Module Name: src
Committed By: christos
Date: Sat May 5 17:54:14 UTC 2012
Modified Files:
src/lib/libm: Makefile
src/lib/libm/man: lgamma.3
src/lib/libm/src: math_private.h
Added Files:
src/lib/libm/src: b_exp.c b_log.c b_tgamma.c s_tgammaf.c
Log Message:
Add tgamma{,f} from FreeBSD via rudolf, netbsd at eq dot cz
To generate a diff of this commit:
cvs rdiff -u -r1.123 -r1.124 src/lib/libm/Makefile
cvs rdiff -u -r1.21 -r1.22 src/lib/libm/man/lgamma.3
cvs rdiff -u -r0 -r1.1 src/lib/libm/src/b_exp.c src/lib/libm/src/b_log.c \
src/lib/libm/src/b_tgamma.c src/lib/libm/src/s_tgammaf.c
cvs rdiff -u -r1.16 -r1.17 src/lib/libm/src/math_private.h
Please note that diffs are not public domain; they are subject to the
copyright notices on the relevant files.
Modified files:
Index: src/lib/libm/Makefile
diff -u src/lib/libm/Makefile:1.123 src/lib/libm/Makefile:1.124
--- src/lib/libm/Makefile:1.123 Wed Apr 4 06:59:46 2012
+++ src/lib/libm/Makefile Sat May 5 13:54:13 2012
@@ -1,4 +1,4 @@
-# $NetBSD: Makefile,v 1.123 2012/04/04 10:59:46 joerg Exp $
+# $NetBSD: Makefile,v 1.124 2012/05/05 17:54:13 christos Exp $
#
# @(#)Makefile 5.1beta 93/09/24
#
@@ -129,7 +129,8 @@ COPTS+= -fno-strict-aliasing
CPPFLAGS+=-DLIBM_SCCS
LIB= m
-COMMON_SRCS+= e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
+COMMON_SRCS+= b_exp.c b_log.c b_tgamma.c \
+ e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c e_j0f.c \
e_j1.c e_j1f.c e_jn.c e_jnf.c e_lgamma_r.c e_lgammaf_r.c e_log.c \
@@ -148,7 +149,7 @@ COMMON_SRCS+= e_acos.c e_acosf.c e_acosh
s_matherr.c s_modff.c s_nextafter.c \
s_nextafterf.c s_remquo.c s_remquof.c s_rint.c s_rintf.c s_round.c s_roundf.c s_scalbn.c \
s_scalbnf.c s_scalbnl.c s_signgam.c s_significand.c s_significandf.c s_sin.c \
- s_sinf.c s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_trunc.c s_truncf.c \
+ s_sinf.c s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \
w_acos.c w_acosf.c w_acosh.c w_acoshf.c w_asin.c w_asinf.c w_atan2.c \
w_atan2f.c w_atanh.c w_atanhf.c w_cosh.c w_coshf.c \
w_drem.c w_dremf.c w_exp.c w_expf.c w_fmod.c w_fmodf.c w_gamma.c \
@@ -269,7 +270,7 @@ MLINKS+=j0.3 j0f.3 j0.3 j1.3 j0.3 j1f.3
j0.3 y0.3 j0.3 y0f.3 j0.3 y1.3 j0.3 y1f.3 j0.3 yn.3 j0.3 ynf.3
MLINKS+=lgamma.3 lgammaf.3 lgamma.3 lgamma_r.3 lgamma.3 lgammaf_r.3 \
lgamma.3 gamma.3 lgamma.3 gammaf.3 lgamma.3 gamma_r.3 \
- lgamma.3 gammaf_r.3
+ lgamma.3 gammaf_r.3 lgamma.3 tgamma.3 lgamma.3 tgammaf.3
MLINKS+=nextafter.3 nextafterf.3 \
nextafter.3 nextafterl.3 \
nextafter.3 nexttoward.3
Index: src/lib/libm/man/lgamma.3
diff -u src/lib/libm/man/lgamma.3:1.21 src/lib/libm/man/lgamma.3:1.22
--- src/lib/libm/man/lgamma.3:1.21 Thu Aug 7 12:44:48 2003
+++ src/lib/libm/man/lgamma.3 Sat May 5 13:54:13 2012
@@ -26,9 +26,9 @@
.\" SUCH DAMAGE.
