125c28e83SPiotr Jasiukajtis /*
225c28e83SPiotr Jasiukajtis * CDDL HEADER START
325c28e83SPiotr Jasiukajtis *
425c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the
525c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License").
625c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License.
725c28e83SPiotr Jasiukajtis *
825c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
925c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
1025c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions
1125c28e83SPiotr Jasiukajtis * and limitations under the License.
1225c28e83SPiotr Jasiukajtis *
1325c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
1425c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
1525c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
1625c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
1725c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
1825c28e83SPiotr Jasiukajtis *
1925c28e83SPiotr Jasiukajtis * CDDL HEADER END
2025c28e83SPiotr Jasiukajtis */
2125c28e83SPiotr Jasiukajtis
2225c28e83SPiotr Jasiukajtis /*
2325c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
2425c28e83SPiotr Jasiukajtis */
2525c28e83SPiotr Jasiukajtis /*
2625c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
2725c28e83SPiotr Jasiukajtis * Use is subject to license terms.
2825c28e83SPiotr Jasiukajtis */
2925c28e83SPiotr Jasiukajtis
30*ddc0e0b5SRichard Lowe #pragma weak __tgammaf = tgammaf
3125c28e83SPiotr Jasiukajtis
3225c28e83SPiotr Jasiukajtis /*
3325c28e83SPiotr Jasiukajtis * True gamma function
3425c28e83SPiotr Jasiukajtis *
3525c28e83SPiotr Jasiukajtis * float tgammaf(float x)
3625c28e83SPiotr Jasiukajtis *
3725c28e83SPiotr Jasiukajtis * Algorithm: see tgamma.c
3825c28e83SPiotr Jasiukajtis *
3925c28e83SPiotr Jasiukajtis * Maximum error observed: 0.87ulp (both positive and negative arguments)
4025c28e83SPiotr Jasiukajtis */
4125c28e83SPiotr Jasiukajtis
4225c28e83SPiotr Jasiukajtis #include "libm.h"
4325c28e83SPiotr Jasiukajtis #include <math.h>
4425c28e83SPiotr Jasiukajtis #if defined(__SUNPRO_C)
4525c28e83SPiotr Jasiukajtis #include <sunmath.h>
4625c28e83SPiotr Jasiukajtis #endif
4725c28e83SPiotr Jasiukajtis #include <sys/isa_defs.h>
4825c28e83SPiotr Jasiukajtis
4925c28e83SPiotr Jasiukajtis #if defined(_BIG_ENDIAN)
5025c28e83SPiotr Jasiukajtis #define HIWORD 0
5125c28e83SPiotr Jasiukajtis #define LOWORD 1
5225c28e83SPiotr Jasiukajtis #else
5325c28e83SPiotr Jasiukajtis #define HIWORD 1
5425c28e83SPiotr Jasiukajtis #define LOWORD 0
5525c28e83SPiotr Jasiukajtis #endif
5625c28e83SPiotr Jasiukajtis #define __HI(x) ((int *) &x)[HIWORD]
5725c28e83SPiotr Jasiukajtis #define __LO(x) ((unsigned *) &x)[LOWORD]
5825c28e83SPiotr Jasiukajtis
5925c28e83SPiotr Jasiukajtis /* Coefficients for primary intervals GTi() */
6025c28e83SPiotr Jasiukajtis static const double cr[] = {
6125c28e83SPiotr Jasiukajtis /* p1 */
6225c28e83SPiotr Jasiukajtis +7.09087253435088360271451613398019280077561279443e-0001,
6325c28e83SPiotr Jasiukajtis -5.17229560788652108545141978238701790105241761089e-0001,
6425c28e83SPiotr Jasiukajtis +5.23403394528150789405825222323770647162337764327e-0001,
6525c28e83SPiotr Jasiukajtis -4.54586308717075010784041566069480411732634814899e-0001,
6625c28e83SPiotr Jasiukajtis +4.20596490915239085459964590559256913498190955233e-0001,
6725c28e83SPiotr Jasiukajtis -3.57307589712377520978332185838241458642142185789e-0001,
6825c28e83SPiotr Jasiukajtis
6925c28e83SPiotr Jasiukajtis /* p2 */
7025c28e83SPiotr Jasiukajtis +4.28486983980295198166056119223984284434264344578e-0001,
7125c28e83SPiotr Jasiukajtis -1.30704539487709138528680121627899735386650103914e-0001,
7225c28e83SPiotr Jasiukajtis +1.60856285038051955072861219352655851542955430871e-0001,
7325c28e83SPiotr Jasiukajtis -9.22285161346010583774458802067371182158937943507e-0002,
