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Implement fmal, some fma bugfixes

This commit is contained in:
Jakub Jelinek 2010-10-15 15:26:06 -04:00 committed by Ulrich Drepper
parent f3f7372de1
commit 3e692e0518
9 changed files with 492 additions and 97 deletions
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25
math/libm-test.inc
View File

@ -2787,8 +2787,24 @@ fma_test (void)
TEST_fff_f (fma, minus_infty, plus_infty, plus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, plus_infty, minus_infty, plus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, minus_infty, minus_infty, minus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, plus_infty, 3.5L, minus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, minus_infty, -7.5L, minus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, -13.5L, plus_infty, plus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, minus_infty, 7.5L, plus_infty, nan_value, INVALID_EXCEPTION);
TEST_fff_f (fma, 1.25L, 0.75L, 0.0625L, 1.0L);
FLOAT fltmax = CHOOSE (LDBL_MAX, DBL_MAX, FLT_MAX,
LDBL_MAX, DBL_MAX, FLT_MAX);
TEST_fff_f (fma, -fltmax, -fltmax, minus_infty, minus_infty);
TEST_fff_f (fma, fltmax / 2, fltmax / 2, minus_infty, minus_infty);
TEST_fff_f (fma, -fltmax, fltmax, plus_infty, plus_infty);
TEST_fff_f (fma, fltmax / 2, -fltmax / 4, plus_infty, plus_infty);
TEST_fff_f (fma, plus_infty, 4, plus_infty, plus_infty);
TEST_fff_f (fma, 2, minus_infty, minus_infty, minus_infty);
TEST_fff_f (fma, minus_infty, minus_infty, plus_infty, plus_infty);
TEST_fff_f (fma, plus_infty, minus_infty, minus_infty, minus_infty);
#if defined (TEST_FLOAT) && FLT_MANT_DIG == 24
TEST_fff_f (fma, 0x1.7ff8p+13, 0x1.000002p+0, 0x1.ffffp-24, 0x1.7ff802p+13);
TEST_fff_f (fma, 0x1.fffp+0, 0x1.00001p+0, -0x1.fffp+0, 0x1.fffp-20);
@ -2818,6 +2834,15 @@ fma_test (void)
TEST_fff_f (fma, -0x1.19cab66d73e17p-959, 0x1.c7108a8c5ff51p-107, -0x0.80b0ad65d9b64p-1022, -0x0.80b0ad65d9d59p-1022);
TEST_fff_f (fma, -0x1.d2eaed6e8e9d3p-979, -0x1.4e066c62ac9ddp-63, -0x0.9245e6b003454p-1022, -0x0.9245c09c5fb5dp-1022);
TEST_fff_f (fma, 0x1.153d650bb9f06p-907, 0x1.2d01230d48407p-125, -0x0.b278d5acfc3cp-1022, -0x0.b22757123bbe9p-1022);
TEST_fff_f (fma, -0x1.fffffffffffffp-711, 0x1.fffffffffffffp-275, 0x1.fffffe00007ffp-983, 0x1.7ffffe00007ffp-983);
#endif
#if defined (TEST_LDOUBLE) && LDBL_MANT_DIG == 64
TEST_fff_f (fma, -0x8.03fcp+3696L, 0xf.fffffffffffffffp-6140L, 0x8.3ffffffffffffffp-2450L, -0x8.01ecp-2440L);
TEST_fff_f (fma, 0x9.fcp+2033L, -0x8.000e1f000ff800fp-3613L, -0xf.fffffffffffc0ffp-1579L, -0xd.fc119fb093ed092p-1577L);
TEST_fff_f (fma, 0xc.7fc000003ffffffp-1194L, 0x8.1e0003fffffffffp+15327L, -0x8.fffep+14072L, 0xc.ae9f164020effffp+14136L);
TEST_fff_f (fma, -0x8.0001fc000000003p+1798L, 0xcp-2230L, 0x8.f7e000000000007p-468L, -0xc.0002f9ffee10404p-429L);
TEST_fff_f (fma, 0xc.0000000000007ffp+10130L, -0x8.000000000000001p+4430L, 0xc.07000000001ffffp+14513L, -0xb.fffffffffffd7e4p+14563L);
TEST_fff_f (fma, 0xb.ffffp-4777L, 0x8.000000fffffffffp-11612L, -0x0.3800fff8p-16385L, 0x5.c7fe80c7ffeffffp-16385L);
#endif
END (fma);