.\"
.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
-.\" $NetBSD: lgamma.3,v 1.21 2003/08/07 16:44:48 agc Exp $
+.\" $NetBSD: lgamma.3,v 1.22 2012/05/05 17:54:13 christos Exp $
.\"
-.Dd December 3, 1992
+.Dd May 4, 2012
.Dt LGAMMA 3
.Os
.Sh NAME
@@ -39,7 +39,9 @@
.Nm gamma ,
.Nm gammaf ,
.Nm gamma_r ,
-.Nm gammaf_r
+.Nm gammaf_r ,
+.Nm tgamma ,
+.Nm tgammaf
.Nd log gamma function
.Sh LIBRARY
.Lb libm
@@ -64,6 +66,10 @@
.Fn gamma_r "double x" "int *sign"
.Ft float
.Fn gammaf_r "float x" "int *sign"
+.Ft double
+.Fn tgamma "double x"
+.Ft float
+.Fn tgammaf "float x"
.Sh DESCRIPTION
.Fn lgamma x
.if t \{\
@@ -90,6 +96,26 @@ pointed to by the
argument and
.Fa signgam
is not modified.
+.Pp
+The
+.Fn tgamma x
+and
+.Fn tgammaf x
+functions return \(*G(x), with no effect on
+.Fa signgam .
+.Pp
+.Fn gamma ,
+.Fn gammaf ,
+.Fn gamma_r ,
+and
+.Fn gammaf_r
+are deprecated aliases for
+.Fn lgamma ,
+.Fn lgammaf ,
+.Fn lgamma_r ,
+and
+.Fn lgammaf_r ,
+respectively.
.Sh IDIOSYNCRASIES
Do not use the expression
.Dq Li signgam\(**exp(lgamma(x))
@@ -107,6 +133,9 @@ has returned can signgam be correct.
returns appropriate values unless an argument is out of range.
Overflow will occur for sufficiently large positive values, and
non-positive integers.
+For large non-integer negative values,
+.Fn tgamma
+will underflow.
On the
.Tn VAX ,
the reserved operator is returned,
@@ -121,3 +150,7 @@ The
.Nm lgamma
function appeared in
.Bx 4.3 .
+The
+.Fn tgamma
+function appeared in
+.Nx 6.0 .
Index: src/lib/libm/src/math_private.h
diff -u src/lib/libm/src/math_private.h:1.16 src/lib/libm/src/math_private.h:1.17
--- src/lib/libm/src/math_private.h:1.16 Thu Sep 16 16:39:50 2010
+++ src/lib/libm/src/math_private.h Sat May 5 13:54:14 2012
@@ -11,7 +11,7 @@
/*
* from: @(#)fdlibm.h 5.1 93/09/24
- * $NetBSD: math_private.h,v 1.16 2010/09/16 20:39:50 drochner Exp $
+ * $NetBSD: math_private.h,v 1.17 2012/05/05 17:54:14 christos Exp $
*/
#ifndef _MATH_PRIVATE_H_
@@ -275,4 +275,33 @@ extern float __kernel_cosf __P((float,fl
extern float __kernel_tanf __P((float,float,int));
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*));
+/*
+ * TRUNC() is a macro that sets the trailing 27 bits in the mantissa of an
+ * IEEE double variable to zero. It must be expression-like for syntactic
+ * reasons, and we implement this expression using an inline function
+ * instead of a pure macro to avoid depending on the gcc feature of
+ * statement-expressions.
+ */
+#define TRUNC(d) (_b_trunc(&(d)))
+
+static __inline void
+_b_trunc(volatile double *_dp)
+{
+ uint32_t _lw;
+
+ GET_LOW_WORD(_lw, *_dp);
+ SET_LOW_WORD(*_dp, _lw & 0xf8000000);
+}
+
+struct Double {
+ double a;
+ double b;
+};
+
+/*
+ * Functions internal to the math package, yet not static.
+ */
+double __exp__D(double, double);
+struct Double __log__D(double);
+
#endif /* _MATH_PRIVATE_H_ */
Added files:
Index: src/lib/libm/src/b_exp.c
diff -u /dev/null src/lib/libm/src/b_exp.c:1.1
--- /dev/null Sat May 5 13:54:14 2012
+++ src/lib/libm/src/b_exp.c Sat May 5 13:54:14 2012
@@ -0,0 +1,137 @@
+/* $NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $ */
+
+/*
+ * Copyright (c) 1985, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+/* @(#)exp.c 8.1 (Berkeley) 6/4/93 */
+#include <sys/cdefs.h>
+#if 0
+__FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_exp.c 176449 2008-02-22 02:26:51Z das $");
+#else
+__RCSID("$NetBSD: b_exp.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
+#endif
+
+
+/* EXP(X)
+ * RETURN THE EXPONENTIAL OF X
+ * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
+ * CODED IN C BY K.C. NG, 1/19/85;
+ * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
+ *
+ * Required system supported functions:
+ * scalb(x,n)
+ * copysign(x,y)
+ * finite(x)
+ *
+ * Method:
+ * 1. Argument Reduction: given the input x, find r and integer k such
+ * that
+ * x = k*ln2 + r, |r| <= 0.5*ln2 .
