4239f144ce
libquadmath sources are mostly based on glibc sources at present, but derived from them by a manual editing / substitution process and with subsequent manual merges. The manual effort involved in merges means they are sometimes incomplete and long-delayed. Since libquadmath was first created, glibc's support for this format has undergone significant changes so that it can also be used in glibc to provide *f128 functions for the _Float128 type from TS 18661-3. This makes it significantly easier to use it for libquadmath in a more automated fashion, since glibc has a float128_private.h header that redefines many identifiers as macros as needed for building *f128 functions. Simply using float128_private.h directly in libquadmath, with unmodified glibc sources except for changing function names in that one header to be *q instead of *f128, would be tricky, given its dependence on lots of other glibc-internal headers (whereas libquadmath supports non-glibc systems), and also given how some libm functions in glibc are built from type-generic templates using a further set of macros rather than from separate function implementations for each type. So instead this patch adds a script update-quadmath.py to convert glibc sources into libquadmath ones, and the script reads float128_private.h to identify many of the substitutions it should make. quadmath-imp.h is updated with various new internal definitions, taken from glibc as needed; this is the main place expected to need updating manually when subsequent merges from glibc are done using the script. No attempt is made to make the script output match the details of existing formatting, although the differences are of a size that makes a rough comparison (ignoring whitespace) possible. Two new public interfaces are added to libquadmath, exp2q and issignalingq, at a new QUADMATH_1.2 symbol version, since those interfaces are used internally by some of the glibc sources being merged into libquadmath; although there is a new symbol version, no change however is made to the libtool version in the libtool-version file. Although there are various other interfaces now in glibc libm but not in libquadmath, this patch does nothing to add such interfaces (although adding many of them would in fact be easy to do, given the script). One internal file (not providing any public interfaces), math/isinf_nsq.c, is removed, as no longer used by anything in libquadmath after the merge. Conditionals in individual source files on <fenv.h> availability or features are moved into quadmath-imp.h (providing trivial macro versions of the functions if real implementations aren't available), to simplify the substitutions in individual source files. Note however that I haven't tested for any configurations lacking <fenv.h>, so further changes could well be needed there. Two files in libquadmath/math/ are based on glibc sources but not updated in this patch: fmaq.c and rem_pio2q.c. Both could be updated after further changes to the script (and quadmath-imp.h as needed); in the case of rem_pio2q.c, based on two separate glibc source files, those separate files would naturally be split out into separate libquadmath source files in the process (as done in this patch with expq_table.h and tanq_kernel.c, where previously two glibc source files had been merged into one libquadmath source file). complex.c, nanq.c and sqrtq.c are not based on glibc sources (though four of the (trivial) functions in complex.c could readily be replaced by instead using the four corresponding files from glibc, if desired). libquadmath also has printf/ and strtod/ sources based on glibc, also mostly not updated for a long time. Again the script could no doubt be made to generate those automatically, although that would be a larger change (effectively some completely separate logic in the script, not sharing much if anything with the existing code). Bootstrapped with no regressions on x86_64-pc-linux-gnu. PR libquadmath/68686 * Makefile.am: (libquadmath_la_SOURCES): Remove math/isinf_nsq.c. Add math/exp2q.c math/issignalingq.c math/lgammaq_neg.c math/lgammaq_product.c math/tanq_kernel.c math/tgammaq_product.c math/casinhq_kernel.c. * Makefile.in: Regenerate. * libquadmath.texi (exp2q, issignalingq): Document. * quadmath-imp.h: Include <errno.h>, <limits.h>, <stdbool.h> and <fenv.h>. (HIGH_ORDER_BIT_IS_SET_FOR_SNAN, FIX_FLT128_LONG_CONVERT_OVERFLOW) (FIX_FLT128_LLONG_CONVERT_OVERFLOW, __quadmath_kernel_tanq) (__quadmath_gamma_productq, __quadmath_gammaq_r) (__quadmath_lgamma_negq, __quadmath_lgamma_productq) (__quadmath_lgammaq_r, __quadmath_kernel_casinhq, mul_splitq) (math_check_force_underflow_complex, __glibc_likely) (__glibc_unlikely, struct rm_ctx, SET_RESTORE_ROUNDF128) (libc_feholdsetround_ctx, libc_feresetround_ctx): New. (feraiseexcept, fenv_t, feholdexcept, fesetround, feupdateenv) (fesetenv, fetestexcept, feclearexcept): Define if not supported through <fenv.h>. (__quadmath_isinf_nsq): Remove. * quadmath.h (exp2q, issignalingq): New. * quadmath.map (QUADMATH_1.2): New. * quadmath_weak.h (exp2q, issignalingq): New. * update-quadmath.py: New file. * math/isinf_nsq.c: Remove file. * math/casinhq_kernel.c, math/exp2q.c, math/expq_table.h, math/issignalingq.c, math/lgammaq_neg.c, math/lgammaq_product.c, math/tanq_kernel.c, math/tgammaq_product.c: New files. Generated from glibc sources with update-quadmath.py. * math/acoshq.c, math/acosq.c, math/asinhq.c, math/asinq.c, math/atan2q.c, math/atanhq.c, math/atanq.c, math/cacoshq.c, math/cacosq.c, math/casinhq.c, math/casinq.c, math/catanhq.c, math/catanq.c, math/cbrtq.c, math/ccoshq.c, math/ceilq.c, math/cexpq.c, math/cimagq.c, math/clog10q.c, math/clogq.c, math/conjq.c, math/copysignq.c, math/coshq.c, math/cosq.c, math/cosq_kernel.c, math/cprojq.c, math/crealq.c, math/csinhq.c, math/csinq.c, math/csqrtq.c, math/ctanhq.c, math/ctanq.c, math/erfq.c, math/expm1q.c, math/expq.c, math/fabsq.c, math/fdimq.c, math/finiteq.c, math/floorq.c, math/fmaxq.c, math/fminq.c, math/fmodq.c, math/frexpq.c, math/hypotq.c, math/ilogbq.c, math/isinfq.c, math/isnanq.c, math/j0q.c, math/j1q.c, math/jnq.c, math/ldexpq.c, math/lgammaq.c, math/llrintq.c, math/llroundq.c, math/log10q.c, math/log1pq.c, math/log2q.c, math/logbq.c, math/logq.c, math/lrintq.c, math/lroundq.c, math/modfq.c, math/nearbyintq.c, math/nextafterq.c, math/powq.c, math/remainderq.c, math/remquoq.c, math/rintq.c, math/roundq.c, math/scalblnq.c, math/scalbnq.c, math/signbitq.c, math/sincos_table.c, math/sincosq.c, math/sincosq_kernel.c, math/sinhq.c, math/sinq.c, math/sinq_kernel.c, math/tanhq.c, math/tanq.c, math/tgammaq.c, math/truncq.c, math/x2y2m1q.c: Regenerate from glibc sources with update-quadmath.py. From-SVN: r265822
1051 lines
31 KiB
C
1051 lines
31 KiB
C
/* lgammal
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*
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* Natural logarithm of gamma function
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*
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, lgammal();
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* extern int sgngam;
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*
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* y = lgammal(x);
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the base e (2.718...) logarithm of the absolute
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* value of the gamma function of the argument.
