Mon Mar 4 20:54:40 1996 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de>
* Makeconfig ($(common-objpfx)config.make): Depend on config.h.in. Mon Mar 4 17:35:09 1996 Roland McGrath <roland@charlie-brown.gnu.ai.mit.edu> * hurd/catch-signal.c (hurd_safe_memmove): New function. (hurd_safe_copyin, hurd_safe_copyout): New functions. * hurd/hurd/sigpreempt.h: Declare them. Sun Mar 3 08:43:44 1996 Roland McGrath <roland@charlie-brown.gnu.ai.mit.edu> Replace math code with fdlibm from Sun as modified for netbsd by JT Conklin and Ian Taylor, including x86 FPU support. * sysdeps/libm-ieee754, sysdeps/libm-i387: New directories. * math/math_private.h: New file. * sysdeps/i386/fpu/Implies: New file. * sysdeps/ieee754/Implies: New file. * math/machine/asm.h, math/machine/endian.h: New files. * math/Makefile, math/math.h: Rewritten. * mathcalls.h, math/mathcalls.h: New file, broken out of math.h. * math/finite.c: File removed. * sysdeps/generic/Makefile [$(subdir)=math]: Frobnication removed. * math/test-math.c: Include errno.h and string.h. * sysdeps/unix/bsd/dirstream.h: File removed. * sysdeps/unix/bsd/readdir.c: File removed.
This commit is contained in:
Roland McGrath
parent
1521668f2a
commit
f7eac6eb50
31
ChangeLog
31
ChangeLog
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@ -1,3 +1,7 @@
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Mon Mar 4 20:54:40 1996 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de>
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* Makeconfig ($(common-objpfx)config.make): Depend on config.h.in.
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Tue Mar 5 12:14:57 1996 Miles Bader <miles@gnu.ai.mit.edu>
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* sysdeps/mach/hurd/select.c (__select): Also don't fault just
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@ -9,7 +13,32 @@ Mon Mar 4 17:35:35 1996 Miles Bader <miles@gnu.ai.mit.edu>
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Don't increment GOT only because READ/WRITE/EXCEPTFDS is 0!
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Don't return without frobbing the bitmasks after a timeout.
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When clearing the bitmasks, only loop from FIRSTFD to LASTFD.
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Mon Mar 4 17:35:09 1996 Roland McGrath <roland@charlie-brown.gnu.ai.mit.edu>
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* hurd/catch-signal.c (hurd_safe_memmove): New function.
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(hurd_safe_copyin, hurd_safe_copyout): New functions.
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* hurd/hurd/sigpreempt.h: Declare them.
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Sun Mar 3 08:43:44 1996 Roland McGrath <roland@charlie-brown.gnu.ai.mit.edu>
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Replace math code with fdlibm from Sun as modified for netbsd by
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JT Conklin and Ian Taylor, including x86 FPU support.
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* sysdeps/libm-ieee754, sysdeps/libm-i387: New directories.
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* math/math_private.h: New file.
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* sysdeps/i386/fpu/Implies: New file.
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* sysdeps/ieee754/Implies: New file.
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* math/machine/asm.h, math/machine/endian.h: New files.
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* math/Makefile, math/math.h: Rewritten.
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* mathcalls.h, math/mathcalls.h: New file, broken out of math.h.
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* math/finite.c: File removed.
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* sysdeps/generic/Makefile [$(subdir)=math]: Frobnication removed.
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* math/test-math.c: Include errno.h and string.h.
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* sysdeps/unix/bsd/dirstream.h: File removed.
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* sysdeps/unix/bsd/readdir.c: File removed.
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Sat Mar 2 16:35:40 1996 Roland McGrath <roland@charlie-brown.gnu.ai.mit.edu>
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* sysdeps/unix/sysv/linux/m68k/profil-counter.h: File removed.
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20
NEWS
20
NEWS
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@ -37,6 +37,11 @@ Version 1.10
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through the interface in <sys/gmon.h>. The profiling code was adapted
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from 4.4 BSD-Lite.
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* The math code has been replaced with a math library based on fdlibm from
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Sun, and modified by JT Conklin with i387 support and by Ian Taylor with
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`float' functions. The math functions now reside in a separate library,
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so programs using them will need to use `-lm' their linking commands.
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* The new functions `strtoq' and `strtouq' parse integer values from
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strings, like `strtol' and `strtoul', but they return `long long int' and
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`unsigned long long int' values, respectively (64-bit quantities).
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@ -53,6 +58,10 @@ Version 1.10
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* The new header <langinfo.h> defines an interface for accessing
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various locale-dependent data (using the locale chosen with `setlocale').
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* Ulrich Drepper has contributed a new suite of functions for operation on
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wide-character and multibyte-character strings; see <wcstr.h> and <mbstr.h>.
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These new functions are intended to conform to the ISO C specification.
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* You can now use positional parameter specifications in format strings
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for the `printf' and `scanf' families of functions. For example,
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`printf ("Number %2$d, Mr %1$s\n", "Jones", 6);'' prints
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@ -163,10 +172,13 @@ Version 1.10
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* New function `getsid' returns session ID number on systems that support it.
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* The 4.4 BSD `db' library has been incorporated into the GNU C library.
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New header files <db.h> and <mpool.h> provide a rich set of functions for
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several types of simple databases stored in memory and in files, and
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<ndbm.h> is an old `ndbm'-compatbile interface using the `db' functions.
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* We have incorporated the 4.4 BSD `db' library (version 1.85). New header
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files <db.h> and <mpool.h> provide a rich set of functions for several
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types of simple databases stored in memory and in files, and <ndbm.h> is
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an old `ndbm'-compatbile interface using the `db' functions.
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* New macro `strdupa' copies a string like `strdup', but uses local stack
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space from `alloca' instead of dynamic heap space from `malloc'.
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Version 1.09
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@ -1,4 +1,6 @@
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# Copyright (C) 1991, 1992, 1994, 1995 Free Software Foundation, Inc.
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# Makefile for the math library.
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# Copyright (C) 1996 Free Software Foundation, Inc.
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# This file is part of the GNU C Library.
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# The GNU C Library is free software; you can redistribute it and/or
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@ -16,24 +18,58 @@
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# not, write to the Free Software Foundation, Inc., 675 Mass Ave,
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# Cambridge, MA 02139, USA.
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#
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# Makefile for math.
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#
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subdir := math
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subdir := math
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headers := math.h __math.h huge_val.h nan.h
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# Installed header files.
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headers := math.h mathcalls.h __math.h huge_val.h nan.h
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# Internal header files.
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distribute := math_private.h machine/asm.h machine/endian.h
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routines := acos asin atan cos sin tan cosh sinh tanh exp fabs ldexp \
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log log10 floor sqrt fmod frexp pow atan2 ceil modf \
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isinf isnan finite infnan copysign drem logb \
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rint hypot cabs cbrt expm1 log1p acosh asinh atanh \
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isinfl isnanl
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tests := # test-math
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install-lib := libm.a
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# Build the -lm library.
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extra-libs := libm
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libm.so-version := .0
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libm-routines := e_acos e_acosf e_acosh e_acoshf e_asin e_asinf \
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e_atan2 e_atan2f e_atanh e_atanhf e_cosh e_coshf \
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e_exp e_expf e_fmod e_fmodf e_hypot e_hypotf e_j0 \
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e_j0f e_j1 e_j1f e_jn e_jnf e_lgamma_r e_lgammaf_r \
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e_log e_log10 e_log10f e_logf e_pow e_powf \
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e_rem_pio2 e_rem_pio2f e_remainder e_remainderf \
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e_scalb e_scalbf e_sinh e_sinhf e_sqrt e_sqrtf k_cos \
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k_cosf k_rem_pio2 k_rem_pio2f k_sin k_sinf \
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k_standard k_tan k_tanf s_asinh s_asinhf s_atan \
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s_atanf s_cbrt s_cbrtf s_ceil s_ceilf s_copysign \
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s_copysignf s_cos s_cosf s_erf s_erff s_expm1 \
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s_expm1f s_fabs s_fabsf s_finite s_finitef s_floor \
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s_floorf s_frexp s_frexpf s_ilogb s_ilogbf \
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s_ldexp s_ldexpf s_lib_version s_log1p s_log1pf \
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s_logb s_logbf s_matherr s_modf s_modff s_nextafter \
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s_nextafterf s_rint s_rintf s_scalbn s_scalbnf \
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s_signgam s_significand s_significandf s_sin s_sinf \
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s_tan s_tanf s_tanh s_tanhf w_acos w_acosf w_acosh \
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w_acoshf w_asin w_asinf w_atan2 w_atan2f w_atanh \
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w_atanhf w_cabs w_cabsf w_cosh w_coshf w_drem \
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w_dremf w_exp w_expf w_fmod w_fmodf w_gamma \
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w_gamma_r w_gammaf w_gammaf_r w_hypot w_hypotf w_j0 \
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w_j0f w_j1 w_j1f w_jn w_jnf w_lgamma w_lgamma_r \
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w_lgammaf w_lgammaf_r w_log w_log10 w_log10f w_logf \
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w_pow w_powf w_remainder w_remainderf w_scalb \
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w_scalbf w_sinh w_sinhf w_sqrt w_sqrtf
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# These functions are in libc instead of libm because __printf_fp
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# calls them, so any program using printf will need them linked in,
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# and we don't want to have to link every program with -lm.
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routines := s_isinf s_isinff s_isnan s_isnanf isinfl isnanl
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include ../Rules
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$(objpfx)libm.a: $(dep-dummy-lib); $(make-dummy-lib)
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lib: $(objpfx)libm.a
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# This file defines the default _LIB_VERSION variable that controls
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# the error return conventions for the math functions.
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CPPFLAGS-s_lib_version.c := -D_POSIX_MODE
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# The fdlibm code generates a lot of these warnings but is otherwise clean.
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override CFLAGS += -Wno-uninitialized -Wno-write-strings
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@ -1,31 +0,0 @@
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/* Copyright (C) 1991, 1992, 1995 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Library General Public License as
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published by the Free Software Foundation; either version 2 of the
|
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License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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License along with the GNU C Library; see the file COPYING.LIB. If
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not, write to the Free Software Foundation, Inc., 675 Mass Ave,
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Cambridge, MA 02139, USA. */
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#include <ansidecl.h>
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#include <math.h>
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#undef __finite
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/* Return nonzero if VALUE is finite and not NaN. */
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int
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DEFUN(__finite, (value), double value)
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{
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return !__isinf (value) && !__isnan (value);
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}
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weak_alias (__finite, finite)
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@ -0,0 +1,10 @@
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/* The libm assembly code wants to include <machine/asm.h> to define the
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ENTRY macro. We define assembly-related macros in sysdep.h and
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asm-syntax.h. */
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#include <sysdep.h>
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#include <asm-syntax.h>
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/* The libm assembly code uses this macro for RCSid strings.
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We don't put RCSid strings into object files. */
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#define RCSID(id) /* ignore them */
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@ -0,0 +1,4 @@
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/* math_private.h wants to include <machine/endian.h>; we provide this
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file so it can, leaving math_private.h unmodified from the original. */
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#include <endian.h>
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292
math/math.h
292
math/math.h
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@ -1,4 +1,5 @@
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/* Copyright (C) 1991, 1992, 1993, 1995 Free Software Foundation, Inc.
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/* Declarations for math functions.
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Copyright (C) 1991, 92, 93, 95, 96 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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@ -30,7 +31,8 @@ __BEGIN_DECLS
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#define __need_Emath
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#include <errno.h>
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/* Get machine-dependent HUGE_VAL value (returned on overflow). */
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/* Get machine-dependent HUGE_VAL value (returned on overflow).
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On all IEEE754 machines, this is +Infinity. */
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#include <huge_val.h>
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/* Get machine-dependent NAN value (returned for some domain errors). */
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@ -39,260 +41,84 @@ __BEGIN_DECLS
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#endif
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/* Trigonometric functions. */
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/* The file <mathcalls.h> contains the prototypes for all the actual
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math functions. These macros are used for those prototypes, so
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we can easily declare each function as both `name' and `__name',
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and can declare the float versions `namef' and `__namef'. */
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/* Arc cosine of X. */
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extern double acos __P ((double __x)) __attribute__ ((__const__));
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/* Arc sine of X. */
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extern double asin __P ((double __x)) __attribute__ ((__const__));
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/* Arc tangent of X. */
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extern double atan __P ((double __x)) __attribute__ ((__const__));
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/* Arc tangent of Y/X. */
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extern double atan2 __P ((double __y, double __x)) __attribute__ ((__const__));
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#define __MATHCALL(function,suffix, args) \
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__MATHDECL (_Mdouble_, function,suffix, args)
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#define __MATHDECL(type, function,suffix, args) \
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__MATHDECL_1(type, function,suffix, args); \
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__MATHDECL_1(type, __##function,suffix, args)
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#define __MATHDECL_1(type, function,suffix, args) \
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extern type __MATH_PRECNAME(function,suffix) args
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/* Cosine of X. */
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extern double cos __P ((double __x)) __attribute__ ((__const__));
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/* Sine of X. */
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extern double sin __P ((double __x)) __attribute__ ((__const__));
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/* Tangent of X. */
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extern double tan __P ((double __x)) __attribute__ ((__const__));
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#define _Mdouble_ double
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#define __MATH_PRECNAME(name,r) name##r
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#include <mathcalls.h>
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#undef _Mdouble_
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#undef __MATH_PRECNAME
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#ifdef __USE_MISC
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/* Include the file of declarations again, this type using `float'
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instead of `double' and appending f to each function name. */
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/* Hyperbolic functions. */
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#define _Mdouble_ float
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#define __MATH_PRECNAME(name,r) name##f##r
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#include <mathcalls.h>
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#undef _Mdouble_
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#undef __MATH_PRECNAME
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#endif
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/* Hyperbolic cosine of X. */
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extern double cosh __P ((double __x)) __attribute__ ((__const__));
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/* Hyperbolic sine of X. */
|
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extern double sinh __P ((double __x)) __attribute__ ((__const__));
|
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/* Hyperbolic tangent of X. */
|
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extern double tanh __P ((double __x)) __attribute__ ((__const__));
|
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|
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#ifdef __USE_MISC
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/* Hyperbolic arc cosine of X. */
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extern double acosh __P ((double __x)) __attribute__ ((__const__));
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/* Hyperbolic arc sine of X. */
|
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extern double asinh __P ((double __x)) __attribute__ ((__const__));
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/* Hyperbolic arc tangent of X. */
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extern double atanh __P ((double __x)) __attribute__ ((__const__));
|
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#endif
|
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/* Support for various different standard error handling behaviors. */
|
||||
|
||||
/* Exponential and logarithmic functions. */
|
||||
typedef enum { _IEEE_ = -1, _SVID_, _XOPEN_, _POSIX_ } _LIB_VERSION_TYPE;
|
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|
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/* Exponentional function of X. */
|
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extern double exp __P ((double __x)) __attribute__ ((__const__));
|
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|
||||
/* Break VALUE into a normalized fraction and an integral power of 2. */
|
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extern double frexp __P ((double __value, int *__exp));
|
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|
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/* X times (two to the EXP power). */
|
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extern double ldexp __P ((double __x, int __exp)) __attribute__ ((__const__));
|
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|
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/* Natural logarithm of X. */
|
||||
extern double log __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
/* Base-ten logarithm of X. */
|
||||
extern double log10 __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
#ifdef __USE_MISC
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||||
/* Return exp(X) - 1. */
|
||||
extern double __expm1 __P ((double __x)) __attribute__ ((__const__));
|
||||
extern double expm1 __P ((double __x)) __attribute__ ((__const__));
|
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|
||||
/* Return log(1 + X). */
|
||||
extern double log1p __P ((double __x)) __attribute__ ((__const__));
|
||||
#endif
|
||||
|
||||
/* Break VALUE into integral and fractional parts. */
|
||||
extern double modf __P ((double __value, double *__iptr));
|
||||
|
||||
|
||||
/* Power functions. */
|
||||
|
||||
/* Return X to the Y power. */
|
||||
extern double pow __P ((double __x, double __y)) __attribute__ ((__const__));
|
||||
|
||||
/* Return the square root of X. */
|
||||
extern double sqrt __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
#ifdef __USE_MISC
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||||
/* Return the cube root of X. */
|
||||
extern double cbrt __P ((double __x)) __attribute__ ((__const__));
|
||||
/* This variable can be changed at run-time to any of the values above to
|
||||
affect floating point error handling behavior (it may also be necessary
|
||||
to change the hardware FPU exception settings). */
|
||||
extern _LIB_VERSION_TYPE _LIB_VERSION;
|
||||
#endif
|
||||
|
||||
|
||||
/* Nearest integer, absolute value, and remainder functions. */
|
||||
#ifdef __USE_SVID
|
||||
/* In SVID error handling, `matherr' is called with this description
|
||||
of the exceptional condition. */
|
||||
struct exception
|
||||
{
|
||||
int type;
|
||||
char *name;
|
||||
double arg1;
|
||||
double arg2;
|
||||
double retval;
|
||||
};
|
||||
|
||||
/* Smallest integral value not less than X. */
|
||||
extern double ceil __P ((double __x)) __attribute__ ((__const__));
|
||||
extern int matherr __P ((struct exception *));
|
||||
|
||||
/* Absolute value of X. */
|
||||
extern double fabs __P ((double __x)) __attribute__ ((__const__));
|
||||
#define X_TLOSS 1.41484755040568800000e+16
|
||||
|
||||
/* Largest integer not greater than X. */
|
||||
extern double floor __P ((double __x)) __attribute__ ((__const__));
|
||||
/* Types of exceptions in the `type' field. */
|
||||
#define DOMAIN 1
|
||||
#define SING 2
|
||||
#define OVERFLOW 3
|
||||
#define UNDERFLOW 4
|
||||
#define TLOSS 5
|
||||
#define PLOSS 6
|
||||
|
||||
/* Floating-point modulo remainder of X/Y. */
|
||||
extern double fmod __P ((double __x, double __y)) __attribute__ ((__const__));
|
||||
/* SVID mode specifies returning this large value instead of infinity. */
|
||||
#define HUGE FLT_MAX
|
||||
#include <float.h> /* Defines FLT_MAX. */
|
||||
|
||||
|
||||
/* Return 0 if VALUE is finite or NaN, +1 if it
|
||||
is +Infinity, -1 if it is -Infinity. */
|
||||
extern int __isinf __P ((double __value)) __attribute__ ((__const__));
|
||||
|
||||
/* Return nonzero if VALUE is not a number. */
|
||||
extern int __isnan __P ((double __value)) __attribute__ ((__const__));
|
||||
|
||||
/* Return nonzero if VALUE is finite and not NaN. */
|
||||
extern int __finite __P ((double __value)) __attribute__ ((__const__));
|
||||
#ifdef __OPTIMIZE__
|
||||
#define __finite(value) (!__isinf(value))
|
||||
#endif
|
||||
|
||||
/* Deal with an infinite or NaN result.
|
||||
If ERROR is ERANGE, result is +Inf;
|
||||
if ERROR is - ERANGE, result is -Inf;
|
||||
otherwise result is NaN.
|
||||
This will set `errno' to either ERANGE or EDOM,
|
||||
and may return an infinity or NaN, or may do something else. */
|
||||
extern double __infnan __P ((int __error));
|
||||
|
||||
/* Return X with its signed changed to Y's. */
|
||||
extern double __copysign __P ((double __x, double __y))
|
||||
__attribute__ ((__const__));
|
||||
|
||||
/* Return X times (2 to the Nth power). */
|
||||
extern double __scalb __P ((double __x, int __n))
|
||||
__attribute__ ((__const__));
|
||||
|
||||
#ifdef __OPTIMIZE__
|
||||
#define __scalb(x, n) ldexp ((x), (n))
|
||||
#endif
|
||||
|
||||
/* Return the remainder of X/Y. */
|
||||
extern double __drem __P ((double __x, double __y))
|
||||
__attribute__ ((__const__));
|
||||
|
||||
/* Return the base 2 signed integral exponent of X. */
|
||||
extern double __logb __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
#ifdef __USE_MISC
|
||||
|
||||
/* Return the integer nearest X in the direction of the
|
||||
prevailing rounding mode. */
|
||||
extern double __rint __P ((double __x)) __attribute__ ((__const__));
|
||||
extern double rint __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
/* Return `sqrt(X*X + Y*Y)'. */
|
||||
extern double hypot __P ((double __x, double __y)) __attribute__ ((__const__));
|
||||
|
||||
struct __cabs_complex
|
||||
{
|
||||
double __x, __y;
|
||||
};
|
||||
|
||||
/* Return `sqrt(X*X + Y*Y)'. */
|
||||
extern double cabs __P ((struct __cabs_complex)) __attribute__ ((__const__));
|
||||
|
||||
extern int isinf __P ((double __value)) __attribute__ ((__const__));
|
||||
extern int isnan __P ((double __value)) __attribute__ ((__const__));
|
||||
extern int finite __P ((double __value)) __attribute__ ((__const__));
|
||||
extern double infnan __P ((int __error)) __attribute__ ((__const__));
|
||||
extern double copysign __P ((double __x, double __y))
|
||||
__attribute__ ((__const__));
|
||||
extern double scalb __P ((double __x, int __n)) __attribute__ ((__const__));
|
||||
extern double drem __P ((double __x, double __y)) __attribute__ ((__const__));
|
||||
extern double logb __P ((double __x)) __attribute__ ((__const__));
|
||||
|
||||
#ifdef __OPTIMIZE__
|
||||
#define isinf(value) __isinf(value)
|
||||
#define isnan(value) __isnan(value)
|
||||
#define infnan(error) __infnan(error)
|
||||
#define finite(value) __finite(value)
|
||||
#define copysign(x, y) __copysign((x), (y))
|
||||
#define scalb(x, n) __scalb((x), (n))
|
||||
#define drem(x, y) __drem((x), (y))
|
||||
#define logb(x) __logb(x)
|
||||
#endif /* Optimizing. */
|
||||
|
||||
#endif /* Use misc. */
|
||||
|
||||
|
||||
#if 0
|
||||
/* The "Future Library Directions" section of the
|
||||
ANSI Standard reserves these as `float' and
|
||||
`long double' versions of the above functions. */
|
||||
|
||||
extern float acosf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float asinf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float atanf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float atan2f __P ((float __y, float __x)) __attribute__ ((__const__));
|
||||
extern float cosf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float sinf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float tanf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float coshf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float sinhf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float tanhf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float expf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float frexpf __P ((float __value, int *__exp));
|
||||
extern float ldexpf __P ((float __x, int __exp)) __attribute__ ((__const__));
|
||||
extern float logf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float log10f __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float modff __P ((float __value, float *__iptr));
|
||||
extern float powf __P ((float __x, float __y)) __attribute__ ((__const__));
|
||||
extern float sqrtf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float ceilf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float fabsf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float floorf __P ((float __x)) __attribute__ ((__const__));
|
||||
extern float fmodf __P ((float __x, float __y)) __attribute__ ((__const__));
|
||||
|
||||
extern __long_double_t acosl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t asinl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t atanl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t atan2l __P ((__long_double_t __y, __long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t cosl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t sinl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t tanl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t coshl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t sinhl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t tanhl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t expl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t frexpl __P ((__long_double_t __value, int *__exp));
|
||||
extern __long_double_t ldexpl __P ((__long_double_t __x, int __exp))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t logl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t log10l __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t modfl __P ((__long_double_t __value,
|
||||
__long_double_t *__ip));
|
||||
extern __long_double_t powl __P ((__long_double_t __x, __long_double_t __y))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t sqrtl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t ceill __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t fabsl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t floorl __P ((__long_double_t __x))
|
||||
__attribute__ ((__const__));
|
||||
extern __long_double_t fmodl __P ((__long_double_t __x, __long_double_t __y))
|
||||
__attribute__ ((__const__));
|
||||
#endif /* 0 */
|
||||
|
||||
/* Get machine-dependent inline versions (if there are any). */
|
||||
#include <__math.h>
|
||||
|
||||
|
||||
__END_DECLS
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,222 @@
|
|||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/*
|
||||
* from: @(#)fdlibm.h 5.1 93/09/24
|
||||
* $Id$
|
||||
*/
|
||||
|
||||
#ifndef _MATH_PRIVATE_H_
|
||||
#define _MATH_PRIVATE_H_
|
||||
|
||||
#include <machine/endian.h>
|
||||
#include <sys/types.h>
|
||||
|
||||
/* The original fdlibm code used statements like:
|
||||
n0 = ((*(int*)&one)>>29)^1; * index of high word *
|
||||
ix0 = *(n0+(int*)&x); * high word of x *
|
||||
ix1 = *((1-n0)+(int*)&x); * low word of x *
|
||||
to dig two 32 bit words out of the 64 bit IEEE floating point
|
||||
value. That is non-ANSI, and, moreover, the gcc instruction
|
||||
scheduler gets it wrong. We instead use the following macros.