+ * r will be represented as r := z+c for better accuracy.
+ *
+ * 2. Compute exp(r) by
+ *
+ * exp(r) = 1 + r + r*R1/(2-R1),
+ * where
+ * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
+ *
+ * 3. exp(x) = 2^k * exp(r) .
+ *
+ * Special cases:
+ * exp(INF) is INF, exp(NaN) is NaN;
+ * exp(-INF)= 0;
+ * for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ * exp(x) returns the exponential of x nearly rounded. In a test run
+ * with 1,156,000 random arguments on a VAX, the maximum observed
+ * error was 0.869 ulps (units in the last place).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double p1 = 0x1.555555555553ep-3;
+static const double p2 = -0x1.6c16c16bebd93p-9;
+static const double p3 = 0x1.1566aaf25de2cp-14;
+static const double p4 = -0x1.bbd41c5d26bf1p-20;
+static const double p5 = 0x1.6376972bea4d0p-25;
+static const double ln2hi = 0x1.62e42fee00000p-1;
+static const double ln2lo = 0x1.a39ef35793c76p-33;
+static const double lnhuge = 0x1.6602b15b7ecf2p9;
+static const double lntiny = -0x1.77af8ebeae354p9;
+static const double invln2 = 0x1.71547652b82fep0;
+
+/* returns exp(r = x + c) for |c| < |x| with no overlap. */
+
+double
+__exp__D(double x, double c)
+{
+ double z,hi,lo;
+ int k;
+
+ if (x != x) /* x is NaN */
+ return(x);
+ if ( x <= lnhuge ) {
+ if ( x >= lntiny ) {
+
+ /* argument reduction : x --> x - k*ln2 */
+ z = invln2*x;
+ k = z + copysign(.5, x);
+
+ /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
+
+ hi=(x-k*ln2hi); /* Exact. */
+ x= hi - (lo = k*ln2lo-c);
+ /* return 2^k*[1+x+x*c/(2+c)] */
+ z=x*x;
+ c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
+ c = (x*c)/(2.0-c);
+
+ return scalb(1.+(hi-(lo - c)), k);
+ }
+ /* end of x > lntiny */
+
+ else
+ /* exp(-big#) underflows to zero */
+ if(finite(x)) return(scalb(1.0,-5000));
+
+ /* exp(-INF) is zero */
+ else return(0.0);
+ }
+ /* end of x < lnhuge */
+
+ else
+ /* exp(INF) is INF, exp(+big#) overflows to INF */
+ return( finite(x) ? scalb(1.0,5000) : x);
+}
Index: src/lib/libm/src/b_log.c
diff -u /dev/null src/lib/libm/src/b_log.c:1.1
--- /dev/null Sat May 5 13:54:14 2012
+++ src/lib/libm/src/b_log.c Sat May 5 13:54:14 2012
@@ -0,0 +1,406 @@
+/* $NetBSD: b_log.c,v 1.1 2012/05/05 17:54:14 christos Exp $ */
+
+/*
+ * Copyright (c) 1992, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+/* @(#)log.c 8.2 (Berkeley) 11/30/93 */
+#include <sys/cdefs.h>
+#if 0
+__FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_log.c 176449 2008-02-22 02:26:51Z das $");
+#else
+__RCSID("$NetBSD: b_log.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
+#endif
+
+#include <errno.h>
+#include "math.h"
+#include "math_private.h"
+
+/* Table-driven natural logarithm.
+ *
+ * This code was derived, with minor modifications, from:
+ * Peter Tang, "Table-Driven Implementation of the
+ * Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
+ * Math Software, vol 16. no 4, pp 378-400, Dec 1990).
+ *
+ * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
+ * where F = j/128 for j an integer in [0, 128].
+ *
+ * log(2^m) = log2_hi*m + log2_tail*m
+ * since m is an integer, the dominant term is exact.
+ * m has at most 10 digits (for subnormal numbers),
+ * and log2_hi has 11 trailing zero bits.
+ *
+ * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
+ * logF_hi[] + 512 is exact.
+ *
+ * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
+ * the leading term is calculated to extra precision in two
+ * parts, the larger of which adds exactly to the dominant
+ * m and F terms.
+ * There are two cases:
+ * 1. when m, j are non-zero (m | j), use absolute
+ * precision for the leading term.
+ * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
+ * In this case, use a relative precision of 24 bits.
+ * (This is done differently in the original paper)
+ *
+ * Special cases:
+ * 0 return signalling -Inf
+ * neg return signalling NaN
+ * +Inf return +Inf
+*/
+
+#define N 128
+
+/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
+ * Used for generation of extend precision logarithms.
+ * The constant 35184372088832 is 2^45, so the divide is exact.
+ * It ensures correct reading of logF_head, even for inaccurate
+ * decimal-to-binary conversion routines. (Everybody gets the
+ * right answer for integers less than 2^53.)
+ * Values for log(F) were generated using error < 10^-57 absolute
+ * with the bc -l package.
+*/
+static const double A1 = .08333333333333178827;
+static const double A2 = .01250000000377174923;
+static const double A3 = .002232139987919447809;
+static const double A4 = .0004348877777076145742;
+
+static const double logF_head[N+1] = {
+ 0.,
+ .007782140442060381246,
+ .015504186535963526694,
+ .023167059281547608406,
+ .030771658666765233647,
+ .038318864302141264488,
+ .045809536031242714670,
+ .053244514518837604555,
+ .060624621816486978786,
+ .067950661908525944454,
+ .075223421237524235039,
+ .082443669210988446138,
+ .089612158689760690322,
+ .096729626458454731618,
+ .103796793681567578460,
+ .110814366340264314203,
+ .117783035656430001836,
+ .124703478501032805070,
+ .131576357788617315236,
+ .138402322859292326029,
+ .145182009844575077295,
+ .151916042025732167530,
+ .158605030176659056451,
+ .165249572895390883786,
+ .171850256926518341060,
+ .178407657472689606947,
+ .184922338493834104156,
+ .191394852999565046047,
+ .197825743329758552135,
+ .204215541428766300668,
+ .210564769107350002741,
+ .216873938300523150246,
+ .223143551314024080056,
+ .229374101064877322642,
+ .235566071312860003672,
+ .241719936886966024758,
+ .247836163904594286577,
+ .253915209980732470285,
+ .259957524436686071567,
+ .265963548496984003577,
+ .271933715484010463114,
+ .277868451003087102435,
+ .283768173130738432519,
+ .289633292582948342896,
+ .295464212893421063199,
+ .301261330578199704177,
+ .307025035294827830512,
+ .312755710004239517729,
+ .318453731118097493890,
+ .324119468654316733591,
+ .329753286372579168528,
+ .335355541920762334484,
+ .340926586970454081892,
+ .346466767346100823488,
+ .351976423156884266063,
+ .357455888922231679316,
+ .362905493689140712376,
+ .368325561158599157352,
+ .373716409793814818840,
+ .379078352934811846353,
+ .384411698910298582632,
+ .389716751140440464951,
+ .394993808240542421117,
+ .400243164127459749579,
+ .405465108107819105498,
+ .410659924985338875558,
+ .415827895143593195825,
+ .420969294644237379543,
+ .426084395310681429691,
+ .431173464818130014464,
+ .436236766774527495726,
+ .441274560805140936281,
+ .446287102628048160113,
+ .451274644139630254358,
+ .456237433481874177232,
+ .461175715122408291790,
+ .466089729924533457960,
+ .470979715219073113985,
+ .475845904869856894947,
+ .480688529345570714212,
+ .485507815781602403149,
+ .490303988045525329653,
+ .495077266798034543171,
+ .499827869556611403822,
+ .504556010751912253908,
+ .509261901790523552335,
+ .513945751101346104405,
+ .518607764208354637958,
+ .523248143765158602036,
+ .527867089620485785417,
+ .532464798869114019908,
+ .537041465897345915436,
+ .541597282432121573947,
+ .546132437597407260909,
+ .550647117952394182793,
+ .555141507540611200965,
+ .559615787935399566777,
+ .564070138285387656651,
+ .568504735352689749561,
+ .572919753562018740922,
+ .577315365035246941260,
+ .581691739635061821900,
+ .586049045003164792433,
+ .590387446602107957005,
+ .594707107746216934174,
+ .599008189645246602594,
+ .603290851438941899687,
+ .607555250224322662688,
+ .611801541106615331955,
+ .616029877215623855590,
+ .620240409751204424537,
+ .624433288012369303032,
+ .628608659422752680256,
+ .632766669570628437213,
+ .636907462236194987781,
+ .641031179420679109171,
+ .645137961373620782978,
+ .649227946625615004450,
+ .653301272011958644725,
+ .657358072709030238911,
+ .661398482245203922502,
+ .665422632544505177065,
+ .669430653942981734871,
+ .673422675212350441142,
+ .677398823590920073911,
+ .681359224807238206267,
+ .685304003098281100392,
+ .689233281238557538017,
+ .693147180560117703862
+};
+
+static const double logF_tail[N+1] = {
+ 0.,
+ -.00000000000000543229938420049,
+ .00000000000000172745674997061,