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* The sign (+1 or -1) of the gamma function is returned in a
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* global (extern) variable named sgngam.
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*
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* The positive domain is partitioned into numerous segments for approximation.
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* For x > 10,
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* log gamma(x) = (x - 0.5) log(x) - x + log sqrt(2 pi) + 1/x R(1/x^2)
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* Near the minimum at x = x0 = 1.46... the approximation is
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* log gamma(x0 + z) = log gamma(x0) + z^2 P(z)/Q(z)
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* for small z.
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* Elsewhere between 0 and 10,
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* log gamma(n + z) = log gamma(n) + z P(z)/Q(z)
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* for various selected n and small z.
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*
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* The cosecant reflection formula is employed for negative arguments.
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*
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*
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*
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* ACCURACY:
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*
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*
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* arithmetic domain # trials peak rms
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* Relative error:
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* IEEE 10, 30 100000 3.9e-34 9.8e-35
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* IEEE 0, 10 100000 3.8e-34 5.3e-35
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* Absolute error:
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* IEEE -10, 0 100000 8.0e-34 8.0e-35
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* IEEE -30, -10 100000 4.4e-34 1.0e-34
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* IEEE -100, 100 100000 1.0e-34
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*
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* The absolute error criterion is the same as relative error
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* when the function magnitude is greater than one but it is absolute
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* when the magnitude is less than one.
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*
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*/
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/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov>
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This 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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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include "quadmath-imp.h"
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#ifdef HAVE_MATH_H_SIGNGAM
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# include <math.h>
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#endif
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__float128
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lgammaq (__float128 x)
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{
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#ifndef HAVE_MATH_H_SIGNGAM
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int signgam;
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#endif
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return __quadmath_lgammaq_r (x, &signgam);
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}
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static const __float128 PIL = 3.1415926535897932384626433832795028841972E0Q;
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static const __float128 MAXLGM = 1.0485738685148938358098967157129705071571E4928Q;
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static const __float128 one = 1;
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static const __float128 huge = FLT128_MAX;
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/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2)
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1/x <= 0.0741 (x >= 13.495...)
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Peak relative error 1.5e-36 */
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static const __float128 ls2pi = 9.1893853320467274178032973640561763986140E-1Q;
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#define NRASY 12
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static const __float128 RASY[NRASY + 1] =
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{
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8.333333333333333333333333333310437112111E-2Q,
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-2.777777777777777777777774789556228296902E-3Q,
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7.936507936507936507795933938448586499183E-4Q,
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-5.952380952380952041799269756378148574045E-4Q,
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8.417508417507928904209891117498524452523E-4Q,
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-1.917526917481263997778542329739806086290E-3Q,
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6.410256381217852504446848671499409919280E-3Q,
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-2.955064066900961649768101034477363301626E-2Q,
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1.796402955865634243663453415388336954675E-1Q,
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-1.391522089007758553455753477688592767741E0Q,
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1.326130089598399157988112385013829305510E1Q,
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-1.420412699593782497803472576479997819149E2Q,