|
||||
Unlike the original code, we determine the endianness at compile
|
||||
time, not at run time; I don't see much benefit to selecting
|
||||
endianness at run time. */
|
||||
|
||||
/* A union which permits us to convert between a double and two 32 bit
|
||||
ints. */
|
||||
|
||||
#if BYTE_ORDER == BIG_ENDIAN
|
||||
|
||||
typedef union
|
||||
{
|
||||
double value;
|
||||
struct
|
||||
{
|
||||
u_int32_t msw;
|
||||
u_int32_t lsw;
|
||||
} parts;
|
||||
} ieee_double_shape_type;
|
||||
|
||||
#endif
|
||||
|
||||
#if BYTE_ORDER == LITTLE_ENDIAN
|
||||
|
||||
typedef union
|
||||
{
|
||||
double value;
|
||||
struct
|
||||
{
|
||||
u_int32_t lsw;
|
||||
u_int32_t msw;
|
||||
} parts;
|
||||
} ieee_double_shape_type;
|
||||
|
||||
#endif
|
||||
|
||||
/* Get two 32 bit ints from a double. */
|
||||
|
||||
#define EXTRACT_WORDS(ix0,ix1,d) \
|
||||
do { \
|
||||
ieee_double_shape_type ew_u; \
|
||||
ew_u.value = (d); \
|
||||
(ix0) = ew_u.parts.msw; \
|
||||
(ix1) = ew_u.parts.lsw; \
|
||||
} while (0)
|
||||
|
||||
/* Get the more significant 32 bit int from a double. */
|
||||
|
||||
#define GET_HIGH_WORD(i,d) \
|
||||
do { \
|
||||
ieee_double_shape_type gh_u; \
|
||||
gh_u.value = (d); \
|
||||
(i) = gh_u.parts.msw; \
|
||||
} while (0)
|
||||
|
||||
/* Get the less significant 32 bit int from a double. */
|
||||
|
||||
#define GET_LOW_WORD(i,d) \
|
||||
do { \
|
||||
ieee_double_shape_type gl_u; \
|
||||
gl_u.value = (d); \
|
||||
(i) = gl_u.parts.lsw; \
|
||||
} while (0)
|
||||
|
||||
/* Set a double from two 32 bit ints. */
|
||||
|
||||
#define INSERT_WORDS(d,ix0,ix1) \
|
||||
do { \
|
||||
ieee_double_shape_type iw_u; \
|
||||
iw_u.parts.msw = (ix0); \
|
||||
iw_u.parts.lsw = (ix1); \
|
||||
(d) = iw_u.value; \
|
||||
} while (0)
|
||||
|
||||
/* Set the more significant 32 bits of a double from an int. */
|
||||
|
||||
#define SET_HIGH_WORD(d,v) \
|
||||
do { \
|
||||
ieee_double_shape_type sh_u; \
|
||||
sh_u.value = (d); \
|
||||
sh_u.parts.msw = (v); \
|
||||
(d) = sh_u.value; \
|
||||
} while (0)
|
||||
|
||||
/* Set the less significant 32 bits of a double from an int. */
|
||||
|
||||
#define SET_LOW_WORD(d,v) \
|
||||
do { \
|
||||
ieee_double_shape_type sl_u; \
|
||||
sl_u.value = (d); \
|
||||
sl_u.parts.lsw = (v); \
|
||||
(d) = sl_u.value; \
|
||||
} while (0)
|
||||
|
||||
/* A union which permits us to convert between a float and a 32 bit
|
||||
int. */
|
||||
|
||||
typedef union
|
||||
{
|
||||
float value;
|
||||
u_int32_t word;
|
||||
} ieee_float_shape_type;
|
||||
|
||||
/* Get a 32 bit int from a float. */
|
||||
|
||||
#define GET_FLOAT_WORD(i,d) \
|
||||
do { \
|
||||
ieee_float_shape_type gf_u; \
|
||||
gf_u.value = (d); \
|
||||
(i) = gf_u.word; \
|
||||
} while (0)
|
||||
|
||||
/* Set a float from a 32 bit int. */
|
||||
|
||||
#define SET_FLOAT_WORD(d,i) \
|
||||
do { \
|
||||
ieee_float_shape_type sf_u; \
|
||||
sf_u.word = (i); \
|
||||
(d) = sf_u.value; \
|
||||
} while (0)
|
||||
|
||||
/* ieee style elementary functions */
|
||||
extern double __ieee754_sqrt __P((double));
|
||||
extern double __ieee754_acos __P((double));
|
||||
extern double __ieee754_acosh __P((double));
|
||||
extern double __ieee754_log __P((double));
|
||||
extern double __ieee754_atanh __P((double));
|
||||
extern double __ieee754_asin __P((double));
|
||||
extern double __ieee754_atan2 __P((double,double));
|
||||
extern double __ieee754_exp __P((double));
|
||||
extern double __ieee754_cosh __P((double));
|
||||
extern double __ieee754_fmod __P((double,double));
|
||||
extern double __ieee754_pow __P((double,double));
|
||||
extern double __ieee754_lgamma_r __P((double,int *));
|
||||
extern double __ieee754_gamma_r __P((double,int *));
|
||||
extern double __ieee754_lgamma __P((double));
|
||||
extern double __ieee754_gamma __P((double));
|
||||
extern double __ieee754_log10 __P((double));
|
||||
extern double __ieee754_sinh __P((double));
|
||||
extern double __ieee754_hypot __P((double,double));
|
||||
extern double __ieee754_j0 __P((double));
|
||||
extern double __ieee754_j1 __P((double));
|
||||
extern double __ieee754_y0 __P((double));
|
||||
extern double __ieee754_y1 __P((double));
|
||||
extern double __ieee754_jn __P((int,double));
|
||||
extern double __ieee754_yn __P((int,double));
|
||||
extern double __ieee754_remainder __P((double,double));
|
||||
extern int __ieee754_rem_pio2 __P((double,double*));
|
||||
extern double __ieee754_scalb __P((double,double));
|
||||
|
||||
/* fdlibm kernel function */
|
||||
extern double __kernel_standard __P((double,double,int));
|
||||
extern double __kernel_sin __P((double,double,int));
|
||||
extern double __kernel_cos __P((double,double));
|
||||
extern double __kernel_tan __P((double,double,int));
|
||||
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
|
||||
|
||||
|
||||
/* ieee style elementary float functions */
|
||||
extern float __ieee754_sqrtf __P((float));
|
||||
extern float __ieee754_acosf __P((float));
|
||||
extern float __ieee754_acoshf __P((float));
|
||||
extern float __ieee754_logf __P((float));
|
||||
extern float __ieee754_atanhf __P((float));
|
||||
extern float __ieee754_asinf __P((float));
|
||||
extern float __ieee754_atan2f __P((float,float));
|
||||
extern float __ieee754_expf __P((float));
|
||||
extern float __ieee754_coshf __P((float));
|
||||
extern float __ieee754_fmodf __P((float,float));
|
||||
extern float __ieee754_powf __P((float,float));
|
||||
extern float __ieee754_lgammaf_r __P((float,int *));
|
||||
extern float __ieee754_gammaf_r __P((float,int *));
|
||||
extern float __ieee754_lgammaf __P((float));
|
||||
extern float __ieee754_gammaf __P((float));
|
||||
extern float __ieee754_log10f __P((float));
|
||||
extern float __ieee754_sinhf __P((float));
|
||||
extern float __ieee754_hypotf __P((float,float));
|
||||
extern float __ieee754_j0f __P((float));
|
||||
extern float __ieee754_j1f __P((float));
|
||||
extern float __ieee754_y0f __P((float));
|
||||
extern float __ieee754_y1f __P((float));
|
||||
extern float __ieee754_jnf __P((int,float));
|
||||
extern float __ieee754_ynf __P((int,float));
|
||||
extern float __ieee754_remainderf __P((float,float));
|
||||
extern int __ieee754_rem_pio2f __P((float,float*));
|
||||
extern float __ieee754_scalbf __P((float,float));
|
||||
|
||||
/* float versions of fdlibm kernel functions */
|
||||
extern float __kernel_sinf __P((float,float,int));
|
||||
extern float __kernel_cosf __P((float,float));
|
||||
extern float __kernel_tanf __P((float,float,int));
|
||||
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*));
|
||||
|
||||
#endif /* _MATH_PRIVATE_H_ */
|
||||
|
|
@ -0,0 +1,232 @@
|
|||
/* Prototype declarations for math functions; helper file for <math.h>.
|
||||
Copyright (C) 1996 Free Software Foundation, Inc.
|
||||
This file is part of the GNU C Library.
|
||||
|
||||
The GNU C Library is free software; you can redistribute it and/or
|
||||
modify it under the terms of the GNU Library General Public License as
|
||||
published by the Free Software Foundation; either version 2 of the
|
||||
License, or (at your option) any later version.
|
||||
|
||||
The GNU C Library is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||
Library General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU Library General Public
|
||||
License along with the GNU C Library; see the file COPYING.LIB. If
|
||||
not, write to the Free Software Foundation, Inc., 675 Mass Ave,
|
||||
Cambridge, MA 02139, USA. */
|
||||
|
||||
/* NOTE: Because of the special way this file is used by <math.h>, this
|
||||
file must NOT be protected from multiple inclusion as header files
|
||||
usually are.
|
||||
|
||||
This file provides prototype declarations for the math functions.
|
||||
Most functions are declared using the macro:
|
||||
|
||||
__MATHCALL (NAME,[_r], (ARGS...));
|
||||
|
||||
This means there is a function `NAME' returning `double' and a function
|
||||
`NAMEf' returning `float'. Each place `_Mdouble_' appears in the
|
||||
prototype, that is actually `double' in the prototype for `NAME' and
|
||||
`float' in the prototype for `NAMEf'. Reentrant variant functions are
|
||||
called `NAME_r' and `NAMEf_r'.
|
||||
|
||||
Functions returning other types like `int' are declared using the macro:
|
||||
|
||||
__MATHDECL (TYPE, NAME,[_r], (ARGS...));
|
||||
|
||||
This is just like __MATHCALL but for a function returning `TYPE'
|
||||
instead of `_Mdouble_'. In all of these cases, there is still
|
||||
both a `NAME' and a `NAMEf' that takes `float' arguments. */
|
||||
|
||||
#ifndef _MATH_H
|
||||
#error "Never include mathcalls.h directly; include <math.h> instead."
|
||||
#endif
|
||||
|
||||
|
||||
/* Trigonometric functions. */
|
||||
|
||||
/* Arc cosine of X. */
|
||||
__MATHCALL (acos,, (_Mdouble_ __x));
|
||||
/* Arc sine of X. */
|
||||
__MATHCALL (asin,, (_Mdouble_ __x));
|
||||
/* Arc tangent of X. */
|
||||
__MATHCALL (atan,, (_Mdouble_ __x));
|
||||
/* Arc tangent of Y/X. */
|
||||
__MATHCALL (atan2,, (_Mdouble_ __y, _Mdouble_ __x));
|
||||
|
||||
/* Cosine of X. */
|
||||
__MATHCALL (cos,, (_Mdouble_ __x));
|
||||
/* Sine of X. */
|
||||
__MATHCALL (sin,, (_Mdouble_ __x));
|
||||
/* Tangent of X. */
|
||||
__MATHCALL (tan,, (_Mdouble_ __x));
|
||||
|
||||
|
||||
/* Hyperbolic functions. */
|
||||
|
||||
/* Hyperbolic cosine of X. */
|
||||
__MATHCALL (cosh,, (_Mdouble_ __x));
|
||||
/* Hyperbolic sine of X. */
|
||||
__MATHCALL (sinh,, (_Mdouble_ __x));
|
||||
/* Hyperbolic tangent of X. */
|
||||
__MATHCALL (tanh,, (_Mdouble_ __x));
|
||||
|
||||
#ifdef __USE_MISC
|
||||
/* Hyperbolic arc cosine of X. */
|
||||
__MATHCALL (acosh,, (_Mdouble_ __x));
|
||||
/* Hyperbolic arc sine of X. */
|
||||
__MATHCALL (asinh,, (_Mdouble_ __x));
|
||||
/* Hyperbolic arc tangent of X. */
|
||||
__MATHCALL (atanh,, (_Mdouble_ __x));
|
||||
#endif
|
||||
|
||||
/* Exponential and logarithmic functions. */
|
||||
|
||||
/* Exponentional function of X. */
|
||||
__MATHCALL (exp,, (_Mdouble_ __x));
|
||||
|
||||
/* Break VALUE into a normalized fraction and an integral power of 2. */
|
||||
__MATHCALL (frexp,, (_Mdouble_ __value, int *__exp));
|
||||
|
||||
/* X times (two to the EXP power). */
|
||||
__MATHCALL (ldexp,, (_Mdouble_ __x, int __exp));
|
||||
|
||||
/* Natural logarithm of X. */
|
||||
__MATHCALL (log,, (_Mdouble_ __x));
|
||||
|
||||
/* Base-ten logarithm of X. */
|
||||
__MATHCALL (log10,, (_Mdouble_ __x));
|
||||
|
||||
#ifdef __USE_MISC
|
||||
/* Return exp(X) - 1. */
|
||||
__MATHCALL (expm1,, (_Mdouble_ __x));
|
||||
|
||||
/* Return log(1 + X). */
|
||||
__MATHCALL (log1p,, (_Mdouble_ __x));
|
||||
#endif
|
||||
|
||||
/* Break VALUE into integral and fractional parts. */
|
||||
__MATHCALL (modf,, (_Mdouble_ __value, _Mdouble_ *__iptr));
|
||||
|
||||
|
||||
/* Power functions. */
|
||||
|
||||
/* Return X to the Y power. */
|
||||
__MATHCALL (pow,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
/* Return the square root of X. */
|
||||
__MATHCALL (sqrt,, (_Mdouble_ __x));
|
||||
|
||||
#ifdef __USE_MISC
|
||||
/* Return the cube root of X. */
|
||||
__MATHCALL (cbrt,, (_Mdouble_ __x));
|
||||
#endif
|
||||
|
||||
|
||||
/* Nearest integer, absolute value, and remainder functions. */
|
||||
|
||||
/* Smallest integral value not less than X. */
|
||||
__MATHCALL (ceil,, (_Mdouble_ __x));
|
||||
|
||||
/* Absolute value of X. */
|
||||
__MATHCALL (fabs,, (_Mdouble_ __x));
|
||||
|
||||
/* Largest integer not greater than X. */
|
||||
__MATHCALL (floor,, (_Mdouble_ __x));
|
||||
|
||||
/* Floating-point modulo remainder of X/Y. */
|
||||
__MATHCALL (fmod,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
|
||||
#ifdef __USE_MISC
|
||||
|
||||
/* Return 0 if VALUE is finite or NaN, +1 if it
|
||||
is +Infinity, -1 if it is -Infinity. */
|
||||
__MATHDECL (int, isinf,, (_Mdouble_ __value));
|
||||
|
||||
/* Return nonzero if VALUE is not a number. */
|
||||
__MATHDECL (int, isnan,, (_Mdouble_ __value));
|
||||
|
||||
/* Return nonzero if VALUE is finite and not NaN. */
|
||||
__MATHDECL (int, finite,, (_Mdouble_ __value));
|
||||
|
||||
/* Deal with an infinite or NaN result.
|
||||
If ERROR is ERANGE, result is +Inf;
|
||||
if ERROR is - ERANGE, result is -Inf;
|
||||
otherwise result is NaN.
|
||||
This will set `errno' to either ERANGE or EDOM,
|
||||
and may return an infinity or NaN, or may do something else. */
|
||||
__MATHCALL (infnan,, (int __error));
|
||||
|
||||
/* Return X with its signed changed to Y's. */
|
||||
__MATHCALL (copysign,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
/* Return X times (2 to the Nth power). */
|
||||
__MATHCALL (scalb,, (_Mdouble_ __x, _Mdouble_ __n));
|
||||
|
||||
/* Return X times (2 to the Nth power). */
|
||||
__MATHCALL (scalbn,, (_Mdouble_ __x, int __n));
|
||||
|
||||
/* Return the remainder of X/Y. */
|
||||
__MATHCALL (drem,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
/* Return the base 2 signed integral exponent of X. */
|
||||
__MATHCALL (logb,, (_Mdouble_ __x));
|
||||
|
||||
/* Return the integer nearest X in the direction of the
|
||||
prevailing rounding mode. */
|
||||
__MATHCALL (rint,, (_Mdouble_ __x));
|
||||
|
||||
/* Return `sqrt(X*X + Y*Y)'. */
|
||||
__MATHCALL (hypot,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
struct __MATH_PRECNAME(__cabs_complex,)
|
||||
{
|
||||
_Mdouble_ x, y;
|
||||
};
|
||||
|
||||
/* Return `sqrt(X*X + Y*Y)'. */
|
||||
__MATHCALL (cabs,, (struct __MATH_PRECNAME(__cabs_complex,)));
|
||||
|
||||
|
||||
/* Return X + epsilon if X < Y, X - epsilon if X > Y. */
|
||||
__MATHCALL (nextafter,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
/* Return the remainder of integer divison X / Y with infinite precision. */
|
||||
__MATHCALL (remainder,, (_Mdouble_ __x, _Mdouble_ __y));
|
||||
|
||||
/* Return the binary exponent of X, which must be nonzero. */
|
||||
__MATHDECL (int, ilogb,, (_Mdouble_ __x));
|
||||
|
||||
/* Return the fractional part of X after dividing out `ilogb (X)'. */
|
||||
__MATHCALL (significand,, (_Mdouble_ __x));
|
||||
|
||||
|
||||
|
||||
/* Error, gamma, and Bessel functions. */
|
||||
__MATHCALL (erf,, (_Mdouble_));
|
||||
__MATHCALL (erfc,, (_Mdouble_));
|
||||
__MATHCALL (gamma,, (_Mdouble_));
|
||||
__MATHCALL (j0,, (_Mdouble_));
|
||||
__MATHCALL (j1,, (_Mdouble_));
|
||||
__MATHCALL (jn,, (int, _Mdouble_));
|
||||
__MATHCALL (lgamma,, (_Mdouble_));
|
||||
__MATHCALL (y0,, (_Mdouble_));
|
||||
__MATHCALL (y1,, (_Mdouble_));
|
||||
__MATHCALL (yn,, (int, _Mdouble_));
|
||||
|
||||
/* This variable is used by `gamma' and `lgamma'. */
|
||||
extern int signgam;
|
||||
|
||||
#ifdef __USE_REENTRANT
|
||||
|
||||
/* Reentrant versions of gamma and lgamma. Those functions use the global
|
||||
variable `signgam'. The reentrant versions instead take a pointer and
|
||||
store the value through it. */
|
||||
__MATHCALL (gamma,_r, (_Mdouble_, int *));
|
||||
__MATHCALL (lgamma,_r, (_Mdouble_, int *));
|
||||
#endif
|
||||
|
||||
#endif /* Use misc. */
|
||||
|
|
@ -0,0 +1 @@
|
|||
#include <math/mathcalls.h>
|
||||
|
|
@ -16,18 +16,6 @@
|
|||
# not, write to the Free Software Foundation, Inc., 675 Mass Ave,
|
||||
# Cambridge, MA 02139, USA.
|
||||
|
||||
ifeq ($(subdir),math)
|
||||
ifndef math-twiddled
|
||||
|
||||
sysdep_routines += sincos asincos exp__E log__L
|
||||
elided-routines += acos asin cos sin
|
||||
|
||||
math-twiddled := t
|
||||
override +gccwarn := -w
|
||||
endif
|
||||
|
||||
endif
|
||||
|
||||
ifeq (,$(filter-out $(sysdep_dir)/stub/ $(common-objpfx),\
|
||||
$(dir $(firstword $(wildcard $(+sysdep_dirs:%=%/bytesex.h))))))
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,2 @@
|
|||
# For x86 machines with FPU, use the i387 port of libm by JT Conklin.
|
||||
libm-i387
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
# For all IEEE machines, use Sun's fdlibm code.
|
||||
libm-ieee754
|
||||
|
|
@ -0,0 +1,20 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_acos.S,v 1.4 1995/05/08 23:44:37 jtc Exp $")
|
||||
|
||||
/* acos = atan (sqrt(1 - x^2) / x) */
|
||||
ENTRY(__ieee754_acos)
|
||||
fldl 4(%esp) /* x */
|
||||
fst %st(1)
|
||||
fmul %st(0) /* x^2 */
|
||||
fld1
|
||||
fsubp /* 1 - x^2 */
|
||||
fsqrt /* sqrt (1 - x^2) */
|
||||
fxch %st(1)
|
||||
fpatan
|
||||
ret
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_asin.S,v 1.4 1995/05/08 23:45:40 jtc Exp $")
|
||||
|
||||
/* asin = atan (x / sqrt(1 - x^2)) */
|
||||
ENTRY(__ieee754_asin)
|
||||
fldl 4(%esp) /* x */
|
||||
fst %st(1)
|
||||
fmul %st(0) /* x^2 */
|
||||
fld1
|
||||
fsubp /* 1 - x^2 */
|
||||
fsqrt /* sqrt (1 - x^2) */
|
||||
fpatan
|
||||
ret
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_atan2.S,v 1.4 1995/05/08 23:46:28 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_atan2)
|
||||
fldl 4(%esp)
|
||||
fldl 12(%esp)
|
||||
fpatan
|
||||
ret
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_atan2f.S,v 1.1 1995/05/08 23:35:10 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_atan2f)
|
||||
flds 4(%esp)
|
||||
flds 8(%esp)
|
||||
fpatan
|
||||
ret
|
||||
|
|
@ -0,0 +1,23 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_exp.S,v 1.4 1995/05/08 23:47:04 jtc Exp $")
|
||||
|
||||
/* e^x = 2^(x * log2(e)) */
|
||||
ENTRY(__ieee754_exp)
|
||||
fldl 4(%esp)
|
||||
fldl2e
|
||||
fmulp /* x * log2(e) */
|
||||
fstl %st(1)
|
||||
frndint /* int(x * log2(e)) */
|
||||
fstl %st(2)
|
||||
fsubrp /* fract(x * log2(e)) */
|
||||
f2xm1 /* 2^(fract(x * log2(e))) - 1 */
|
||||
fld1
|
||||
faddp /* 2^(fract(x * log2(e))) */
|
||||
fscale /* e^x */
|
||||
ret
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_fmod.S,v 1.4 1995/05/08 23:47:56 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_fmod)
|
||||
fldl 12(%esp)
|
||||
fldl 4(%esp)
|
||||
1: fprem
|
||||
fstsw %ax
|
||||
sahf
|
||||
jp 1b
|
||||
fstpl %st(1)
|
||||
ret
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_log.S,v 1.4 1995/05/08 23:48:39 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_log)
|
||||
fldln2
|
||||
fldl 4(%esp)
|
||||
fyl2x
|
||||
ret
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_log10.S,v 1.4 1995/05/08 23:49:24 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_log10)
|
||||
fldlg2
|
||||
fldl 4(%esp)
|
||||
fyl2x
|
||||
ret
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_remainder.S,v 1.4 1995/05/08 23:49:37 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_remainder)
|
||||
fldl 12(%esp)
|
||||
fldl 4(%esp)
|
||||
1: fprem1
|
||||
fstsw %ax
|
||||
sahf
|
||||
jp 1b
|
||||
fstpl %st(1)
|
||||
ret
|
||||
|
|
@ -0,0 +1,18 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_remainderf.S,v 1.2 1995/05/08 23:49:47 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_remainderf)
|
||||
flds 8(%esp)
|
||||
flds 4(%esp)
|
||||
1: fprem1
|
||||
fstsw %ax
|
||||
sahf
|
||||
jp 1b
|
||||
fstpl %st(1)
|
||||
ret
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_scalb.S,v 1.4 1995/05/08 23:49:52 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_scalb)
|
||||
fldl 12(%esp)
|
||||
fldl 4(%esp)
|
||||
fscale
|
||||
ret
|
||||
|
|
@ -0,0 +1,13 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_sqrt.S,v 1.4 1995/05/08 23:49:57 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_sqrt)
|
||||
fldl 4(%esp)
|
||||
fsqrt
|
||||
ret
|
||||
|
|
@ -0,0 +1,13 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: e_sqrtf.S,v 1.2 1995/05/08 23:50:14 jtc Exp $")
|
||||
|
||||
ENTRY(__ieee754_sqrtf)
|
||||
flds 4(%esp)
|
||||
fsqrt
|
||||
ret
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_atan.S,v 1.4 1995/05/08 23:50:41 jtc Exp $")
|
||||
|
||||
ENTRY(__atan)
|
||||
fldl 4(%esp)
|
||||
fld1
|
||||
fpatan
|
||||
ret
|
||||
weak_alias (__atan, atan)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_atanf.S,v 1.3 1995/05/08 23:51:33 jtc Exp $")
|
||||
|
||||
ENTRY(__atanf)
|
||||
flds 4(%esp)
|
||||
fld1
|
||||
fpatan
|
||||
ret
|
||||
weak_alias (__atanf, atanf)
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_ceil.S,v 1.4 1995/05/08 23:52:13 jtc Exp $")
|
||||
|
||||
ENTRY(__ceil)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $8,%esp
|
||||
|
||||
fstcw -12(%ebp) /* store fpu control word */
|
||||
movw -12(%ebp),%dx
|
||||
orw $0x0800,%dx /* round towards +oo */
|
||||
andw $0xfbff,%dx
|
||||
movw %dx,-16(%ebp)
|
||||
fldcw -16(%ebp) /* load modfied control word */
|
||||
|
||||
fldl 8(%ebp); /* round */
|
||||
frndint
|
||||
|
||||
fldcw -12(%ebp) /* restore original control word */
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__ceil, ceil)
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_ceilf.S,v 1.3 1995/05/08 23:52:44 jtc Exp $")
|
||||
|
||||
ENTRY(__ceilf)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $8,%esp
|
||||
|
||||
fstcw -12(%ebp) /* store fpu control word */
|
||||
movw -12(%ebp),%dx
|
||||
orw $0x0800,%dx /* round towards +oo */
|
||||
andw $0xfbff,%dx
|
||||
movw %dx,-16(%ebp)
|
||||
fldcw -16(%ebp) /* load modfied control word */
|
||||
|
||||
flds 8(%ebp); /* round */
|
||||
frndint
|
||||
|
||||
fldcw -12(%ebp) /* restore original control word */
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__ceilf, ceilf)
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_copysign.S,v 1.4 1995/05/08 23:53:02 jtc Exp $")
|
||||
|
||||
ENTRY(__copysign)
|
||||
movl 16(%esp),%edx
|
||||
andl $0x80000000,%edx
|
||||
movl 8(%esp),%eax
|
||||
andl $0x7fffffff,%eax
|
||||
orl %edx,%eax
|
||||
movl %eax,8(%esp)
|
||||
fldl 4(%esp)
|
||||
ret
|
||||
weak_alias (__copysign, copysign)
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_copysignf.S,v 1.3 1995/05/08 23:53:25 jtc Exp $")
|
||||
|
||||
ENTRY(__copysignf)
|
||||
movl 8(%esp),%edx
|
||||
andl $0x80000000,%edx
|
||||
movl 4(%esp),%eax
|
||||
andl $0x7fffffff,%eax
|
||||
orl %edx,%eax
|
||||
movl %eax,4(%esp)
|
||||
flds 4(%esp)
|
||||
ret
|
||||
weak_alias (__copysignf, copysignf)
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_cos.S,v 1.5 1995/05/08 23:54:00 jtc Exp $")
|
||||
|
||||
ENTRY(__cos)
|
||||
fldl 4(%esp)
|
||||
fcos
|
||||
fnstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 1f
|
||||
ret
|
||||
1: fldpi
|
||||
fadd %st(0)
|
||||
fxch %st(1)
|
||||
2: fprem1
|
||||
fnstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 2b
|
||||
fstp %st(1)
|
||||
fcos
|
||||
ret
|
||||
weak_alias (__cos, cos)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_cosf.S,v 1.3 1995/05/08 23:55:16 jtc Exp $")
|
||||
|
||||
/* A float's domain isn't large enough to require argument reduction. */
|
||||
ENTRY(__cosf)
|
||||
flds 4(%esp)
|
||||
fcos
|
||||
ret
|
||||
weak_alias (__cosf, cosf)
|
||||
|
|
@ -0,0 +1,17 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_finite.S,v 1.4 1995/05/08 23:57:41 jtc Exp $")
|
||||
|
||||
ENTRY(__finite)
|
||||
movl 8(%esp),%eax
|
||||
andl $0x7ff00000, %eax
|
||||
cmpl $0x7ff00000, %eax
|
||||
setnel %al
|
||||
andl $0x000000ff, %eax
|
||||
ret
|
||||
weak_alias (__finite, finite)
|
||||
|
|
@ -0,0 +1,17 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_finitef.S,v 1.3 1995/05/09 00:00:02 jtc Exp $")
|
||||
|
||||
ENTRY(__finitef)
|
||||
movl 4(%esp),%eax
|
||||
andl $0x7ff00000, %eax
|
||||
cmpl $0x7ff00000, %eax
|
||||
setnel %al
|
||||
andl $0x000000ff, %eax
|
||||
ret
|
||||
weak_alias (__finitef, finitef)
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_floor.S,v 1.4 1995/05/09 00:01:59 jtc Exp $")
|
||||
|
||||
ENTRY(__floor)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $8,%esp
|
||||
|
||||
fstcw -12(%ebp) /* store fpu control word */
|
||||
movw -12(%ebp),%dx
|
||||
orw $0x0400,%dx /* round towards -oo */
|
||||
andw $0xf7ff,%dx
|
||||
movw %dx,-16(%ebp)
|
||||
fldcw -16(%ebp) /* load modfied control word */
|
||||
|
||||
fldl 8(%ebp); /* round */
|
||||
frndint
|
||||
|
||||
fldcw -12(%ebp) /* restore original control word */
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__floor, floor)
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_floorf.S,v 1.3 1995/05/09 00:04:32 jtc Exp $")
|
||||
|
||||
ENTRY(__floorf)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $8,%esp
|
||||
|
||||
fstcw -12(%ebp) /* store fpu control word */
|
||||
movw -12(%ebp),%dx
|
||||
orw $0x0400,%dx /* round towards -oo */
|
||||
andw $0xf7ff,%dx
|
||||
movw %dx,-16(%ebp)
|
||||
fldcw -16(%ebp) /* load modfied control word */
|
||||
|
||||
flds 8(%ebp); /* round */
|
||||
frndint
|
||||
|
||||
fldcw -12(%ebp) /* restore original control word */
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__floorf, floorf)
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_ilogb.S,v 1.5 1995/10/12 15:53:09 jtc Exp $")
|
||||
|
||||
ENTRY(__ilogb)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $4,%esp
|
||||
|
||||
fldl 8(%ebp)
|
||||
fxtract
|
||||
fstpl %st
|
||||
|
||||
fistpl -4(%ebp)
|
||||
movl -4(%ebp),%eax
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__ilogb, ilogb)
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_ilogbf.S,v 1.4 1995/10/22 20:32:43 pk Exp $")
|
||||
|
||||
ENTRY(__ilogbf)
|
||||
pushl %ebp
|
||||
movl %esp,%ebp
|
||||
subl $4,%esp
|
||||
|
||||
flds 8(%ebp)
|
||||
fxtract
|
||||
fstpl %st
|
||||
|
||||
fistpl -4(%ebp)
|
||||
movl -4(%ebp),%eax
|
||||
|
||||
leave
|
||||
ret
|
||||
weak_alias (__ilogbf, ilogbf)
|
||||
|
|
@ -0,0 +1,23 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_log1p.S,v 1.7 1995/05/09 00:10:58 jtc Exp $")
|
||||
|
||||
/*
|
||||
* Since the fyl2xp1 instruction has such a limited range:
|
||||
* -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1
|
||||
* it's not worth trying to use it.
