/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */

/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak __tgammaf = tgammaf

/*
 * True gamma function
 *
 * float tgammaf(float x)
 *
 * Algorithm: see tgamma.c
 *
 * Maximum error observed: 0.87ulp (both positive and negative arguments)
 */

#include "libm.h"
#include <math.h>
#if defined(__SUNPRO_C)
#include <sunmath.h>
#endif
#include <sys/isa_defs.h>

#if defined(_BIG_ENDIAN)
#define HIWORD  0
#define LOWORD  1
#else
#define HIWORD  1
#define LOWORD  0
#endif
#define __HI(x) ((int *) &x)[HIWORD]
#define __LO(x) ((unsigned *) &x)[LOWORD]

/* Coefficients for primary intervals GTi() */
static const double cr[] = {
        /* p1 */
        +7.09087253435088360271451613398019280077561279443e-0001,
        -5.17229560788652108545141978238701790105241761089e-0001,
        +5.23403394528150789405825222323770647162337764327e-0001,
        -4.54586308717075010784041566069480411732634814899e-0001,
        +4.20596490915239085459964590559256913498190955233e-0001,
        -3.57307589712377520978332185838241458642142185789e-0001,

        /* p2 */
        +4.28486983980295198166056119223984284434264344578e-0001,
        -1.30704539487709138528680121627899735386650103914e-0001,
        +1.60856285038051955072861219352655851542955430871e-0001,
        -9.22285161346010583774458802067371182158937943507e-0002,
        +7.19240511767225260740890292605070595560626179357e-0002,
        -4.88158265593355093703112238534484636193260459574e-0002,

        /* p3 */
        +3.82409531118807759081121479786092134814808872880e-0001,
        +2.65309888180188647956400403013495759365167853426e-0002,
        +8.06815109775079171923561169415370309376296739835e-0002,
        -1.54821591666137613928840890835174351674007764799e-0002,
        +1.76308239242717268530498313416899188157165183405e-0002,

        /* GZi and TZi */
        +0.9382046279096824494097535615803269576988,    /* GZ1 */
        +0.8856031944108887002788159005825887332080,    /* GZ2 */
        +0.9367814114636523216188468970808378497426,    /* GZ3 */
        -0.3517214357852935791015625,   /* TZ1 */
        +0.280530631542205810546875,    /* TZ3 */
};

#define P10     cr[0]
#define P11     cr[1]
#define P12     cr[2]
#define P13     cr[3]
#define P14     cr[4]
#define P15     cr[5]
#define P20     cr[6]
#define P21     cr[7]
#define P22     cr[8]
#define P23     cr[9]
#define P24     cr[10]
#define P25     cr[11]
#define P30     cr[12]
#define P31     cr[13]
#define P32     cr[14]
#define P33     cr[15]
#define P34     cr[16]
#define GZ1     cr[17]
#define GZ2     cr[18]
#define GZ3     cr[19]
#define TZ1     cr[20]
#define TZ3     cr[21]

/* compute gamma(y) for y in GT1 = [1.0000, 1.2845] */
static double
GT1(double y) {
        double z, r;

        z = y * y;
        r = TZ1 * y + z * ((P10 + y * P11 + z * P12) + (z * y) * (P13 + y *
                P14 + z * P15));
        return (GZ1 + r);
}

/* compute gamma(y) for y in GT2 = [1.2844, 1.6374] */
static double
GT2(double y) {
        double z;

        z = y * y;
        return (GZ2 + z * ((P20 + y * P21 + z * P22) + (z * y) * (P23 + y *
                P24 + z * P25)));
}

/* compute gamma(y) for y in GT3 = [1.6373, 2.0000] */
static double
GT3(double y) {
double z, r;

        z = y * y;
        r = TZ3 * y + z * ((P30 + y * P31 + z * P32) + (z * y) * (P33 + y *
                P34));
        return (GZ3 + r);
}

/* INDENT OFF */
static const double c[] = {
+1.0,
+2.0,
+0.5,
+1.0e-300,
+6.666717231848518054693623697539230e-0001,                     /* A1=T3[0] */
+8.33333330959694065245736888749042811909994573178e-0002,       /* GP[0] */
-2.77765545601667179767706600890361535225507762168e-0003,       /* GP[1] */
+7.77830853479775281781085278324621033523037489883e-0004,       /* GP[2] */
+4.18938533204672741744150788368695779923320328369e-0001,       /* hln2pi   */
+2.16608493924982901946e-02,                                    /* ln2_32 */
+4.61662413084468283841e+01,                                    /* invln2_32 */
+5.00004103388988968841156421415669985414073453720e-0001,       /* Et1 */
+1.66667656752800761782778277828110208108687545908e-0001,       /* Et2 */
};