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1.218058922427762808938869872528846787020E3Q
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};
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/* log gamma(x+13) = log gamma(13) + x P(x)/Q(x)
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-0.5 <= x <= 0.5
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12.5 <= x+13 <= 13.5
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Peak relative error 1.1e-36 */
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static const __float128 lgam13a = 1.9987213134765625E1Q;
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static const __float128 lgam13b = 1.3608962611495173623870550785125024484248E-6Q;
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#define NRN13 7
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static const __float128 RN13[NRN13 + 1] =
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{
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8.591478354823578150238226576156275285700E11Q,
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2.347931159756482741018258864137297157668E11Q,
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2.555408396679352028680662433943000804616E10Q,
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1.408581709264464345480765758902967123937E9Q,
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4.126759849752613822953004114044451046321E7Q,
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6.133298899622688505854211579222889943778E5Q,
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3.929248056293651597987893340755876578072E3Q,
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6.850783280018706668924952057996075215223E0Q
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};
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#define NRD13 6
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static const __float128 RD13[NRD13 + 1] =
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{
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3.401225382297342302296607039352935541669E11Q,
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8.756765276918037910363513243563234551784E10Q,
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8.873913342866613213078554180987647243903E9Q,
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4.483797255342763263361893016049310017973E8Q,
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1.178186288833066430952276702931512870676E7Q,
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1.519928623743264797939103740132278337476E5Q,
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7.989298844938119228411117593338850892311E2Q
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/* 1.0E0L */
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};
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/* log gamma(x+12) = log gamma(12) + x P(x)/Q(x)
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-0.5 <= x <= 0.5
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11.5 <= x+12 <= 12.5
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Peak relative error 4.1e-36 */
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static const __float128 lgam12a = 1.75023040771484375E1Q;
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static const __float128 lgam12b = 3.7687254483392876529072161996717039575982E-6Q;
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#define NRN12 7
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static const __float128 RN12[NRN12 + 1] =
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{
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4.709859662695606986110997348630997559137E11Q,
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1.398713878079497115037857470168777995230E11Q,
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1.654654931821564315970930093932954900867E10Q,
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9.916279414876676861193649489207282144036E8Q,
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3.159604070526036074112008954113411389879E7Q,
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5.109099197547205212294747623977502492861E5Q,
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3.563054878276102790183396740969279826988E3Q,
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6.769610657004672719224614163196946862747E0Q
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};
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#define NRD12 6
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static const __float128 RD12[NRD12 + 1] =
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{
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1.928167007860968063912467318985802726613E11Q,
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5.383198282277806237247492369072266389233E10Q,
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5.915693215338294477444809323037871058363E9Q,
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3.241438287570196713148310560147925781342E8Q,
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9.236680081763754597872713592701048455890E6Q,
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1.292246897881650919242713651166596478850E5Q,
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7.366532445427159272584194816076600211171E2Q
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/* 1.0E0L */
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};
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/* log gamma(x+11) = log gamma(11) + x P(x)/Q(x)
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-0.5 <= x <= 0.5
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10.5 <= x+11 <= 11.5
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Peak relative error 1.8e-35 */
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static const __float128 lgam11a = 1.5104400634765625E1Q;
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static const __float128 lgam11b = 1.1938309890295225709329251070371882250744E-5Q;
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#define NRN11 7
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static const __float128 RN11[NRN11 + 1] =
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{