|
||||
*/
|
||||
|
||||
ENTRY(__log1p)
|
||||
fldln2
|
||||
fldl 4(%esp)
|
||||
fld1
|
||||
faddp
|
||||
fyl2x
|
||||
ret
|
||||
weak_alias (__log1p, log1p)
|
||||
|
|
@ -0,0 +1,23 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_log1pf.S,v 1.4 1995/05/09 00:13:05 jtc Exp $")
|
||||
|
||||
/*
|
||||
* Since the fyl2xp1 instruction has such a limited range:
|
||||
* -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1
|
||||
* it's not worth trying to use it.
|
||||
*/
|
||||
|
||||
ENTRY(__log1pf)
|
||||
fldln2
|
||||
flds 4(%esp)
|
||||
fld1
|
||||
faddp
|
||||
fyl2x
|
||||
ret
|
||||
weak_alias (__log1pf, log1pf)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_logb.S,v 1.4 1995/05/09 00:14:30 jtc Exp $")
|
||||
|
||||
ENTRY(__logb)
|
||||
fldl 4(%esp)
|
||||
fxtract
|
||||
fstpl %st
|
||||
ret
|
||||
weak_alias (__logb, logb)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_logbf.S,v 1.3 1995/05/09 00:15:12 jtc Exp $")
|
||||
|
||||
ENTRY(__logbf)
|
||||
flds 4(%esp)
|
||||
fxtract
|
||||
fstpl %st
|
||||
ret
|
||||
weak_alias (__logbf, logbf)
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_rint.S,v 1.4 1995/05/09 00:16:08 jtc Exp $")
|
||||
|
||||
ENTRY(__rint)
|
||||
fldl 4(%esp)
|
||||
frndint
|
||||
ret
|
||||
weak_alias (__rint, rint)
|
||||
|
|
@ -0,0 +1,14 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_rintf.S,v 1.3 1995/05/09 00:17:22 jtc Exp $")
|
||||
|
||||
ENTRY(__rintf)
|
||||
flds 4(%esp)
|
||||
frndint
|
||||
ret
|
||||
weak_alias (__rintf, rintf)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_scalbn.S,v 1.4 1995/05/09 00:19:06 jtc Exp $")
|
||||
|
||||
ENTRY(__scalbn)
|
||||
fildl 12(%esp)
|
||||
fldl 4(%esp)
|
||||
fscale
|
||||
ret
|
||||
weak_alias (__scalbn, scalbn)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_scalbnf.S,v 1.3 1995/05/09 00:19:59 jtc Exp $")
|
||||
|
||||
ENTRY(__scalbnf)
|
||||
fildl 8(%esp)
|
||||
flds 4(%esp)
|
||||
fscale
|
||||
ret
|
||||
weak_alias (__scalbnf, scalbnf)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_significand.S,v 1.4 1995/05/09 00:21:47 jtc Exp $")
|
||||
|
||||
ENTRY(__significand)
|
||||
fldl 4(%esp)
|
||||
fxtract
|
||||
fstpl %st(1)
|
||||
ret
|
||||
weak_alias (__significand, significand)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_significandf.S,v 1.3 1995/05/09 00:24:07 jtc Exp $")
|
||||
|
||||
ENTRY(__significandf)
|
||||
flds 4(%esp)
|
||||
fxtract
|
||||
fstpl %st(1)
|
||||
ret
|
||||
weak_alias (__significandf, significandf)
|
||||
|
|
@ -0,0 +1,27 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_sin.S,v 1.5 1995/05/09 00:25:54 jtc Exp $")
|
||||
|
||||
ENTRY(__sin)
|
||||
fldl 4(%esp)
|
||||
fsin
|
||||
fnstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 1f
|
||||
ret
|
||||
1: fldpi
|
||||
fadd %st(0)
|
||||
fxch %st(1)
|
||||
2: fprem1
|
||||
fnstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 2b
|
||||
fstp %st(1)
|
||||
fsin
|
||||
ret
|
||||
weak_alias (__sin, sin)
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_sinf.S,v 1.3 1995/05/09 00:27:53 jtc Exp $")
|
||||
|
||||
/* A float's domain isn't large enough to require argument reduction. */
|
||||
ENTRY(__sinf)
|
||||
flds 4(%esp)
|
||||
fsin
|
||||
ret
|
||||
weak_alias (__sinf, sinf)
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_tan.S,v 1.5 1995/05/09 00:30:00 jtc Exp $")
|
||||
|
||||
ENTRY(__tan)
|
||||
fldl 4(%esp)
|
||||
fptan
|
||||
fnstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 1f
|
||||
fstp %st(0)
|
||||
ret
|
||||
1: fldpi
|
||||
fadd %st(0)
|
||||
fxch %st(1)
|
||||
2: fprem1
|
||||
fstsw %ax
|
||||
andw $0x400,%ax
|
||||
jnz 2b
|
||||
fstp %st(1)
|
||||
fptan
|
||||
fstp %st(0)
|
||||
ret
|
||||
weak_alias (__tan, tan)
|
||||
|
|
@ -0,0 +1,16 @@
|
|||
/*
|
||||
* Written by J.T. Conklin <jtc@netbsd.org>.
|
||||
* Public domain.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
|
||||
RCSID("$NetBSD: s_tanf.S,v 1.3 1995/05/09 00:31:09 jtc Exp $")
|
||||
|
||||
/* A float's domain isn't large enough to require argument reduction. */
|
||||
ENTRY(__tanf)
|
||||
flds 4(%esp)
|
||||
fptan
|
||||
fstp %st(0)
|
||||
ret
|
||||
weak_alias (__tanf, tanf)
|
||||
|
|
@ -0,0 +1,111 @@
|
|||
/* @(#)e_acos.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_acos(x)
|
||||
* Method :
|
||||
* acos(x) = pi/2 - asin(x)
|
||||
* acos(-x) = pi/2 + asin(x)
|
||||
* For |x|<=0.5
|
||||
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
|
||||
* For x>0.5
|
||||
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
|
||||
* = 2asin(sqrt((1-x)/2))
|
||||
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
|
||||
* = 2f + (2c + 2s*z*R(z))
|
||||
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
|
||||
* for f so that f+c ~ sqrt(z).
|
||||
* For x<-0.5
|
||||
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
|
||||
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
* Function needed: __ieee754_sqrt
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_acos(double x)
|
||||
#else
|
||||
double __ieee754_acos(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z,p,q,r,w,s,c,df;
|
||||
int32_t hx,ix;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x3ff00000) { /* |x| >= 1 */
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
|
||||
}
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3fe00000) { /* |x| < 0.5 */
|
||||
if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = __ieee754_sqrt(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - 2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
z = (one-x)*0.5;
|
||||
s = __ieee754_sqrt(z);
|
||||
df = s;
|
||||
SET_LOW_WORD(df,0);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return 2.0*(df+w);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,89 @@
|
|||
/* e_acosf.c -- float version of e_acos.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_acosf.c,v 1.5 1995/05/12 04:57:16 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
|
||||
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
|
||||
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
|
||||
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
|
||||
pS3 = -4.0055535734e-02, /* 0xbd241146 */
|
||||
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
|
||||
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
|
||||
qS1 = -2.4033949375e+00, /* 0xc019d139 */
|
||||
qS2 = 2.0209457874e+00, /* 0x4001572d */
|
||||
qS3 = -6.8828397989e-01, /* 0xbf303361 */
|
||||
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_acosf(float x)
|
||||
#else
|
||||
float __ieee754_acosf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z,p,q,r,w,s,c,df;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix==0x3f800000) { /* |x|==1 */
|
||||
if(hx>0) return 0.0; /* acos(1) = 0 */
|
||||
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
|
||||
} else if(ix>0x3f800000) { /* |x| >= 1 */
|
||||
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
|
||||
}
|
||||
if(ix<0x3f000000) { /* |x| < 0.5 */
|
||||
if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
|
||||
z = x*x;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
return pio2_hi - (x - (pio2_lo-x*r));
|
||||
} else if (hx<0) { /* x < -0.5 */
|
||||
z = (one+x)*(float)0.5;
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
s = __ieee754_sqrtf(z);
|
||||
r = p/q;
|
||||
w = r*s-pio2_lo;
|
||||
return pi - (float)2.0*(s+w);
|
||||
} else { /* x > 0.5 */
|
||||
int32_t idf;
|
||||
z = (one-x)*(float)0.5;
|
||||
s = __ieee754_sqrtf(z);
|
||||
df = s;
|
||||
GET_FLOAT_WORD(idf,df);
|
||||
SET_FLOAT_WORD(df,idf&0xfffff000);
|
||||
c = (z-df*df)/(s+df);
|
||||
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
|
||||
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
|
||||
r = p/q;
|
||||
w = r*s+c;
|
||||
return (float)2.0*(df+w);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,69 @@
|
|||
/* @(#)e_acosh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_acosh.c,v 1.9 1995/05/12 04:57:18 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_acosh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
||||
* we have
|
||||
* acosh(x) := log(x)+ln2, if x is large; else
|
||||
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
|
||||
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
|
||||
*
|
||||
* Special cases:
|
||||
* acosh(x) is NaN with signal if x<1.
|
||||
* acosh(NaN) is NaN without signal.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_acosh(double x)
|
||||
#else
|
||||
double __ieee754_acosh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t;
|
||||
int32_t hx;
|
||||
u_int32_t lx;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
if(hx<0x3ff00000) { /* x < 1 */
|
||||
return (x-x)/(x-x);
|
||||
} else if(hx >=0x41b00000) { /* x > 2**28 */
|
||||
if(hx >=0x7ff00000) { /* x is inf of NaN */
|
||||
return x+x;
|
||||
} else
|
||||
return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
|
||||
} else if(((hx-0x3ff00000)|lx)==0) {
|
||||
return 0.0; /* acosh(1) = 0 */
|
||||
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
||||
t=x*x;
|
||||
return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
|
||||
} else { /* 1<x<2 */
|
||||
t = x-one;
|
||||
return __log1p(t+__sqrt(2.0*t+t*t));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,57 @@
|
|||
/* e_acoshf.c -- float version of e_acosh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_acoshf.c,v 1.5 1995/05/12 04:57:20 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
one = 1.0,
|
||||
ln2 = 6.9314718246e-01; /* 0x3f317218 */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_acoshf(float x)
|
||||
#else
|
||||
float __ieee754_acoshf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float t;
|
||||
int32_t hx;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
if(hx<0x3f800000) { /* x < 1 */
|
||||
return (x-x)/(x-x);
|
||||
} else if(hx >=0x4d800000) { /* x > 2**28 */
|
||||
if(hx >=0x7f800000) { /* x is inf of NaN */
|
||||
return x+x;
|
||||
} else
|
||||
return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */
|
||||
} else if (hx==0x3f800000) {
|
||||
return 0.0; /* acosh(1) = 0 */
|
||||
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
||||
t=x*x;
|
||||
return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one)));
|
||||
} else { /* 1<x<2 */
|
||||
t = x-one;
|
||||
return __log1pf(t+__sqrtf((float)2.0*t+t*t));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,120 @@
|
|||
/* @(#)e_asin.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_asin(x)
|
||||
* Method :
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
||||
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
huge = 1.000e+300,
|
||||
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
|
||||
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
|
||||
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
|
||||
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
|
||||
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
|
||||
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
|
||||
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
|
||||
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
|
||||
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
|
||||
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
|
||||
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_asin(double x)
|
||||
#else
|
||||
double __ieee754_asin(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w,p,q,c,r,s;
|
||||
int32_t hx,ix;
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>= 0x3ff00000) { /* |x|>= 1 */
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3fe00000) { /* |x|<0.5 */
|
||||
if(ix<0x3e400000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabs(x);
|
||||
t = w*0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = __ieee754_sqrt(t);
|
||||
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
w = s;
|
||||
SET_LOW_WORD(w,0);
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = 2.0*s*r-(pio2_lo-2.0*c);
|
||||
q = pio4_hi-2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,92 @@
|
|||
/* e_asinf.c -- float version of e_asin.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_asinf.c,v 1.5 1995/05/12 04:57:25 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
one = 1.0000000000e+00, /* 0x3F800000 */
|
||||
huge = 1.000e+30,
|
||||
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
|
||||
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
|
||||
pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */
|
||||
/* coefficient for R(x^2) */
|
||||
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
|
||||
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
|
||||
pS3 = -4.0055535734e-02, /* 0xbd241146 */
|
||||
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
|
||||
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
|
||||
qS1 = -2.4033949375e+00, /* 0xc019d139 */
|
||||
qS2 = 2.0209457874e+00, /* 0x4001572d */
|
||||
qS3 = -6.8828397989e-01, /* 0xbf303361 */
|
||||
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_asinf(float x)
|
||||
#else
|
||||
float __ieee754_asinf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float t,w,p,q,c,r,s;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix==0x3f800000) {
|
||||
/* asin(1)=+-pi/2 with inexact */
|
||||
return x*pio2_hi+x*pio2_lo;
|
||||
} else if(ix> 0x3f800000) { /* |x|>= 1 */
|
||||
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
|
||||
} else if (ix<0x3f000000) { /* |x|<0.5 */
|
||||
if(ix<0x32000000) { /* if |x| < 2**-27 */
|
||||
if(huge+x>one) return x;/* return x with inexact if x!=0*/
|
||||
} else
|
||||
t = x*x;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
w = p/q;
|
||||
return x+x*w;
|
||||
}
|
||||
/* 1> |x|>= 0.5 */
|
||||
w = one-fabsf(x);
|
||||
t = w*(float)0.5;
|
||||
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
|
||||
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
|
||||
s = __ieee754_sqrtf(t);
|
||||
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
|
||||
w = p/q;
|
||||
t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
|
||||
} else {
|
||||
int32_t iw;
|
||||
w = s;
|
||||
GET_FLOAT_WORD(iw,w);
|
||||
SET_FLOAT_WORD(w,iw&0xfffff000);
|
||||
c = (t-w*w)/(s+w);
|
||||
r = p/q;
|
||||
p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
|
||||
q = pio4_hi-(float)2.0*w;
|
||||
t = pio4_hi-(p-q);
|
||||
}
|
||||
if(hx>0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,130 @@
|
|||
/* @(#)e_atan2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_atan2(y,x)
|
||||
* Method :
|
||||
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
||||
* 2. Reduce x to positive by (if x and y are unexceptional):
|
||||
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
||||
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
||||
*
|
||||
* Special cases:
|
||||
*
|
||||
* ATAN2((anything), NaN ) is NaN;
|
||||
* ATAN2(NAN , (anything) ) is NaN;
|
||||
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
||||
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
||||
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
||||
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
||||
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
||||
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
||||
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
||||
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
tiny = 1.0e-300,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
|
||||
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
|
||||
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
|
||||
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_atan2(double y, double x)
|
||||
#else
|
||||
double __ieee754_atan2(y,x)
|
||||
double y,x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int32_t k,m,hx,hy,ix,iy;
|
||||
u_int32_t lx,ly;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
iy = hy&0x7fffffff;
|
||||
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
|
||||
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if((iy|ly)==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7ff00000) {
|
||||
if(iy==0x7ff00000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>20;
|
||||
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=atan(fabs(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: {
|
||||
u_int32_t zh;
|
||||
GET_HIGH_WORD(zh,z);
|
||||
SET_HIGH_WORD(z,zh ^ 0x80000000);
|
||||
}
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,105 @@
|
|||
/* e_atan2f.c -- float version of e_atan2.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_atan2f.c,v 1.4 1995/05/10 20:44:53 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
tiny = 1.0e-30,
|
||||
zero = 0.0,
|
||||
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
|
||||
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
|
||||
pi = 3.1415925026e+00, /* 0x40490fda */
|
||||
pi_lo = 1.5099578832e-07; /* 0x34222168 */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_atan2f(float y, float x)
|
||||
#else
|
||||
float __ieee754_atan2f(y,x)
|
||||
float y,x;
|
||||
#endif
|
||||
{
|
||||
float z;
|
||||
int32_t k,m,hx,hy,ix,iy;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
iy = hy&0x7fffffff;
|
||||
if((ix>0x7f800000)||
|
||||
(iy>0x7f800000)) /* x or y is NaN */
|
||||
return x+y;
|
||||
if(hx==0x3f800000) return atanf(y); /* x=1.0 */
|
||||
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if(iy==0) {
|
||||
switch(m) {
|
||||
case 0:
|
||||
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
||||
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
||||
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* when x is INF */
|
||||
if(ix==0x7f800000) {
|
||||
if(iy==0x7f800000) {
|
||||
switch(m) {
|
||||
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
||||
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
||||
case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
||||
case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
||||
}
|
||||
} else {
|
||||
switch(m) {
|
||||
case 0: return zero ; /* atan(+...,+INF) */
|
||||
case 1: return -zero ; /* atan(-...,+INF) */
|
||||
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
||||
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
||||
|
||||
/* compute y/x */
|
||||
k = (iy-ix)>>23;
|
||||
if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
|
||||
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
||||
else z=atanf(fabsf(y/x)); /* safe to do y/x */
|
||||
switch (m) {
|
||||
case 0: return z ; /* atan(+,+) */
|
||||
case 1: {
|
||||
u_int32_t zh;
|
||||
GET_FLOAT_WORD(zh,z);
|
||||
SET_FLOAT_WORD(z,zh ^ 0x80000000);
|
||||
}
|
||||
return z ; /* atan(-,+) */
|
||||
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
||||
default: /* case 3 */
|
||||
return (z-pi_lo)-pi;/* atan(-,-) */
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,74 @@
|
|||
/* @(#)e_atanh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_atanh(x)
|
||||
* Method :
|
||||
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
|
||||
* 2.For x>=0.5
|
||||
* 1 2x x
|
||||
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
|
||||
* 2 1 - x 1 - x
|
||||
*
|
||||
* For x<0.5
|
||||
* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
|
||||
*
|
||||
* Special cases:
|
||||
* atanh(x) is NaN if |x| > 1 with signal;
|
||||
* atanh(NaN) is that NaN with no signal;
|
||||
* atanh(+-1) is +-INF with signal.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, huge = 1e300;
|
||||
#else
|
||||
static double one = 1.0, huge = 1e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_atanh(double x)
|
||||
#else
|
||||
double __ieee754_atanh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t;
|
||||
int32_t hx,ix;
|
||||
u_int32_t lx;
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
|
||||
return (x-x)/(x-x);
|
||||
if(ix==0x3ff00000)
|
||||
return x/zero;
|
||||
if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
|
||||
SET_HIGH_WORD(x,ix);
|
||||
if(ix<0x3fe00000) { /* x < 0.5 */
|
||||
t = x+x;
|
||||
t = 0.5*__log1p(t+t*x/(one-x));
|
||||
} else
|
||||
t = 0.5*__log1p((x+x)/(one-x));
|
||||
if(hx>=0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,58 @@
|
|||
/* e_atanhf.c -- float version of e_atanh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_atanhf.c,v 1.4 1995/05/10 20:44:56 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float one = 1.0, huge = 1e30;
|
||||
#else
|
||||
static float one = 1.0, huge = 1e30;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_atanhf(float x)
|
||||
#else
|
||||
float __ieee754_atanhf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float t;
|
||||
int32_t hx,ix;
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if (ix>0x3f800000) /* |x|>1 */
|
||||
return (x-x)/(x-x);
|
||||
if(ix==0x3f800000)
|
||||
return x/zero;
|
||||
if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */
|
||||
SET_FLOAT_WORD(x,ix);
|
||||
if(ix<0x3f000000) { /* x < 0.5 */
|
||||
t = x+x;
|
||||
t = (float)0.5*__log1pf(t+t*x/(one-x));
|
||||
} else
|
||||
t = (float)0.5*__log1pf((x+x)/(one-x));
|
||||
if(hx>=0) return t; else return -t;
|
||||
}
|
||||
|
|
@ -0,0 +1,93 @@
|
|||
/* @(#)e_cosh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_cosh(x)
|
||||
* Method :
|
||||
* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
|
||||
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
|
||||
* 2.
|
||||
* [ exp(x) - 1 ]^2
|
||||
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
|
||||
* 2*exp(x)
|
||||
*
|
||||
* exp(x) + 1/exp(x)
|
||||
* ln2/2 <= x <= 22 : cosh(x) := -------------------
|
||||
* 2
|
||||
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : cosh(x) := huge*huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* cosh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only cosh(0)=1 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, half=0.5, huge = 1.0e300;
|
||||
#else
|
||||
static double one = 1.0, half=0.5, huge = 1.0e300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_cosh(double x)
|
||||
#else
|
||||
double __ieee754_cosh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w;
|
||||
int32_t ix;
|
||||
u_int32_t lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
|
||||
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
||||
if(ix<0x3fd62e43) {
|
||||
t = __expm1(fabs(x));
|
||||
w = one+t;
|
||||
if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
|
||||
return one+(t*t)/(w+w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
||||
if (ix < 0x40360000) {
|
||||
t = __ieee754_exp(fabs(x));
|
||||
return half*t+half/t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
|
||||
if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
GET_LOW_WORD(lx,x);
|
||||
if (ix<0x408633CE ||
|
||||
(ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
|
||||
w = __ieee754_exp(half*fabs(x));
|
||||
t = half*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge*huge;
|
||||
}
|
||||
|
|
@ -0,0 +1,72 @@
|
|||
/* e_coshf.c -- float version of e_cosh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_coshf.c,v 1.5 1995/05/10 20:45:01 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const volatile float huge = 1.0e30;
|
||||
static const float one = 1.0, half=0.5;
|
||||
#else
|
||||
static float one = 1.0, half=0.5, huge = 1.0e30;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_coshf(float x)
|
||||
#else
|
||||
float __ieee754_coshf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float t,w;
|
||||
int32_t ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7f800000) return x*x;
|
||||
|
||||
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
|
||||
if(ix<0x3eb17218) {
|
||||
t = __expm1f(fabsf(x));
|
||||
w = one+t;
|
||||
if (ix<0x24000000) return w; /* cosh(tiny) = 1 */
|
||||
return one+(t*t)/(w+w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
|
||||
if (ix < 0x41b00000) {
|
||||
t = __ieee754_expf(fabsf(x));
|
||||
return half*t+half/t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
|
||||
if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
if (ix<=0x42b2d4fc) {
|
||||
w = __ieee754_expf(half*fabsf(x));
|
||||
t = half*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge*huge;
|
||||
}
|
||||
|
|
@ -0,0 +1,167 @@
|
|||
/* @(#)e_exp.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_exp.c,v 1.8 1995/05/10 20:45:03 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_exp(x)
|
||||
* Returns the exponential of x.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2.
|
||||
*
|
||||
* Here r will be represented as r = hi-lo for better
|
||||
* accuracy.