7425c28e83SPiotr Jasiukajtis +7.19240511767225260740890292605070595560626179357e-0002,
7525c28e83SPiotr Jasiukajtis -4.88158265593355093703112238534484636193260459574e-0002,
7625c28e83SPiotr Jasiukajtis
7725c28e83SPiotr Jasiukajtis /* p3 */
7825c28e83SPiotr Jasiukajtis +3.82409531118807759081121479786092134814808872880e-0001,
7925c28e83SPiotr Jasiukajtis +2.65309888180188647956400403013495759365167853426e-0002,
8025c28e83SPiotr Jasiukajtis +8.06815109775079171923561169415370309376296739835e-0002,
8125c28e83SPiotr Jasiukajtis -1.54821591666137613928840890835174351674007764799e-0002,
8225c28e83SPiotr Jasiukajtis +1.76308239242717268530498313416899188157165183405e-0002,
8325c28e83SPiotr Jasiukajtis
8425c28e83SPiotr Jasiukajtis /* GZi and TZi */
8525c28e83SPiotr Jasiukajtis +0.9382046279096824494097535615803269576988, /* GZ1 */
8625c28e83SPiotr Jasiukajtis +0.8856031944108887002788159005825887332080, /* GZ2 */
8725c28e83SPiotr Jasiukajtis +0.9367814114636523216188468970808378497426, /* GZ3 */
8825c28e83SPiotr Jasiukajtis -0.3517214357852935791015625, /* TZ1 */
8925c28e83SPiotr Jasiukajtis +0.280530631542205810546875, /* TZ3 */
9025c28e83SPiotr Jasiukajtis };
9125c28e83SPiotr Jasiukajtis
9225c28e83SPiotr Jasiukajtis #define P10 cr[0]
9325c28e83SPiotr Jasiukajtis #define P11 cr[1]
9425c28e83SPiotr Jasiukajtis #define P12 cr[2]
9525c28e83SPiotr Jasiukajtis #define P13 cr[3]
9625c28e83SPiotr Jasiukajtis #define P14 cr[4]
9725c28e83SPiotr Jasiukajtis #define P15 cr[5]
9825c28e83SPiotr Jasiukajtis #define P20 cr[6]
9925c28e83SPiotr Jasiukajtis #define P21 cr[7]
10025c28e83SPiotr Jasiukajtis #define P22 cr[8]
10125c28e83SPiotr Jasiukajtis #define P23 cr[9]
10225c28e83SPiotr Jasiukajtis #define P24 cr[10]
10325c28e83SPiotr Jasiukajtis #define P25 cr[11]
10425c28e83SPiotr Jasiukajtis #define P30 cr[12]
10525c28e83SPiotr Jasiukajtis #define P31 cr[13]
10625c28e83SPiotr Jasiukajtis #define P32 cr[14]
10725c28e83SPiotr Jasiukajtis #define P33 cr[15]
10825c28e83SPiotr Jasiukajtis #define P34 cr[16]
10925c28e83SPiotr Jasiukajtis #define GZ1 cr[17]
11025c28e83SPiotr Jasiukajtis #define GZ2 cr[18]
11125c28e83SPiotr Jasiukajtis #define GZ3 cr[19]
11225c28e83SPiotr Jasiukajtis #define TZ1 cr[20]
11325c28e83SPiotr Jasiukajtis #define TZ3 cr[21]
11425c28e83SPiotr Jasiukajtis
11525c28e83SPiotr Jasiukajtis /* compute gamma(y) for y in GT1 = [1.0000, 1.2845] */
11625c28e83SPiotr Jasiukajtis static double
GT1(double y)11725c28e83SPiotr Jasiukajtis GT1(double y) {
11825c28e83SPiotr Jasiukajtis double z, r;
11925c28e83SPiotr Jasiukajtis
12025c28e83SPiotr Jasiukajtis z = y * y;
12125c28e83SPiotr Jasiukajtis r = TZ1 * y + z * ((P10 + y * P11 + z * P12) + (z * y) * (P13 + y *
12225c28e83SPiotr Jasiukajtis P14 + z * P15));
12325c28e83SPiotr Jasiukajtis return (GZ1 + r);
12425c28e83SPiotr Jasiukajtis }
12525c28e83SPiotr Jasiukajtis
12625c28e83SPiotr Jasiukajtis /* compute gamma(y) for y in GT2 = [1.2844, 1.6374] */
12725c28e83SPiotr Jasiukajtis static double
GT2(double y)12825c28e83SPiotr Jasiukajtis GT2(double y) {
12925c28e83SPiotr Jasiukajtis double z;
13025c28e83SPiotr Jasiukajtis
13125c28e83SPiotr Jasiukajtis z = y * y;
13225c28e83SPiotr Jasiukajtis return (GZ2 + z * ((P20 + y * P21 + z * P22) + (z * y) * (P23 + y *
13325c28e83SPiotr Jasiukajtis P24 + z * P25)));
13425c28e83SPiotr Jasiukajtis }
13525c28e83SPiotr Jasiukajtis
13625c28e83SPiotr Jasiukajtis /* compute gamma(y) for y in GT3 = [1.6373, 2.0000] */
13725c28e83SPiotr Jasiukajtis static double
GT3(double y)13825c28e83SPiotr Jasiukajtis GT3(double y) {
13925c28e83SPiotr Jasiukajtis double z, r;
14025c28e83SPiotr Jasiukajtis
14125c28e83SPiotr Jasiukajtis z = y * y;
14225c28e83SPiotr Jasiukajtis r = TZ3 * y + z * ((P30 + y * P31 + z * P32) + (z * y) * (P33 + y *
14325c28e83SPiotr Jasiukajtis P34));
14425c28e83SPiotr Jasiukajtis return (GZ3 + r);
14525c28e83SPiotr Jasiukajtis }