31
sysdeps/i386/fpu/s_fma.S
View File

@ -1,31 +0,0 @@
/* Compute (X * Y) + Z as ternary operation.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <sysdep.h>
.text
ENTRY(__fma)
fldl 4(%esp) // x
fmull 12(%esp) // x * y
fldl 20(%esp) // z : x * y
faddp // (x * y) + z
ret
END(__fma)
weak_alias (__fma, fma)

31
sysdeps/i386/fpu/s_fmaf.S
View File

@ -1,31 +0,0 @@
/* Compute (X * Y) + Z as ternary operation.
Copyright (C) 1997 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <sysdep.h>
.text
ENTRY(__fmaf)
flds 4(%esp) // x
fmuls 8(%esp) // x * y
flds 12(%esp) // z : x * y
faddp // (x * y) + z
ret
END(__fmaf)
weak_alias (__fmaf, fmaf)

32
sysdeps/i386/fpu/s_fmal.S
View File

@ -1,32 +0,0 @@
/* Compute (X * Y) + Z as ternary operation.
Copyright (C) 1997 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <sysdep.h>
.text
ENTRY(__fmal)
fldt 4(%esp) // x
fldt 16(%esp) // x : y
fmulp // x * y
fldt 28(%esp) // z : x * y
faddp // (x * y) + z
ret
END(__fmal)
weak_alias (__fmal, fmal)

8
sysdeps/ieee754/dbl-64/s_fma.c
View File

@ -43,6 +43,12 @@ __fma (double x, double y, double z)
|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0))
{
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (w.ieee.exponent == 0x7ff
&& u.ieee.exponent != 0x7ff
&& v.ieee.exponent != 0x7ff)
return (z + x) + y;
/* If x or y or z is Inf/NaN, or if fma will certainly overflow,
or if x * y is less than half of DBL_DENORM_MIN,
compute as x * y + z. */
@ -165,6 +171,8 @@ __fma (double x, double y, double z)
}
else
{
if ((u.ieee.mantissa1 & 1) == 0)
u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
v.d = a1 + u.d;
int j = fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);