|
||||
*
|
||||
* 2. Approximation of exp(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Write
|
||||
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
||||
* We use a special Reme algorithm on [0,0.34658] to generate
|
||||
* a polynomial of degree 5 to approximate R. The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
huge = 1.0e+300,
|
||||
twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
|
||||
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
|
||||
u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
|
||||
ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
|
||||
ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
|
||||
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_exp(double x) /* default IEEE double exp */
|
||||
#else
|
||||
double __ieee754_exp(x) /* default IEEE double exp */
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,hi,lo,c,t;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
|
||||
if(hx>=0x7ff00000) {
|
||||
u_int32_t lx;
|
||||
GET_LOW_WORD(lx,x);
|
||||
if(((hx&0xfffff)|lx)!=0)
|
||||
return x+x; /* NaN */
|
||||
else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
}
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom1000*twom1000; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = invln2*x+halF[xsb];
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-2.0)-x);
|
||||
else y = one-((lo-(x*c)/(2.0-c))-hi);
|
||||
if(k >= -1021) {
|
||||
u_int32_t hy;
|
||||
GET_HIGH_WORD(hy,y);
|
||||
SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
u_int32_t hy;
|
||||
GET_HIGH_WORD(hy,y);
|
||||
SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
|
||||
return y*twom1000;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,104 @@
|
|||
/* e_expf.c -- float version of e_exp.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_expf.c,v 1.5 1995/05/10 20:45:05 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const volatile float huge = 1.0e+30;
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
one = 1.0,
|
||||
halF[2] = {0.5,-0.5,},
|
||||
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
|
||||
o_threshold= 8.8721679688e+01, /* 0x42b17180 */
|
||||
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
|
||||
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
|
||||
-6.9313812256e-01,}, /* 0xbf317180 */
|
||||
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
-9.0580006145e-06,}, /* 0xb717f7d1 */
|
||||
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
|
||||
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
||||
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
||||
P5 = 4.1381369442e-08; /* 0x3331bb4c */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_expf(float x) /* default IEEE double exp */
|
||||
#else
|
||||
float __ieee754_expf(x) /* default IEEE double exp */
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float y,hi,lo,c,t;
|
||||
int32_t k,xsb;
|
||||
u_int32_t hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
xsb = (hx>>31)&1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
||||
if(hx>0x7f800000)
|
||||
return x+x; /* NaN */
|
||||
if(hx==0x7f800000)
|
||||
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
|
||||
if(x > o_threshold) return huge*huge; /* overflow */
|
||||
if(x < u_threshold) return twom100*twom100; /* underflow */
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
||||
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
||||
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
||||
} else {
|
||||
k = invln2*x+halF[xsb];
|
||||
t = k;
|
||||
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
|
||||
lo = t*ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if(hx < 0x31800000) { /* when |x|<2**-28 */
|
||||
if(huge+x>one) return one+x;/* trigger inexact */
|
||||
}
|
||||
else k = 0;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x*x;
|
||||
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
|
||||
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
|
||||
if(k >= -125) {
|
||||
u_int32_t hy;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
u_int32_t hy;
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
|
||||
return y*twom100;
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,140 @@
|
|||
/* @(#)e_fmod.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_fmod.c,v 1.8 1995/05/10 20:45:07 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_fmod(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#else
|
||||
static double one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_fmod(double x, double y)
|
||||
#else
|
||||
double __ieee754_fmod(x,y)
|
||||
double x,y ;
|
||||
#endif
|
||||
{
|
||||
int32_t n,hx,hy,hz,ix,iy,sx,i;
|
||||
u_int32_t lx,ly,lz;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
sx = hx&0x80000000; /* sign of x */
|
||||
hx ^=sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
|
||||
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
|
||||
return (x*y)/(x*y);
|
||||
if(hx<=hy) {
|
||||
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
|
||||
if(lx==ly)
|
||||
return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
|
||||
}
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if(hx<0x00100000) { /* subnormal x */
|
||||
if(hx==0) {
|
||||
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
|
||||
} else {
|
||||
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
|
||||
}
|
||||
} else ix = (hx>>20)-1023;
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if(hy<0x00100000) { /* subnormal y */
|
||||
if(hy==0) {
|
||||
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
|
||||
} else {
|
||||
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
|
||||
}
|
||||
} else iy = (hy>>20)-1023;
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if(ix >= -1022)
|
||||
hx = 0x00100000|(0x000fffff&hx);
|
||||
else { /* subnormal x, shift x to normal */
|
||||
n = -1022-ix;
|
||||
if(n<=31) {
|
||||
hx = (hx<<n)|(lx>>(32-n));
|
||||
lx <<= n;
|
||||
} else {
|
||||
hx = lx<<(n-32);
|
||||
lx = 0;
|
||||
}
|
||||
}
|
||||
if(iy >= -1022)
|
||||
hy = 0x00100000|(0x000fffff&hy);
|
||||
else { /* subnormal y, shift y to normal */
|
||||
n = -1022-iy;
|
||||
if(n<=31) {
|
||||
hy = (hy<<n)|(ly>>(32-n));
|
||||
ly <<= n;
|
||||
} else {
|
||||
hy = ly<<(n-32);
|
||||
ly = 0;
|
||||
}
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while(n--) {
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
|
||||
else {
|
||||
if((hz|lz)==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
hx = hz+hz+(lz>>31); lx = lz+lz;
|
||||
}
|
||||
}
|
||||
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
||||
if(hz>=0) {hx=hz;lx=lz;}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if((hx|lx)==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
while(hx<0x00100000) { /* normalize x */
|
||||
hx = hx+hx+(lx>>31); lx = lx+lx;
|
||||
iy -= 1;
|
||||
}
|
||||
if(iy>= -1022) { /* normalize output */
|
||||
hx = ((hx-0x00100000)|((iy+1023)<<20));
|
||||
INSERT_WORDS(x,hx|sx,lx);
|
||||
} else { /* subnormal output */
|
||||
n = -1022 - iy;
|
||||
if(n<=20) {
|
||||
lx = (lx>>n)|((u_int32_t)hx<<(32-n));
|
||||
hx >>= n;
|
||||
} else if (n<=31) {
|
||||
lx = (hx<<(32-n))|(lx>>n); hx = sx;
|
||||
} else {
|
||||
lx = hx>>(n-32); hx = sx;
|
||||
}
|
||||
INSERT_WORDS(x,hx|sx,lx);
|
||||
x *= one; /* create necessary signal */
|
||||
}
|
||||
return x; /* exact output */
|
||||
}
|
||||
|
|
@ -0,0 +1,113 @@
|
|||
/* e_fmodf.c -- float version of e_fmod.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_fmodf.c,v 1.4 1995/05/10 20:45:10 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_fmodf(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#else
|
||||
static float one = 1.0, Zero[] = {0.0, -0.0,};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_fmodf(float x, float y)
|
||||
#else
|
||||
float __ieee754_fmodf(x,y)
|
||||
float x,y ;
|
||||
#endif
|
||||
{
|
||||
int32_t n,hx,hy,hz,ix,iy,sx,i;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
sx = hx&0x80000000; /* sign of x */
|
||||
hx ^=sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
|
||||
(hy>0x7f800000)) /* or y is NaN */
|
||||
return (x*y)/(x*y);
|
||||
if(hx<hy) return x; /* |x|<|y| return x */
|
||||
if(hx==hy)
|
||||
return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if(hx<0x00800000) { /* subnormal x */
|
||||
for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
|
||||
} else ix = (hx>>23)-127;
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if(hy<0x00800000) { /* subnormal y */
|
||||
for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
|
||||
} else iy = (hy>>23)-127;
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if(ix >= -126)
|
||||
hx = 0x00800000|(0x007fffff&hx);
|
||||
else { /* subnormal x, shift x to normal */
|
||||
n = -126-ix;
|
||||
hx = hx<<n;
|
||||
}
|
||||
if(iy >= -126)
|
||||
hy = 0x00800000|(0x007fffff&hy);
|
||||
else { /* subnormal y, shift y to normal */
|
||||
n = -126-iy;
|
||||
hy = hy<<n;
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while(n--) {
|
||||
hz=hx-hy;
|
||||
if(hz<0){hx = hx+hx;}
|
||||
else {
|
||||
if(hz==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
hx = hz+hz;
|
||||
}
|
||||
}
|
||||
hz=hx-hy;
|
||||
if(hz>=0) {hx=hz;}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if(hx==0) /* return sign(x)*0 */
|
||||
return Zero[(u_int32_t)sx>>31];
|
||||
while(hx<0x00800000) { /* normalize x */
|
||||
hx = hx+hx;
|
||||
iy -= 1;
|
||||
}
|
||||
if(iy>= -126) { /* normalize output */
|
||||
hx = ((hx-0x00800000)|((iy+127)<<23));
|
||||
SET_FLOAT_WORD(x,hx|sx);
|
||||
} else { /* subnormal output */
|
||||
n = -126 - iy;
|
||||
hx >>= n;
|
||||
SET_FLOAT_WORD(x,hx|sx);
|
||||
x *= one; /* create necessary signal */
|
||||
}
|
||||
return x; /* exact output */
|
||||
}
|
||||
|
|
@ -0,0 +1,128 @@
|
|||
/* @(#)e_hypot.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_hypot.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_hypot(x,y)
|
||||
*
|
||||
* Method :
|
||||
* If (assume round-to-nearest) z=x*x+y*y
|
||||
* has error less than sqrt(2)/2 ulp, than
|
||||
* sqrt(z) has error less than 1 ulp (exercise).
|
||||
*
|
||||
* So, compute sqrt(x*x+y*y) with some care as
|
||||
* follows to get the error below 1 ulp:
|
||||
*
|
||||
* Assume x>y>0;
|
||||
* (if possible, set rounding to round-to-nearest)
|
||||
* 1. if x > 2y use
|
||||
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
|
||||
* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
|
||||
* 2. if x <= 2y use
|
||||
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
|
||||
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
|
||||
* y1= y with lower 32 bits chopped, y2 = y-y1.
|
||||
*
|
||||
* NOTE: scaling may be necessary if some argument is too
|
||||
* large or too tiny
|
||||
*
|
||||
* Special cases:
|
||||
* hypot(x,y) is INF if x or y is +INF or -INF; else
|
||||
* hypot(x,y) is NAN if x or y is NAN.
|
||||
*
|
||||
* Accuracy:
|
||||
* hypot(x,y) returns sqrt(x^2+y^2) with error less
|
||||
* than 1 ulps (units in the last place)
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_hypot(double x, double y)
|
||||
#else
|
||||
double __ieee754_hypot(x,y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double a=x,b=y,t1,t2,y1,y2,w;
|
||||
int32_t j,k,ha,hb;
|
||||
|
||||
GET_HIGH_WORD(ha,x);
|
||||
ha &= 0x7fffffff;
|
||||
GET_HIGH_WORD(hb,y);
|
||||
hb &= 0x7fffffff;
|
||||
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
|
||||
SET_HIGH_WORD(a,ha); /* a <- |a| */
|
||||
SET_HIGH_WORD(b,hb); /* b <- |b| */
|
||||
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
|
||||
k=0;
|
||||
if(ha > 0x5f300000) { /* a>2**500 */
|
||||
if(ha >= 0x7ff00000) { /* Inf or NaN */
|
||||
u_int32_t low;
|
||||
w = a+b; /* for sNaN */
|
||||
GET_LOW_WORD(low,a);
|
||||
if(((ha&0xfffff)|low)==0) w = a;
|
||||
GET_LOW_WORD(low,b);
|
||||
if(((hb^0x7ff00000)|low)==0) w = b;
|
||||
return w;
|
||||
}
|
||||
/* scale a and b by 2**-600 */
|
||||
ha -= 0x25800000; hb -= 0x25800000; k += 600;
|
||||
SET_HIGH_WORD(a,ha);
|
||||
SET_HIGH_WORD(b,hb);
|
||||
}
|
||||
if(hb < 0x20b00000) { /* b < 2**-500 */
|
||||
if(hb <= 0x000fffff) { /* subnormal b or 0 */
|
||||
u_int32_t low;
|
||||
GET_LOW_WORD(low,b);
|
||||
if((hb|low)==0) return a;
|
||||
t1=0;
|
||||
SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
|
||||
b *= t1;
|
||||
a *= t1;
|
||||
k -= 1022;
|
||||
} else { /* scale a and b by 2^600 */
|
||||
ha += 0x25800000; /* a *= 2^600 */
|
||||
hb += 0x25800000; /* b *= 2^600 */
|
||||
k -= 600;
|
||||
SET_HIGH_WORD(a,ha);
|
||||
SET_HIGH_WORD(b,hb);
|
||||
}
|
||||
}
|
||||
/* medium size a and b */
|
||||
w = a-b;
|
||||
if (w>b) {
|
||||
t1 = 0;
|
||||
SET_HIGH_WORD(t1,ha);
|
||||
t2 = a-t1;
|
||||
w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
|
||||
} else {
|
||||
a = a+a;
|
||||
y1 = 0;
|
||||
SET_HIGH_WORD(y1,hb);
|
||||
y2 = b - y1;
|
||||
t1 = 0;
|
||||
SET_HIGH_WORD(t1,ha+0x00100000);
|
||||
t2 = a - t1;
|
||||
w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
|
||||
}
|
||||
if(k!=0) {
|
||||
u_int32_t high;
|
||||
t1 = 1.0;
|
||||
GET_HIGH_WORD(high,t1);
|
||||
SET_HIGH_WORD(t1,high+(k<<20));
|
||||
return t1*w;
|
||||
} else return w;
|
||||
}
|
||||
|
|
@ -0,0 +1,87 @@
|
|||
/* e_hypotf.c -- float version of e_hypot.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_hypotf.c,v 1.5 1995/05/12 04:57:30 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_hypotf(float x, float y)
|
||||
#else
|
||||
float __ieee754_hypot(x,y)
|
||||
float x, y;
|
||||
#endif
|
||||
{
|
||||
float a=x,b=y,t1,t2,y1,y2,w;
|
||||
int32_t j,k,ha,hb;
|
||||
|
||||
GET_FLOAT_WORD(ha,x);
|
||||
ha &= 0x7fffffff;
|
||||
GET_FLOAT_WORD(hb,y);
|
||||
hb &= 0x7fffffff;
|
||||
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
|
||||
SET_FLOAT_WORD(a,ha); /* a <- |a| */
|
||||
SET_FLOAT_WORD(b,hb); /* b <- |b| */
|
||||
if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
|
||||
k=0;
|
||||
if(ha > 0x58800000) { /* a>2**50 */
|
||||
if(ha >= 0x7f800000) { /* Inf or NaN */
|
||||
w = a+b; /* for sNaN */
|
||||
if(ha == 0x7f800000) w = a;
|
||||
if(hb == 0x7f800000) w = b;
|
||||
return w;
|
||||
}
|
||||
/* scale a and b by 2**-60 */
|
||||
ha -= 0x5d800000; hb -= 0x5d800000; k += 60;
|
||||
SET_FLOAT_WORD(a,ha);
|
||||
SET_FLOAT_WORD(b,hb);
|
||||
}
|
||||
if(hb < 0x26800000) { /* b < 2**-50 */
|
||||
if(hb <= 0x007fffff) { /* subnormal b or 0 */
|
||||
if(hb==0) return a;
|
||||
SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */
|
||||
b *= t1;
|
||||
a *= t1;
|
||||
k -= 126;
|
||||
} else { /* scale a and b by 2^60 */
|
||||
ha += 0x5d800000; /* a *= 2^60 */
|
||||
hb += 0x5d800000; /* b *= 2^60 */
|
||||
k -= 60;
|
||||
SET_FLOAT_WORD(a,ha);
|
||||
SET_FLOAT_WORD(b,hb);
|
||||
}
|
||||
}
|
||||
/* medium size a and b */
|
||||
w = a-b;
|
||||
if (w>b) {
|
||||
SET_FLOAT_WORD(t1,ha&0xfffff000);
|
||||
t2 = a-t1;
|
||||
w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
|
||||
} else {
|
||||
a = a+a;
|
||||
SET_FLOAT_WORD(y1,hb&0xfffff000);
|
||||
y2 = b - y1;
|
||||
SET_FLOAT_WORD(t1,ha+0x00800000);
|
||||
t2 = a - t1;
|
||||
w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
|
||||
}
|
||||
if(k!=0) {
|
||||
SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
|
||||
return t1*w;
|
||||
} else return w;
|
||||
}
|
||||
|
|
@ -0,0 +1,487 @@
|
|||
/* @(#)e_j0.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_j0(x), __ieee754_y0(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j0(x):
|
||||
* 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
|
||||
* 2. Reduce x to |x| since j0(x)=j0(-x), and
|
||||
* for x in (0,2)
|
||||
* j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x;
|
||||
* (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
|
||||
* for x in (2,inf)
|
||||
* j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* as follow:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (cos(x) + sin(x))
|
||||
* sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j0(nan)= nan
|
||||
* j0(0) = 1
|
||||
* j0(inf) = 0
|
||||
*
|
||||
* Method -- y0(x):
|
||||
* 1. For x<2.
|
||||
* Since
|
||||
* y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
|
||||
* therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
|
||||
* We use the following function to approximate y0,
|
||||
* y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
|
||||
* where
|
||||
* U(z) = u00 + u01*z + ... + u06*z^6
|
||||
* V(z) = 1 + v01*z + ... + v04*z^4
|
||||
* with absolute approximation error bounded by 2**-72.
|
||||
* Note: For tiny x, U/V = u0 and j0(x)~1, hence
|
||||
* y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
|
||||
* 2. For x>=2.
|
||||
* y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
|
||||
* where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
|
||||
* by the method mentioned above.
|
||||
* 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pzero(double), qzero(double);
|
||||
#else
|
||||
static double pzero(), qzero();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0, 2.00] */
|
||||
R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
|
||||
R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
|
||||
R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
|
||||
R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
|
||||
S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
|
||||
S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
|
||||
S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
|
||||
S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_j0(double x)
|
||||
#else
|
||||
double __ieee754_j0(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/(x*x);
|
||||
x = fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sin(x);
|
||||
c = __cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -__cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*cc-v*ss)/__sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<0x3f200000) { /* |x| < 2**-13 */
|
||||
if(huge+x>one) { /* raise inexact if x != 0 */
|
||||
if(ix<0x3e400000) return one; /* |x|<2**-27 */
|
||||
else return one - 0.25*x*x;
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(R02+z*(R03+z*(R04+z*R05)));
|
||||
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
|
||||
if(ix < 0x3FF00000) { /* |x| < 1.00 */
|
||||
return one + z*(-0.25+(r/s));
|
||||
} else {
|
||||
u = 0.5*x;
|
||||
return((one+u)*(one-u)+z*(r/s));
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
|
||||
u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
|
||||
u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
|
||||
u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
|
||||
u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
|
||||
u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
|
||||
u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
|
||||
v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
|
||||
v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
|
||||
v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
|
||||
v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_y0(double x)
|
||||
#else
|
||||
double __ieee754_y0(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix,lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
|
||||
* where x0 = x-pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) + cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
s = __sin(x);
|
||||
c = __cos(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = -__cos(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x);
|
||||
else {
|
||||
u = pzero(x); v = qzero(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/__sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3e400000) { /* x < 2**-27 */
|
||||
return(u00 + tpi*__ieee754_log(x));
|
||||
}
|
||||
z = x*x;
|
||||
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
||||
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
|
||||
return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
|
||||
}
|
||||
|
||||
/* The asymptotic expansions of pzero is
|
||||
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
|
||||
* For x >= 2, We approximate pzero by
|
||||
* pzero(x) = 1 + (R/S)
|
||||
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
|
||||
* S = 1 + pS0*s^2 + ... + pS4*s^10
|
||||
* and
|
||||
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
|
||||
-8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
|
||||
-2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
|
||||
-2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
|
||||
-5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS8[5] = {
|
||||
#else
|
||||
static double pS8[5] = {
|
||||
#endif
|
||||
1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
|
||||
3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
|
||||
4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
|
||||
1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
|
||||
4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
|
||||
-7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
|
||||
-4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
|
||||
-6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
|
||||
-3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
|
||||
-3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS5[5] = {
|
||||
#else
|
||||
static double pS5[5] = {
|
||||
#endif
|
||||
6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
|
||||
1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
|
||||
5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
|
||||
9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
|
||||
2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
|
||||
-7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
|
||||
-2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
|
||||
-2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
|
||||
-5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
|
||||
-3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS3[5] = {
|
||||
#else
|
||||
static double pS3[5] = {
|
||||
#endif
|
||||
3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
|
||||
3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
|
||||
1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
|
||||
1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
|
||||
1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
|
||||
-7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
|
||||
-1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
|
||||
-7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
|
||||
-1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
|
||||
-3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double pS2[5] = {
|
||||
#else
|
||||
static double pS2[5] = {
|
||||
#endif
|
||||
2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
|
||||
1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
|
||||
2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
|
||||
1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
|
||||
1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pzero(double x)
|
||||
#else
|
||||
static double pzero(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double z,r,s;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = pR8; q= pS8;}
|
||||
else if(ix>=0x40122E8B){p = pR5; q= pS5;}
|
||||
else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
|
||||
else if(ix>=0x40000000){p = pR2; q= pS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qzero is
|
||||
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pzero by
|
||||
* qzero(x) = s*(-1.25 + (R/S))
|
||||
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
|
||||
* S = 1 + qS0*s^2 + ... + qS5*s^12
|
||||
* and
|
||||
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
|
||||
1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
|
||||
5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
|
||||
8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
|
||||
3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS8[6] = {
|
||||
#else
|
||||
static double qS8[6] = {
|
||||
#endif
|
||||
1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
|
||||
8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
|
||||
1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
|
||||
8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
|
||||
8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
|
||||
-3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
|
||||
7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
|
||||
5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
|
||||
1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
|
||||
1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
|
||||
1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS5[6] = {
|
||||
#else
|
||||
static double qS5[6] = {
|
||||
#endif
|
||||
8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
|
||||
2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
|
||||
1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
|
||||
5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
|
||||
3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
|
||||
-5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
|
||||
7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
|
||||
3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
|
||||
4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
|
||||
1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
|
||||
1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS3[6] = {
|
||||
#else
|
||||
static double qS3[6] = {
|
||||
#endif
|
||||
4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
|
||||
7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
|
||||
3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
|
||||
6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
|
||||
2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
|
||||
-1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
|
||||
7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
|
||||
1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
|
||||
1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
|
||||
3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
|
||||
1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qS2[6] = {
|
||||
#else
|
||||
static double qS2[6] = {
|
||||
#endif
|
||||
3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
|
||||
2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
|
||||
8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
|
||||
8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
|
||||
2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
|
||||
-5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double qzero(double x)
|
||||
#else
|
||||
static double qzero(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double s,r,z;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = qR8; q= qS8;}
|
||||
else if(ix>=0x40122E8B){p = qR5; q= qS5;}
|
||||
else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
|
||||
else if(ix>=0x40000000){p = qR2; q= qS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (-.125 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,444 @@
|
|||
/* e_j0f.c -- float version of e_j0.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_j0f.c,v 1.4 1995/05/10 20:45:25 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static float pzerof(float), qzerof(float);
|
||||
#else
|
||||
static float pzerof(), qzerof();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
huge = 1e30,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
tpi = 6.3661974669e-01, /* 0x3f22f983 */
|
||||
/* R0/S0 on [0, 2.00] */
|
||||
R02 = 1.5625000000e-02, /* 0x3c800000 */
|
||||
R03 = -1.8997929874e-04, /* 0xb947352e */
|
||||
R04 = 1.8295404516e-06, /* 0x35f58e88 */
|
||||
R05 = -4.6183270541e-09, /* 0xb19eaf3c */
|
||||
S01 = 1.5619102865e-02, /* 0x3c7fe744 */
|
||||
S02 = 1.1692678527e-04, /* 0x38f53697 */
|
||||
S03 = 5.1354652442e-07, /* 0x3509daa6 */
|
||||
S04 = 1.1661400734e-09; /* 0x30a045e8 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_j0f(float x)
|
||||
#else
|
||||
float __ieee754_j0f(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z, s,c,ss,cc,r,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return one/(x*x);
|
||||
x = fabsf(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sinf(x);
|
||||
c = __cosf(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = -__cosf(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x80000000) z = (invsqrtpi*cc)/__sqrtf(x);
|
||||
else {
|
||||
u = pzerof(x); v = qzerof(x);
|
||||
z = invsqrtpi*(u*cc-v*ss)/__sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<0x39000000) { /* |x| < 2**-13 */
|
||||
if(huge+x>one) { /* raise inexact if x != 0 */
|
||||
if(ix<0x32000000) return one; /* |x|<2**-27 */
|
||||
else return one - (float)0.25*x*x;
|
||||
}
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(R02+z*(R03+z*(R04+z*R05)));
|
||||
s = one+z*(S01+z*(S02+z*(S03+z*S04)));
|
||||
if(ix < 0x3F800000) { /* |x| < 1.00 */
|
||||
return one + z*((float)-0.25+(r/s));
|
||||
} else {
|
||||
u = (float)0.5*x;
|
||||
return((one+u)*(one-u)+z*(r/s));
|
||||
}
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
u00 = -7.3804296553e-02, /* 0xbd9726b5 */
|
||||
u01 = 1.7666645348e-01, /* 0x3e34e80d */
|
||||
u02 = -1.3818567619e-02, /* 0xbc626746 */
|
||||
u03 = 3.4745343146e-04, /* 0x39b62a69 */
|
||||
u04 = -3.8140706238e-06, /* 0xb67ff53c */
|
||||
u05 = 1.9559013964e-08, /* 0x32a802ba */
|
||||
u06 = -3.9820518410e-11, /* 0xae2f21eb */
|
||||
v01 = 1.2730483897e-02, /* 0x3c509385 */
|
||||
v02 = 7.6006865129e-05, /* 0x389f65e0 */
|
||||
v03 = 2.5915085189e-07, /* 0x348b216c */
|
||||
v04 = 4.4111031494e-10; /* 0x2ff280c2 */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_y0f(float x)
|
||||
#else
|
||||
float __ieee754_y0f(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */
|
||||
if(ix>=0x7f800000) return one/(x+x*x);
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
|
||||
* where x0 = x-pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) + cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
s = __sinf(x);
|
||||
c = __cosf(x);
|
||||
ss = s-c;
|
||||
cc = s+c;
|
||||
/*
|
||||
* j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
|
||||
* y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = -__cosf(x+x);
|
||||
if ((s*c)<zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
if(ix>0x80000000) z = (invsqrtpi*ss)/__sqrtf(x);
|
||||
else {
|
||||
u = pzerof(x); v = qzerof(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x32000000) { /* x < 2**-27 */
|
||||
return(u00 + tpi*__ieee754_logf(x));
|
||||
}
|
||||
z = x*x;
|
||||
u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
||||
v = one+z*(v01+z*(v02+z*(v03+z*v04)));
|
||||
return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
|
||||
}
|
||||
|
||||
/* The asymptotic expansions of pzero is
|
||||
* 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x.