+ -.00000000000001323017818229233,
+ -.00000000000001154527628289872,
+ -.00000000000000466529469958300,
+ .00000000000005148849572685810,
+ -.00000000000002532168943117445,
+ -.00000000000005213620639136504,
+ -.00000000000001819506003016881,
+ .00000000000006329065958724544,
+ .00000000000008614512936087814,
+ -.00000000000007355770219435028,
+ .00000000000009638067658552277,
+ .00000000000007598636597194141,
+ .00000000000002579999128306990,
+ -.00000000000004654729747598444,
+ -.00000000000007556920687451336,
+ .00000000000010195735223708472,
+ -.00000000000017319034406422306,
+ -.00000000000007718001336828098,
+ .00000000000010980754099855238,
+ -.00000000000002047235780046195,
+ -.00000000000008372091099235912,
+ .00000000000014088127937111135,
+ .00000000000012869017157588257,
+ .00000000000017788850778198106,
+ .00000000000006440856150696891,
+ .00000000000016132822667240822,
+ -.00000000000007540916511956188,
+ -.00000000000000036507188831790,
+ .00000000000009120937249914984,
+ .00000000000018567570959796010,
+ -.00000000000003149265065191483,
+ -.00000000000009309459495196889,
+ .00000000000017914338601329117,
+ -.00000000000001302979717330866,
+ .00000000000023097385217586939,
+ .00000000000023999540484211737,
+ .00000000000015393776174455408,
+ -.00000000000036870428315837678,
+ .00000000000036920375082080089,
+ -.00000000000009383417223663699,
+ .00000000000009433398189512690,
+ .00000000000041481318704258568,
+ -.00000000000003792316480209314,
+ .00000000000008403156304792424,
+ -.00000000000034262934348285429,
+ .00000000000043712191957429145,
+ -.00000000000010475750058776541,
+ -.00000000000011118671389559323,
+ .00000000000037549577257259853,
+ .00000000000013912841212197565,
+ .00000000000010775743037572640,
+ .00000000000029391859187648000,
+ -.00000000000042790509060060774,
+ .00000000000022774076114039555,
+ .00000000000010849569622967912,
+ -.00000000000023073801945705758,
+ .00000000000015761203773969435,
+ .00000000000003345710269544082,
+ -.00000000000041525158063436123,
+ .00000000000032655698896907146,
+ -.00000000000044704265010452446,
+ .00000000000034527647952039772,
+ -.00000000000007048962392109746,
+ .00000000000011776978751369214,
+ -.00000000000010774341461609578,
+ .00000000000021863343293215910,
+ .00000000000024132639491333131,
+ .00000000000039057462209830700,
+ -.00000000000026570679203560751,
+ .00000000000037135141919592021,
+ -.00000000000017166921336082431,
+ -.00000000000028658285157914353,
+ -.00000000000023812542263446809,
+ .00000000000006576659768580062,
+ -.00000000000028210143846181267,
+ .00000000000010701931762114254,
+ .00000000000018119346366441110,
+ .00000000000009840465278232627,
+ -.00000000000033149150282752542,
+ -.00000000000018302857356041668,
+ -.00000000000016207400156744949,
+ .00000000000048303314949553201,
+ -.00000000000071560553172382115,
+ .00000000000088821239518571855,
+ -.00000000000030900580513238244,
+ -.00000000000061076551972851496,
+ .00000000000035659969663347830,
+ .00000000000035782396591276383,
+ -.00000000000046226087001544578,
+ .00000000000062279762917225156,
+ .00000000000072838947272065741,
+ .00000000000026809646615211673,
+ -.00000000000010960825046059278,
+ .00000000000002311949383800537,
+ -.00000000000058469058005299247,
+ -.00000000000002103748251144494,
+ -.00000000000023323182945587408,
+ -.00000000000042333694288141916,
+ -.00000000000043933937969737844,
+ .00000000000041341647073835565,
+ .00000000000006841763641591466,
+ .00000000000047585534004430641,
+ .00000000000083679678674757695,
+ -.00000000000085763734646658640,
+ .00000000000021913281229340092,
+ -.00000000000062242842536431148,
+ -.00000000000010983594325438430,
+ .00000000000065310431377633651,
+ -.00000000000047580199021710769,
+ -.00000000000037854251265457040,
+ .00000000000040939233218678664,
+ .00000000000087424383914858291,
+ .00000000000025218188456842882,
+ -.00000000000003608131360422557,
+ -.00000000000050518555924280902,
+ .00000000000078699403323355317,
+ -.00000000000067020876961949060,
+ .00000000000016108575753932458,
+ .00000000000058527188436251509,
+ -.00000000000035246757297904791,
+ -.00000000000018372084495629058,
+ .00000000000088606689813494916,
+ .00000000000066486268071468700,
+ .00000000000063831615170646519,
+ .00000000000025144230728376072,
+ -.00000000000017239444525614834
+};
+
+/*
+ * Extra precision variant, returning struct {double a, b;};
+ * log(x) = a+b to 63 bits, with a rounded to 26 bits.