221
sysdeps/ieee754/ldbl-128/s_fmal.c Normal file
View File

@ -0,0 +1,221 @@
/* Compute x * y + z as ternary operation.
Copyright (C) 2010 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <float.h>
#include <math.h>
#include <fenv.h>
#include <ieee754.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
http://www.lri.fr/~melquion/doc/08-tc.pdf */
long double
__fmal (long double x, long double y, long double z)
{
union ieee854_long_double u, v, w;
int adjust = 0;
u.d = x;
v.d = y;
w.d = z;
if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
- LDBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
{
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (w.ieee.exponent == 0x7fff
&& u.ieee.exponent != 0x7fff
&& v.ieee.exponent != 0x7fff)
return (z + x) + y;
/* If x or y or z is Inf/NaN, or if fma will certainly overflow,
or if x * y is less than half of LDBL_DENORM_MIN,
compute as x * y + z. */
if (u.ieee.exponent == 0x7fff
|| v.ieee.exponent == 0x7fff
|| w.ieee.exponent == 0x7fff
|| u.ieee.exponent + v.ieee.exponent
> 0x7fff + IEEE854_LONG_DOUBLE_BIAS
|| u.ieee.exponent + v.ieee.exponent
< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
return x * y + z;
if (u.ieee.exponent + v.ieee.exponent
>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
{
/* Compute 1p-113 times smaller result and multiply
at the end. */
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent -= LDBL_MANT_DIG;
else
v.ieee.exponent -= LDBL_MANT_DIG;
/* If x + y exponent is very large and z exponent is very small,
it doesn't matter if we don't adjust it. */
if (w.ieee.exponent > LDBL_MANT_DIG)
w.ieee.exponent -= LDBL_MANT_DIG;
adjust = 1;
}
else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
/* Similarly.
If z exponent is very large and x and y exponents are
very small, it doesn't matter if we don't adjust it. */
if (u.ieee.exponent > v.ieee.exponent)
{
if (u.ieee.exponent > LDBL_MANT_DIG)
u.ieee.exponent -= LDBL_MANT_DIG;
}
else if (v.ieee.exponent > LDBL_MANT_DIG)
v.ieee.exponent -= LDBL_MANT_DIG;
w.ieee.exponent -= LDBL_MANT_DIG;
adjust = 1;
}
else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
u.ieee.exponent -= LDBL_MANT_DIG;
if (v.ieee.exponent)
v.ieee.exponent += LDBL_MANT_DIG;
else
v.d *= 0x1p113L;
}
else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
v.ieee.exponent -= LDBL_MANT_DIG;
if (u.ieee.exponent)
u.ieee.exponent += LDBL_MANT_DIG;
else
u.d *= 0x1p113L;
}
else /* if (u.ieee.exponent + v.ieee.exponent
<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
{
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent += 2 * LDBL_MANT_DIG;
else
v.ieee.exponent += 2 * LDBL_MANT_DIG;
if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 4)
{
if (w.ieee.exponent)
w.ieee.exponent += 2 * LDBL_MANT_DIG;
else
w.d *= 0x1p226L;
adjust = -1;
}
/* Otherwise x * y should just affect inexact
and nothing else. */
}
x = u.d;
y = v.d;
z = w.d;
}
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
long double x1 = x * C;
long double y1 = y * C;
long double m1 = x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
long double x2 = x - x1;
long double y2 = y - y1;
long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
long double a1 = z + m1;
long double t1 = a1 - z;
long double t2 = a1 - t1;
t1 = m1 - t1;
t2 = z - t2;
long double a2 = t1 + t2;
fenv_t env;
feholdexcept (&env);
fesetround (FE_TOWARDZERO);
/* Perform m2 + a2 addition with round to odd. */
u.d = a2 + m2;
if (__builtin_expect (adjust == 0, 1))
{
if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Result is a1 + u.d. */
return a1 + u.d;
}
else if (__builtin_expect (adjust > 0, 1))
{
if ((u.ieee.mantissa3 & 1) == 0 && u.ieee.exponent != 0x7fff)
u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Result is a1 + u.d, scaled up. */
return (a1 + u.d) * 0x1p113L;
}
else
{
if ((u.ieee.mantissa3 & 1) == 0)
u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0;
v.d = a1 + u.d;
int j = fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Ensure the following computations are performed in default rounding
mode instead of just reusing the round to zero computation. */
asm volatile ("" : "=m" (u) : "m" (u));
/* If a1 + u.d is exact, the only rounding happens during
scaling down. */
if (j == 0)
return v.d * 0x1p-226L;
/* If result rounded to zero is not subnormal, no double
rounding will occur. */
if (v.ieee.exponent > 226)
return (a1 + u.d) * 0x1p-226L;
/* If v.d * 0x1p-226L with round to zero is a subnormal above
or equal to LDBL_MIN / 2, then v.d * 0x1p-226L shifts mantissa
down just by 1 bit, which means v.ieee.mantissa3 |= j would
change the round bit, not sticky or guard bit.
v.d * 0x1p-226L never normalizes by shifting up,
so round bit plus sticky bit should be already enough
for proper rounding. */
if (v.ieee.exponent == 226)
{
/* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa3 & 1 is the round bit and j is our sticky
bit. In round-to-nearest 001 rounds down like 00,
011 rounds up, even though 01 rounds down (thus we need
to adjust), 101 rounds down like 10 and 111 rounds up
like 11. */
if ((v.ieee.mantissa3 & 3) == 1)
{
v.d *= 0x1p-226L;
if (v.ieee.negative)
return v.d - 0x1p-16493L /* __LDBL_DENORM_MIN__ */;
else
return v.d + 0x1p-16493L /* __LDBL_DENORM_MIN__ */;
}
else
return v.d * 0x1p-226L;
}
v.ieee.mantissa3 |= j;
return v.d * 0x1p-226L;
}
}
weak_alias (__fmal, fmal)