|
||||
* For x >= 2, We approximate pzero by
|
||||
* pzero(x) = 1 + (R/S)
|
||||
* where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
|
||||
* S = 1 + pS0*s^2 + ... + pS4*s^10
|
||||
* and
|
||||
* | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
-7.0312500000e-02, /* 0xbd900000 */
|
||||
-8.0816707611e+00, /* 0xc1014e86 */
|
||||
-2.5706311035e+02, /* 0xc3808814 */
|
||||
-2.4852163086e+03, /* 0xc51b5376 */
|
||||
-5.2530439453e+03, /* 0xc5a4285a */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float pS8[5] = {
|
||||
#else
|
||||
static float pS8[5] = {
|
||||
#endif
|
||||
1.1653436279e+02, /* 0x42e91198 */
|
||||
3.8337448730e+03, /* 0x456f9beb */
|
||||
4.0597855469e+04, /* 0x471e95db */
|
||||
1.1675296875e+05, /* 0x47e4087c */
|
||||
4.7627726562e+04, /* 0x473a0bba */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-1.1412546255e-11, /* 0xad48c58a */
|
||||
-7.0312492549e-02, /* 0xbd8fffff */
|
||||
-4.1596107483e+00, /* 0xc0851b88 */
|
||||
-6.7674766541e+01, /* 0xc287597b */
|
||||
-3.3123129272e+02, /* 0xc3a59d9b */
|
||||
-3.4643338013e+02, /* 0xc3ad3779 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float pS5[5] = {
|
||||
#else
|
||||
static float pS5[5] = {
|
||||
#endif
|
||||
6.0753936768e+01, /* 0x42730408 */
|
||||
1.0512523193e+03, /* 0x44836813 */
|
||||
5.9789707031e+03, /* 0x45bad7c4 */
|
||||
9.6254453125e+03, /* 0x461665c8 */
|
||||
2.4060581055e+03, /* 0x451660ee */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-2.5470459075e-09, /* 0xb12f081b */
|
||||
-7.0311963558e-02, /* 0xbd8fffb8 */
|
||||
-2.4090321064e+00, /* 0xc01a2d95 */
|
||||
-2.1965976715e+01, /* 0xc1afba52 */
|
||||
-5.8079170227e+01, /* 0xc2685112 */
|
||||
-3.1447946548e+01, /* 0xc1fb9565 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float pS3[5] = {
|
||||
#else
|
||||
static float pS3[5] = {
|
||||
#endif
|
||||
3.5856033325e+01, /* 0x420f6c94 */
|
||||
3.6151397705e+02, /* 0x43b4c1ca */
|
||||
1.1936077881e+03, /* 0x44953373 */
|
||||
1.1279968262e+03, /* 0x448cffe6 */
|
||||
1.7358093262e+02, /* 0x432d94b8 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-8.8753431271e-08, /* 0xb3be98b7 */
|
||||
-7.0303097367e-02, /* 0xbd8ffb12 */
|
||||
-1.4507384300e+00, /* 0xbfb9b1cc */
|
||||
-7.6356959343e+00, /* 0xc0f4579f */
|
||||
-1.1193166733e+01, /* 0xc1331736 */
|
||||
-3.2336456776e+00, /* 0xc04ef40d */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float pS2[5] = {
|
||||
#else
|
||||
static float pS2[5] = {
|
||||
#endif
|
||||
2.2220300674e+01, /* 0x41b1c32d */
|
||||
1.3620678711e+02, /* 0x430834f0 */
|
||||
2.7047027588e+02, /* 0x43873c32 */
|
||||
1.5387539673e+02, /* 0x4319e01a */
|
||||
1.4657617569e+01, /* 0x416a859a */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static float pzerof(float x)
|
||||
#else
|
||||
static float pzerof(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const float *p,*q;
|
||||
#else
|
||||
float *p,*q;
|
||||
#endif
|
||||
float z,r,s;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = pR8; q= pS8;}
|
||||
else if(ix>=0x40f71c58){p = pR5; q= pS5;}
|
||||
else if(ix>=0x4036db68){p = pR3; q= pS3;}
|
||||
else if(ix>=0x40000000){p = pR2; q= pS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qzero is
|
||||
* -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pzero by
|
||||
* qzero(x) = s*(-1.25 + (R/S))
|
||||
* where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
|
||||
* S = 1 + qS0*s^2 + ... + qS5*s^12
|
||||
* and
|
||||
* | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
7.3242187500e-02, /* 0x3d960000 */
|
||||
1.1768206596e+01, /* 0x413c4a93 */
|
||||
5.5767340088e+02, /* 0x440b6b19 */
|
||||
8.8591972656e+03, /* 0x460a6cca */
|
||||
3.7014625000e+04, /* 0x471096a0 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qS8[6] = {
|
||||
#else
|
||||
static float qS8[6] = {
|
||||
#endif
|
||||
1.6377603149e+02, /* 0x4323c6aa */
|
||||
8.0983447266e+03, /* 0x45fd12c2 */
|
||||
1.4253829688e+05, /* 0x480b3293 */
|
||||
8.0330925000e+05, /* 0x49441ed4 */
|
||||
8.4050156250e+05, /* 0x494d3359 */
|
||||
-3.4389928125e+05, /* 0xc8a7eb69 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.8408595828e-11, /* 0x2da1ec79 */
|
||||
7.3242180049e-02, /* 0x3d95ffff */
|
||||
5.8356351852e+00, /* 0x40babd86 */
|
||||
1.3511157227e+02, /* 0x43071c90 */
|
||||
1.0272437744e+03, /* 0x448067cd */
|
||||
1.9899779053e+03, /* 0x44f8bf4b */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qS5[6] = {
|
||||
#else
|
||||
static float qS5[6] = {
|
||||
#endif
|
||||
8.2776611328e+01, /* 0x42a58da0 */
|
||||
2.0778142090e+03, /* 0x4501dd07 */
|
||||
1.8847289062e+04, /* 0x46933e94 */
|
||||
5.6751113281e+04, /* 0x475daf1d */
|
||||
3.5976753906e+04, /* 0x470c88c1 */
|
||||
-5.3543427734e+03, /* 0xc5a752be */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#else
|
||||
static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
4.3774099900e-09, /* 0x3196681b */
|
||||
7.3241114616e-02, /* 0x3d95ff70 */
|
||||
3.3442313671e+00, /* 0x405607e3 */
|
||||
4.2621845245e+01, /* 0x422a7cc5 */
|
||||
1.7080809021e+02, /* 0x432acedf */
|
||||
1.6673394775e+02, /* 0x4326bbe4 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qS3[6] = {
|
||||
#else
|
||||
static float qS3[6] = {
|
||||
#endif
|
||||
4.8758872986e+01, /* 0x42430916 */
|
||||
7.0968920898e+02, /* 0x44316c1c */
|
||||
3.7041481934e+03, /* 0x4567825f */
|
||||
6.4604252930e+03, /* 0x45c9e367 */
|
||||
2.5163337402e+03, /* 0x451d4557 */
|
||||
-1.4924745178e+02, /* 0xc3153f59 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.5044444979e-07, /* 0x342189db */
|
||||
7.3223426938e-02, /* 0x3d95f62a */
|
||||
1.9981917143e+00, /* 0x3fffc4bf */
|
||||
1.4495602608e+01, /* 0x4167edfd */
|
||||
3.1666231155e+01, /* 0x41fd5471 */
|
||||
1.6252708435e+01, /* 0x4182058c */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qS2[6] = {
|
||||
#else
|
||||
static float qS2[6] = {
|
||||
#endif
|
||||
3.0365585327e+01, /* 0x41f2ecb8 */
|
||||
2.6934811401e+02, /* 0x4386ac8f */
|
||||
8.4478375244e+02, /* 0x44533229 */
|
||||
8.8293585205e+02, /* 0x445cbbe5 */
|
||||
2.1266638184e+02, /* 0x4354aa98 */
|
||||
-5.3109550476e+00, /* 0xc0a9f358 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static float qzerof(float x)
|
||||
#else
|
||||
static float qzerof(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const float *p,*q;
|
||||
#else
|
||||
float *p,*q;
|
||||
#endif
|
||||
float s,r,z;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = qR8; q= qS8;}
|
||||
else if(ix>=0x40f71c58){p = qR5; q= qS5;}
|
||||
else if(ix>=0x4036db68){p = qR3; q= qS3;}
|
||||
else if(ix>=0x40000000){p = qR2; q= qS2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (-(float).125 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,486 @@
|
|||
/* @(#)e_j1.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_j1(x), __ieee754_y1(x)
|
||||
* Bessel function of the first and second kinds of order zero.
|
||||
* Method -- j1(x):
|
||||
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
|
||||
* 2. Reduce x to |x| since j1(x)=-j1(-x), and
|
||||
* for x in (0,2)
|
||||
* j1(x) = x/2 + x*z*R0/S0, where z = x*x;
|
||||
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
|
||||
* for x in (2,inf)
|
||||
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* as follow:
|
||||
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (sin(x) + cos(x))
|
||||
* (To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.)
|
||||
*
|
||||
* 3 Special cases
|
||||
* j1(nan)= nan
|
||||
* j1(0) = 0
|
||||
* j1(inf) = 0
|
||||
*
|
||||
* Method -- y1(x):
|
||||
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
|
||||
* 2. For x<2.
|
||||
* Since
|
||||
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
|
||||
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
|
||||
* We use the following function to approximate y1,
|
||||
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
|
||||
* where for x in [0,2] (abs err less than 2**-65.89)
|
||||
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
|
||||
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
|
||||
* Note: For tiny x, 1/x dominate y1 and hence
|
||||
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
|
||||
* 3. For x>=2.
|
||||
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
|
||||
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
|
||||
* by method mentioned above.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pone(double), qone(double);
|
||||
#else
|
||||
static double pone(), qone();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
huge = 1e300,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
/* R0/S0 on [0,2] */
|
||||
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
|
||||
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
|
||||
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
|
||||
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
|
||||
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
|
||||
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
|
||||
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
|
||||
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
|
||||
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_j1(double x)
|
||||
#else
|
||||
double __ieee754_j1(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,r,u,v,y;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_HIGH_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return one/x;
|
||||
y = fabs(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sin(y);
|
||||
c = __cos(y);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure y+y not overflow */
|
||||
z = __cos(y+y);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
|
||||
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*cc)/__sqrt(y);
|
||||
else {
|
||||
u = pone(y); v = qone(y);
|
||||
z = invsqrtpi*(u*cc-v*ss)/__sqrt(y);
|
||||
}
|
||||
if(hx<0) return -z;
|
||||
else return z;
|
||||
}
|
||||
if(ix<0x3e400000) { /* |x|<2**-27 */
|
||||
if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(r00+z*(r01+z*(r02+z*r03)));
|
||||
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
|
||||
r *= x;
|
||||
return(x*0.5+r/s);
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double U0[5] = {
|
||||
#else
|
||||
static double U0[5] = {
|
||||
#endif
|
||||
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
|
||||
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
|
||||
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
|
||||
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
|
||||
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double V0[5] = {
|
||||
#else
|
||||
static double V0[5] = {
|
||||
#endif
|
||||
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
|
||||
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
|
||||
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
|
||||
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
|
||||
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_y1(double x)
|
||||
#else
|
||||
double __ieee754_y1(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix,lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
|
||||
if(ix>=0x7ff00000) return one/(x+x*x);
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sin(x);
|
||||
c = __cos(x);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7fe00000) { /* make sure x+x not overflow */
|
||||
z = __cos(x+x);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
|
||||
* where x0 = x-3pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (cos(x) + sin(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrt(x);
|
||||
else {
|
||||
u = pone(x); v = qone(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/__sqrt(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x3c900000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
z = x*x;
|
||||
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
|
||||
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
|
||||
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
|
||||
}
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of pone is
|
||||
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* pone(x) = 1 + (R/S)
|
||||
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
|
||||
* S = 1 + ps0*s^2 + ... + ps4*s^10
|
||||
* and
|
||||
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
|
||||
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
|
||||
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
|
||||
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
|
||||
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps8[5] = {
|
||||
#else
|
||||
static double ps8[5] = {
|
||||
#endif
|
||||
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
|
||||
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
|
||||
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
|
||||
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
|
||||
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
|
||||
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
|
||||
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
|
||||
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
|
||||
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
|
||||
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps5[5] = {
|
||||
#else
|
||||
static double ps5[5] = {
|
||||
#endif
|
||||
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
|
||||
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
|
||||
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
|
||||
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
|
||||
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr3[6] = {
|
||||
#else
|
||||
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
|
||||
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
|
||||
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
|
||||
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
|
||||
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
|
||||
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps3[5] = {
|
||||
#else
|
||||
static double ps3[5] = {
|
||||
#endif
|
||||
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
|
||||
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
|
||||
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
|
||||
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
|
||||
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
|
||||
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
|
||||
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
|
||||
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
|
||||
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
|
||||
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double ps2[5] = {
|
||||
#else
|
||||
static double ps2[5] = {
|
||||
#endif
|
||||
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
|
||||
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
|
||||
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
|
||||
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
|
||||
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double pone(double x)
|
||||
#else
|
||||
static double pone(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double z,r,s;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = pr8; q= ps8;}
|
||||
else if(ix>=0x40122E8B){p = pr5; q= ps5;}
|
||||
else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
|
||||
else if(ix>=0x40000000){p = pr2; q= ps2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* qone(x) = s*(0.375 + (R/S))
|
||||
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
|
||||
* S = 1 + qs1*s^2 + ... + qs6*s^12
|
||||
* and
|
||||
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
|
||||
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
|
||||
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
|
||||
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
|
||||
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs8[6] = {
|
||||
#else
|
||||
static double qs8[6] = {
|
||||
#endif
|
||||
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
|
||||
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
|
||||
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
|
||||
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
|
||||
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
|
||||
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
|
||||
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
|
||||
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
|
||||
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
|
||||
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
|
||||
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs5[6] = {
|
||||
#else
|
||||
static double qs5[6] = {
|
||||
#endif
|
||||
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
|
||||
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
|
||||
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
|
||||
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
|
||||
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
|
||||
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr3[6] = {
|
||||
#else
|
||||
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
|
||||
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
|
||||
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
|
||||
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
|
||||
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
|
||||
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs3[6] = {
|
||||
#else
|
||||
static double qs3[6] = {
|
||||
#endif
|
||||
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
|
||||
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
|
||||
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
|
||||
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
|
||||
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
|
||||
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
|
||||
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
|
||||
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
|
||||
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
|
||||
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
|
||||
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const double qs2[6] = {
|
||||
#else
|
||||
static double qs2[6] = {
|
||||
#endif
|
||||
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
|
||||
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
|
||||
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
|
||||
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
|
||||
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
|
||||
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static double qone(double x)
|
||||
#else
|
||||
static double qone(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const double *p,*q;
|
||||
#else
|
||||
double *p,*q;
|
||||
#endif
|
||||
double s,r,z;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = qr8; q= qs8;}
|
||||
else if(ix>=0x40122E8B){p = qr5; q= qs5;}
|
||||
else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
|
||||
else if(ix>=0x40000000){p = qr2; q= qs2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return (.375 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,444 @@
|
|||
/* e_j1f.c -- float version of e_j1.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_j1f.c,v 1.4 1995/05/10 20:45:31 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static float ponef(float), qonef(float);
|
||||
#else
|
||||
static float ponef(), qonef();
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
huge = 1e30,
|
||||
one = 1.0,
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
tpi = 6.3661974669e-01, /* 0x3f22f983 */
|
||||
/* R0/S0 on [0,2] */
|
||||
r00 = -6.2500000000e-02, /* 0xbd800000 */
|
||||
r01 = 1.4070566976e-03, /* 0x3ab86cfd */
|
||||
r02 = -1.5995563444e-05, /* 0xb7862e36 */
|
||||
r03 = 4.9672799207e-08, /* 0x335557d2 */
|
||||
s01 = 1.9153760746e-02, /* 0x3c9ce859 */
|
||||
s02 = 1.8594678841e-04, /* 0x3942fab6 */
|
||||
s03 = 1.1771846857e-06, /* 0x359dffc2 */
|
||||
s04 = 5.0463624390e-09, /* 0x31ad6446 */
|
||||
s05 = 1.2354227016e-11; /* 0x2d59567e */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_j1f(float x)
|
||||
#else
|
||||
float __ieee754_j1f(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z, s,c,ss,cc,r,u,v,y;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return one/x;
|
||||
y = fabsf(x);
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sinf(y);
|
||||
c = __cosf(y);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7f000000) { /* make sure y+y not overflow */
|
||||
z = __cosf(y+y);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/*
|
||||
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
|
||||
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
|
||||
*/
|
||||
if(ix>0x80000000) z = (invsqrtpi*cc)/__sqrtf(y);
|
||||
else {
|
||||
u = ponef(y); v = qonef(y);
|
||||
z = invsqrtpi*(u*cc-v*ss)/__sqrtf(y);
|
||||
}
|
||||
if(hx<0) return -z;
|
||||
else return z;
|
||||
}
|
||||
if(ix<0x32000000) { /* |x|<2**-27 */
|
||||
if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(r00+z*(r01+z*(r02+z*r03)));
|
||||
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
|
||||
r *= x;
|
||||
return(x*(float)0.5+r/s);
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float U0[5] = {
|
||||
#else
|
||||
static float U0[5] = {
|
||||
#endif
|
||||
-1.9605709612e-01, /* 0xbe48c331 */
|
||||
5.0443872809e-02, /* 0x3d4e9e3c */
|
||||
-1.9125689287e-03, /* 0xbafaaf2a */
|
||||
2.3525259166e-05, /* 0x37c5581c */
|
||||
-9.1909917899e-08, /* 0xb3c56003 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float V0[5] = {
|
||||
#else
|
||||
static float V0[5] = {
|
||||
#endif
|
||||
1.9916731864e-02, /* 0x3ca3286a */
|
||||
2.0255257550e-04, /* 0x3954644b */
|
||||
1.3560879779e-06, /* 0x35b602d4 */
|
||||
6.2274145840e-09, /* 0x31d5f8eb */
|
||||
1.6655924903e-11, /* 0x2d9281cf */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_y1f(float x)
|
||||
#else
|
||||
float __ieee754_y1f(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z, s,c,ss,cc,u,v;
|
||||
int32_t hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
|
||||
if(ix>=0x7f800000) return one/(x+x*x);
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
if(ix >= 0x40000000) { /* |x| >= 2.0 */
|
||||
s = __sinf(x);
|
||||
c = __cosf(x);
|
||||
ss = -s-c;
|
||||
cc = s-c;
|
||||
if(ix<0x7f000000) { /* make sure x+x not overflow */
|
||||
z = __cosf(x+x);
|
||||
if ((s*c)>zero) cc = z/ss;
|
||||
else ss = z/cc;
|
||||
}
|
||||
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
|
||||
* where x0 = x-3pi/4
|
||||
* Better formula:
|
||||
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
|
||||
* = 1/sqrt(2) * (sin(x) - cos(x))
|
||||
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
|
||||
* = -1/sqrt(2) * (cos(x) + sin(x))
|
||||
* To avoid cancellation, use
|
||||
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
|
||||
* to compute the worse one.
|
||||
*/
|
||||
if(ix>0x48000000) z = (invsqrtpi*ss)/__sqrtf(x);
|
||||
else {
|
||||
u = ponef(x); v = qonef(x);
|
||||
z = invsqrtpi*(u*ss+v*cc)/__sqrtf(x);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
if(ix<=0x24800000) { /* x < 2**-54 */
|
||||
return(-tpi/x);
|
||||
}
|
||||
z = x*x;
|
||||
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
|
||||
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
|
||||
return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
|
||||
}
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of pone is
|
||||
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* pone(x) = 1 + (R/S)
|
||||
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
|
||||
* S = 1 + ps0*s^2 + ... + ps4*s^10
|
||||
* and
|
||||
* | pone(x)-1-R/S | <= 2 ** ( -60.06)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
1.1718750000e-01, /* 0x3df00000 */
|
||||
1.3239480972e+01, /* 0x4153d4ea */
|
||||
4.1205184937e+02, /* 0x43ce06a3 */
|
||||
3.8747453613e+03, /* 0x45722bed */
|
||||
7.9144794922e+03, /* 0x45f753d6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float ps8[5] = {
|
||||
#else
|
||||
static float ps8[5] = {
|
||||
#endif
|
||||
1.1420736694e+02, /* 0x42e46a2c */
|
||||
3.6509309082e+03, /* 0x45642ee5 */
|
||||
3.6956207031e+04, /* 0x47105c35 */
|
||||
9.7602796875e+04, /* 0x47bea166 */
|
||||
3.0804271484e+04, /* 0x46f0a88b */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
1.3199052094e-11, /* 0x2d68333f */
|
||||
1.1718749255e-01, /* 0x3defffff */
|
||||
6.8027510643e+00, /* 0x40d9b023 */
|
||||
1.0830818176e+02, /* 0x42d89dca */
|
||||
5.1763616943e+02, /* 0x440168b7 */
|
||||
5.2871520996e+02, /* 0x44042dc6 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float ps5[5] = {
|
||||
#else
|
||||
static float ps5[5] = {
|
||||
#endif
|
||||
5.9280597687e+01, /* 0x426d1f55 */
|
||||
9.9140142822e+02, /* 0x4477d9b1 */
|
||||
5.3532670898e+03, /* 0x45a74a23 */
|
||||
7.8446904297e+03, /* 0x45f52586 */
|
||||
1.5040468750e+03, /* 0x44bc0180 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pr3[6] = {
|
||||
#else
|
||||
static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
3.0250391081e-09, /* 0x314fe10d */
|
||||
1.1718686670e-01, /* 0x3defffab */
|
||||
3.9329774380e+00, /* 0x407bb5e7 */
|
||||
3.5119403839e+01, /* 0x420c7a45 */
|
||||
9.1055007935e+01, /* 0x42b61c2a */
|
||||
4.8559066772e+01, /* 0x42423c7c */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float ps3[5] = {
|
||||
#else
|
||||
static float ps3[5] = {
|
||||
#endif
|
||||
3.4791309357e+01, /* 0x420b2a4d */
|
||||
3.3676245117e+02, /* 0x43a86198 */
|
||||
1.0468714600e+03, /* 0x4482dbe3 */
|
||||
8.9081134033e+02, /* 0x445eb3ed */
|
||||
1.0378793335e+02, /* 0x42cf936c */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
1.0771083225e-07, /* 0x33e74ea8 */
|
||||
1.1717621982e-01, /* 0x3deffa16 */
|
||||
2.3685150146e+00, /* 0x401795c0 */
|
||||
1.2242610931e+01, /* 0x4143e1bc */
|
||||
1.7693971634e+01, /* 0x418d8d41 */
|
||||
5.0735230446e+00, /* 0x40a25a4d */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float ps2[5] = {
|
||||
#else
|
||||
static float ps2[5] = {
|
||||
#endif
|
||||
2.1436485291e+01, /* 0x41ab7dec */
|
||||
1.2529022980e+02, /* 0x42fa9499 */
|
||||
2.3227647400e+02, /* 0x436846c7 */
|
||||
1.1767937469e+02, /* 0x42eb5bd7 */
|
||||
8.3646392822e+00, /* 0x4105d590 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static float ponef(float x)
|
||||
#else
|
||||
static float ponef(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const float *p,*q;
|
||||
#else
|
||||
float *p,*q;
|
||||
#endif
|
||||
float z,r,s;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x41000000) {p = pr8; q= ps8;}
|
||||
else if(ix>=0x40f71c58){p = pr5; q= ps5;}
|
||||
else if(ix>=0x4036db68){p = pr3; q= ps3;}
|
||||
else if(ix>=0x40000000){p = pr2; q= ps2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
|
||||
return one+ r/s;
|
||||
}
|
||||
|
||||
|
||||
/* For x >= 8, the asymptotic expansions of qone is
|
||||
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
|
||||
* We approximate pone by
|
||||
* qone(x) = s*(0.375 + (R/S))
|
||||
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
|
||||
* S = 1 + qs1*s^2 + ... + qs6*s^12
|
||||
* and
|
||||
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#else
|
||||
static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
||||
#endif
|
||||
0.0000000000e+00, /* 0x00000000 */
|
||||
-1.0253906250e-01, /* 0xbdd20000 */
|
||||
-1.6271753311e+01, /* 0xc1822c8d */
|
||||
-7.5960174561e+02, /* 0xc43de683 */
|
||||
-1.1849806641e+04, /* 0xc639273a */
|
||||
-4.8438511719e+04, /* 0xc73d3683 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qs8[6] = {
|
||||
#else
|
||||
static float qs8[6] = {
|
||||
#endif
|
||||
1.6139537048e+02, /* 0x43216537 */
|
||||
7.8253862305e+03, /* 0x45f48b17 */
|
||||
1.3387534375e+05, /* 0x4802bcd6 */
|
||||
7.1965775000e+05, /* 0x492fb29c */
|
||||
6.6660125000e+05, /* 0x4922be94 */
|
||||
-2.9449025000e+05, /* 0xc88fcb48 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#else
|
||||
static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
||||
#endif
|
||||
-2.0897993405e-11, /* 0xadb7d219 */
|
||||
-1.0253904760e-01, /* 0xbdd1fffe */
|
||||
-8.0564479828e+00, /* 0xc100e736 */
|
||||
-1.8366960144e+02, /* 0xc337ab6b */
|
||||
-1.3731937256e+03, /* 0xc4aba633 */
|
||||
-2.6124443359e+03, /* 0xc523471c */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qs5[6] = {
|
||||
#else
|
||||
static float qs5[6] = {
|
||||
#endif
|
||||
8.1276550293e+01, /* 0x42a28d98 */
|
||||
1.9917987061e+03, /* 0x44f8f98f */
|
||||
1.7468484375e+04, /* 0x468878f8 */
|
||||
4.9851425781e+04, /* 0x4742bb6d */
|
||||
2.7948074219e+04, /* 0x46da5826 */
|
||||
-4.7191835938e+03, /* 0xc5937978 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qr3[6] = {
|
||||
#else
|
||||
static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
||||
#endif
|
||||
-5.0783124372e-09, /* 0xb1ae7d4f */
|
||||
-1.0253783315e-01, /* 0xbdd1ff5b */
|
||||
-4.6101160049e+00, /* 0xc0938612 */
|
||||
-5.7847221375e+01, /* 0xc267638e */
|
||||
-2.2824453735e+02, /* 0xc3643e9a */
|
||||
-2.1921012878e+02, /* 0xc35b35cb */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qs3[6] = {
|
||||
#else
|
||||
static float qs3[6] = {
|
||||
#endif
|
||||
4.7665153503e+01, /* 0x423ea91e */
|
||||
6.7386511230e+02, /* 0x4428775e */
|
||||
3.3801528320e+03, /* 0x45534272 */
|
||||
5.5477290039e+03, /* 0x45ad5dd5 */
|
||||
1.9031191406e+03, /* 0x44ede3d0 */
|
||||
-1.3520118713e+02, /* 0xc3073381 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#else
|
||||
static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
||||
#endif
|
||||
-1.7838172539e-07, /* 0xb43f8932 */
|
||||
-1.0251704603e-01, /* 0xbdd1f475 */
|
||||
-2.7522056103e+00, /* 0xc0302423 */
|
||||
-1.9663616180e+01, /* 0xc19d4f16 */
|
||||
-4.2325313568e+01, /* 0xc2294d1f */
|
||||
-2.1371921539e+01, /* 0xc1aaf9b2 */
|
||||
};
|
||||
#ifdef __STDC__
|
||||
static const float qs2[6] = {
|
||||
#else
|
||||
static float qs2[6] = {
|
||||
#endif
|
||||
2.9533363342e+01, /* 0x41ec4454 */
|
||||
2.5298155212e+02, /* 0x437cfb47 */
|
||||
7.5750280762e+02, /* 0x443d602e */
|
||||
7.3939318848e+02, /* 0x4438d92a */
|
||||
1.5594900513e+02, /* 0x431bf2f2 */
|
||||
-4.9594988823e+00, /* 0xc09eb437 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static float qonef(float x)
|
||||
#else
|
||||
static float qonef(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
#ifdef __STDC__
|
||||
const float *p,*q;
|
||||
#else
|
||||
float *p,*q;
|
||||
#endif
|
||||
float s,r,z;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
if(ix>=0x40200000) {p = qr8; q= qs8;}
|
||||
else if(ix>=0x40f71c58){p = qr5; q= qs5;}
|
||||
else if(ix>=0x4036db68){p = qr3; q= qs3;}
|
||||
else if(ix>=0x40000000){p = qr2; q= qs2;}
|
||||
z = one/(x*x);
|
||||
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
|
||||
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
|
||||
return ((float).375 + r/s)/x;
|
||||
}
|
||||
|
|
@ -0,0 +1,281 @@
|
|||
/* @(#)e_jn.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_jn.c,v 1.9 1995/05/10 20:45:34 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_jn(n, x), __ieee754_yn(n, x)
|
||||
* floating point Bessel's function of the 1st and 2nd kind
|
||||
* of order n
|
||||
*
|
||||
* Special cases:
|
||||
* y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
|
||||
* y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
|
||||
* Note 2. About jn(n,x), yn(n,x)
|
||||
* For n=0, j0(x) is called,
|
||||
* for n=1, j1(x) is called,
|
||||
* for n<x, forward recursion us used starting
|
||||
* from values of j0(x) and j1(x).
|
||||
* for n>x, a continued fraction approximation to
|
||||
* j(n,x)/j(n-1,x) is evaluated and then backward
|
||||
* recursion is used starting from a supposed value
|
||||
* for j(n,x). The resulting value of j(0,x) is
|
||||
* compared with the actual value to correct the
|
||||
* supposed value of j(n,x).
|
||||
*
|
||||
* yn(n,x) is similar in all respects, except
|
||||
* that forward recursion is used for all
|
||||
* values of n>1.