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2.446960438029415837384622675816736622795E11Q,
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7.955444974446413315803799763901729640350E10Q,
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1.030555327949159293591618473447420338444E10Q,
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6.765022131195302709153994345470493334946E8Q,
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2.361892792609204855279723576041468347494E7Q,
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4.186623629779479136428005806072176490125E5Q,
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3.202506022088912768601325534149383594049E3Q,
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6.681356101133728289358838690666225691363E0Q
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};
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#define NRD11 6
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static const __float128 RD11[NRD11 + 1] =
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{
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1.040483786179428590683912396379079477432E11Q,
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3.172251138489229497223696648369823779729E10Q,
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3.806961885984850433709295832245848084614E9Q,
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2.278070344022934913730015420611609620171E8Q,
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7.089478198662651683977290023829391596481E6Q,
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1.083246385105903533237139380509590158658E5Q,
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6.744420991491385145885727942219463243597E2Q
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/* 1.0E0L */
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};
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/* log gamma(x+10) = log gamma(10) + x P(x)/Q(x)
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-0.5 <= x <= 0.5
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9.5 <= x+10 <= 10.5
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Peak relative error 5.4e-37 */
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static const __float128 lgam10a = 1.280181884765625E1Q;
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static const __float128 lgam10b = 8.6324252196112077178745667061642811492557E-6Q;
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#define NRN10 7
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static const __float128 RN10[NRN10 + 1] =
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{
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-1.239059737177249934158597996648808363783E14Q,
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-4.725899566371458992365624673357356908719E13Q,
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-7.283906268647083312042059082837754850808E12Q,
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-5.802855515464011422171165179767478794637E11Q,
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-2.532349691157548788382820303182745897298E10Q,
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-5.884260178023777312587193693477072061820E8Q,
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-6.437774864512125749845840472131829114906E6Q,
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-2.350975266781548931856017239843273049384E4Q
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};
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#define NRD10 7
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static const __float128 RD10[NRD10 + 1] =
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{
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-5.502645997581822567468347817182347679552E13Q,
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-1.970266640239849804162284805400136473801E13Q,
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-2.819677689615038489384974042561531409392E12Q,
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-2.056105863694742752589691183194061265094E11Q,
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-8.053670086493258693186307810815819662078E9Q,
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-1.632090155573373286153427982504851867131E8Q,
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-1.483575879240631280658077826889223634921E6Q,
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-4.002806669713232271615885826373550502510E3Q
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/* 1.0E0L */
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};
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/* log gamma(x+9) = log gamma(9) + x P(x)/Q(x)
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-0.5 <= x <= 0.5
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8.5 <= x+9 <= 9.5
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Peak relative error 3.6e-36 */
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static const __float128 lgam9a = 1.06045989990234375E1Q;
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static const __float128 lgam9b = 3.9037218127284172274007216547549861681400E-6Q;
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#define NRN9 7
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static const __float128 RN9[NRN9 + 1] =
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{
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-4.936332264202687973364500998984608306189E13Q,
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-2.101372682623700967335206138517766274855E13Q,
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-3.615893404644823888655732817505129444195E12Q,
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-3.217104993800878891194322691860075472926E11Q,
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-1.568465330337375725685439173603032921399E10Q,
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-4.073317518162025744377629219101510217761E8Q,
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-4.983232096406156139324846656819246974500E6Q,
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-2.036280038903695980912289722995505277253E4Q