+ */
+struct Double
+__log__D(double x)
+{
+ int m, j;
+ double F, f, g, q, u, v, u2;
+ volatile double u1;
+ struct Double r;
+
+ /* Argument reduction: 1 <= g < 2; x/2^m = g; */
+ /* y = F*(1 + f/F) for |f| <= 2^-8 */
+
+ m = logb(x);
+ g = ldexp(x, -m);
+ if (m == -1022) {
+ j = logb(g), m += j;
+ g = ldexp(g, -j);
+ }
+ j = N*(g-1) + .5;
+ F = (1.0/N) * j + 1;
+ f = g - F;
+
+ g = 1/(2*F+f);
+ u = 2*f*g;
+ v = u*u;
+ q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
+ if (m | j)
+ u1 = u + 513, u1 -= 513;
+ else
+ u1 = u, TRUNC(u1);
+ u2 = (2.0*(f - F*u1) - u1*f) * g;
+
+ u1 += m*logF_head[N] + logF_head[j];
+
+ u2 += logF_tail[j]; u2 += q;
+ u2 += logF_tail[N]*m;
+ r.a = u1 + u2; /* Only difference is here */
+ TRUNC(r.a);
+ r.b = (u1 - r.a) + u2;
+ return (r);
+}
Index: src/lib/libm/src/b_tgamma.c
diff -u /dev/null src/lib/libm/src/b_tgamma.c:1.1
--- /dev/null Sat May 5 13:54:14 2012
+++ src/lib/libm/src/b_tgamma.c Sat May 5 13:54:14 2012
@@ -0,0 +1,317 @@
+/* $NetBSD: b_tgamma.c,v 1.1 2012/05/05 17:54:14 christos Exp $ */
+
+/*-
+ * Copyright (c) 1992, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+/* @(#)gamma.c 8.1 (Berkeley) 6/4/93 */
+#include <sys/cdefs.h>
+#if 0
+__FBSDID("$FreeBSD: release/9.0.0/lib/msun/bsdsrc/b_tgamma.c 176449 2008-02-22 02:26:51Z das $");
+#else
+__RCSID("$NetBSD: b_tgamma.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
+#endif
+
+/*
+ * This code by P. McIlroy, Oct 1992;
+ *
+ * The financial support of UUNET Communications Services is greatfully
+ * acknowledged.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/* METHOD:
+ * x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x))
+ * At negative integers, return NaN and raise invalid.
+ *
+ * x < 6.5:
+ * Use argument reduction G(x+1) = xG(x) to reach the
+ * range [1.066124,2.066124]. Use a rational
+ * approximation centered at the minimum (x0+1) to
+ * ensure monotonicity.
+ *
+ * x >= 6.5: Use the asymptotic approximation (Stirling's formula)
+ * adjusted for equal-ripples:
+ *
+ * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x))
+ *
+ * Keep extra precision in multiplying (x-.5)(log(x)-1), to
+ * avoid premature round-off.
+ *
+ * Special values:
+ * -Inf: return NaN and raise invalid;
+ * negative integer: return NaN and raise invalid;
+ * other x ~< 177.79: return +-0 and raise underflow;
+ * +-0: return +-Inf and raise divide-by-zero;
+ * finite x ~> 171.63: return +Inf and raise overflow;
+ * +Inf: return +Inf;
+ * NaN: return NaN.
+ *
+ * Accuracy: tgamma(x) is accurate to within
+ * x > 0: error provably < 0.9ulp.
+ * Maximum observed in 1,000,000 trials was .87ulp.
+ * x < 0:
+ * Maximum observed error < 4ulp in 1,000,000 trials.