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
|
||||
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.00000000000000000000e+00;
|
||||
#else
|
||||
static double zero = 0.00000000000000000000e+00;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_jn(int n, double x)
|
||||
#else
|
||||
double __ieee754_jn(n,x)
|
||||
int n; double x;
|
||||
#endif
|
||||
{
|
||||
int32_t i,hx,ix,lx, sgn;
|
||||
double a, b, temp, di;
|
||||
double z, w;
|
||||
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if J(n,NaN) is NaN */
|
||||
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
x = -x;
|
||||
hx ^= 0x80000000;
|
||||
}
|
||||
if(n==0) return(__ieee754_j0(x));
|
||||
if(n==1) return(__ieee754_j1(x));
|
||||
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fabs(x);
|
||||
if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */
|
||||
b = zero;
|
||||
else if((double)n<=x) {
|
||||
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = __cos(x)+__sin(x); break;
|
||||
case 1: temp = -__cos(x)+__sin(x); break;
|
||||
case 2: temp = -__cos(x)-__sin(x); break;
|
||||
case 3: temp = __cos(x)-__sin(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/__sqrt(x);
|
||||
} else {
|
||||
a = __ieee754_j0(x);
|
||||
b = __ieee754_j1(x);
|
||||
for(i=1;i<n;i++){
|
||||
temp = b;
|
||||
b = b*((double)(i+i)/x) - a; /* avoid underflow */
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
if(ix<0x3e100000) { /* x < 2**-29 */
|
||||
/* x is tiny, return the first Taylor expansion of J(n,x)
|
||||
* J(n,x) = 1/n!*(x/2)^n - ...
|
||||
*/
|
||||
if(n>33) /* underflow */
|
||||
b = zero;
|
||||
else {
|
||||
temp = x*0.5; b = temp;
|
||||
for (a=one,i=2;i<=n;i++) {
|
||||
a *= (double)i; /* a = n! */
|
||||
b *= temp; /* b = (x/2)^n */
|
||||
}
|
||||
b = b/a;
|
||||
}
|
||||
} else {
|
||||
/* use backward recurrence */
|
||||
/* x x^2 x^2
|
||||
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
|
||||
* 2n - 2(n+1) - 2(n+2)
|
||||
*
|
||||
* 1 1 1
|
||||
* (for large x) = ---- ------ ------ .....
|
||||
* 2n 2(n+1) 2(n+2)
|
||||
* -- - ------ - ------ -
|
||||
* x x x
|
||||
*
|
||||
* Let w = 2n/x and h=2/x, then the above quotient
|
||||
* is equal to the continued fraction:
|
||||
* 1
|
||||
* = -----------------------
|
||||
* 1
|
||||
* w - -----------------
|
||||
* 1
|
||||
* w+h - ---------
|
||||
* w+2h - ...
|
||||
*
|
||||
* To determine how many terms needed, let
|
||||
* Q(0) = w, Q(1) = w(w+h) - 1,
|
||||
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
|
||||
* When Q(k) > 1e4 good for single
|
||||
* When Q(k) > 1e9 good for double
|
||||
* When Q(k) > 1e17 good for quadruple
|
||||
*/
|
||||
/* determine k */
|
||||
double t,v;
|
||||
double q0,q1,h,tmp; int32_t k,m;
|
||||
w = (n+n)/(double)x; h = 2.0/(double)x;
|
||||
q0 = w; z = w+h; q1 = w*z - 1.0; k=1;
|
||||
while(q1<1.0e9) {
|
||||
k += 1; z += h;
|
||||
tmp = z*q1 - q0;
|
||||
q0 = q1;
|
||||
q1 = tmp;
|
||||
}
|
||||
m = n+n;
|
||||
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
|
||||
a = t;
|
||||
b = one;
|
||||
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
|
||||
* Hence, if n*(log(2n/x)) > ...
|
||||
* single 8.8722839355e+01
|
||||
* double 7.09782712893383973096e+02
|
||||
* long double 1.1356523406294143949491931077970765006170e+04
|
||||
* then recurrent value may overflow and the result is
|
||||
* likely underflow to zero
|
||||
*/
|
||||
tmp = n;
|
||||
v = two/x;
|
||||
tmp = tmp*__ieee754_log(fabs(v*tmp));
|
||||
if(tmp<7.09782712893383973096e+02) {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
}
|
||||
} else {
|
||||
for(i=n-1,di=(double)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
/* scale b to avoid spurious overflow */
|
||||
if(b>1e100) {
|
||||
a /= b;
|
||||
t /= b;
|
||||
b = one;
|
||||
}
|
||||
}
|
||||
}
|
||||
b = (t*__ieee754_j0(x)/b);
|
||||
}
|
||||
}
|
||||
if(sgn==1) return -b; else return b;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_yn(int n, double x)
|
||||
#else
|
||||
double __ieee754_yn(n,x)
|
||||
int n; double x;
|
||||
#endif
|
||||
{
|
||||
int32_t i,hx,ix,lx;
|
||||
int32_t sign;
|
||||
double a, b, temp;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
|
||||
if((ix|lx)==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
sign = 1;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
sign = 1 - ((n&1)<<1);
|
||||
}
|
||||
if(n==0) return(__ieee754_y0(x));
|
||||
if(n==1) return(sign*__ieee754_y1(x));
|
||||
if(ix==0x7ff00000) return zero;
|
||||
if(ix>=0x52D00000) { /* x > 2**302 */
|
||||
/* (x >> n**2)
|
||||
* Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
|
||||
* Let s=sin(x), c=cos(x),
|
||||
* xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
|
||||
*
|
||||
* n sin(xn)*sqt2 cos(xn)*sqt2
|
||||
* ----------------------------------
|
||||
* 0 s-c c+s
|
||||
* 1 -s-c -c+s
|
||||
* 2 -s+c -c-s
|
||||
* 3 s+c c-s
|
||||
*/
|
||||
switch(n&3) {
|
||||
case 0: temp = __sin(x)-__cos(x); break;
|
||||
case 1: temp = -__sin(x)-__cos(x); break;
|
||||
case 2: temp = -__sin(x)+__cos(x); break;
|
||||
case 3: temp = __sin(x)+__cos(x); break;
|
||||
}
|
||||
b = invsqrtpi*temp/__sqrt(x);
|
||||
} else {
|
||||
u_int32_t high;
|
||||
a = __ieee754_y0(x);
|
||||
b = __ieee754_y1(x);
|
||||
/* quit if b is -inf */
|
||||
GET_HIGH_WORD(high,b);
|
||||
for(i=1;i<n&&high!=0xfff00000;i++){
|
||||
temp = b;
|
||||
b = ((double)(i+i)/x)*b - a;
|
||||
GET_HIGH_WORD(high,b);
|
||||
a = temp;
|
||||
}
|
||||
}
|
||||
if(sign>0) return b; else return -b;
|
||||
}
|
||||
|
|
@ -0,0 +1,212 @@
|
|||
/* e_jnf.c -- float version of e_jn.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_jnf.c,v 1.5 1995/05/10 20:45:37 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
|
||||
two = 2.0000000000e+00, /* 0x40000000 */
|
||||
one = 1.0000000000e+00; /* 0x3F800000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0000000000e+00;
|
||||
#else
|
||||
static float zero = 0.0000000000e+00;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_jnf(int n, float x)
|
||||
#else
|
||||
float __ieee754_jnf(n,x)
|
||||
int n; float x;
|
||||
#endif
|
||||
{
|
||||
int32_t i,hx,ix, sgn;
|
||||
float a, b, temp, di;
|
||||
float z, w;
|
||||
|
||||
/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
|
||||
* Thus, J(-n,x) = J(n,-x)
|
||||
*/
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if J(n,NaN) is NaN */
|
||||
if(ix>0x7f800000) return x+x;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
x = -x;
|
||||
hx ^= 0x80000000;
|
||||
}
|
||||
if(n==0) return(__ieee754_j0f(x));
|
||||
if(n==1) return(__ieee754_j1f(x));
|
||||
sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
|
||||
x = fabsf(x);
|
||||
if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */
|
||||
b = zero;
|
||||
else if((float)n<=x) {
|
||||
/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
|
||||
a = __ieee754_j0f(x);
|
||||
b = __ieee754_j1f(x);
|
||||
for(i=1;i<n;i++){
|
||||
temp = b;
|
||||
b = b*((float)(i+i)/x) - a; /* avoid underflow */
|
||||
a = temp;
|
||||
}
|
||||
} else {
|
||||
if(ix<0x30800000) { /* x < 2**-29 */
|
||||
/* x is tiny, return the first Taylor expansion of J(n,x)
|
||||
* J(n,x) = 1/n!*(x/2)^n - ...
|
||||
*/
|
||||
if(n>33) /* underflow */
|
||||
b = zero;
|
||||
else {
|
||||
temp = x*(float)0.5; b = temp;
|
||||
for (a=one,i=2;i<=n;i++) {
|
||||
a *= (float)i; /* a = n! */
|
||||
b *= temp; /* b = (x/2)^n */
|
||||
}
|
||||
b = b/a;
|
||||
}
|
||||
} else {
|
||||
/* use backward recurrence */
|
||||
/* x x^2 x^2
|
||||
* J(n,x)/J(n-1,x) = ---- ------ ------ .....
|
||||
* 2n - 2(n+1) - 2(n+2)
|
||||
*
|
||||
* 1 1 1
|
||||
* (for large x) = ---- ------ ------ .....
|
||||
* 2n 2(n+1) 2(n+2)
|
||||
* -- - ------ - ------ -
|
||||
* x x x
|
||||
*
|
||||
* Let w = 2n/x and h=2/x, then the above quotient
|
||||
* is equal to the continued fraction:
|
||||
* 1
|
||||
* = -----------------------
|
||||
* 1
|
||||
* w - -----------------
|
||||
* 1
|
||||
* w+h - ---------
|
||||
* w+2h - ...
|
||||
*
|
||||
* To determine how many terms needed, let
|
||||
* Q(0) = w, Q(1) = w(w+h) - 1,
|
||||
* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
|
||||
* When Q(k) > 1e4 good for single
|
||||
* When Q(k) > 1e9 good for double
|
||||
* When Q(k) > 1e17 good for quadruple
|
||||
*/
|
||||
/* determine k */
|
||||
float t,v;
|
||||
float q0,q1,h,tmp; int32_t k,m;
|
||||
w = (n+n)/(float)x; h = (float)2.0/(float)x;
|
||||
q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
|
||||
while(q1<(float)1.0e9) {
|
||||
k += 1; z += h;
|
||||
tmp = z*q1 - q0;
|
||||
q0 = q1;
|
||||
q1 = tmp;
|
||||
}
|
||||
m = n+n;
|
||||
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
|
||||
a = t;
|
||||
b = one;
|
||||
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
|
||||
* Hence, if n*(log(2n/x)) > ...
|
||||
* single 8.8722839355e+01
|
||||
* double 7.09782712893383973096e+02
|
||||
* long double 1.1356523406294143949491931077970765006170e+04
|
||||
* then recurrent value may overflow and the result is
|
||||
* likely underflow to zero
|
||||
*/
|
||||
tmp = n;
|
||||
v = two/x;
|
||||
tmp = tmp*__ieee754_logf(fabsf(v*tmp));
|
||||
if(tmp<(float)8.8721679688e+01) {
|
||||
for(i=n-1,di=(float)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
}
|
||||
} else {
|
||||
for(i=n-1,di=(float)(i+i);i>0;i--){
|
||||
temp = b;
|
||||
b *= di;
|
||||
b = b/x - a;
|
||||
a = temp;
|
||||
di -= two;
|
||||
/* scale b to avoid spurious overflow */
|
||||
if(b>(float)1e10) {
|
||||
a /= b;
|
||||
t /= b;
|
||||
b = one;
|
||||
}
|
||||
}
|
||||
}
|
||||
b = (t*__ieee754_j0f(x)/b);
|
||||
}
|
||||
}
|
||||
if(sgn==1) return -b; else return b;
|
||||
}
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_ynf(int n, float x)
|
||||
#else
|
||||
float __ieee754_ynf(n,x)
|
||||
int n; float x;
|
||||
#endif
|
||||
{
|
||||
int32_t i,hx,ix,ib;
|
||||
int32_t sign;
|
||||
float a, b, temp;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = 0x7fffffff&hx;
|
||||
/* if Y(n,NaN) is NaN */
|
||||
if(ix>0x7f800000) return x+x;
|
||||
if(ix==0) return -one/zero;
|
||||
if(hx<0) return zero/zero;
|
||||
sign = 1;
|
||||
if(n<0){
|
||||
n = -n;
|
||||
sign = 1 - ((n&1)<<1);
|
||||
}
|
||||
if(n==0) return(__ieee754_y0f(x));
|
||||
if(n==1) return(sign*__ieee754_y1f(x));
|
||||
if(ix==0x7f800000) return zero;
|
||||
|
||||
a = __ieee754_y0f(x);
|
||||
b = __ieee754_y1f(x);
|
||||
/* quit if b is -inf */
|
||||
GET_FLOAT_WORD(ib,b);
|
||||
for(i=1;i<n&&ib!=0xff800000;i++){
|
||||
temp = b;
|
||||
b = ((float)(i+i)/x)*b - a;
|
||||
GET_FLOAT_WORD(ib,b);
|
||||
a = temp;
|
||||
}
|
||||
if(sign>0) return b; else return -b;
|
||||
}
|
||||
|
|
@ -0,0 +1,312 @@
|
|||
/* @(#)er_lgamma.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_lgamma_r.c,v 1.7 1995/05/10 20:45:42 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_lgamma_r(x, signgamp)
|
||||
* Reentrant version of the logarithm of the Gamma function
|
||||
* with user provide pointer for the sign of Gamma(x).
|
||||
*
|
||||
* Method:
|
||||
* 1. Argument Reduction for 0 < x <= 8
|
||||
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
|
||||
* reduce x to a number in [1.5,2.5] by
|
||||
* lgamma(1+s) = log(s) + lgamma(s)
|
||||
* for example,
|
||||
* lgamma(7.3) = log(6.3) + lgamma(6.3)
|
||||
* = log(6.3*5.3) + lgamma(5.3)
|
||||
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
|
||||
* 2. Polynomial approximation of lgamma around its
|
||||
* minimun ymin=1.461632144968362245 to maintain monotonicity.
|
||||
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
|
||||
* Let z = x-ymin;
|
||||
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
|
||||
* where
|
||||
* poly(z) is a 14 degree polynomial.
|
||||
* 2. Rational approximation in the primary interval [2,3]
|
||||
* We use the following approximation:
|
||||
* s = x-2.0;
|
||||
* lgamma(x) = 0.5*s + s*P(s)/Q(s)
|
||||
* with accuracy
|
||||
* |P/Q - (lgamma(x)-0.5s)| < 2**-61.71
|
||||
* Our algorithms are based on the following observation
|
||||
*
|
||||
* zeta(2)-1 2 zeta(3)-1 3
|
||||
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
|
||||
* 2 3
|
||||
*
|
||||
* where Euler = 0.5771... is the Euler constant, which is very
|
||||
* close to 0.5.
|
||||
*
|
||||
* 3. For x>=8, we have
|
||||
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
|
||||
* (better formula:
|
||||
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
|
||||
* Let z = 1/x, then we approximation
|
||||
* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
|
||||
* by
|
||||
* 3 5 11
|
||||
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
|
||||
* where
|
||||
* |w - f(z)| < 2**-58.74
|
||||
*
|
||||
* 4. For negative x, since (G is gamma function)
|
||||
* -x*G(-x)*G(x) = pi/sin(pi*x),
|
||||
* we have
|
||||
* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
|
||||
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
|
||||
* Hence, for x<0, signgam = sign(sin(pi*x)) and
|
||||
* lgamma(x) = log(|Gamma(x)|)
|
||||
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
|
||||
* Note: one should avoid compute pi*(-x) directly in the
|
||||
* computation of sin(pi*(-x)).
|
||||
*
|
||||
* 5. Special Cases
|
||||
* lgamma(2+s) ~ s*(1-Euler) for tiny s
|
||||
* lgamma(1)=lgamma(2)=0
|
||||
* lgamma(x) ~ -log(x) for tiny x
|
||||
* lgamma(0) = lgamma(inf) = inf
|
||||
* lgamma(-integer) = +-inf
|
||||
*
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
|
||||
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
|
||||
a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
|
||||
a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
|
||||
a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
|
||||
a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
|
||||
a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
|
||||
a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
|
||||
a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
|
||||
a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
|
||||
a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
|
||||
a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
|
||||
a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
|
||||
a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
|
||||
tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
|
||||
tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
|
||||
t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
|
||||
t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
|
||||
t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
|
||||
t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
|
||||
t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
|
||||
t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
|
||||
t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
|
||||
t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
|
||||
t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
|
||||
t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
|
||||
t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
|
||||
t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
|
||||
t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
|
||||
t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
|
||||
t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
|
||||
u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
|
||||
u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
|
||||
u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
|
||||
u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
|
||||
u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
|
||||
v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
|
||||
v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
|
||||
v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
|
||||
v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
|
||||
v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
|
||||
s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
|
||||
s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
|
||||
s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
|
||||
s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
|
||||
s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
|
||||
s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
|
||||
s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
|
||||
r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
|
||||
r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
|
||||
r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
|
||||
r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
|
||||
r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
|
||||
r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
|
||||
w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
|
||||
w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
|
||||
w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
|
||||
w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
|
||||
w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
|
||||
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
|
||||
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero= 0.00000000000000000000e+00;
|
||||
#else
|
||||
static double zero= 0.00000000000000000000e+00;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static double sin_pi(double x)
|
||||
#else
|
||||
static double sin_pi(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,z;
|
||||
int n,ix;
|
||||
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = __floor(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= 0.5;
|
||||
y = 2.0*(y - __floor(y)); /* y = |x| mod 2.0 */
|
||||
n = (int) (y*4.0);
|
||||
} else {
|
||||
if(ix>=0x43400000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x43300000) z = y+two52; /* exact */
|
||||
GET_LOW_WORD(n,z);
|
||||
n &= 1;
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sin(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cos(pi*(0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sin(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cos(pi*(y-1.5),zero); break;
|
||||
default: y = __kernel_sin(pi*(y-2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_lgamma_r(double x, int *signgamp)
|
||||
#else
|
||||
double __ieee754_lgamma_r(x,signgamp)
|
||||
double x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,lx,ix;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7ff00000) return x*x;
|
||||
if((ix|lx)==0) return one/zero;
|
||||
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_log(-x);
|
||||
} else return -__ieee754_log(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pi(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_log(pi/fabs(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_log(x);
|
||||
if(ix>=0x3FE76944) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x40200000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(double)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+2.0); /* FALLTHRU */
|
||||
r += __ieee754_log(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x43900000) {
|
||||
t = __ieee754_log(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_log(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
|
|
@ -0,0 +1,248 @@
|
|||
/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_lgammaf_r.c,v 1.3 1995/05/10 20:45:47 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
two23= 8.3886080000e+06, /* 0x4b000000 */
|
||||
half= 5.0000000000e-01, /* 0x3f000000 */
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
pi = 3.1415927410e+00, /* 0x40490fdb */
|
||||
a0 = 7.7215664089e-02, /* 0x3d9e233f */
|
||||
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
|
||||
a2 = 6.7352302372e-02, /* 0x3d89f001 */
|
||||
a3 = 2.0580807701e-02, /* 0x3ca89915 */
|
||||
a4 = 7.3855509982e-03, /* 0x3bf2027e */
|
||||
a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
|
||||
a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
|
||||
a7 = 5.1006977446e-04, /* 0x3a05b634 */
|
||||
a8 = 2.2086278477e-04, /* 0x39679767 */
|
||||
a9 = 1.0801156895e-04, /* 0x38e28445 */
|
||||
a10 = 2.5214456400e-05, /* 0x37d383a2 */
|
||||
a11 = 4.4864096708e-05, /* 0x383c2c75 */
|
||||
tc = 1.4616321325e+00, /* 0x3fbb16c3 */
|
||||
tf = -1.2148628384e-01, /* 0xbdf8cdcd */
|
||||
/* tt = -(tail of tf) */
|
||||
tt = 6.6971006518e-09, /* 0x31e61c52 */
|
||||
t0 = 4.8383611441e-01, /* 0x3ef7b95e */
|
||||
t1 = -1.4758771658e-01, /* 0xbe17213c */
|
||||
t2 = 6.4624942839e-02, /* 0x3d845a15 */
|
||||
t3 = -3.2788541168e-02, /* 0xbd064d47 */
|
||||
t4 = 1.7970675603e-02, /* 0x3c93373d */
|
||||
t5 = -1.0314224288e-02, /* 0xbc28fcfe */
|
||||
t6 = 6.1005386524e-03, /* 0x3bc7e707 */
|
||||
t7 = -3.6845202558e-03, /* 0xbb7177fe */
|
||||
t8 = 2.2596477065e-03, /* 0x3b141699 */
|
||||
t9 = -1.4034647029e-03, /* 0xbab7f476 */
|
||||
t10 = 8.8108185446e-04, /* 0x3a66f867 */
|
||||
t11 = -5.3859531181e-04, /* 0xba0d3085 */
|
||||
t12 = 3.1563205994e-04, /* 0x39a57b6b */
|
||||
t13 = -3.1275415677e-04, /* 0xb9a3f927 */
|
||||
t14 = 3.3552918467e-04, /* 0x39afe9f7 */
|
||||
u0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
u1 = 6.3282704353e-01, /* 0x3f2200f4 */
|
||||
u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
|
||||
u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
|
||||
u4 = 2.2896373272e-01, /* 0x3e6a7578 */
|
||||
u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
|
||||
v1 = 2.4559779167e+00, /* 0x401d2ebe */
|
||||
v2 = 2.1284897327e+00, /* 0x4008392d */
|
||||
v3 = 7.6928514242e-01, /* 0x3f44efdf */
|
||||
v4 = 1.0422264785e-01, /* 0x3dd572af */
|
||||
v5 = 3.2170924824e-03, /* 0x3b52d5db */
|
||||
s0 = -7.7215664089e-02, /* 0xbd9e233f */
|
||||
s1 = 2.1498242021e-01, /* 0x3e5c245a */
|
||||
s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
|
||||
s3 = 1.4635047317e-01, /* 0x3e15dce6 */
|
||||
s4 = 2.6642270386e-02, /* 0x3cda40e4 */
|
||||
s5 = 1.8402845599e-03, /* 0x3af135b4 */
|
||||
s6 = 3.1947532989e-05, /* 0x3805ff67 */
|
||||
r1 = 1.3920053244e+00, /* 0x3fb22d3b */
|
||||
r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
|
||||
r3 = 1.7193385959e-01, /* 0x3e300f6e */
|
||||
r4 = 1.8645919859e-02, /* 0x3c98bf54 */
|
||||
r5 = 7.7794247773e-04, /* 0x3a4beed6 */
|
||||
r6 = 7.3266842264e-06, /* 0x36f5d7bd */
|
||||
w0 = 4.1893854737e-01, /* 0x3ed67f1d */
|
||||
w1 = 8.3333335817e-02, /* 0x3daaaaab */
|
||||
w2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
w3 = 7.9365057172e-04, /* 0x3a500cfd */
|
||||
w4 = -5.9518753551e-04, /* 0xba1c065c */
|
||||
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
|
||||
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero= 0.0000000000e+00;
|
||||
#else
|
||||
static float zero= 0.0000000000e+00;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static float sin_pif(float x)
|
||||
#else
|
||||
static float sin_pif(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float y,z;
|
||||
int n,ix;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
|
||||
y = -x; /* x is assume negative */
|
||||
|
||||
/*
|
||||
* argument reduction, make sure inexact flag not raised if input
|
||||
* is an integer
|
||||
*/
|
||||
z = __floorf(y);
|
||||
if(z!=y) { /* inexact anyway */
|
||||
y *= (float)0.5;
|
||||
y = (float)2.0*(y - __floorf(y)); /* y = |x| mod 2.0 */
|
||||
n = (int) (y*(float)4.0);
|
||||
} else {
|
||||
if(ix>=0x4b800000) {
|
||||
y = zero; n = 0; /* y must be even */
|
||||
} else {
|
||||
if(ix<0x4b000000) z = y+two23; /* exact */
|
||||
GET_FLOAT_WORD(n,z);
|
||||
n &= 1;
|
||||
y = n;
|
||||
n<<= 2;
|
||||
}
|
||||
}
|
||||
switch (n) {
|
||||
case 0: y = __kernel_sinf(pi*y,zero,0); break;
|
||||
case 1:
|
||||
case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break;
|
||||
case 3:
|
||||
case 4: y = __kernel_sinf(pi*(one-y),zero,0); break;
|
||||
case 5:
|
||||
case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
|
||||
default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
|
||||
}
|
||||
return -y;
|
||||
}
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_lgammaf_r(float x, int *signgamp)
|
||||
#else
|
||||
float __ieee754_lgammaf_r(x,signgamp)
|
||||
float x; int *signgamp;
|
||||
#endif
|
||||
{
|
||||
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
|
||||
int i,hx,ix;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
/* purge off +-inf, NaN, +-0, and negative arguments */
|
||||
*signgamp = 1;
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix>=0x7f800000) return x*x;
|
||||
if(ix==0) return one/zero;
|
||||
if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */
|
||||
if(hx<0) {
|
||||
*signgamp = -1;
|
||||
return -__ieee754_logf(-x);
|
||||
} else return -__ieee754_logf(x);
|
||||
}
|
||||
if(hx<0) {
|
||||
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
|
||||
return one/zero;
|
||||
t = sin_pif(x);
|
||||
if(t==zero) return one/zero; /* -integer */
|
||||
nadj = __ieee754_logf(pi/fabsf(t*x));
|
||||
if(t<zero) *signgamp = -1;
|
||||
x = -x;
|
||||
}
|
||||
|
||||
/* purge off 1 and 2 */
|
||||
if (ix==0x3f800000||ix==0x40000000) r = 0;
|
||||
/* for x < 2.0 */
|
||||
else if(ix<0x40000000) {
|
||||
if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
|
||||
r = -__ieee754_logf(x);
|
||||
if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
|
||||
else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
|
||||
else {y = x; i=2;}
|
||||
} else {
|
||||
r = zero;
|
||||
if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
|
||||
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
|
||||
else {y=x-one;i=2;}
|
||||
}
|
||||
switch(i) {
|
||||
case 0:
|
||||
z = y*y;
|
||||
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
|
||||
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
|
||||
p = y*p1+p2;
|
||||
r += (p-(float)0.5*y); break;
|
||||
case 1:
|
||||
z = y*y;
|
||||
w = z*y;
|
||||
p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
|
||||
p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
|
||||
p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
|
||||
p = z*p1-(tt-w*(p2+y*p3));
|
||||
r += (tf + p); break;
|
||||
case 2:
|
||||
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
|
||||
p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
|
||||
r += (-(float)0.5*y + p1/p2);
|
||||
}
|
||||
}
|
||||
else if(ix<0x41000000) { /* x < 8.0 */
|
||||
i = (int)x;
|
||||
t = zero;
|
||||
y = x-(float)i;
|
||||
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
|
||||
q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
|
||||
r = half*y+p/q;
|
||||
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
|
||||
switch(i) {
|
||||
case 7: z *= (y+(float)6.0); /* FALLTHRU */
|
||||
case 6: z *= (y+(float)5.0); /* FALLTHRU */
|
||||
case 5: z *= (y+(float)4.0); /* FALLTHRU */
|
||||
case 4: z *= (y+(float)3.0); /* FALLTHRU */
|
||||
case 3: z *= (y+(float)2.0); /* FALLTHRU */
|
||||
r += __ieee754_logf(z); break;
|
||||
}
|
||||
/* 8.0 <= x < 2**58 */
|
||||
} else if (ix < 0x5c800000) {
|
||||
t = __ieee754_logf(x);
|
||||
z = one/x;
|
||||
y = z*z;
|
||||
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
|
||||
r = (x-half)*(t-one)+w;
|
||||
} else
|
||||
/* 2**58 <= x <= inf */
|
||||
r = x*(__ieee754_logf(x)-one);
|
||||
if(hx<0) r = nadj - r;
|
||||
return r;
|
||||
}
|
||||
|
|
@ -0,0 +1,146 @@
|
|||
/* @(#)e_log.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_log(x)
|
||||
* Return the logrithm of x
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* 2. Approximation of log(1+f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
||||
* (the values of Lg1 to Lg7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lg1*s +...+Lg7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log(1+f) = f - s*(f - R) (if f is not too large)
|
||||
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
||||
*
|
||||
* 3. Finally, log(x) = k*ln2 + log(1+f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log(x) is NaN with signal if x < 0 (including -INF) ;
|
||||
* log(+INF) is +INF; log(0) is -INF with signal;
|
||||
* log(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
|
||||
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
|
||||
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
|
||||
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
|
||||
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
|
||||
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
|
||||
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
|
||||
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
|
||||
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
|
||||
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_log(double x)
|
||||
#else
|
||||
double __ieee754_log(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,hx,i,j;
|
||||
u_int32_t lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx+0x95f64)&0x100000;
|
||||
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
|
||||
k += (i>>20);
|
||||
f = x-1.0;
|
||||
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
|
||||
if(f==zero) if(k==0) return zero; else {dk=(double)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
R = f*f*(0.5-0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(double)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/(2.0+f);
|
||||
dk = (double)k;
|
||||
z = s*s;
|
||||
i = hx-0x6147a;
|
||||
w = z*z;
|
||||
j = 0x6b851-hx;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
/* @(#)e_log10.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_log10(x)
|
||||
* Return the base 10 logarithm of x
|
||||
*
|
||||
* Method :
|
||||
* Let log10_2hi = leading 40 bits of log10(2) and
|
||||
* log10_2lo = log10(2) - log10_2hi,
|
||||
* ivln10 = 1/log(10) rounded.
|
||||
* Then
|
||||
* n = ilogb(x),
|
||||
* if(n<0) n = n+1;
|
||||
* x = scalbn(x,-n);
|
||||
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
||||
*
|
||||
* Note 1:
|
||||
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
||||
* mode must set to Round-to-Nearest.
|
||||
* Note 2:
|
||||
* [1/log(10)] rounded to 53 bits has error .198 ulps;
|
||||
* log10 is monotonic at all binary break points.
|
||||
*
|
||||
* Special cases:
|
||||
* log10(x) is NaN with signal if x < 0;
|
||||
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
|
||||
* log10(NaN) is that NaN with no signal;
|
||||
* log10(10**N) = N for N=0,1,...,22.