14625c28e83SPiotr Jasiukajtis
14725c28e83SPiotr Jasiukajtis /* INDENT OFF */
14825c28e83SPiotr Jasiukajtis static const double c[] = {
14925c28e83SPiotr Jasiukajtis +1.0,
15025c28e83SPiotr Jasiukajtis +2.0,
15125c28e83SPiotr Jasiukajtis +0.5,
15225c28e83SPiotr Jasiukajtis +1.0e-300,
15325c28e83SPiotr Jasiukajtis +6.666717231848518054693623697539230e-0001, /* A1=T3[0] */
15425c28e83SPiotr Jasiukajtis +8.33333330959694065245736888749042811909994573178e-0002, /* GP[0] */
15525c28e83SPiotr Jasiukajtis -2.77765545601667179767706600890361535225507762168e-0003, /* GP[1] */
15625c28e83SPiotr Jasiukajtis +7.77830853479775281781085278324621033523037489883e-0004, /* GP[2] */
15725c28e83SPiotr Jasiukajtis +4.18938533204672741744150788368695779923320328369e-0001, /* hln2pi */
15825c28e83SPiotr Jasiukajtis +2.16608493924982901946e-02, /* ln2_32 */
15925c28e83SPiotr Jasiukajtis +4.61662413084468283841e+01, /* invln2_32 */
16025c28e83SPiotr Jasiukajtis +5.00004103388988968841156421415669985414073453720e-0001, /* Et1 */
16125c28e83SPiotr Jasiukajtis +1.66667656752800761782778277828110208108687545908e-0001, /* Et2 */
16225c28e83SPiotr Jasiukajtis };
16325c28e83SPiotr Jasiukajtis
16425c28e83SPiotr Jasiukajtis #define one c[0]
16525c28e83SPiotr Jasiukajtis #define two c[1]
16625c28e83SPiotr Jasiukajtis #define half c[2]
16725c28e83SPiotr Jasiukajtis #define tiny c[3]
16825c28e83SPiotr Jasiukajtis #define A1 c[4]
16925c28e83SPiotr Jasiukajtis #define GP0 c[5]
17025c28e83SPiotr Jasiukajtis #define GP1 c[6]
17125c28e83SPiotr Jasiukajtis #define GP2 c[7]
17225c28e83SPiotr Jasiukajtis #define hln2pi c[8]
17325c28e83SPiotr Jasiukajtis #define ln2_32 c[9]
17425c28e83SPiotr Jasiukajtis #define invln2_32 c[10]
17525c28e83SPiotr Jasiukajtis #define Et1 c[11]
17625c28e83SPiotr Jasiukajtis #define Et2 c[12]
17725c28e83SPiotr Jasiukajtis
17825c28e83SPiotr Jasiukajtis /* S[j] = 2**(j/32.) for the final computation of exp(w) */
17925c28e83SPiotr Jasiukajtis static const double S[] = {
18025c28e83SPiotr Jasiukajtis +1.00000000000000000000e+00, /* 3FF0000000000000 */
18125c28e83SPiotr Jasiukajtis +1.02189714865411662714e+00, /* 3FF059B0D3158574 */
18225c28e83SPiotr Jasiukajtis +1.04427378242741375480e+00, /* 3FF0B5586CF9890F */
18325c28e83SPiotr Jasiukajtis +1.06714040067682369717e+00, /* 3FF11301D0125B51 */
18425c28e83SPiotr Jasiukajtis +1.09050773266525768967e+00, /* 3FF172B83C7D517B */
18525c28e83SPiotr Jasiukajtis +1.11438674259589243221e+00, /* 3FF1D4873168B9AA */
18625c28e83SPiotr Jasiukajtis +1.13878863475669156458e+00, /* 3FF2387A6E756238 */
18725c28e83SPiotr Jasiukajtis +1.16372485877757747552e+00, /* 3FF29E9DF51FDEE1 */
18825c28e83SPiotr Jasiukajtis +1.18920711500272102690e+00, /* 3FF306FE0A31B715 */
18925c28e83SPiotr Jasiukajtis +1.21524735998046895524e+00, /* 3FF371A7373AA9CB */
19025c28e83SPiotr Jasiukajtis +1.24185781207348400201e+00, /* 3FF3DEA64C123422 */
19125c28e83SPiotr Jasiukajtis +1.26905095719173321989e+00, /* 3FF44E086061892D */
19225c28e83SPiotr Jasiukajtis +1.29683955465100964055e+00, /* 3FF4BFDAD5362A27 */
19325c28e83SPiotr Jasiukajtis +1.32523664315974132322e+00, /* 3FF5342B569D4F82 */
19425c28e83SPiotr Jasiukajtis +1.35425554693689265129e+00, /* 3FF5AB07DD485429 */
19525c28e83SPiotr Jasiukajtis +1.38390988196383202258e+00, /* 3FF6247EB03A5585 */
19625c28e83SPiotr Jasiukajtis +1.41421356237309514547e+00, /* 3FF6A09E667F3BCD */
19725c28e83SPiotr Jasiukajtis +1.44518080697704665027e+00, /* 3FF71F75E8EC5F74 */
19825c28e83SPiotr Jasiukajtis +1.47682614593949934623e+00, /* 3FF7A11473EB0187 */
19925c28e83SPiotr Jasiukajtis +1.50916442759342284141e+00, /* 3FF82589994CCE13 */
20025c28e83SPiotr Jasiukajtis +1.54221082540794074411e+00, /* 3FF8ACE5422AA0DB */
20125c28e83SPiotr Jasiukajtis +1.57598084510788649659e+00, /* 3FF93737B0CDC5E5 */
20225c28e83SPiotr Jasiukajtis +1.61049033194925428347e+00, /* 3FF9C49182A3F090 */