5
sysdeps/ieee754/ldbl-64-128/s_fmal.c Normal file
View File

@ -0,0 +1,5 @@
#include <math_ldbl_opt.h>
#undef weak_alias
#define weak_alias(n,a)
#include <sysdeps/ieee754/ldbl-128/s_fmal.c>
long_double_symbol (libm, __fmal, fmal);

15
sysdeps/ieee754/ldbl-96/s_fma.c
View File

@ -30,11 +30,20 @@
double
__fma (double x, double y, double z)
{
if (__builtin_expect (isinf (z), 0))
{
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (finite (x) && finite (y))
return (z + x) + y;
return (x * y) + z;
}
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
#define C ((1ULL << (LDBL_MANT_DIG + 1) / 2) + 1)
long double x1 = x * C;
long double y1 = y * C;
long double m1 = x * y;
long double x1 = (long double) x * C;
long double y1 = (long double) y * C;
long double m1 = (long double) x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
long double x2 = x - x1;

221
sysdeps/ieee754/ldbl-96/s_fmal.c Normal file
View File

@ -0,0 +1,221 @@
/* Compute x * y + z as ternary operation.
Copyright (C) 2010 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
#include <float.h>
#include <math.h>
#include <fenv.h>
#include <ieee754.h>
/* This implementation uses rounding to odd to avoid problems with
double rounding. See a paper by Boldo and Melquiond:
http://www.lri.fr/~melquion/doc/08-tc.pdf */
long double
__fmal (long double x, long double y, long double z)
{
union ieee854_long_double u, v, w;
int adjust = 0;
u.d = x;
v.d = y;
w.d = z;
if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
- LDBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
{
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (w.ieee.exponent == 0x7fff
&& u.ieee.exponent != 0x7fff
&& v.ieee.exponent != 0x7fff)
return (z + x) + y;
/* If x or y or z is Inf/NaN, or if fma will certainly overflow,
or if x * y is less than half of LDBL_DENORM_MIN,
compute as x * y + z. */
if (u.ieee.exponent == 0x7fff
|| v.ieee.exponent == 0x7fff
|| w.ieee.exponent == 0x7fff
|| u.ieee.exponent + v.ieee.exponent
> 0x7fff + IEEE854_LONG_DOUBLE_BIAS
|| u.ieee.exponent + v.ieee.exponent
< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
return x * y + z;
if (u.ieee.exponent + v.ieee.exponent
>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
{
/* Compute 1p-64 times smaller result and multiply
at the end. */
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent -= LDBL_MANT_DIG;
else
v.ieee.exponent -= LDBL_MANT_DIG;
/* If x + y exponent is very large and z exponent is very small,
it doesn't matter if we don't adjust it. */
if (w.ieee.exponent > LDBL_MANT_DIG)
w.ieee.exponent -= LDBL_MANT_DIG;
adjust = 1;
}
else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
/* Similarly.
If z exponent is very large and x and y exponents are
very small, it doesn't matter if we don't adjust it. */
if (u.ieee.exponent > v.ieee.exponent)
{
if (u.ieee.exponent > LDBL_MANT_DIG)
u.ieee.exponent -= LDBL_MANT_DIG;
}
else if (v.ieee.exponent > LDBL_MANT_DIG)
v.ieee.exponent -= LDBL_MANT_DIG;
w.ieee.exponent -= LDBL_MANT_DIG;
adjust = 1;
}
else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