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following constants.
|
||||
* The decimal values may be used, provided that the compiler will convert
|
||||
* from decimal to binary accurately enough to produce the hexadecimal values
|
||||
* shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
|
||||
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
|
||||
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_log10(double x)
|
||||
#else
|
||||
double __ieee754_log10(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double y,z;
|
||||
int32_t i,k,hx;
|
||||
u_int32_t lx;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00100000) { /* x < 2**-1022 */
|
||||
if (((hx&0x7fffffff)|lx)==0)
|
||||
return -two54/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 54; x *= two54; /* subnormal number, scale up x */
|
||||
GET_HIGH_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7ff00000) return x+x;
|
||||
k += (hx>>20)-1023;
|
||||
i = ((u_int32_t)k&0x80000000)>>31;
|
||||
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
|
||||
y = (double)(k+i);
|
||||
SET_HIGH_WORD(x,hx);
|
||||
z = y*log10_2lo + ivln10*__ieee754_log(x);
|
||||
return z+y*log10_2hi;
|
||||
}
|
||||
|
|
@ -0,0 +1,67 @@
|
|||
/* e_log10f.c -- float version of e_log10.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_log10f.c,v 1.5 1995/05/10 20:45:53 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
two25 = 3.3554432000e+07, /* 0x4c000000 */
|
||||
ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
|
||||
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
|
||||
log10_2lo = 7.9034151668e-07; /* 0x355427db */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_log10f(float x)
|
||||
#else
|
||||
float __ieee754_log10f(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float y,z;
|
||||
int32_t i,k,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
|
||||
k=0;
|
||||
if (hx < 0x00800000) { /* x < 2**-126 */
|
||||
if ((hx&0x7fffffff)==0)
|
||||
return -two25/zero; /* log(+-0)=-inf */
|
||||
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
}
|
||||
if (hx >= 0x7f800000) return x+x;
|
||||
k += (hx>>23)-127;
|
||||
i = ((u_int32_t)k&0x80000000)>>31;
|
||||
hx = (hx&0x007fffff)|((0x7f-i)<<23);
|
||||
y = (float)(k+i);
|
||||
SET_FLOAT_WORD(x,hx);
|
||||
z = y*log10_2lo + ivln10*__ieee754_logf(x);
|
||||
return z+y*log10_2hi;
|
||||
}
|
||||
|
|
@ -0,0 +1,97 @@
|
|||
/* e_logf.c -- float version of e_log.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_logf.c,v 1.4 1995/05/10 20:45:54 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||
two25 = 3.355443200e+07, /* 0x4c000000 */
|
||||
Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
|
||||
Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
|
||||
Lg3 = 2.8571429849e-01, /* 3E924925 */
|
||||
Lg4 = 2.2222198546e-01, /* 3E638E29 */
|
||||
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
|
||||
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
|
||||
Lg7 = 1.4798198640e-01; /* 3E178897 */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_logf(float x)
|
||||
#else
|
||||
float __ieee754_logf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float hfsq,f,s,z,R,w,t1,t2,dk;
|
||||
int32_t k,ix,i,j;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
k=0;
|
||||
if (ix < 0x00800000) { /* x < 2**-126 */
|
||||
if ((ix&0x7fffffff)==0)
|
||||
return -two25/zero; /* log(+-0)=-inf */
|
||||
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
|
||||
k -= 25; x *= two25; /* subnormal number, scale up x */
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
}
|
||||
if (ix >= 0x7f800000) return x+x;
|
||||
k += (ix>>23)-127;
|
||||
ix &= 0x007fffff;
|
||||
i = (ix+(0x95f64<<3))&0x800000;
|
||||
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
|
||||
k += (i>>23);
|
||||
f = x-(float)1.0;
|
||||
if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
|
||||
if(f==zero) if(k==0) return zero; else {dk=(float)k;
|
||||
return dk*ln2_hi+dk*ln2_lo;}
|
||||
R = f*f*((float)0.5-(float)0.33333333333333333*f);
|
||||
if(k==0) return f-R; else {dk=(float)k;
|
||||
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
|
||||
}
|
||||
s = f/((float)2.0+f);
|
||||
dk = (float)k;
|
||||
z = s*s;
|
||||
i = ix-(0x6147a<<3);
|
||||
w = z*z;
|
||||
j = (0x6b851<<3)-ix;
|
||||
t1= w*(Lg2+w*(Lg4+w*Lg6));
|
||||
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
|
||||
i |= j;
|
||||
R = t2+t1;
|
||||
if(i>0) {
|
||||
hfsq=(float)0.5*f*f;
|
||||
if(k==0) return f-(hfsq-s*(hfsq+R)); else
|
||||
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
|
||||
} else {
|
||||
if(k==0) return f-s*(f-R); else
|
||||
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,308 @@
|
|||
/* @(#)e_pow.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_pow(x,y) return x**y
|
||||
*
|
||||
* n
|
||||
* Method: Let x = 2 * (1+f)
|
||||
* 1. Compute and return log2(x) in two pieces:
|
||||
* log2(x) = w1 + w2,
|
||||
* where w1 has 53-24 = 29 bit trailing zeros.
|
||||
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
|
||||
* arithmetic, where |y'|<=0.5.
|
||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||
*
|
||||
* Special cases:
|
||||
* 1. (anything) ** 0 is 1
|
||||
* 2. (anything) ** 1 is itself
|
||||
* 3. (anything) ** NAN is NAN
|
||||
* 4. NAN ** (anything except 0) is NAN
|
||||
* 5. +-(|x| > 1) ** +INF is +INF
|
||||
* 6. +-(|x| > 1) ** -INF is +0
|
||||
* 7. +-(|x| < 1) ** +INF is +0
|
||||
* 8. +-(|x| < 1) ** -INF is +INF
|
||||
* 9. +-1 ** +-INF is NAN
|
||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||
*
|
||||
* Accuracy:
|
||||
* pow(x,y) returns x**y nearly rounded. In particular
|
||||
* pow(integer,integer)
|
||||
* always returns the correct integer provided it is
|
||||
* representable.
|
||||
*
|
||||
* Constants :
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
|
||||
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
|
||||
huge = 1.0e300,
|
||||
tiny = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_pow(double x, double y)
|
||||
#else
|
||||
double __ieee754_pow(x,y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double z,ax,z_h,z_l,p_h,p_l;
|
||||
double y1,t1,t2,r,s,t,u,v,w;
|
||||
int32_t i,j,k,yisint,n;
|
||||
int32_t hx,hy,ix,iy;
|
||||
u_int32_t lx,ly;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hy,ly,y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if((iy|ly)==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
|
||||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x43400000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3ff00000) {
|
||||
k = (iy>>20)-0x3ff; /* exponent */
|
||||
if(k>20) {
|
||||
j = ly>>(52-k);
|
||||
if((j<<(52-k))==ly) yisint = 2-(j&1);
|
||||
} else if(ly==0) {
|
||||
j = iy>>(20-k);
|
||||
if((j<<(20-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if(ly==0) {
|
||||
if (iy==0x7ff00000) { /* y is +-inf */
|
||||
if(((ix-0x3ff00000)|lx)==0)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3ff00000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3fe00000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return __ieee754_sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fabs(x);
|
||||
/* special value of x */
|
||||
if(lx==0) {
|
||||
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3ff00000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x41e00000) { /* if |y| > 2**31 */
|
||||
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
|
||||
if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = x-1; /* t has 20 trailing zeros */
|
||||
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
SET_LOW_WORD(t1,0);
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
double s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00100000)
|
||||
{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
|
||||
n += ((ix)>>20)-0x3ff;
|
||||
j = ix&0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3ff00000; /* normalize ix */
|
||||
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00100000;}
|
||||
SET_HIGH_WORD(ax,ix);
|
||||
|
||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
s = u*v;
|
||||
s_h = s;
|
||||
SET_LOW_WORD(s_h,0);
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = s*s;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+s);
|
||||
s2 = s_h*s_h;
|
||||
t_h = 3.0+s2+r;
|
||||
SET_LOW_WORD(t_h,0);
|
||||
t_l = r-((t_h-3.0)-s2);
|
||||
/* u+v = s*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*s;
|
||||
/* 2/(3log2)*(s+...) */
|
||||
p_h = u+v;
|
||||
SET_LOW_WORD(p_h,0);
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
SET_LOW_WORD(t1,0);
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
|
||||
s = -one;/* (-ve)**(odd int) */
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
y1 = y;
|
||||
SET_LOW_WORD(y1,0);
|
||||
p_l = (y-y1)*t1+y*t2;
|
||||
p_h = y1*t1;
|
||||
z = p_l+p_h;
|
||||
EXTRACT_WORDS(j,i,z);
|
||||
if (j>=0x40900000) { /* z >= 1024 */
|
||||
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else {
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
|
||||
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
else {
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>20)-0x3ff;
|
||||
n = 0;
|
||||
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00100000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
SET_HIGH_WORD(t,n&~(0x000fffff>>k));
|
||||
n = ((n&0x000fffff)|0x00100000)>>(20-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
SET_LOW_WORD(t,0);
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
GET_HIGH_WORD(j,z);
|
||||
j += (n<<20);
|
||||
if((j>>20)<=0) z = __scalbn(z,n); /* subnormal output */
|
||||
else SET_HIGH_WORD(z,j);
|
||||
return s*z;
|
||||
}
|
||||
|
|
@ -0,0 +1,253 @@
|
|||
/* e_powf.c -- float version of e_pow.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_powf.c,v 1.6 1995/05/12 04:57:35 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
static const volatile float huge = 1.0e+30, tiny = 1.0e-30;
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
bp[] = {1.0, 1.5,},
|
||||
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
||||
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two = 2.0,
|
||||
two24 = 16777216.0, /* 0x4b800000 */
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 6.0000002384e-01, /* 0x3f19999a */
|
||||
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
||||
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
||||
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
||||
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
||||
L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
||||
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
||||
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
||||
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
||||
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
||||
P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
||||
lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
||||
lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
||||
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
||||
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
||||
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
||||
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
|
||||
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
|
||||
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
||||
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
||||
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_powf(float x, float y)
|
||||
#else
|
||||
float __ieee754_powf(x,y)
|
||||
float x, y;
|
||||
#endif
|
||||
{
|
||||
float z,ax,z_h,z_l,p_h,p_l;
|
||||
float y1,t1,t2,r,s,t,u,v,w;
|
||||
int32_t i,j,k,yisint,n;
|
||||
int32_t hx,hy,ix,iy,is;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hy,y);
|
||||
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if(iy==0) return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if(ix > 0x7f800000 ||
|
||||
iy > 0x7f800000)
|
||||
return x+y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx<0) {
|
||||
if(iy>=0x4b800000) yisint = 2; /* even integer y */
|
||||
else if(iy>=0x3f800000) {
|
||||
k = (iy>>23)-0x7f; /* exponent */
|
||||
j = iy>>(23-k);
|
||||
if((j<<(23-k))==iy) yisint = 2-(j&1);
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if (iy==0x7f800000) { /* y is +-inf */
|
||||
if (ix==0x3f800000)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy>=0)? y: zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy<0)?-y: zero;
|
||||
}
|
||||
if(iy==0x3f800000) { /* y is +-1 */
|
||||
if(hy<0) return one/x; else return x;
|
||||
}
|
||||
if(hy==0x40000000) return x*x; /* y is 2 */
|
||||
if(hy==0x3f000000) { /* y is 0.5 */
|
||||
if(hx>=0) /* x >= +0 */
|
||||
return __ieee754_sqrtf(x);
|
||||
}
|
||||
|
||||
ax = fabsf(x);
|
||||
/* special value of x */
|
||||
if(ix==0x7f800000||ix==0||ix==0x3f800000){
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy<0) z = one/z; /* z = (1/|x|) */
|
||||
if(hx<0) {
|
||||
if(((ix-0x3f800000)|yisint)==0) {
|
||||
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint==1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
|
||||
|
||||
/* |y| is huge */
|
||||
if(iy>0x4d000000) { /* if |y| > 2**27 */
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
|
||||
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = x-1; /* t has 20 trailing zeros */
|
||||
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
|
||||
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
|
||||
v = t*ivln2_l-w*ivln2;
|
||||
t1 = u+v;
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = v-(t1-u);
|
||||
} else {
|
||||
float s2,s_h,s_l,t_h,t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix<0x00800000)
|
||||
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
|
||||
n += ((ix)>>23)-0x7f;
|
||||
j = ix&0x007fffff;
|
||||
/* determine interval */
|
||||
ix = j|0x3f800000; /* normalize ix */
|
||||
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
|
||||
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
|
||||
else {k=0;n+=1;ix -= 0x00800000;}
|
||||
SET_FLOAT_WORD(ax,ix);
|
||||
|
||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one/(ax+bp[k]);
|
||||
s = u*v;
|
||||
s_h = s;
|
||||
GET_FLOAT_WORD(is,s_h);
|
||||
SET_FLOAT_WORD(s_h,is&0xfffff000);
|
||||
/* t_h=ax+bp[k] High */
|
||||
SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
|
||||
t_l = ax - (t_h-bp[k]);
|
||||
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = s*s;
|
||||
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
||||
r += s_l*(s_h+s);
|
||||
s2 = s_h*s_h;
|
||||
t_h = (float)3.0+s2+r;
|
||||
GET_FLOAT_WORD(is,t_h);
|
||||
SET_FLOAT_WORD(t_h,is&0xfffff000);
|
||||
t_l = r-((t_h-(float)3.0)-s2);
|
||||
/* u+v = s*(1+...) */
|
||||
u = s_h*t_h;
|
||||
v = s_l*t_h+t_l*s;
|
||||
/* 2/(3log2)*(s+...) */
|
||||
p_h = u+v;
|
||||
GET_FLOAT_WORD(is,p_h);
|
||||
SET_FLOAT_WORD(p_h,is&0xfffff000);
|
||||
p_l = v-(p_h-u);
|
||||
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (float)n;
|
||||
t1 = (((z_h+z_l)+dp_h[k])+t);
|
||||
GET_FLOAT_WORD(is,t1);
|
||||
SET_FLOAT_WORD(t1,is&0xfffff000);
|
||||
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
|
||||
s = -one; /* (-ve)**(odd int) */
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
GET_FLOAT_WORD(is,y);
|
||||
SET_FLOAT_WORD(y1,is&0xfffff000);
|
||||
p_l = (y-y1)*t1+y*t2;
|
||||
p_h = y1*t1;
|
||||
z = p_l+p_h;
|
||||
GET_FLOAT_WORD(j,z);
|
||||
if (j>0x43000000) /* if z > 128 */
|
||||
return s*huge*huge; /* overflow */
|
||||
else if (j==0x43000000) { /* if z == 128 */
|
||||
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
||||
}
|
||||
else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
|
||||
return s*tiny*tiny; /* underflow */
|
||||
else if (j==0xc3160000){ /* z == -150 */
|
||||
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j&0x7fffffff;
|
||||
k = (i>>23)-0x7f;
|
||||
n = 0;
|
||||
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j+(0x00800000>>(k+1));
|
||||
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
|
||||
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
|
||||
n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
||||
if(j<0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l+p_h;
|
||||
GET_FLOAT_WORD(is,t);
|
||||
SET_FLOAT_WORD(t,is&0xfffff000);
|
||||
u = t*lg2_h;
|
||||
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
||||
z = u+v;
|
||||
w = v-(z-u);
|
||||
t = z*z;
|
||||
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
||||
r = (z*t1)/(t1-two)-(w+z*w);
|
||||
z = one-(r-z);
|
||||
GET_FLOAT_WORD(j,z);
|
||||
j += (n<<23);
|
||||
if((j>>23)<=0) z = __scalbnf(z,n); /* subnormal output */
|
||||
else SET_FLOAT_WORD(z,j);
|
||||
return s*z;
|
||||
}
|
||||
|
|
@ -0,0 +1,183 @@
|
|||
/* @(#)e_rem_pio2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_rem_pio2(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2()
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const int32_t two_over_pi[] = {
|
||||
#else
|
||||
static int32_t two_over_pi[] = {
|
||||
#endif
|
||||
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
||||
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
||||
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
||||
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
||||
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
||||
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
||||
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
||||
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
||||
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
||||
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
||||
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int32_t npio2_hw[] = {
|
||||
#else
|
||||
static int32_t npio2_hw[] = {
|
||||
#endif
|
||||
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
||||
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
||||
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
||||
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
||||
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
||||
0x404858EB, 0x404921FB,
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 53 bits of 2/pi
|
||||
* pio2_1: first 33 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 33 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 33 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
||||
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
||||
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
||||
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
||||
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
||||
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
||||
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
||||
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int32_t __ieee754_rem_pio2(double x, double *y)
|
||||
#else
|
||||
int32_t __ieee754_rem_pio2(x,y)
|
||||
double x,y[];
|
||||
#endif
|
||||
{
|
||||
double z,w,t,r,fn;
|
||||
double tx[3];
|
||||
int32_t e0,i,j,nx,n,ix,hx;
|
||||
u_int32_t low;
|
||||
|
||||
GET_HIGH_WORD(hx,x); /* high word of x */
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 33+33+53 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
||||
t = fabs(x);
|
||||
n = (int32_t) (t*invpio2+half);
|
||||
fn = (double)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
||||
if(n<32&&ix!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
u_int32_t high;
|
||||
j = ix>>20;
|
||||
y[0] = r-w;
|
||||
GET_HIGH_WORD(high,y[0]);
|
||||
i = j-((high>>20)&0x7ff);
|
||||
if(i>16) { /* 2nd iteration needed, good to 118 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
GET_HIGH_WORD(high,y[0]);
|
||||
i = j-((high>>20)&0x7ff);
|
||||
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-23) */
|
||||
GET_LOW_WORD(low,x);
|
||||
SET_LOW_WORD(z,low);
|
||||
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
|
||||
SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (double)((int32_t)(z));
|
||||
z = (z-tx[i])*two24;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
|
|
@ -0,0 +1,196 @@
|
|||
/* e_rem_pio2f.c -- float version of e_rem_pio2.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_rem_pio2f(x,y)
|
||||
*
|
||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
||||
* use __kernel_rem_pio2f()
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/*
|
||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
||||
*/
|
||||
#ifdef __STDC__
|
||||
static const int32_t two_over_pi[] = {
|
||||
#else
|
||||
static int32_t two_over_pi[] = {
|
||||
#endif
|
||||
0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
|
||||
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
|
||||
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
|
||||
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
|
||||
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
|
||||
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
|
||||
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
|
||||
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
|
||||
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
|
||||
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
|
||||
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
|
||||
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
|
||||
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
|
||||
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
|
||||
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
|
||||
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
|
||||
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
|
||||
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
|
||||
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
|
||||
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
|
||||
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
|
||||
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
|
||||
};
|
||||
|
||||
/* This array is like the one in e_rem_pio2.c, but the numbers are
|
||||
single precision and the last 8 bits are forced to 0. */
|
||||
#ifdef __STDC__
|
||||
static const int32_t npio2_hw[] = {
|
||||
#else
|
||||
static int32_t npio2_hw[] = {
|
||||
#endif
|
||||
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
|
||||
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
|
||||
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
|
||||
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
|
||||
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
|
||||
0x4242c700, 0x42490f00
|
||||
};
|
||||
|
||||
/*
|
||||
* invpio2: 24 bits of 2/pi
|
||||
* pio2_1: first 17 bit of pi/2
|
||||
* pio2_1t: pi/2 - pio2_1
|
||||
* pio2_2: second 17 bit of pi/2
|
||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
||||
* pio2_3: third 17 bit of pi/2
|
||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
||||
*/
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
zero = 0.0000000000e+00, /* 0x00000000 */
|
||||
half = 5.0000000000e-01, /* 0x3f000000 */
|
||||
two8 = 2.5600000000e+02, /* 0x43800000 */
|
||||
invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
|
||||
pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
|
||||
pio2_1t = 1.0804334124e-05, /* 0x37354443 */
|
||||
pio2_2 = 1.0804273188e-05, /* 0x37354400 */
|
||||
pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
|
||||
pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
|
||||
pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int32_t __ieee754_rem_pio2f(float x, float *y)
|
||||
#else
|
||||
int32_t __ieee754_rem_pio2f(x,y)
|
||||
float x,y[];
|
||||
#endif
|
||||
{
|
||||
float z,w,t,r,fn;
|
||||
float tx[3];
|
||||
int32_t e0,i,j,nx,n,ix,hx;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
ix = hx&0x7fffffff;
|
||||
if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
|
||||
{y[0] = x; y[1] = 0; return 0;}
|
||||
if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
|
||||
if(hx>0) {
|
||||
z = x - pio2_1;
|
||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
||||
y[0] = z - pio2_1t;
|
||||
y[1] = (z-y[0])-pio2_1t;
|
||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
||||
z -= pio2_2;
|
||||
y[0] = z - pio2_2t;
|
||||
y[1] = (z-y[0])-pio2_2t;
|
||||
}
|
||||
return 1;
|
||||
} else { /* negative x */
|
||||
z = x + pio2_1;
|
||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
||||
y[0] = z + pio2_1t;
|
||||
y[1] = (z-y[0])+pio2_1t;
|
||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
||||
z += pio2_2;
|
||||
y[0] = z + pio2_2t;
|
||||
y[1] = (z-y[0])+pio2_2t;
|
||||
}
|
||||
return -1;
|
||||
}
|
||||
}
|
||||
if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
|
||||
t = fabsf(x);
|
||||
n = (int32_t) (t*invpio2+half);
|
||||
fn = (float)n;
|
||||
r = t-fn*pio2_1;
|
||||
w = fn*pio2_1t; /* 1st round good to 40 bit */
|
||||
if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
|
||||
y[0] = r-w; /* quick check no cancellation */
|
||||
} else {
|
||||
u_int32_t high;
|
||||
j = ix>>23;
|
||||
y[0] = r-w;
|
||||
GET_FLOAT_WORD(high,y[0]);
|
||||
i = j-((high>>23)&0xff);
|
||||
if(i>8) { /* 2nd iteration needed, good to 57 */
|
||||
t = r;
|
||||
w = fn*pio2_2;
|
||||
r = t-w;
|
||||
w = fn*pio2_2t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
GET_FLOAT_WORD(high,y[0]);
|
||||
i = j-((high>>23)&0xff);
|
||||
if(i>25) { /* 3rd iteration need, 74 bits acc */
|
||||
t = r; /* will cover all possible cases */
|
||||
w = fn*pio2_3;
|
||||
r = t-w;
|
||||
w = fn*pio2_3t-((t-r)-w);
|
||||
y[0] = r-w;
|
||||
}
|
||||
}
|
||||
}
|
||||
y[1] = (r-y[0])-w;
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
else return n;
|
||||
}
|
||||
/*
|
||||
* all other (large) arguments
|
||||
*/
|
||||
if(ix>=0x7f800000) { /* x is inf or NaN */
|
||||
y[0]=y[1]=x-x; return 0;
|
||||
}
|
||||
/* set z = scalbn(|x|,ilogb(x)-7) */
|
||||
e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */
|
||||
SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
|
||||
for(i=0;i<2;i++) {
|
||||
tx[i] = (float)((int32_t)(z));
|
||||
z = (z-tx[i])*two8;
|
||||
}
|
||||
tx[2] = z;
|
||||
nx = 3;
|
||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
||||
n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
|
||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
||||
return n;
|
||||
}
|
||||
|
|
@ -0,0 +1,80 @@
|
|||
/* @(#)e_remainder.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_remainder.c,v 1.8 1995/05/10 20:46:05 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_remainder(x,p)
|
||||
* Return :
|
||||
* returns x REM p = x - [x/p]*p as if in infinite
|
||||
* precise arithmetic, where [x/p] is the (infinite bit)
|
||||
* integer nearest x/p (in half way case choose the even one).