20325c28e83SPiotr Jasiukajtis +1.64575547815396494578e+00, /* 3FFA5503B23E255D */
20425c28e83SPiotr Jasiukajtis +1.68179283050742900407e+00, /* 3FFAE89F995AD3AD */
20525c28e83SPiotr Jasiukajtis +1.71861929812247793414e+00, /* 3FFB7F76F2FB5E47 */
20625c28e83SPiotr Jasiukajtis +1.75625216037329945351e+00, /* 3FFC199BDD85529C */
20725c28e83SPiotr Jasiukajtis +1.79470907500310716820e+00, /* 3FFCB720DCEF9069 */
20825c28e83SPiotr Jasiukajtis +1.83400808640934243066e+00, /* 3FFD5818DCFBA487 */
20925c28e83SPiotr Jasiukajtis +1.87416763411029996256e+00, /* 3FFDFC97337B9B5F */
21025c28e83SPiotr Jasiukajtis +1.91520656139714740007e+00, /* 3FFEA4AFA2A490DA */
21125c28e83SPiotr Jasiukajtis +1.95714412417540017941e+00, /* 3FFF50765B6E4540 */
21225c28e83SPiotr Jasiukajtis };
21325c28e83SPiotr Jasiukajtis /* INDENT ON */
21425c28e83SPiotr Jasiukajtis
21525c28e83SPiotr Jasiukajtis /* INDENT OFF */
21625c28e83SPiotr Jasiukajtis /*
21725c28e83SPiotr Jasiukajtis * return tgammaf(x) in double for 8<x<=35.040096283... using Stirling's formula
21825c28e83SPiotr Jasiukajtis * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + (1/x)*P(1/(x*x))
21925c28e83SPiotr Jasiukajtis */
22025c28e83SPiotr Jasiukajtis /*
22125c28e83SPiotr Jasiukajtis * compute ss = log(x)-1
22225c28e83SPiotr Jasiukajtis *
22325c28e83SPiotr Jasiukajtis * log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y, 1<=y<2,
22425c28e83SPiotr Jasiukajtis * j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
22525c28e83SPiotr Jasiukajtis * T1(n-3) = n*log(2)-1, n=3,4,5
22625c28e83SPiotr Jasiukajtis * T2(j) = log(z[j]),
22725c28e83SPiotr Jasiukajtis * T3(s) = 2s + A1*s^3
22825c28e83SPiotr Jasiukajtis * Note
22925c28e83SPiotr Jasiukajtis * (1) Remez error for T3(s) is bounded by 2**(-35.8)
23025c28e83SPiotr Jasiukajtis * (see mpremez/work/Log/tgamma_log_2_outr1)
23125c28e83SPiotr Jasiukajtis */
23225c28e83SPiotr Jasiukajtis
23325c28e83SPiotr Jasiukajtis static const double T1[] = { /* T1[j]=(j+3)*log(2)-1 */
23425c28e83SPiotr Jasiukajtis +1.079441541679835928251696364375e+00,
23525c28e83SPiotr Jasiukajtis +1.772588722239781237668928485833e+00,
23625c28e83SPiotr Jasiukajtis +2.465735902799726547086160607291e+00,
23725c28e83SPiotr Jasiukajtis };
23825c28e83SPiotr Jasiukajtis
23925c28e83SPiotr Jasiukajtis static const double T2[] = { /* T2[j]=log(1+j/64+1/128) */
24025c28e83SPiotr Jasiukajtis +7.782140442054948947462900061137e-03,
24125c28e83SPiotr Jasiukajtis +2.316705928153437822879916096229e-02,
24225c28e83SPiotr Jasiukajtis +3.831886430213659919375532512380e-02,
24325c28e83SPiotr Jasiukajtis +5.324451451881228286587019378653e-02,
24425c28e83SPiotr Jasiukajtis +6.795066190850774939456527777263e-02,
24525c28e83SPiotr Jasiukajtis +8.244366921107459126816006866831e-02,
24625c28e83SPiotr Jasiukajtis +9.672962645855111229557105648746e-02,
24725c28e83SPiotr Jasiukajtis +1.108143663402901141948061693232e-01,
24825c28e83SPiotr Jasiukajtis +1.247034785009572358634065153809e-01,
24925c28e83SPiotr Jasiukajtis +1.384023228591191356853258736016e-01,
25025c28e83SPiotr Jasiukajtis +1.519160420258419750718034248969e-01,
25125c28e83SPiotr Jasiukajtis +1.652495728953071628756114492772e-01,
25225c28e83SPiotr Jasiukajtis +1.784076574728182971194002415109e-01,
25325c28e83SPiotr Jasiukajtis +1.913948529996294546092988075613e-01,
25425c28e83SPiotr Jasiukajtis +2.042155414286908915038203861962e-01,
25525c28e83SPiotr Jasiukajtis +2.168739383006143596190895257443e-01,
25625c28e83SPiotr Jasiukajtis +2.293741010648458299914807250461e-01,
25725c28e83SPiotr Jasiukajtis +2.417199368871451681443075159135e-01,
25825c28e83SPiotr Jasiukajtis +2.539152099809634441373232979066e-01,
25925c28e83SPiotr Jasiukajtis +2.659635484971379413391259265375e-01,
26025c28e83SPiotr Jasiukajtis +2.778684510034563061863500329234e-01,