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};
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#define NRD9 7
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static const __float128 RD9[NRD9 + 1] =
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{
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-2.306006080437656357167128541231915480393E13Q,
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-9.183606842453274924895648863832233799950E12Q,
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-1.461857965935942962087907301194381010380E12Q,
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-1.185728254682789754150068652663124298303E11Q,
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-5.166285094703468567389566085480783070037E9Q,
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-1.164573656694603024184768200787835094317E8Q,
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-1.177343939483908678474886454113163527909E6Q,
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-3.529391059783109732159524500029157638736E3Q
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/* 1.0E0L */
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};
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|
|
/* log gamma(x+8) = log gamma(8) + x P(x)/Q(x)
|
|
-0.5 <= x <= 0.5
|
|
7.5 <= x+8 <= 8.5
|
|
Peak relative error 2.4e-37 */
|
|
static const __float128 lgam8a = 8.525146484375E0Q;
|
|
static const __float128 lgam8b = 1.4876690414300165531036347125050759667737E-5Q;
|
|
#define NRN8 8
|
|
static const __float128 RN8[NRN8 + 1] =
|
|
{
|
|
6.600775438203423546565361176829139703289E11Q,
|
|
3.406361267593790705240802723914281025800E11Q,
|
|
7.222460928505293914746983300555538432830E10Q,
|
|
8.102984106025088123058747466840656458342E9Q,
|
|
5.157620015986282905232150979772409345927E8Q,
|
|
1.851445288272645829028129389609068641517E7Q,
|
|
3.489261702223124354745894067468953756656E5Q,
|
|
2.892095396706665774434217489775617756014E3Q,
|
|
6.596977510622195827183948478627058738034E0Q
|
|
};
|
|
#define NRD8 7
|
|
static const __float128 RD8[NRD8 + 1] =
|
|
{
|
|
3.274776546520735414638114828622673016920E11Q,
|
|
1.581811207929065544043963828487733970107E11Q,
|
|
3.108725655667825188135393076860104546416E10Q,
|
|
3.193055010502912617128480163681842165730E9Q,
|
|
1.830871482669835106357529710116211541839E8Q,
|
|
5.790862854275238129848491555068073485086E6Q,
|
|
9.305213264307921522842678835618803553589E4Q,
|
|
6.216974105861848386918949336819572333622E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+7) = log gamma(7) + x P(x)/Q(x)
|
|
-0.5 <= x <= 0.5
|
|
6.5 <= x+7 <= 7.5
|
|
Peak relative error 3.2e-36 */
|
|
static const __float128 lgam7a = 6.5792388916015625E0Q;
|
|
static const __float128 lgam7b = 1.2320408538495060178292903945321122583007E-5Q;
|
|
#define NRN7 8
|
|
static const __float128 RN7[NRN7 + 1] =
|
|
{
|
|
2.065019306969459407636744543358209942213E11Q,
|
|
1.226919919023736909889724951708796532847E11Q,
|
|
2.996157990374348596472241776917953749106E10Q,
|
|
3.873001919306801037344727168434909521030E9Q,
|
|
2.841575255593761593270885753992732145094E8Q,
|
|
1.176342515359431913664715324652399565551E7Q,
|
|
2.558097039684188723597519300356028511547E5Q,
|
|
2.448525238332609439023786244782810774702E3Q,
|
|
6.460280377802030953041566617300902020435E0Q
|
|
};
|
|
#define NRD7 7
|
|
static const __float128 RD7[NRD7 + 1] =
|
|
{
|
|
1.102646614598516998880874785339049304483E11Q,
|
|
6.099297512712715445879759589407189290040E10Q,
|
|
1.372898136289611312713283201112060238351E10Q,
|
|
1.615306270420293159907951633566635172343E9Q,
|
|
1.061114435798489135996614242842561967459E8Q,
|
|
3.845638971184305248268608902030718674691E6Q,
|
|
7.081730675423444975703917836972720495507E4Q,
|
|
5.423122582741398226693137276201344096370E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+6) = log gamma(6) + x P(x)/Q(x)
|
|
-0.5 <= x <= 0.5
|
|
5.5 <= x+6 <= 6.5
|
|
Peak relative error 6.2e-37 */
|
|
static const __float128 lgam6a = 4.7874908447265625E0Q;
|
|
static const __float128 lgam6b = 8.9805548349424770093452324304839959231517E-7Q;
|
|
#define NRN6 8
|
|
static const __float128 RN6[NRN6 + 1] =
|
|
{
|
|
-3.538412754670746879119162116819571823643E13Q,
|
|
-2.613432593406849155765698121483394257148E13Q,
|
|
-8.020670732770461579558867891923784753062E12Q,
|
|
-1.322227822931250045347591780332435433420E12Q,
|
|
-1.262809382777272476572558806855377129513E11Q,
|
|
-7.015006277027660872284922325741197022467E9Q,
|
|
-2.149320689089020841076532186783055727299E8Q,
|
|
-3.167210585700002703820077565539658995316E6Q,
|
|
-1.576834867378554185210279285358586385266E4Q
|
|
};
|
|
#define NRD6 8
|
|
static const __float128 RD6[NRD6 + 1] =
|
|
{
|
|
-2.073955870771283609792355579558899389085E13Q,
|
|
-1.421592856111673959642750863283919318175E13Q,
|
|
-4.012134994918353924219048850264207074949E12Q,
|
|
-6.013361045800992316498238470888523722431E11Q,
|
|
-5.145382510136622274784240527039643430628E10Q,
|
|
-2.510575820013409711678540476918249524123E9Q,
|
|
-6.564058379709759600836745035871373240904E7Q,
|
|
-7.861511116647120540275354855221373571536E5Q,
|
|
-2.821943442729620524365661338459579270561E3Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+5) = log gamma(5) + x P(x)/Q(x)
|
|
-0.5 <= x <= 0.5
|
|
4.5 <= x+5 <= 5.5
|
|
Peak relative error 3.4e-37 */
|
|
static const __float128 lgam5a = 3.17803955078125E0Q;
|
|
static const __float128 lgam5b = 1.4279566695619646941601297055408873990961E-5Q;
|
|
#define NRN5 9
|
|
static const __float128 RN5[NRN5 + 1] =
|
|
{
|
|
2.010952885441805899580403215533972172098E11Q,
|
|
1.916132681242540921354921906708215338584E11Q,
|
|
7.679102403710581712903937970163206882492E10Q,
|
|
1.680514903671382470108010973615268125169E10Q,
|
|
2.181011222911537259440775283277711588410E9Q,
|
|
1.705361119398837808244780667539728356096E8Q,
|
|
7.792391565652481864976147945997033946360E6Q,
|
|
1.910741381027985291688667214472560023819E5Q,
|
|
2.088138241893612679762260077783794329559E3Q,
|
|
6.330318119566998299106803922739066556550E0Q
|
|
};
|
|
#define NRD5 8
|
|
static const __float128 RD5[NRD5 + 1] =
|
|
{
|
|
1.335189758138651840605141370223112376176E11Q,
|
|
1.174130445739492885895466097516530211283E11Q,
|
|