+ */
+
+static double neg_gam(double);
+static double small_gam(double);
+static double smaller_gam(double);
+static struct Double large_gam(double);
+static struct Double ratfun_gam(double, double);
+
+/*
+ * Rational approximation, A0 + x*x*P(x)/Q(x), on the interval
+ * [1.066.., 2.066..] accurate to 4.25e-19.
+ */
+#define LEFT -.3955078125 /* left boundary for rat. approx */
+#define x0 .461632144968362356785 /* xmin - 1 */
+
+#define a0_hi 0.88560319441088874992
+#define a0_lo -.00000000000000004996427036469019695
+#define P0 6.21389571821820863029017800727e-01
+#define P1 2.65757198651533466104979197553e-01
+#define P2 5.53859446429917461063308081748e-03
+#define P3 1.38456698304096573887145282811e-03
+#define P4 2.40659950032711365819348969808e-03
+#define Q0 1.45019531250000000000000000000e+00
+#define Q1 1.06258521948016171343454061571e+00
+#define Q2 -2.07474561943859936441469926649e-01
+#define Q3 -1.46734131782005422506287573015e-01
+#define Q4 3.07878176156175520361557573779e-02
+#define Q5 5.12449347980666221336054633184e-03
+#define Q6 -1.76012741431666995019222898833e-03
+#define Q7 9.35021023573788935372153030556e-05
+#define Q8 6.13275507472443958924745652239e-06
+/*
+ * Constants for large x approximation (x in [6, Inf])
+ * (Accurate to 2.8*10^-19 absolute)
+ */
+#define lns2pi_hi 0.418945312500000
+#define lns2pi_lo -.000006779295327258219670263595
+#define Pa0 8.33333333333333148296162562474e-02
+#define Pa1 -2.77777777774548123579378966497e-03
+#define Pa2 7.93650778754435631476282786423e-04
+#define Pa3 -5.95235082566672847950717262222e-04
+#define Pa4 8.41428560346653702135821806252e-04
+#define Pa5 -1.89773526463879200348872089421e-03
+#define Pa6 5.69394463439411649408050664078e-03
+#define Pa7 -1.44705562421428915453880392761e-02
+
+static const double zero = 0., one = 1.0, tiny = 1e-300;
+
+double
+tgamma(double x)
+{
+ struct Double u;
+
+ if (x >= 6) {
+ if(x > 171.63)
+ return (x / zero);
+ u = large_gam(x);
+ return(__exp__D(u.a, u.b));
+ } else if (x >= 1.0 + LEFT + x0)
+ return (small_gam(x));
+ else if (x > 1.e-17)
+ return (smaller_gam(x));
+ else if (x > -1.e-17) {
+ if (x != 0.0)
+ u.a = one - tiny; /* raise inexact */
+ return (one/x);
+ } else if (!finite(x))
+ return (x - x); /* x is NaN or -Inf */
+ else
+ return (neg_gam(x));
+}
+/*
+ * Accurate to max(ulp(1/128) absolute, 2^-66 relative) error.
+ */
+static struct Double
+large_gam(double x)
+{
+ double z, p;
+ struct Double t, u, v;
+
+ z = one/(x*x);
+ p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7))))));
+ p = p/x;
+
+ u = __log__D(x);
+ u.a -= one;
+ v.a = (x -= .5);
+ TRUNC(v.a);
+ v.b = x - v.a;
+ t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */
+ t.b = v.b*u.a + x*u.b;
+ /* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */
+ t.b += lns2pi_lo; t.b += p;
+ u.a = lns2pi_hi + t.b; u.a += t.a;
+ u.b = t.a - u.a;
+ u.b += lns2pi_hi; u.b += t.b;
+ return (u);
+}
+/*
+ * Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.)
+ * It also has correct monotonicity.
+ */
+static double
+small_gam(double x)
+{
+ double y, ym1, t;
+ struct Double yy, r;
+ y = x - one;
+ ym1 = y - one;
+ if (y <= 1.0 + (LEFT + x0)) {
+ yy = ratfun_gam(y - x0, 0);
+ return (yy.a + yy.b);
+ }
+ r.a = y;
+ TRUNC(r.a);
+ yy.a = r.a - one;
+ y = ym1;
+ yy.b = r.b = y - yy.a;
+ /* Argument reduction: G(x+1) = x*G(x) */
+ for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) {
+ t = r.a*yy.a;
+ r.b = r.a*yy.b + y*r.b;
+ r.a = t;
+ TRUNC(r.a);
+ r.b += (t - r.a);
+ }
+ /* Return r*tgamma(y). */
+ yy = ratfun_gam(y - x0, 0);
+ y = r.b*(yy.a + yy.b) + r.a*yy.b;
+ y += yy.a*r.a;
+ return (y);
+}
+/*
+ * Good on (0, 1+x0+LEFT]. Accurate to 1ulp.