26125c28e83SPiotr Jasiukajtis +2.896332925830426768788930555257e-01,
26225c28e83SPiotr Jasiukajtis +3.012613305781617810128755382338e-01,
26325c28e83SPiotr Jasiukajtis +3.127557100038968883862465596883e-01,
26425c28e83SPiotr Jasiukajtis +3.241194686542119760906707604350e-01,
26525c28e83SPiotr Jasiukajtis +3.353555419211378302571795798142e-01,
26625c28e83SPiotr Jasiukajtis +3.464667673462085809184621884258e-01,
26725c28e83SPiotr Jasiukajtis +3.574558889218037742260094901409e-01,
26825c28e83SPiotr Jasiukajtis +3.683255611587076530482301540504e-01,
26925c28e83SPiotr Jasiukajtis +3.790783529349694583908533456310e-01,
27025c28e83SPiotr Jasiukajtis +3.897167511400252133704636040035e-01,
27125c28e83SPiotr Jasiukajtis +4.002431641270127069293251019951e-01,
27225c28e83SPiotr Jasiukajtis +4.106599249852683859343062031758e-01,
27325c28e83SPiotr Jasiukajtis +4.209692946441296361288671615068e-01,
27425c28e83SPiotr Jasiukajtis +4.311734648183713408591724789556e-01,
27525c28e83SPiotr Jasiukajtis +4.412745608048752294894964416613e-01,
27625c28e83SPiotr Jasiukajtis +4.512746441394585851446923830790e-01,
27725c28e83SPiotr Jasiukajtis +4.611757151221701663679999255979e-01,
27825c28e83SPiotr Jasiukajtis +4.709797152187910125468978560564e-01,
27925c28e83SPiotr Jasiukajtis +4.806885293457519076766184554480e-01,
28025c28e83SPiotr Jasiukajtis +4.903039880451938381503461596457e-01,
28125c28e83SPiotr Jasiukajtis +4.998278695564493298213314152470e-01,
28225c28e83SPiotr Jasiukajtis +5.092619017898079468040749192283e-01,
28325c28e83SPiotr Jasiukajtis +5.186077642080456321529769963648e-01,
28425c28e83SPiotr Jasiukajtis +5.278670896208423851138922177783e-01,
28525c28e83SPiotr Jasiukajtis +5.370414658968836545667292441538e-01,
28625c28e83SPiotr Jasiukajtis +5.461324375981356503823972092312e-01,
28725c28e83SPiotr Jasiukajtis +5.551415075405015927154803595159e-01,
28825c28e83SPiotr Jasiukajtis +5.640701382848029660713842900902e-01,
28925c28e83SPiotr Jasiukajtis +5.729197535617855090927567266263e-01,
29025c28e83SPiotr Jasiukajtis +5.816917396346224825206107537254e-01,
29125c28e83SPiotr Jasiukajtis +5.903874466021763746419167081236e-01,
29225c28e83SPiotr Jasiukajtis +5.990081896460833993816000244617e-01,
29325c28e83SPiotr Jasiukajtis +6.075552502245417955010851527911e-01,
29425c28e83SPiotr Jasiukajtis +6.160298772155140196475659281967e-01,
29525c28e83SPiotr Jasiukajtis +6.244332880118935010425387440547e-01,
29625c28e83SPiotr Jasiukajtis +6.327666695710378295457864685036e-01,
29725c28e83SPiotr Jasiukajtis +6.410311794209312910556013344054e-01,
29825c28e83SPiotr Jasiukajtis +6.492279466251098188908399699053e-01,
29925c28e83SPiotr Jasiukajtis +6.573580727083600301418900232459e-01,
30025c28e83SPiotr Jasiukajtis +6.654226325450904489500926100067e-01,
30125c28e83SPiotr Jasiukajtis +6.734226752121667202979603888010e-01,
30225c28e83SPiotr Jasiukajtis +6.813592248079030689480715595681e-01,
30325c28e83SPiotr Jasiukajtis +6.892332812388089803249143378146e-01,
30425c28e83SPiotr Jasiukajtis };
30525c28e83SPiotr Jasiukajtis /* INDENT ON */
30625c28e83SPiotr Jasiukajtis
30725c28e83SPiotr Jasiukajtis static double
large_gam(double x)30825c28e83SPiotr Jasiukajtis large_gam(double x) {
30925c28e83SPiotr Jasiukajtis double ss, zz, z, t1, t2, w, y, u;
31025c28e83SPiotr Jasiukajtis unsigned lx;
31125c28e83SPiotr Jasiukajtis int k, ix, j, m;
31225c28e83SPiotr Jasiukajtis
31325c28e83SPiotr Jasiukajtis ix = __HI(x);
31425c28e83SPiotr Jasiukajtis lx = __LO(x);
31525c28e83SPiotr Jasiukajtis m = (ix >> 20) - 0x3ff; /* exponent of x, range:3-5 */
31625c28e83SPiotr Jasiukajtis ix = (ix & 0x000fffff) | 0x3ff00000; /* y = scale x to [1,2] */
31725c28e83SPiotr Jasiukajtis __HI(y) = ix;
31825c28e83SPiotr Jasiukajtis __LO(y) = lx;
31925c28e83SPiotr Jasiukajtis __HI(z) = (ix & 0xffffc000) | 0x2000; /* z[j]=1+j/64+1/128 */
32025c28e83SPiotr Jasiukajtis __LO(z) = 0;