4.308006619274572338118732154886328519910E10Q,
|
|
8.547402888692578655814445003283720677468E9Q,
|
|
9.934628078575618309542580800421370730906E8Q,
|
|
6.847107420092173812998096295422311820672E7Q,
|
|
2.698552646016599923609773122139463150403E6Q,
|
|
5.526516251532464176412113632726150253215E4Q,
|
|
4.772343321713697385780533022595450486932E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+4) = log gamma(4) + x P(x)/Q(x)
|
|
-0.5 <= x <= 0.5
|
|
3.5 <= x+4 <= 4.5
|
|
Peak relative error 6.7e-37 */
|
|
static const __float128 lgam4a = 1.791748046875E0Q;
|
|
static const __float128 lgam4b = 1.1422353055000812477358380702272722990692E-5Q;
|
|
#define NRN4 9
|
|
static const __float128 RN4[NRN4 + 1] =
|
|
{
|
|
-1.026583408246155508572442242188887829208E13Q,
|
|
-1.306476685384622809290193031208776258809E13Q,
|
|
-7.051088602207062164232806511992978915508E12Q,
|
|
-2.100849457735620004967624442027793656108E12Q,
|
|
-3.767473790774546963588549871673843260569E11Q,
|
|
-4.156387497364909963498394522336575984206E10Q,
|
|
-2.764021460668011732047778992419118757746E9Q,
|
|
-1.036617204107109779944986471142938641399E8Q,
|
|
-1.895730886640349026257780896972598305443E6Q,
|
|
-1.180509051468390914200720003907727988201E4Q
|
|
};
|
|
#define NRD4 9
|
|
static const __float128 RD4[NRD4 + 1] =
|
|
{
|
|
-8.172669122056002077809119378047536240889E12Q,
|
|
-9.477592426087986751343695251801814226960E12Q,
|
|
-4.629448850139318158743900253637212801682E12Q,
|
|
-1.237965465892012573255370078308035272942E12Q,
|
|
-1.971624313506929845158062177061297598956E11Q,
|
|
-1.905434843346570533229942397763361493610E10Q,
|
|
-1.089409357680461419743730978512856675984E9Q,
|
|
-3.416703082301143192939774401370222822430E7Q,
|
|
-4.981791914177103793218433195857635265295E5Q,
|
|
-2.192507743896742751483055798411231453733E3Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+3) = log gamma(3) + x P(x)/Q(x)
|
|
-0.25 <= x <= 0.5
|
|
2.75 <= x+3 <= 3.5
|
|
Peak relative error 6.0e-37 */
|
|
static const __float128 lgam3a = 6.93145751953125E-1Q;
|
|
static const __float128 lgam3b = 1.4286068203094172321214581765680755001344E-6Q;
|
|
|
|
#define NRN3 9
|
|
static const __float128 RN3[NRN3 + 1] =
|
|
{
|
|
-4.813901815114776281494823863935820876670E11Q,
|
|
-8.425592975288250400493910291066881992620E11Q,
|
|
-6.228685507402467503655405482985516909157E11Q,
|
|
-2.531972054436786351403749276956707260499E11Q,
|
|
-6.170200796658926701311867484296426831687E10Q,
|
|
-9.211477458528156048231908798456365081135E9Q,
|
|
-8.251806236175037114064561038908691305583E8Q,
|
|
-4.147886355917831049939930101151160447495E7Q,
|
|
-1.010851868928346082547075956946476932162E6Q,
|
|
-8.333374463411801009783402800801201603736E3Q
|
|
};
|
|
#define NRD3 9
|
|
static const __float128 RD3[NRD3 + 1] =
|
|
{
|
|
-5.216713843111675050627304523368029262450E11Q,
|
|
-8.014292925418308759369583419234079164391E11Q,
|
|
-5.180106858220030014546267824392678611990E11Q,
|
|
-1.830406975497439003897734969120997840011E11Q,
|
|
-3.845274631904879621945745960119924118925E10Q,
|
|
-4.891033385370523863288908070309417710903E9Q,
|
|
-3.670172254411328640353855768698287474282E8Q,
|
|
-1.505316381525727713026364396635522516989E7Q,
|
|
-2.856327162923716881454613540575964890347E5Q,
|
|
-1.622140448015769906847567212766206894547E3Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x)
|
|
-0.125 <= x <= 0.25
|
|
2.375 <= x+2.5 <= 2.75 */
|
|
static const __float128 lgam2r5a = 2.8466796875E-1Q;
|
|
static const __float128 lgam2r5b = 1.4901722919159632494669682701924320137696E-5Q;
|
|
#define NRN2r5 8
|
|
static const __float128 RN2r5[NRN2r5 + 1] =
|
|
{
|
|
-4.676454313888335499356699817678862233205E9Q,
|
|
-9.361888347911187924389905984624216340639E9Q,
|
|
-7.695353600835685037920815799526540237703E9Q,
|
|
-3.364370100981509060441853085968900734521E9Q,
|
|
-8.449902011848163568670361316804900559863E8Q,
|
|
-1.225249050950801905108001246436783022179E8Q,
|
|
-9.732972931077110161639900388121650470926E6Q,
|
|
-3.695711763932153505623248207576425983573E5Q,
|
|
-4.717341584067827676530426007495274711306E3Q
|
|
};
|
|
#define NRD2r5 8
|
|
static const __float128 RD2r5[NRD2r5 + 1] =
|
|
{
|
|
-6.650657966618993679456019224416926875619E9Q,
|
|
-1.099511409330635807899718829033488771623E10Q,
|
|
-7.482546968307837168164311101447116903148E9Q,
|
|
-2.702967190056506495988922973755870557217E9Q,
|
|
-5.570008176482922704972943389590409280950E8Q,
|
|
-6.536934032192792470926310043166993233231E7Q,
|
|
-4.101991193844953082400035444146067511725E6Q,
|
|
-1.174082735875715802334430481065526664020E5Q,
|
|
-9.932840389994157592102947657277692978511E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+2) = x P(x)/Q(x)
|
|
-0.125 <= x <= +0.375
|
|
1.875 <= x+2 <= 2.375
|
|
Peak relative error 4.6e-36 */
|
|
#define NRN2 9
|
|
static const __float128 RN2[NRN2 + 1] =
|
|
{
|
|
-3.716661929737318153526921358113793421524E9Q,
|
|
-1.138816715030710406922819131397532331321E10Q,
|
|
-1.421017419363526524544402598734013569950E10Q,
|
|
-9.510432842542519665483662502132010331451E9Q,
|
|
-3.747528562099410197957514973274474767329E9Q,
|
|
-8.923565763363912474488712255317033616626E8Q,
|
|
-1.261396653700237624185350402781338231697E8Q,
|
|
-9.918402520255661797735331317081425749014E6Q,
|
|
-3.753996255897143855113273724233104768831E5Q,
|
|
-4.778761333044147141559311805999540765612E3Q
|
|
};
|
|
#define NRD2 9
|
|
static const __float128 RD2[NRD2 + 1] =
|
|
{
|
|
-8.790916836764308497770359421351673950111E9Q,
|
|
-2.023108608053212516399197678553737477486E10Q,
|
|
-1.958067901852022239294231785363504458367E10Q,
|
|
-1.035515043621003101254252481625188704529E10Q,
|
|
-3.253884432621336737640841276619272224476E9Q,
|
|
-6.186383531162456814954947669274235815544E8Q,
|
|
-6.932557847749518463038934953605969951466E7Q,
|
|
-4.240731768287359608773351626528479703758E6Q,
|
|
-1.197343995089189188078944689846348116630E5Q,
|
|
-1.004622911670588064824904487064114090920E3Q
|
|
/* 1.0E0 */
|
|
};
|
|
|
|
|
|
/* log gamma(x+1.75) = log gamma(1.75) + x P(x)/Q(x)
|
|
-0.125 <= x <= +0.125
|
|
1.625 <= x+1.75 <= 1.875
|
|
Peak relative error 9.2e-37 */
|
|
static const __float128 lgam1r75a = -8.441162109375E-2Q;
|
|
static const __float128 lgam1r75b = 1.0500073264444042213965868602268256157604E-5Q;