|
||||
* Method :
|
||||
* Based on fmod() return x-[x/p]chopped*p exactlp.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double zero = 0.0;
|
||||
#else
|
||||
static double zero = 0.0;
|
||||
#endif
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_remainder(double x, double p)
|
||||
#else
|
||||
double __ieee754_remainder(x,p)
|
||||
double x,p;
|
||||
#endif
|
||||
{
|
||||
int32_t hx,hp;
|
||||
u_int32_t sx,lx,lp;
|
||||
double p_half;
|
||||
|
||||
EXTRACT_WORDS(hx,lx,x);
|
||||
EXTRACT_WORDS(hp,lp,p);
|
||||
sx = hx&0x80000000;
|
||||
hp &= 0x7fffffff;
|
||||
hx &= 0x7fffffff;
|
||||
|
||||
/* purge off exception values */
|
||||
if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */
|
||||
if((hx>=0x7ff00000)|| /* x not finite */
|
||||
((hp>=0x7ff00000)&& /* p is NaN */
|
||||
(((hp-0x7ff00000)|lp)!=0)))
|
||||
return (x*p)/(x*p);
|
||||
|
||||
|
||||
if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */
|
||||
if (((hx-hp)|(lx-lp))==0) return zero*x;
|
||||
x = fabs(x);
|
||||
p = fabs(p);
|
||||
if (hp<0x00200000) {
|
||||
if(x+x>p) {
|
||||
x-=p;
|
||||
if(x+x>=p) x -= p;
|
||||
}
|
||||
} else {
|
||||
p_half = 0.5*p;
|
||||
if(x>p_half) {
|
||||
x-=p;
|
||||
if(x>=p_half) x -= p;
|
||||
}
|
||||
}
|
||||
GET_HIGH_WORD(hx,x);
|
||||
SET_HIGH_WORD(x,hx^sx);
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,73 @@
|
|||
/* e_remainderf.c -- float version of e_remainder.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_remainderf.c,v 1.4 1995/05/10 20:46:08 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float zero = 0.0;
|
||||
#else
|
||||
static float zero = 0.0;
|
||||
#endif
|
||||
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_remainderf(float x, float p)
|
||||
#else
|
||||
float __ieee754_remainderf(x,p)
|
||||
float x,p;
|
||||
#endif
|
||||
{
|
||||
int32_t hx,hp;
|
||||
u_int32_t sx;
|
||||
float p_half;
|
||||
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
GET_FLOAT_WORD(hp,p);
|
||||
sx = hx&0x80000000;
|
||||
hp &= 0x7fffffff;
|
||||
hx &= 0x7fffffff;
|
||||
|
||||
/* purge off exception values */
|
||||
if(hp==0) return (x*p)/(x*p); /* p = 0 */
|
||||
if((hx>=0x7f800000)|| /* x not finite */
|
||||
((hp>0x7f800000))) /* p is NaN */
|
||||
return (x*p)/(x*p);
|
||||
|
||||
|
||||
if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */
|
||||
if ((hx-hp)==0) return zero*x;
|
||||
x = fabsf(x);
|
||||
p = fabsf(p);
|
||||
if (hp<0x01000000) {
|
||||
if(x+x>p) {
|
||||
x-=p;
|
||||
if(x+x>=p) x -= p;
|
||||
}
|
||||
} else {
|
||||
p_half = (float)0.5*p;
|
||||
if(x>p_half) {
|
||||
x-=p;
|
||||
if(x>=p_half) x -= p;
|
||||
}
|
||||
}
|
||||
GET_FLOAT_WORD(hx,x);
|
||||
SET_FLOAT_WORD(x,hx^sx);
|
||||
return x;
|
||||
}
|
||||
|
|
@ -0,0 +1,55 @@
|
|||
/* @(#)e_scalb.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_scalb.c,v 1.6 1995/05/10 20:46:09 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __ieee754_scalb(x, fn) is provide for
|
||||
* passing various standard test suite. One
|
||||
* should use scalbn() instead.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef _SCALB_INT
|
||||
#ifdef __STDC__
|
||||
double __ieee754_scalb(double x, int fn)
|
||||
#else
|
||||
double __ieee754_scalb(x,fn)
|
||||
double x; int fn;
|
||||
#endif
|
||||
#else
|
||||
#ifdef __STDC__
|
||||
double __ieee754_scalb(double x, double fn)
|
||||
#else
|
||||
double __ieee754_scalb(x,fn)
|
||||
double x, fn;
|
||||
#endif
|
||||
#endif
|
||||
{
|
||||
#ifdef _SCALB_INT
|
||||
return scalbn(x,fn);
|
||||
#else
|
||||
if (isnan(x)||isnan(fn)) return x*fn;
|
||||
if (!finite(fn)) {
|
||||
if(fn>0.0) return x*fn;
|
||||
else return x/(-fn);
|
||||
}
|
||||
if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
|
||||
if ( fn > 65000.0) return scalbn(x, 65000);
|
||||
if (-fn > 65000.0) return scalbn(x,-65000);
|
||||
return scalbn(x,(int)fn);
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,52 @@
|
|||
/* e_scalbf.c -- float version of e_scalb.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_scalbf.c,v 1.3 1995/05/10 20:46:12 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef _SCALB_INT
|
||||
#ifdef __STDC__
|
||||
float __ieee754_scalbf(float x, int fn)
|
||||
#else
|
||||
float __ieee754_scalbf(x,fn)
|
||||
float x; int fn;
|
||||
#endif
|
||||
#else
|
||||
#ifdef __STDC__
|
||||
float __ieee754_scalbf(float x, float fn)
|
||||
#else
|
||||
float __ieee754_scalbf(x,fn)
|
||||
float x, fn;
|
||||
#endif
|
||||
#endif
|
||||
{
|
||||
#ifdef _SCALB_INT
|
||||
return __scalbnf(x,fn);
|
||||
#else
|
||||
if (__isnanf(x)||__isnanf(fn)) return x*fn;
|
||||
if (!__finitef(fn)) {
|
||||
if(fn>(float)0.0) return x*fn;
|
||||
else return x/(-fn);
|
||||
}
|
||||
if (__rintf(fn)!=fn) return (fn-fn)/(fn-fn);
|
||||
if ( fn > (float)65000.0) return __scalbnf(x, 65000);
|
||||
if (-fn > (float)65000.0) return __scalbnf(x,-65000);
|
||||
return __scalbnf(x,(int)fn);
|
||||
#endif
|
||||
}
|
||||
|
|
@ -0,0 +1,86 @@
|
|||
/* @(#)e_sinh.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_sinh(x)
|
||||
* Method :
|
||||
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : sinh(x) := x*shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0)=0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, shuge = 1.0e307;
|
||||
#else
|
||||
static double one = 1.0, shuge = 1.0e307;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sinh(double x)
|
||||
#else
|
||||
double __ieee754_sinh(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double t,w,h;
|
||||
int32_t ix,jx;
|
||||
u_int32_t lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
GET_HIGH_WORD(jx,x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7ff00000) return x+x;
|
||||
|
||||
h = 0.5;
|
||||
if (jx<0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x40360000) { /* |x|<22 */
|
||||
if (ix<0x3e300000) /* |x|<2**-28 */
|
||||
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = __expm1(fabs(x));
|
||||
if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
|
||||
return h*(t+t/(t+one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
GET_LOW_WORD(lx,x);
|
||||
if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
|
||||
w = __ieee754_exp(0.5*fabs(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*shuge;
|
||||
}
|
||||
|
|
@ -0,0 +1,68 @@
|
|||
/* e_sinhf.c -- float version of e_sinh.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_sinhf.c,v 1.4 1995/05/10 20:46:15 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float one = 1.0, shuge = 1.0e37;
|
||||
#else
|
||||
static float one = 1.0, shuge = 1.0e37;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_sinhf(float x)
|
||||
#else
|
||||
float __ieee754_sinhf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float t,w,h;
|
||||
int32_t ix,jx;
|
||||
|
||||
GET_FLOAT_WORD(jx,x);
|
||||
ix = jx&0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if(ix>=0x7f800000) return x+x;
|
||||
|
||||
h = 0.5;
|
||||
if (jx<0) h = -h;
|
||||
/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
|
||||
if (ix < 0x41b00000) { /* |x|<22 */
|
||||
if (ix<0x31800000) /* |x|<2**-28 */
|
||||
if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
|
||||
t = __expm1f(fabsf(x));
|
||||
if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
|
||||
return h*(t+t/(t+one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x));
|
||||
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
if (ix<=0x42b2d4fc) {
|
||||
w = __ieee754_expf((float)0.5*fabsf(x));
|
||||
t = h*w;
|
||||
return t*w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x*shuge;
|
||||
}
|
||||
|
|
@ -0,0 +1,453 @@
|
|||
/* @(#)e_sqrt.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/* __ieee754_sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods : see the appended file at the end of the program below.
|
||||
*---------------
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double one = 1.0, tiny=1.0e-300;
|
||||
#else
|
||||
static double one = 1.0, tiny=1.0e-300;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
double __ieee754_sqrt(double x)
|
||||
#else
|
||||
double __ieee754_sqrt(x)
|
||||
double x;
|
||||
#endif
|
||||
{
|
||||
double z;
|
||||
int32_t sign = (int)0x80000000;
|
||||
int32_t ix0,s0,q,m,t,i;
|
||||
u_int32_t r,t1,s1,ix1,q1;
|
||||
|
||||
EXTRACT_WORDS(ix0,ix1,x);
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix0&0x7ff00000)==0x7ff00000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix0<=0) {
|
||||
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix0<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0>>20);
|
||||
if(m==0) { /* subnormal x */
|
||||
while(ix0==0) {
|
||||
m -= 21;
|
||||
ix0 |= (ix1>>11); ix1 <<= 21;
|
||||
}
|
||||
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
|
||||
m -= i-1;
|
||||
ix0 |= (ix1>>(32-i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0&0x000fffff)|0x00100000;
|
||||
if(m&1){ /* odd m, double x to make it even */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s0+r;
|
||||
if(t<=ix0) {
|
||||
s0 = t+r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while(r!=0) {
|
||||
t1 = s1+r;
|
||||
t = s0;
|
||||
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
|
||||
s1 = t1+r;
|
||||
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
|
||||
ix0 -= t;
|
||||
if (ix1 < t1) ix0 -= 1;
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1&sign)>>31);
|
||||
ix1 += ix1;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if((ix0|ix1)!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
|
||||
else if (z>one) {
|
||||
if (q1==(u_int32_t)0xfffffffe) q+=1;
|
||||
q1+=2;
|
||||
} else
|
||||
q1 += (q1&1);
|
||||
}
|
||||
}
|
||||
ix0 = (q>>1)+0x3fe00000;
|
||||
ix1 = q1>>1;
|
||||
if ((q&1)==1) ix1 |= sign;
|
||||
ix0 += (m <<20);
|
||||
INSERT_WORDS(z,ix0,ix1);
|
||||
return z;
|
||||
}
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper then the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
|
||||
*/
|
||||
|
||||
|
|
@ -0,0 +1,97 @@
|
|||
/* e_sqrtf.c -- float version of e_sqrt.c.
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: e_sqrtf.c,v 1.4 1995/05/10 20:46:19 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float one = 1.0, tiny=1.0e-30;
|
||||
#else
|
||||
static float one = 1.0, tiny=1.0e-30;
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
float __ieee754_sqrtf(float x)
|
||||
#else
|
||||
float __ieee754_sqrtf(x)
|
||||
float x;
|
||||
#endif
|
||||
{
|
||||
float z;
|
||||
int32_t sign = (int)0x80000000;
|
||||
int32_t ix,s,q,m,t,i;
|
||||
u_int32_t r;
|
||||
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if((ix&0x7f800000)==0x7f800000) {
|
||||
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
|
||||
sqrt(-inf)=sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if(ix<=0) {
|
||||
if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
|
||||
else if(ix<0)
|
||||
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix>>23);
|
||||
if(m==0) { /* subnormal x */
|
||||
for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
|
||||
m -= i-1;
|
||||
}
|
||||
m -= 127; /* unbias exponent */
|
||||
ix = (ix&0x007fffff)|0x00800000;
|
||||
if(m&1) /* odd m, double x to make it even */
|
||||
ix += ix;
|
||||
m >>= 1; /* m = [m/2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix += ix;
|
||||
q = s = 0; /* q = sqrt(x) */
|
||||
r = 0x01000000; /* r = moving bit from right to left */
|
||||
|
||||
while(r!=0) {
|
||||
t = s+r;
|
||||
if(t<=ix) {
|
||||
s = t+r;
|
||||
ix -= t;
|
||||
q += r;
|
||||
}
|
||||
ix += ix;
|
||||
r>>=1;
|
||||
}
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if(ix!=0) {
|
||||
z = one-tiny; /* trigger inexact flag */
|
||||
if (z>=one) {
|
||||
z = one+tiny;
|
||||
if (z>one)
|
||||
q += 2;
|
||||
else
|
||||
q += (q&1);
|
||||
}
|
||||
}
|
||||
ix = (q>>1)+0x3f000000;
|
||||
ix += (m <<23);
|
||||
SET_FLOAT_WORD(z,ix);
|
||||
return z;
|
||||
}
|
||||
|
|
@ -0,0 +1,96 @@
|
|||
/* @(#)k_cos.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __kernel_cos( x, y )
|
||||
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
|
||||
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
* Input y is the tail of x.
|
||||
*
|
||||
* Algorithm
|
||||
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
|
||||
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
|
||||
* 3. cos(x) is approximated by a polynomial of degree 14 on
|
||||
* [0,pi/4]
|
||||
* 4 14
|
||||
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
|
||||
* where the remez error is
|
||||
*
|
||||
* | 2 4 6 8 10 12 14 | -58
|
||||
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
|
||||
* | |
|
||||
*
|
||||
* 4 6 8 10 12 14
|
||||
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
|
||||
* cos(x) = 1 - x*x/2 + r
|
||||
* since cos(x+y) ~ cos(x) - sin(x)*y
|
||||
* ~ cos(x) - x*y,
|
||||
* a correction term is necessary in cos(x) and hence
|
||||
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
|
||||
* For better accuracy when x > 0.3, let qx = |x|/4 with
|
||||
* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
|
||||
* Then
|
||||
* cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
|
||||
* Note that 1-qx and (x*x/2-qx) is EXACT here, and the
|
||||
* magnitude of the latter is at least a quarter of x*x/2,
|
||||
* thus, reducing the rounding error in the subtraction.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
||||
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
|
||||
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
|
||||
C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
|
||||
C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
|
||||
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
|
||||
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
|
||||
|
||||
#ifdef __STDC__
|
||||
double __kernel_cos(double x, double y)
|
||||
#else
|
||||
double __kernel_cos(x, y)
|
||||
double x,y;
|
||||
#endif
|
||||
{
|
||||
double a,hz,z,r,qx;
|
||||
int32_t ix;
|
||||
GET_HIGH_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x3e400000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3FD33333) /* if |x| < 0.3 */
|
||||
return one - (0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3fe90000) { /* x > 0.78125 */
|
||||
qx = 0.28125;
|
||||
} else {
|
||||
INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
|
||||
}
|
||||
hz = 0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,64 @@
|
|||
/* k_cosf.c -- float version of k_cos.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
|
||||
C2 = -1.3888889225e-03, /* 0xbab60b61 */
|
||||
C3 = 2.4801587642e-05, /* 0x37d00d01 */
|
||||
C4 = -2.7557314297e-07, /* 0xb493f27c */
|
||||
C5 = 2.0875723372e-09, /* 0x310f74f6 */
|
||||
C6 = -1.1359647598e-11; /* 0xad47d74e */
|
||||
|
||||
#ifdef __STDC__
|
||||
float __kernel_cosf(float x, float y)
|
||||
#else
|
||||
float __kernel_cosf(x, y)
|
||||
float x,y;
|
||||
#endif
|
||||
{
|
||||
float a,hz,z,r,qx;
|
||||
int32_t ix;
|
||||
GET_FLOAT_WORD(ix,x);
|
||||
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
||||
if(ix<0x32000000) { /* if x < 2**27 */
|
||||
if(((int)x)==0) return one; /* generate inexact */
|
||||
}
|
||||
z = x*x;
|
||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||
if(ix < 0x3e99999a) /* if |x| < 0.3 */
|
||||
return one - ((float)0.5*z - (z*r - x*y));
|
||||
else {
|
||||
if(ix > 0x3f480000) { /* x > 0.78125 */
|
||||
qx = (float)0.28125;
|
||||
} else {
|
||||
SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
|
||||
}
|
||||
hz = (float)0.5*z-qx;
|
||||
a = one-qx;
|
||||
return a - (hz - (z*r-x*y));
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,320 @@
|
|||
/* @(#)k_rem_pio2.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
|
||||
#endif
|
||||
|
||||
/*
|
||||
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
* double x[],y[]; int e0,nx,prec; int ipio2[];
|
||||
*
|
||||
* __kernel_rem_pio2 return the last three digits of N with
|
||||
* y = x - N*pi/2
|
||||
* so that |y| < pi/2.
|
||||
*
|
||||
* The method is to compute the integer (mod 8) and fraction parts of
|
||||
* (2/pi)*x without doing the full multiplication. In general we
|
||||
* skip the part of the product that are known to be a huge integer (
|
||||
* more accurately, = 0 mod 8 ). Thus the number of operations are
|
||||
* independent of the exponent of the input.
|
||||
*
|
||||
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
|
||||
*
|
||||
* Input parameters:
|
||||
* x[] The input value (must be positive) is broken into nx
|
||||
* pieces of 24-bit integers in double precision format.
|
||||
* x[i] will be the i-th 24 bit of x. The scaled exponent
|
||||
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
|
||||
* match x's up to 24 bits.
|
||||
*
|
||||
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
|
||||
* e0 = ilogb(z)-23
|
||||
* z = scalbn(z,-e0)
|
||||
* for i = 0,1,2
|
||||
* x[i] = floor(z)
|
||||
* z = (z-x[i])*2**24
|
||||
*
|
||||
*
|
||||
* y[] ouput result in an array of double precision numbers.
|
||||
* The dimension of y[] is:
|
||||
* 24-bit precision 1
|
||||
* 53-bit precision 2
|
||||
* 64-bit precision 2
|
||||
* 113-bit precision 3
|
||||
* The actual value is the sum of them. Thus for 113-bit
|
||||
* precison, one may have to do something like:
|
||||
*
|
||||
* long double t,w,r_head, r_tail;
|
||||
* t = (long double)y[2] + (long double)y[1];
|
||||
* w = (long double)y[0];
|
||||
* r_head = t+w;
|
||||
* r_tail = w - (r_head - t);
|
||||
*
|
||||
* e0 The exponent of x[0]
|
||||
*
|
||||
* nx dimension of x[]
|
||||
*
|
||||
* prec an integer indicating the precision:
|
||||
* 0 24 bits (single)
|
||||
* 1 53 bits (double)
|
||||
* 2 64 bits (extended)
|
||||
* 3 113 bits (quad)
|
||||
*
|
||||
* ipio2[]
|
||||
* integer array, contains the (24*i)-th to (24*i+23)-th
|
||||
* bit of 2/pi after binary point. The corresponding
|
||||
* floating value is
|
||||
*
|
||||
* ipio2[i] * 2^(-24(i+1)).
|
||||
*
|
||||
* External function:
|
||||
* double scalbn(), floor();
|
||||
*
|
||||
*
|
||||
* Here is the description of some local variables:
|
||||
*
|
||||
* jk jk+1 is the initial number of terms of ipio2[] needed
|
||||
* in the computation. The recommended value is 2,3,4,
|
||||
* 6 for single, double, extended,and quad.
|
||||
*
|
||||
* jz local integer variable indicating the number of
|
||||
* terms of ipio2[] used.
|
||||
*
|
||||
* jx nx - 1
|
||||
*
|
||||
* jv index for pointing to the suitable ipio2[] for the
|
||||
* computation. In general, we want
|
||||
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
|
||||
* is an integer. Thus
|
||||
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
|
||||
* Hence jv = max(0,(e0-3)/24).
|
||||
*
|
||||
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
|
||||
*
|
||||
* q[] double array with integral value, representing the
|
||||
* 24-bits chunk of the product of x and 2/pi.
|
||||
*
|
||||
* q0 the corresponding exponent of q[0]. Note that the
|
||||
* exponent for q[i] would be q0-24*i.
|
||||
*
|
||||
* PIo2[] double precision array, obtained by cutting pi/2
|
||||
* into 24 bits chunks.
|
||||
*
|
||||
* f[] ipio2[] in floating point
|
||||
*
|
||||
* iq[] integer array by breaking up q[] in 24-bits chunk.
|
||||
*
|
||||
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
|
||||
*
|
||||
* ih integer. If >0 it indicates q[] is >= 0.5, hence
|
||||
* it also indicates the *sign* of the result.
|
||||
*
|
||||
*/
|
||||
|
||||
|
||||
/*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
||||
#else
|
||||
static int init_jk[] = {2,3,4,6};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double PIo2[] = {
|
||||
#else
|
||||
static double PIo2[] = {
|
||||
#endif
|
||||
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
||||
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
||||
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
||||
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
|
||||
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
||||
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
||||
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
||||
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const double
|
||||
#else
|
||||
static double
|
||||
#endif
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
||||
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
|
||||
#else
|
||||
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
|
||||
double x[], y[]; int e0,nx,prec; int32_t ipio2[];
|
||||
#endif
|
||||
{
|
||||
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
double z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/24; if(jv<0) jv=0;
|
||||
q0 = e0-24*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (double)((int32_t)(twon24* z));
|
||||
iq[i] = (int32_t)(z-two24*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = __scalbn(z,q0); /* actual value of z */
|
||||
z -= 8.0*__floor(z*0.125); /* trim off integer >= 8 */
|
||||
n = (int32_t) z;
|
||||
z -= (double)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(24-q0)); n += i;
|
||||
iq[jz-1] -= i<<(24-q0);
|
||||
ih = iq[jz-1]>>(23-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>23;
|
||||
else if(z>=0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x1000000- j;
|
||||
}
|
||||
} else iq[i] = 0xffffff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7fffff; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3fffff; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= __scalbn(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (double) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==0.0) {
|
||||
jz -= 1; q0 -= 24;
|
||||
while(iq[jz]==0) { jz--; q0-=24;}
|
||||
} else { /* break z into 24-bit if necessary */
|
||||
z = __scalbn(z,-q0);
|
||||
if(z>=two24) {
|
||||
fw = (double)((int32_t)(twon24*z));
|
||||
iq[jz] = (int32_t)(z-two24*fw);
|
||||
jz += 1; q0 += 24;
|
||||
iq[jz] = (int32_t) fw;
|
||||
} else iq[jz] = (int32_t) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = __scalbn(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(double)iq[i]; fw*=twon24;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
|
|
@ -0,0 +1,213 @@
|
|||
/* k_rem_pio2f.c -- float version of k_rem_pio2.c
|
||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||
*/
|
||||
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
#if defined(LIBM_SCCS) && !defined(lint)
|
||||
static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $";
|
||||
#endif
|
||||
|
||||
#include "math.h"
|
||||
#include "math_private.h"
|
||||
|
||||
/* In the float version, the input parameter x contains 8 bit
|
||||
integers, not 24 bit integers. 113 bit precision is not supported. */
|
||||
|
||||
#ifdef __STDC__
|
||||
static const int init_jk[] = {4,7,9}; /* initial value for jk */
|
||||
#else
|
||||
static int init_jk[] = {4,7,9};
|
||||
#endif
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float PIo2[] = {
|
||||
#else
|
||||
static float PIo2[] = {
|
||||
#endif
|
||||
1.5703125000e+00, /* 0x3fc90000 */
|
||||
4.5776367188e-04, /* 0x39f00000 */
|
||||
2.5987625122e-05, /* 0x37da0000 */
|
||||
7.5437128544e-08, /* 0x33a20000 */
|
||||
6.0026650317e-11, /* 0x2e840000 */
|
||||
7.3896444519e-13, /* 0x2b500000 */
|
||||
5.3845816694e-15, /* 0x27c20000 */
|
||||
5.6378512969e-18, /* 0x22d00000 */
|
||||
8.3009228831e-20, /* 0x1fc40000 */
|
||||
3.2756352257e-22, /* 0x1bc60000 */
|
||||
6.3331015649e-25, /* 0x17440000 */
|
||||
};
|
||||
|
||||
#ifdef __STDC__
|
||||
static const float
|
||||
#else
|
||||
static float
|
||||
#endif
|
||||
zero = 0.0,
|
||||
one = 1.0,
|
||||
two8 = 2.5600000000e+02, /* 0x43800000 */
|
||||
twon8 = 3.9062500000e-03; /* 0x3b800000 */
|
||||
|
||||
#ifdef __STDC__
|
||||
int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
|
||||
#else
|
||||
int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
|
||||
float x[], y[]; int e0,nx,prec; int32_t ipio2[];
|
||||
#endif
|
||||
{
|
||||
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||
float z,fw,f[20],fq[20],q[20];
|
||||
|
||||
/* initialize jk*/
|
||||
jk = init_jk[prec];
|
||||
jp = jk;
|
||||
|
||||
/* determine jx,jv,q0, note that 3>q0 */
|
||||
jx = nx-1;
|
||||
jv = (e0-3)/8; if(jv<0) jv=0;
|
||||
q0 = e0-8*(jv+1);
|
||||
|
||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||
j = jv-jx; m = jx+jk;
|
||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
|
||||
|
||||
/* compute q[0],q[1],...q[jk] */
|
||||
for (i=0;i<=jk;i++) {
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||
}
|
||||
|
||||
jz = jk;
|
||||
recompute:
|
||||
/* distill q[] into iq[] reversingly */
|
||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||
fw = (float)((int32_t)(twon8* z));
|
||||
iq[i] = (int32_t)(z-two8*fw);
|
||||
z = q[j-1]+fw;
|
||||
}
|
||||
|
||||
/* compute n */
|
||||
z = __scalbnf(z,q0); /* actual value of z */
|
||||
z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
|
||||
n = (int32_t) z;
|
||||
z -= (float)n;
|
||||
ih = 0;
|
||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||
i = (iq[jz-1]>>(8-q0)); n += i;
|
||||
iq[jz-1] -= i<<(8-q0);
|
||||
ih = iq[jz-1]>>(7-q0);
|
||||
}
|
||||
else if(q0==0) ih = iq[jz-1]>>8;
|
||||
else if(z>=(float)0.5) ih=2;
|
||||
|
||||
if(ih>0) { /* q > 0.5 */
|
||||
n += 1; carry = 0;
|
||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||
j = iq[i];
|
||||
if(carry==0) {
|
||||
if(j!=0) {
|
||||
carry = 1; iq[i] = 0x100- j;
|
||||
}
|
||||
} else iq[i] = 0xff - j;
|
||||
}
|
||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||
switch(q0) {
|
||||
case 1:
|
||||
iq[jz-1] &= 0x7f; break;
|
||||
case 2:
|
||||
iq[jz-1] &= 0x3f; break;
|
||||
}
|
||||
}
|
||||
if(ih==2) {
|
||||
z = one - z;
|
||||
if(carry!=0) z -= __scalbnf(one,q0);
|
||||
}
|
||||
}
|
||||
|
||||
/* check if recomputation is needed */
|
||||
if(z==zero) {
|
||||
j = 0;
|
||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||
if(j==0) { /* need recomputation */
|
||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||
|
||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||
f[jx+i] = (float) ipio2[jv+i];
|
||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||
q[i] = fw;
|
||||
}
|
||||
jz += k;
|
||||
goto recompute;
|
||||
}
|
||||
}
|
||||
|
||||
/* chop off zero terms */
|
||||
if(z==(float)0.0) {
|
||||
jz -= 1; q0 -= 8;
|
||||
while(iq[jz]==0) { jz--; q0-=8;}
|
||||
} else { /* break z into 8-bit if necessary */
|
||||
z = __scalbnf(z,-q0);
|
||||
if(z>=two8) {
|
||||
fw = (float)((int32_t)(twon8*z));
|
||||
iq[jz] = (int32_t)(z-two8*fw);
|
||||
jz += 1; q0 += 8;
|
||||
iq[jz] = (int32_t) fw;
|
||||
} else iq[jz] = (int32_t) z ;
|
||||
}
|
||||
|
||||
/* convert integer "bit" chunk to floating-point value */
|
||||
fw = __scalbnf(one,q0);
|
||||
for(i=jz;i>=0;i--) {
|
||||
q[i] = fw*(float)iq[i]; fw*=twon8;
|
||||
}
|
||||
|
||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||
for(i=jz;i>=0;i--) {
|
||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||
fq[jz-i] = fw;
|
||||
}
|
||||
|
||||
/* compress fq[] into y[] */
|
||||
switch(prec) {
|
||||
case 0:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 1:
|
||||
case 2:
|
||||
fw = 0.0;
|
||||
for (i=jz;i>=0;i--) fw += fq[i];
|
||||
y[0] = (ih==0)? fw: -fw;
|
||||
fw = fq[0]-fw;
|
||||
for (i=1;i<=jz;i++) fw += fq[i];
|
||||
y[1] = (ih==0)? fw: -fw;
|
||||
break;
|
||||
case 3: /* painful */
|
||||
for (i=jz;i>0;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (i=jz;i>1;i--) {
|
||||
fw = fq[i-1]+fq[i];
|
||||
fq[i] += fq[i-1]-fw;
|
||||
fq[i-1] = fw;
|
||||
}
|
||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||
if(ih==0) {
|
||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||
} else {
|
||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||
}
|
||||
}
|
||||
return n&7;
|
||||
}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Loading…
Reference in New Issue