32125c28e83SPiotr Jasiukajtis j = (ix >> 14) & 0x3f;
32225c28e83SPiotr Jasiukajtis t1 = y + z;
32325c28e83SPiotr Jasiukajtis t2 = y - z;
32425c28e83SPiotr Jasiukajtis u = t2 / t1;
32525c28e83SPiotr Jasiukajtis ss = T1[m - 3] + T2[j] + u * (two + A1 * (u * u));
32625c28e83SPiotr Jasiukajtis /* ss = log(x)-1 */
32725c28e83SPiotr Jasiukajtis /*
32825c28e83SPiotr Jasiukajtis * compute ww = (x-.5)*(log(x)-1) + .5*(log(2pi)-1) + 1/x*(P(1/x^2)))
32925c28e83SPiotr Jasiukajtis * where ss = log(x) - 1
33025c28e83SPiotr Jasiukajtis */
33125c28e83SPiotr Jasiukajtis z = one / x;
33225c28e83SPiotr Jasiukajtis zz = z * z;
33325c28e83SPiotr Jasiukajtis w = ((x - half) * ss + hln2pi) + z * (GP0 + zz * GP1 + (zz * zz) * GP2);
33425c28e83SPiotr Jasiukajtis k = (int) (w * invln2_32 + half);
33525c28e83SPiotr Jasiukajtis
33625c28e83SPiotr Jasiukajtis /* compute the exponential of w */
33725c28e83SPiotr Jasiukajtis j = k & 0x1f;
33825c28e83SPiotr Jasiukajtis m = k >> 5;
33925c28e83SPiotr Jasiukajtis z = w - (double) k *ln2_32;
34025c28e83SPiotr Jasiukajtis zz = S[j] * (one + z + (z * z) * (Et1 + z * Et2));
34125c28e83SPiotr Jasiukajtis __HI(zz) += m << 20;
34225c28e83SPiotr Jasiukajtis return (zz);
34325c28e83SPiotr Jasiukajtis }
34425c28e83SPiotr Jasiukajtis /* INDENT OFF */
34525c28e83SPiotr Jasiukajtis /*
34625c28e83SPiotr Jasiukajtis * kpsin(x)= sin(pi*x)/pi
34725c28e83SPiotr Jasiukajtis * 3 5 7 9
34825c28e83SPiotr Jasiukajtis * = x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x
34925c28e83SPiotr Jasiukajtis */
35025c28e83SPiotr Jasiukajtis static const double ks[] = {
35125c28e83SPiotr Jasiukajtis -1.64493404985645811354476665052005342839447790544e+0000,
35225c28e83SPiotr Jasiukajtis +8.11740794458351064092797249069438269367389272270e-0001,
35325c28e83SPiotr Jasiukajtis -1.90703144603551216933075809162889536878854055202e-0001,
35425c28e83SPiotr Jasiukajtis +2.55742333994264563281155312271481108635575331201e-0002,
35525c28e83SPiotr Jasiukajtis };
35625c28e83SPiotr Jasiukajtis /* INDENT ON */
35725c28e83SPiotr Jasiukajtis
35825c28e83SPiotr Jasiukajtis static double
kpsin(double x)35925c28e83SPiotr Jasiukajtis kpsin(double x) {
36025c28e83SPiotr Jasiukajtis double z;
36125c28e83SPiotr Jasiukajtis
36225c28e83SPiotr Jasiukajtis z = x * x;
36325c28e83SPiotr Jasiukajtis return (x + (x * z) * ((ks[0] + z * ks[1]) + (z * z) * (ks[2] + z *
36425c28e83SPiotr Jasiukajtis ks[3])));
36525c28e83SPiotr Jasiukajtis }
36625c28e83SPiotr Jasiukajtis
36725c28e83SPiotr Jasiukajtis /* INDENT OFF */
36825c28e83SPiotr Jasiukajtis /*
36925c28e83SPiotr Jasiukajtis * kpcos(x)= cos(pi*x)/pi
37025c28e83SPiotr Jasiukajtis * 2 4 6
37125c28e83SPiotr Jasiukajtis * = kc[0]+kc[1]*x +kc[2]*x +kc[3]*x
37225c28e83SPiotr Jasiukajtis */
37325c28e83SPiotr Jasiukajtis static const double kc[] = {
37425c28e83SPiotr Jasiukajtis +3.18309886183790671537767526745028724068919291480e-0001,
37525c28e83SPiotr Jasiukajtis -1.57079581447762568199467875065854538626594937791e+0000,
37625c28e83SPiotr Jasiukajtis +1.29183528092558692844073004029568674027807393862e+0000,
37725c28e83SPiotr Jasiukajtis -4.20232949771307685981015914425195471602739075537e-0001,
37825c28e83SPiotr Jasiukajtis };
37925c28e83SPiotr Jasiukajtis /* INDENT ON */
38025c28e83SPiotr Jasiukajtis
38125c28e83SPiotr Jasiukajtis static double
kpcos(double x)38225c28e83SPiotr Jasiukajtis kpcos(double x) {
38325c28e83SPiotr Jasiukajtis double z;
38425c28e83SPiotr Jasiukajtis
38525c28e83SPiotr Jasiukajtis z = x * x;
38625c28e83SPiotr Jasiukajtis return (kc[0] + z * (kc[1] + z * kc[2] + (z * z) * kc[3]));
38725c28e83SPiotr Jasiukajtis }
38825c28e83SPiotr Jasiukajtis
38925c28e83SPiotr Jasiukajtis /* INDENT OFF */
39025c28e83SPiotr Jasiukajtis static const double
39125c28e83SPiotr Jasiukajtis t0z1 = 0.134861805732790769689793935774652917006,
39225c28e83SPiotr Jasiukajtis t0z2 = 0.461632144968362341262659542325721328468,