|
|
#define NRN1r75 8
|
|
static const __float128 RN1r75[NRN1r75 + 1] =
|
|
{
|
|
-5.221061693929833937710891646275798251513E7Q,
|
|
-2.052466337474314812817883030472496436993E8Q,
|
|
-2.952718275974940270675670705084125640069E8Q,
|
|
-2.132294039648116684922965964126389017840E8Q,
|
|
-8.554103077186505960591321962207519908489E7Q,
|
|
-1.940250901348870867323943119132071960050E7Q,
|
|
-2.379394147112756860769336400290402208435E6Q,
|
|
-1.384060879999526222029386539622255797389E5Q,
|
|
-2.698453601378319296159355612094598695530E3Q
|
|
};
|
|
#define NRD1r75 8
|
|
static const __float128 RD1r75[NRD1r75 + 1] =
|
|
{
|
|
-2.109754689501705828789976311354395393605E8Q,
|
|
-5.036651829232895725959911504899241062286E8Q,
|
|
-4.954234699418689764943486770327295098084E8Q,
|
|
-2.589558042412676610775157783898195339410E8Q,
|
|
-7.731476117252958268044969614034776883031E7Q,
|
|
-1.316721702252481296030801191240867486965E7Q,
|
|
-1.201296501404876774861190604303728810836E6Q,
|
|
-5.007966406976106636109459072523610273928E4Q,
|
|
-6.155817990560743422008969155276229018209E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+x0) = y0 + x^2 P(x)/Q(x)
|
|
-0.0867 <= x <= +0.1634
|
|
1.374932... <= x+x0 <= 1.625032...
|
|
Peak relative error 4.0e-36 */
|
|
static const __float128 x0a = 1.4616241455078125Q;
|
|
static const __float128 x0b = 7.9994605498412626595423257213002588621246E-6Q;
|
|
static const __float128 y0a = -1.21490478515625E-1Q;
|
|
static const __float128 y0b = 4.1879797753919044854428223084178486438269E-6Q;
|
|
#define NRN1r5 8
|
|
static const __float128 RN1r5[NRN1r5 + 1] =
|
|
{
|
|
6.827103657233705798067415468881313128066E5Q,
|
|
1.910041815932269464714909706705242148108E6Q,
|
|
2.194344176925978377083808566251427771951E6Q,
|
|
1.332921400100891472195055269688876427962E6Q,
|
|
4.589080973377307211815655093824787123508E5Q,
|
|
8.900334161263456942727083580232613796141E4Q,
|
|
9.053840838306019753209127312097612455236E3Q,
|
|
4.053367147553353374151852319743594873771E2Q,
|
|
5.040631576303952022968949605613514584950E0Q
|
|
};
|
|
#define NRD1r5 8
|
|
static const __float128 RD1r5[NRD1r5 + 1] =
|
|
{
|
|
1.411036368843183477558773688484699813355E6Q,
|
|
4.378121767236251950226362443134306184849E6Q,
|
|
5.682322855631723455425929877581697918168E6Q,
|
|
3.999065731556977782435009349967042222375E6Q,
|
|
1.653651390456781293163585493620758410333E6Q,
|
|
4.067774359067489605179546964969435858311E5Q,
|
|
5.741463295366557346748361781768833633256E4Q,
|
|
4.226404539738182992856094681115746692030E3Q,
|
|
1.316980975410327975566999780608618774469E2Q,
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x+1.25) = log gamma(1.25) + x P(x)/Q(x)
|
|
-.125 <= x <= +.125
|
|
1.125 <= x+1.25 <= 1.375
|
|
Peak relative error = 4.9e-36 */
|
|
static const __float128 lgam1r25a = -9.82818603515625E-2Q;
|
|
static const __float128 lgam1r25b = 1.0023929749338536146197303364159774377296E-5Q;
|
|
#define NRN1r25 9
|
|
static const __float128 RN1r25[NRN1r25 + 1] =
|
|
{
|
|
-9.054787275312026472896002240379580536760E4Q,
|
|
-8.685076892989927640126560802094680794471E4Q,
|
|
2.797898965448019916967849727279076547109E5Q,
|
|
6.175520827134342734546868356396008898299E5Q,
|
|
5.179626599589134831538516906517372619641E5Q,
|
|
2.253076616239043944538380039205558242161E5Q,
|
|
5.312653119599957228630544772499197307195E4Q,
|
|
6.434329437514083776052669599834938898255E3Q,
|
|
3.385414416983114598582554037612347549220E2Q,
|
|
4.907821957946273805080625052510832015792E0Q
|
|
};
|
|
#define NRD1r25 8
|
|
static const __float128 RD1r25[NRD1r25 + 1] =
|
|
{
|
|
3.980939377333448005389084785896660309000E5Q,
|
|
1.429634893085231519692365775184490465542E6Q,
|
|
2.145438946455476062850151428438668234336E6Q,
|
|
1.743786661358280837020848127465970357893E6Q,
|
|
8.316364251289743923178092656080441655273E5Q,
|
|
2.355732939106812496699621491135458324294E5Q,
|
|
3.822267399625696880571810137601310855419E4Q,
|
|
3.228463206479133236028576845538387620856E3Q,
|
|
1.152133170470059555646301189220117965514E2Q
|
|
/* 1.0E0L */
|
|
};
|
|
|
|
|
|
/* log gamma(x + 1) = x P(x)/Q(x)
|
|
0.0 <= x <= +0.125
|
|
1.0 <= x+1 <= 1.125
|
|
Peak relative error 1.1e-35 */
|
|
#define NRN1 8
|
|
static const __float128 RN1[NRN1 + 1] =
|
|
{
|
|
-9.987560186094800756471055681088744738818E3Q,
|
|
-2.506039379419574361949680225279376329742E4Q,
|
|
-1.386770737662176516403363873617457652991E4Q,
|
|
1.439445846078103202928677244188837130744E4Q,
|
|
2.159612048879650471489449668295139990693E4Q,
|
|
1.047439813638144485276023138173676047079E4Q,
|
|
2.250316398054332592560412486630769139961E3Q,
|
|
1.958510425467720733041971651126443864041E2Q,
|
|
4.516830313569454663374271993200291219855E0Q
|
|
};
|
|
#define NRD1 7
|
|
static const __float128 RD1[NRD1 + 1] =
|
|
{
|
|
1.730299573175751778863269333703788214547E4Q,
|
|
6.807080914851328611903744668028014678148E4Q,
|
|
1.090071629101496938655806063184092302439E5Q,
|
|
9.124354356415154289343303999616003884080E4Q,
|
|
4.262071638655772404431164427024003253954E4Q,
|
|
1.096981664067373953673982635805821283581E4Q,
|
|
1.431229503796575892151252708527595787588E3Q,
|
|
7.734110684303689320830401788262295992921E1Q
|
|
/* 1.0E0 */
|
|
};
|
|
|
|
|
|
/* log gamma(x + 1) = x P(x)/Q(x)
|
|
-0.125 <= x <= 0
|
|
0.875 <= x+1 <= 1.0
|
|
Peak relative error 7.0e-37 */
|
|
#define NRNr9 8
|
|
static const __float128 RNr9[NRNr9 + 1] =
|
|
{
|
|
4.441379198241760069548832023257571176884E5Q,
|
|
1.273072988367176540909122090089580368732E6Q,
|
|
9.732422305818501557502584486510048387724E5Q,
|
|
-5.040539994443998275271644292272870348684E5Q,
|
|
-1.208719055525609446357448132109723786736E6Q,
|
|
-7.434275365370936547146540554419058907156E5Q,
|
|
-2.075642969983377738209203358199008185741E5Q,
|
|
-2.565534860781128618589288075109372218042E4Q,
|
|
-1.032901669542994124131223797515913955938E3Q,
|
|
};
|
|
#define NRDr9 8
|
|
static const __float128 RDr9[NRDr9 + 1] =
|
|
{
|
|
-7.694488331323118759486182246005193998007E5Q,
|
|
-3.301918855321234414232308938454112213751E6Q,
|
|
-5.856830900232338906742924836032279404702E6Q,
|
|
-5.540672519616151584486240871424021377540E6Q,
|
|
-3.006530901041386626148342989181721176919E6Q,
|
|
-9.350378280513062139466966374330795935163E5Q,
|
|