u.ieee.exponent -= LDBL_MANT_DIG;
if (v.ieee.exponent)
v.ieee.exponent += LDBL_MANT_DIG;
else
v.d *= 0x1p64L;
}
else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
{
v.ieee.exponent -= LDBL_MANT_DIG;
if (u.ieee.exponent)
u.ieee.exponent += LDBL_MANT_DIG;
else
u.d *= 0x1p64L;
}
else /* if (u.ieee.exponent + v.ieee.exponent
<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
{
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent += 2 * LDBL_MANT_DIG;
else
v.ieee.exponent += 2 * LDBL_MANT_DIG;
if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 4)
{
if (w.ieee.exponent)
w.ieee.exponent += 2 * LDBL_MANT_DIG;
else
w.d *= 0x1p128L;
adjust = -1;
}
/* Otherwise x * y should just affect inexact
and nothing else. */
}
x = u.d;
y = v.d;
z = w.d;
}
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
long double x1 = x * C;
long double y1 = y * C;
long double m1 = x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
long double x2 = x - x1;
long double y2 = y - y1;
long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
long double a1 = z + m1;
long double t1 = a1 - z;
long double t2 = a1 - t1;
t1 = m1 - t1;
t2 = z - t2;
long double a2 = t1 + t2;
fenv_t env;
feholdexcept (&env);
fesetround (FE_TOWARDZERO);
/* Perform m2 + a2 addition with round to odd. */
u.d = a2 + m2;
if (__builtin_expect (adjust == 0, 1))
{
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Result is a1 + u.d. */
return a1 + u.d;
}
else if (__builtin_expect (adjust > 0, 1))
{
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Result is a1 + u.d, scaled up. */
return (a1 + u.d) * 0x1p64L;
}
else
{
if ((u.ieee.mantissa1 & 1) == 0)
u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
v.d = a1 + u.d;
int j = fetestexcept (FE_INEXACT) != 0;
feupdateenv (&env);
/* Ensure the following computations are performed in default rounding
mode instead of just reusing the round to zero computation. */
asm volatile ("" : "=m" (u) : "m" (u));
/* If a1 + u.d is exact, the only rounding happens during
scaling down. */
if (j == 0)
return v.d * 0x1p-128L;
/* If result rounded to zero is not subnormal, no double
rounding will occur. */
if (v.ieee.exponent > 128)
return (a1 + u.d) * 0x1p-128L;
/* If v.d * 0x1p-128L with round to zero is a subnormal above
or equal to LDBL_MIN / 2, then v.d * 0x1p-128L shifts mantissa
down just by 1 bit, which means v.ieee.mantissa1 |= j would
change the round bit, not sticky or guard bit.
v.d * 0x1p-128L never normalizes by shifting up,
so round bit plus sticky bit should be already enough
for proper rounding. */
if (v.ieee.exponent == 128)
{
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
bit. In round-to-nearest 001 rounds down like 00,
011 rounds up, even though 01 rounds down (thus we need
to adjust), 101 rounds down like 10 and 111 rounds up
like 11. */
if ((v.ieee.mantissa1 & 3) == 1)
{
v.d *= 0x1p-128L;
if (v.ieee.negative)
return v.d - 0x1p-16445L /* __LDBL_DENORM_MIN__ */;
else
return v.d + 0x1p-16445L /* __LDBL_DENORM_MIN__ */;
}
else
return v.d * 0x1p-128L;
}
v.ieee.mantissa1 |= j;
return v.d * 0x1p-128L;
}
}
weak_alias (__fmal, fmal)