39325c28e83SPiotr Jasiukajtis t0z3 = 0.819773101100500601787868704921606996312;
39425c28e83SPiotr Jasiukajtis /* 1.134861805732790769689793935774652917006 */
39525c28e83SPiotr Jasiukajtis /* INDENT ON */
39625c28e83SPiotr Jasiukajtis
39725c28e83SPiotr Jasiukajtis /*
39825c28e83SPiotr Jasiukajtis * gamma(x+i) for 0 <= x < 1
39925c28e83SPiotr Jasiukajtis */
40025c28e83SPiotr Jasiukajtis static double
gam_n(int i,double x)40125c28e83SPiotr Jasiukajtis gam_n(int i, double x) {
40225c28e83SPiotr Jasiukajtis double rr = 0.0L, yy;
40325c28e83SPiotr Jasiukajtis double z1, z2;
40425c28e83SPiotr Jasiukajtis
40525c28e83SPiotr Jasiukajtis /* compute yy = gamma(x+1) */
40625c28e83SPiotr Jasiukajtis if (x > 0.2845) {
40725c28e83SPiotr Jasiukajtis if (x > 0.6374)
40825c28e83SPiotr Jasiukajtis yy = GT3(x - t0z3);
40925c28e83SPiotr Jasiukajtis else
41025c28e83SPiotr Jasiukajtis yy = GT2(x - t0z2);
41125c28e83SPiotr Jasiukajtis } else
41225c28e83SPiotr Jasiukajtis yy = GT1(x - t0z1);
41325c28e83SPiotr Jasiukajtis
41425c28e83SPiotr Jasiukajtis /* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */
41525c28e83SPiotr Jasiukajtis switch (i) {
41625c28e83SPiotr Jasiukajtis case 0: /* yy/x */
41725c28e83SPiotr Jasiukajtis rr = yy / x;
41825c28e83SPiotr Jasiukajtis break;
41925c28e83SPiotr Jasiukajtis case 1: /* yy */
42025c28e83SPiotr Jasiukajtis rr = yy;
42125c28e83SPiotr Jasiukajtis break;
42225c28e83SPiotr Jasiukajtis case 2: /* (x+1)*yy */
42325c28e83SPiotr Jasiukajtis rr = (x + one) * yy;
42425c28e83SPiotr Jasiukajtis break;
42525c28e83SPiotr Jasiukajtis case 3: /* (x+2)*(x+1)*yy */
42625c28e83SPiotr Jasiukajtis rr = (x + one) * (x + two) * yy;
42725c28e83SPiotr Jasiukajtis break;
42825c28e83SPiotr Jasiukajtis
42925c28e83SPiotr Jasiukajtis case 4: /* (x+1)*(x+3)*(x+2)*yy */
43025c28e83SPiotr Jasiukajtis rr = (x + one) * (x + two) * ((x + 3.0) * yy);
43125c28e83SPiotr Jasiukajtis break;
43225c28e83SPiotr Jasiukajtis case 5: /* ((x+1)*(x+4)*(x+2)*(x+3))*yy */
43325c28e83SPiotr Jasiukajtis z1 = (x + two) * (x + 3.0) * yy;
43425c28e83SPiotr Jasiukajtis z2 = (x + one) * (x + 4.0);
43525c28e83SPiotr Jasiukajtis rr = z1 * z2;
43625c28e83SPiotr Jasiukajtis break;
43725c28e83SPiotr Jasiukajtis case 6: /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5))*yy */
43825c28e83SPiotr Jasiukajtis z1 = (x + two) * (x + 3.0);
43925c28e83SPiotr Jasiukajtis z2 = (x + 5.0) * yy;
44025c28e83SPiotr Jasiukajtis rr = z1 * (z1 - two) * z2;
44125c28e83SPiotr Jasiukajtis break;
44225c28e83SPiotr Jasiukajtis case 7: /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5)*(x+6))*yy */
44325c28e83SPiotr Jasiukajtis z1 = (x + two) * (x + 3.0);
44425c28e83SPiotr Jasiukajtis z2 = (x + 5.0) * (x + 6.0) * yy;
44525c28e83SPiotr Jasiukajtis rr = z1 * (z1 - two) * z2;
44625c28e83SPiotr Jasiukajtis break;
44725c28e83SPiotr Jasiukajtis }
44825c28e83SPiotr Jasiukajtis return (rr);
44925c28e83SPiotr Jasiukajtis }
45025c28e83SPiotr Jasiukajtis
45125c28e83SPiotr Jasiukajtis float
tgammaf(float xf)45225c28e83SPiotr Jasiukajtis tgammaf(float xf) {
45325c28e83SPiotr Jasiukajtis float zf;
45425c28e83SPiotr Jasiukajtis double ss, ww;
45525c28e83SPiotr Jasiukajtis double x, y, z;
45625c28e83SPiotr Jasiukajtis int i, j, k, ix, hx, xk;
45725c28e83SPiotr Jasiukajtis
45825c28e83SPiotr Jasiukajtis hx = *(int *) &xf;
45925c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff;
46025c28e83SPiotr Jasiukajtis
46125c28e83SPiotr Jasiukajtis x = (double) xf;
46225c28e83SPiotr Jasiukajtis if (ix < 0x33800000)
46325c28e83SPiotr Jasiukajtis return (1.0F / xf); /* |x| < 2**-24 */
46425c28e83SPiotr Jasiukajtis
46525c28e83SPiotr Jasiukajtis if (ix >= 0x7f800000)
46625c28e83SPiotr Jasiukajtis return (xf * ((hx < 0)? 0.0F : xf)); /* +-Inf or NaN */
46725c28e83SPiotr Jasiukajtis