-1.566179100031063346901755685375732739511E5Q,
|
|
-1.205016539620260779274902967231510804992E4Q,
|
|
-2.724583156305709733221564484006088794284E2Q
|
|
/* 1.0E0 */
|
|
};
|
|
|
|
|
|
/* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */
|
|
|
|
static __float128
|
|
neval (__float128 x, const __float128 *p, int n)
|
|
{
|
|
__float128 y;
|
|
|
|
p += n;
|
|
y = *p--;
|
|
do
|
|
{
|
|
y = y * x + *p--;
|
|
}
|
|
while (--n > 0);
|
|
return y;
|
|
}
|
|
|
|
|
|
/* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */
|
|
|
|
static __float128
|
|
deval (__float128 x, const __float128 *p, int n)
|
|
{
|
|
__float128 y;
|
|
|
|
p += n;
|
|
y = x + *p--;
|
|
do
|
|
{
|
|
y = y * x + *p--;
|
|
}
|
|
while (--n > 0);
|
|
return y;
|
|
}
|
|
|
|
|
|
__float128
|
|
__quadmath_lgammaq_r (__float128 x, int *signgamp)
|
|
{
|
|
__float128 p, q, w, z, nx;
|
|
int i, nn;
|
|
|
|
*signgamp = 1;
|
|
|
|
if (! finiteq (x))
|
|
return x * x;
|
|
|
|
if (x == 0)
|
|
{
|
|
if (signbitq (x))
|
|
*signgamp = -1;
|
|
}
|
|
|
|
if (x < 0)
|
|
{
|
|
if (x < -2 && x > -50)
|
|
return __quadmath_lgamma_negq (x, signgamp);
|
|
q = -x;
|
|
p = floorq (q);
|
|
if (p == q)
|
|
return (one / fabsq (p - p));
|
|
__float128 halfp = p * 0.5Q;
|
|
if (halfp == floorq (halfp))
|
|
*signgamp = -1;
|
|
else
|
|
*signgamp = 1;
|
|
if (q < 0x1p-120Q)
|
|
return -logq (q);
|
|
z = q - p;
|
|
if (z > 0.5Q)
|
|
{
|
|
p += 1;
|
|
z = p - q;
|
|
}
|
|
z = q * sinq (PIL * z);
|
|
w = __quadmath_lgammaq_r (q, &i);
|
|
z = logq (PIL / z) - w;
|
|
return (z);
|
|
}
|
|
|
|
if (x < 13.5Q)
|
|
{
|
|
p = 0;
|
|
nx = floorq (x + 0.5Q);
|
|
nn = nx;
|
|
switch (nn)
|
|
{
|
|
case 0:
|
|
/* log gamma (x + 1) = log(x) + log gamma(x) */
|
|
if (x < 0x1p-120Q)
|
|
return -logq (x);
|
|
else if (x <= 0.125)
|
|
{
|
|
p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1);
|
|
}
|
|
else if (x <= 0.375)
|
|
{
|
|
z = x - 0.25Q;
|
|
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
|
|
p += lgam1r25b;
|
|
p += lgam1r25a;
|
|
}
|
|
else if (x <= 0.625)
|
|
{
|
|
z = x + (1 - x0a);
|
|
z = z - x0b;
|
|
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
|
p = p * z * z;
|
|
p = p + y0b;
|
|
p = p + y0a;
|
|
}
|
|
else if (x <= 0.875)
|
|
{
|
|
z = x - 0.75Q;
|
|
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
|
|
p += lgam1r75b;
|
|
p += lgam1r75a;
|
|
}
|
|
else
|
|
{
|
|
z = x - 1;
|
|
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
|
}
|
|
p = p - logq (x);
|
|
break;
|
|
|
|
case 1:
|
|
if (x < 0.875Q)
|
|
{
|
|
if (x <= 0.625)
|
|
{
|
|
z = x + (1 - x0a);
|
|
z = z - x0b;
|
|
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
|
p = p * z * z;
|
|
p = p + y0b;
|
|
p = p + y0a;
|
|
}
|
|
else if (x <= 0.875)
|
|
{
|
|
z = x - 0.75Q;
|
|
p = z * neval (z, RN1r75, NRN1r75)
|
|
/ deval (z, RD1r75, NRD1r75);
|
|
p += lgam1r75b;
|
|
p += lgam1r75a;
|
|
}
|
|
else
|
|
{
|
|
z = x - 1;
|
|
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
|
}
|
|
p = p - logq (x);
|
|
}
|
|
else if (x < 1)
|
|
{
|
|
z = x - 1;
|
|
p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9);
|
|
}
|
|
else if (x == 1)
|
|
p = 0;
|
|
else if (x <= 1.125Q)
|
|
{
|
|
z = x - 1;
|
|
p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1);
|
|
}
|
|
else if (x <= 1.375)
|
|
{
|
|
z = x - 1.25Q;
|
|
p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25);
|
|
p += lgam1r25b;
|
|
p += lgam1r25a;
|
|
}
|
|
else
|
|
{
|
|
/* 1.375 <= x+x0 <= 1.625 */
|
|
z = x - x0a;
|
|
z = z - x0b;
|
|
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
|
p = p * z * z;
|
|
p = p + y0b;
|
|
p = p + y0a;
|
|
}
|
|
break;
|
|
|
|
case 2:
|
|
if (x < 1.625Q)
|
|
{
|
|
z = x - x0a;
|
|
z = z - x0b;
|
|
p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5);
|
|
p = p * z * z;
|
|
p = p + y0b;
|
|
p = p + y0a;
|
|
}
|
|
else if (x < 1.875Q)
|
|
{
|
|
z = x - 1.75Q;
|
|
p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75);
|
|
p += lgam1r75b;
|
|
p += lgam1r75a;
|
|
}
|
|
else if (x == 2)
|
|
p = 0;
|
|
else if (x < 2.375Q)
|
|
{
|
|
z = x - 2;
|
|
p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2);
|
|
}
|
|
else
|
|
{
|
|
z = x - 2.5Q;
|
|
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
|
|
p += lgam2r5b;
|
|
p += lgam2r5a;
|
|
}
|
|
break;
|
|
|
|
case 3:
|
|
if (x < 2.75)
|
|
{
|
|
z = x - 2.5Q;
|
|
p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5);
|
|
p += lgam2r5b;
|
|
p += lgam2r5a;
|
|
}
|
|
else
|
|
{
|
|
z = x - 3;
|
|
p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3);
|
|
p += lgam3b;
|
|
p += lgam3a;
|
|
}
|
|
break;
|
|
|
|
case 4:
|
|
z = x - 4;
|
|
p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4);
|
|
p += lgam4b;
|
|
p += lgam4a;
|
|
break;
|
|
|
|
case 5:
|
|
z = x - 5;
|
|
p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5);
|
|
p += lgam5b;
|
|
p += lgam5a;
|
|
break;
|
|
|
|
case 6:
|
|
z = x - 6;
|
|
p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6);
|
|
p += lgam6b;
|
|
p += lgam6a;
|
|
break;
|
|
|
|
case 7:
|
|
z = x - 7;
|
|
p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7);
|
|
p += lgam7b;
|
|
p += lgam7a;
|
|
break;
|
|
|
|
case 8:
|
|
z = x - 8;
|
|
p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8);
|
|
p += lgam8b;
|
|
p += lgam8a;
|
|
break;
|
|
|
|
case 9:
|
|
z = x - 9;
|
|
p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9);
|
|
p += lgam9b;
|
|
p += lgam9a;
|
|
break;
|
|
|
|
case 10:
|
|
z = x - 10;
|
|
p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10);
|
|
p += lgam10b;
|
|
p += lgam10a;
|
|
break;
|
|
|
|
case 11:
|
|
z = x - 11;
|
|
p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11);
|
|
p += lgam11b;
|
|
p += lgam11a;
|
|
break;
|
|
|
|
case 12:
|
|
z = x - 12;
|
|
p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12);
|
|
p += lgam12b;
|
|
p += lgam12a;
|
|
break;
|
|
|
|
case 13:
|
|
z = x - 13;
|
|
p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13);
|
|
p += lgam13b;
|
|
p += lgam13a;
|
|
break;
|
|
}
|
|
return p;
|
|
}
|
|
|
|
if (x > MAXLGM)
|
|
return (*signgamp * huge * huge);
|
|
|
|
if (x > 0x1p120Q)
|
|
return x * (logq (x) - 1);
|
|
q = ls2pi - x;
|
|
q = (x - 0.5Q) * logq (x) + q;
|
|
if (x > 1.0e18Q)
|
|
return (q);
|
|
|
|
p = 1 / (x * x);
|
|
q += neval (p, RASY, NRASY) / x;
|
|
return (q);
|
|
}
|