+ */
+static double
+smaller_gam(double x)
+{
+ double t, d;
+ struct Double r, xx;
+ if (x < x0 + LEFT) {
+ t = x, TRUNC(t);
+ d = (t+x)*(x-t);
+ t *= t;
+ xx.a = (t + x), TRUNC(xx.a);
+ xx.b = x - xx.a; xx.b += t; xx.b += d;
+ t = (one-x0); t += x;
+ d = (one-x0); d -= t; d += x;
+ x = xx.a + xx.b;
+ } else {
+ xx.a = x, TRUNC(xx.a);
+ xx.b = x - xx.a;
+ t = x - x0;
+ d = (-x0 -t); d += x;
+ }
+ r = ratfun_gam(t, d);
+ d = r.a/x, TRUNC(d);
+ r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b;
+ return (d + r.a/x);
+}
+/*
+ * returns (z+c)^2 * P(z)/Q(z) + a0
+ */
+static struct Double
+ratfun_gam(double z, double c)
+{
+ double p, q;
+ struct Double r, t;
+
+ q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8)))))));
+ p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4)));
+
+ /* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */
+ p = p/q;
+ t.a = z, TRUNC(t.a); /* t ~= z + c */
+ t.b = (z - t.a) + c;
+ t.b *= (t.a + z);
+ q = (t.a *= t.a); /* t = (z+c)^2 */
+ TRUNC(t.a);
+ t.b += (q - t.a);
+ r.a = p, TRUNC(r.a); /* r = P/Q */
+ r.b = p - r.a;
+ t.b = t.b*p + t.a*r.b + a0_lo;
+ t.a *= r.a; /* t = (z+c)^2*(P/Q) */
+ r.a = t.a + a0_hi, TRUNC(r.a);
+ r.b = ((a0_hi-r.a) + t.a) + t.b;
+ return (r); /* r = a0 + t */
+}
+
+static double
+neg_gam(double x)
+{
+ int sgn = 1;
+ struct Double lg, lsine;
+ double y, z;
+
+ y = ceil(x);
+ if (y == x) /* Negative integer. */
+ return ((x - x) / zero);
+ z = y - x;
+ if (z > 0.5)
+ z = one - z;
+ y = 0.5 * y;
+ if (y == ceil(y))
+ sgn = -1;
+ if (z < .25)
+ z = sin(M_PI*z);
+ else
+ z = cos(M_PI*(0.5-z));
+ /* Special case: G(1-x) = Inf; G(x) may be nonzero. */
+ if (x < -170) {
+ if (x < -190)
+ return ((double)sgn*tiny*tiny);
+ y = one - x; /* exact: 128 < |x| < 255 */
+ lg = large_gam(y);
+ lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */
+ lg.a -= lsine.a; /* exact (opposite signs) */
+ lg.b -= lsine.b;
+ y = -(lg.a + lg.b);
+ z = (y + lg.a) + lg.b;
+ y = __exp__D(y, z);
+ if (sgn < 0) y = -y;
+ return (y);
+ }
+ y = one-x;
+ if (one-y == x)
+ y = tgamma(y);
+ else /* 1-x is inexact */
+ y = -x*tgamma(-x);
+ if (sgn < 0) y = -y;
+ return (M_PI / (y*z));
+}
Index: src/lib/libm/src/s_tgammaf.c
diff -u /dev/null src/lib/libm/src/s_tgammaf.c:1.1
--- /dev/null Sat May 5 13:54:14 2012
+++ src/lib/libm/src/s_tgammaf.c Sat May 5 13:54:14 2012
@@ -0,0 +1,47 @@
+/*-
+ * Copyright (c) 2008 David Schultz <d...@freebsd.org>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include <sys/cdefs.h>
+#if 0
+__FBSDID("$FreeBSD: release/9.0.0/lib/msun/src/s_tgammaf.c 176388 2008-02-18 17:27:11Z das $");
+#else
+__RCSID("$NetBSD: s_tgammaf.c,v 1.1 2012/05/05 17:54:14 christos Exp $");
+#endif
+
+#include <math.h>
+
+/*
+ * We simply call tgamma() rather than bloating the math library with
+ * a float-optimized version of it. The reason is that tgammaf() is
+ * essentially useless, since the function is superexponential and
+ * floats have very limited range.
+ */
+float
+tgammaf(float x)
+{
+
+ return (tgamma(x));
+}