46825c28e83SPiotr Jasiukajtis if (hx > 0x420C290F) /* x > 35.040096283... overflow */
46925c28e83SPiotr Jasiukajtis return (float)(x / tiny);
47025c28e83SPiotr Jasiukajtis
47125c28e83SPiotr Jasiukajtis if (hx >= 0x41000000) /* x >= 8 */
47225c28e83SPiotr Jasiukajtis return ((float) large_gam(x));
47325c28e83SPiotr Jasiukajtis
47425c28e83SPiotr Jasiukajtis if (hx > 0) { /* 0 < x < 8 */
47525c28e83SPiotr Jasiukajtis i = (int) xf;
47625c28e83SPiotr Jasiukajtis return ((float) gam_n(i, x - (double) i));
47725c28e83SPiotr Jasiukajtis }
47825c28e83SPiotr Jasiukajtis
47925c28e83SPiotr Jasiukajtis /* negative x */
48025c28e83SPiotr Jasiukajtis /* INDENT OFF */
48125c28e83SPiotr Jasiukajtis /*
48225c28e83SPiotr Jasiukajtis * compute xk =
48325c28e83SPiotr Jasiukajtis * -2 ... x is an even int (-inf is considered even)
48425c28e83SPiotr Jasiukajtis * -1 ... x is an odd int
48525c28e83SPiotr Jasiukajtis * +0 ... x is not an int but chopped to an even int
48625c28e83SPiotr Jasiukajtis * +1 ... x is not an int but chopped to an odd int
48725c28e83SPiotr Jasiukajtis */
48825c28e83SPiotr Jasiukajtis /* INDENT ON */
48925c28e83SPiotr Jasiukajtis xk = 0;
49025c28e83SPiotr Jasiukajtis if (ix >= 0x4b000000) {
49125c28e83SPiotr Jasiukajtis if (ix > 0x4b000000)
49225c28e83SPiotr Jasiukajtis xk = -2;
49325c28e83SPiotr Jasiukajtis else
49425c28e83SPiotr Jasiukajtis xk = -2 + (ix & 1);
49525c28e83SPiotr Jasiukajtis } else if (ix >= 0x3f800000) {
49625c28e83SPiotr Jasiukajtis k = (ix >> 23) - 0x7f;
49725c28e83SPiotr Jasiukajtis j = ix >> (23 - k);
49825c28e83SPiotr Jasiukajtis if ((j << (23 - k)) == ix)
49925c28e83SPiotr Jasiukajtis xk = -2 + (j & 1);
50025c28e83SPiotr Jasiukajtis else
50125c28e83SPiotr Jasiukajtis xk = j & 1;
50225c28e83SPiotr Jasiukajtis }
50325c28e83SPiotr Jasiukajtis if (xk < 0) {
50425c28e83SPiotr Jasiukajtis /* 0/0 invalid NaN, ideally gamma(-n)= (-1)**(n+1) * inf */
50525c28e83SPiotr Jasiukajtis zf = xf - xf;
50625c28e83SPiotr Jasiukajtis return (zf / zf);
50725c28e83SPiotr Jasiukajtis }
50825c28e83SPiotr Jasiukajtis
50925c28e83SPiotr Jasiukajtis /* negative underflow thresold */
51025c28e83SPiotr Jasiukajtis if (ix > 0x4224000B) { /* x < -(41+11ulp) */
51125c28e83SPiotr Jasiukajtis if (xk == 0)
51225c28e83SPiotr Jasiukajtis z = -tiny;
51325c28e83SPiotr Jasiukajtis else
51425c28e83SPiotr Jasiukajtis z = tiny;
51525c28e83SPiotr Jasiukajtis return ((float)z);
51625c28e83SPiotr Jasiukajtis }
51725c28e83SPiotr Jasiukajtis
51825c28e83SPiotr Jasiukajtis /* INDENT OFF */
51925c28e83SPiotr Jasiukajtis /* now compute gamma(x) by -1/((sin(pi*y)/pi)*gamma(1+y)), y = -x */
52025c28e83SPiotr Jasiukajtis /*
52125c28e83SPiotr Jasiukajtis * First compute ss = -sin(pi*y)/pi , so that
52225c28e83SPiotr Jasiukajtis * gamma(x) = 1/(ss*gamma(1+y))
52325c28e83SPiotr Jasiukajtis */
52425c28e83SPiotr Jasiukajtis /* INDENT ON */
52525c28e83SPiotr Jasiukajtis y = -x;
52625c28e83SPiotr Jasiukajtis j = (int) y;
52725c28e83SPiotr Jasiukajtis z = y - (double) j;
52825c28e83SPiotr Jasiukajtis if (z > 0.3183098861837906715377675)
52925c28e83SPiotr Jasiukajtis if (z > 0.6816901138162093284622325)
53025c28e83SPiotr Jasiukajtis ss = kpsin(one - z);
53125c28e83SPiotr Jasiukajtis else
53225c28e83SPiotr Jasiukajtis ss = kpcos(0.5 - z);
53325c28e83SPiotr Jasiukajtis else
53425c28e83SPiotr Jasiukajtis ss = kpsin(z);
53525c28e83SPiotr Jasiukajtis if (xk == 0)
53625c28e83SPiotr Jasiukajtis ss = -ss;
53725c28e83SPiotr Jasiukajtis
53825c28e83SPiotr Jasiukajtis /* Then compute ww = gamma(1+y) */
53925c28e83SPiotr Jasiukajtis if (j < 7)
54025c28e83SPiotr Jasiukajtis ww = gam_n(j + 1, z);
54125c28e83SPiotr Jasiukajtis else
54225c28e83SPiotr Jasiukajtis ww = large_gam(y + one);
54325c28e83SPiotr Jasiukajtis
54425c28e83SPiotr Jasiukajtis /* return 1/(ss*ww) */
54525c28e83SPiotr Jasiukajtis return ((float) (one / (ww * ss)));
54625c28e83SPiotr Jasiukajtis }
547