#define one             c[0]
#define two             c[1]
#define half            c[2]
#define tiny            c[3]
#define A1              c[4]
#define GP0             c[5]
#define GP1             c[6]
#define GP2             c[7]
#define hln2pi          c[8]
#define ln2_32          c[9]
#define invln2_32       c[10]
#define Et1             c[11]
#define Et2             c[12]

/* S[j] = 2**(j/32.) for the final computation of exp(w) */
static const double S[] = {
+1.00000000000000000000e+00,    /* 3FF0000000000000 */
+1.02189714865411662714e+00,    /* 3FF059B0D3158574 */
+1.04427378242741375480e+00,    /* 3FF0B5586CF9890F */
+1.06714040067682369717e+00,    /* 3FF11301D0125B51 */
+1.09050773266525768967e+00,    /* 3FF172B83C7D517B */
+1.11438674259589243221e+00,    /* 3FF1D4873168B9AA */
+1.13878863475669156458e+00,    /* 3FF2387A6E756238 */
+1.16372485877757747552e+00,    /* 3FF29E9DF51FDEE1 */
+1.18920711500272102690e+00,    /* 3FF306FE0A31B715 */
+1.21524735998046895524e+00,    /* 3FF371A7373AA9CB */
+1.24185781207348400201e+00,    /* 3FF3DEA64C123422 */
+1.26905095719173321989e+00,    /* 3FF44E086061892D */
+1.29683955465100964055e+00,    /* 3FF4BFDAD5362A27 */
+1.32523664315974132322e+00,    /* 3FF5342B569D4F82 */
+1.35425554693689265129e+00,    /* 3FF5AB07DD485429 */
+1.38390988196383202258e+00,    /* 3FF6247EB03A5585 */
+1.41421356237309514547e+00,    /* 3FF6A09E667F3BCD */
+1.44518080697704665027e+00,    /* 3FF71F75E8EC5F74 */
+1.47682614593949934623e+00,    /* 3FF7A11473EB0187 */
+1.50916442759342284141e+00,    /* 3FF82589994CCE13 */
+1.54221082540794074411e+00,    /* 3FF8ACE5422AA0DB */
+1.57598084510788649659e+00,    /* 3FF93737B0CDC5E5 */
+1.61049033194925428347e+00,    /* 3FF9C49182A3F090 */
+1.64575547815396494578e+00,    /* 3FFA5503B23E255D */
+1.68179283050742900407e+00,    /* 3FFAE89F995AD3AD */
+1.71861929812247793414e+00,    /* 3FFB7F76F2FB5E47 */
+1.75625216037329945351e+00,    /* 3FFC199BDD85529C */
+1.79470907500310716820e+00,    /* 3FFCB720DCEF9069 */
+1.83400808640934243066e+00,    /* 3FFD5818DCFBA487 */
+1.87416763411029996256e+00,    /* 3FFDFC97337B9B5F */
+1.91520656139714740007e+00,    /* 3FFEA4AFA2A490DA */
+1.95714412417540017941e+00,    /* 3FFF50765B6E4540 */
};
/* INDENT ON */

/* INDENT OFF */
/*
 * return tgammaf(x) in double for 8<x<=35.040096283... using Stirling's formula
 *     log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + (1/x)*P(1/(x*x))
 */
/*
 * compute ss = log(x)-1
 *
 *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
 *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
 *       T1(n-3) = n*log(2)-1,  n=3,4,5
 *       T2(j) = log(z[j]),
 *       T3(s) = 2s + A1*s^3
 *  Note
 *  (1) Remez error for T3(s) is bounded by 2**(-35.8)
 *      (see mpremez/work/Log/tgamma_log_2_outr1)
 */

static const double T1[] = { /* T1[j]=(j+3)*log(2)-1 */
+1.079441541679835928251696364375e+00,
+1.772588722239781237668928485833e+00,
+2.465735902799726547086160607291e+00,
};

static const double T2[] = {   /* T2[j]=log(1+j/64+1/128) */
+7.782140442054948947462900061137e-03,
+2.316705928153437822879916096229e-02,
+3.831886430213659919375532512380e-02,
+5.324451451881228286587019378653e-02,
+6.795066190850774939456527777263e-02,
+8.244366921107459126816006866831e-02,
+9.672962645855111229557105648746e-02,
+1.108143663402901141948061693232e-01,
+1.247034785009572358634065153809e-01,
+1.384023228591191356853258736016e-01,
+1.519160420258419750718034248969e-01,
+1.652495728953071628756114492772e-01,
+1.784076574728182971194002415109e-01,
+1.913948529996294546092988075613e-01,
+2.042155414286908915038203861962e-01,
+2.168739383006143596190895257443e-01,
+2.293741010648458299914807250461e-01,
+2.417199368871451681443075159135e-01,
+2.539152099809634441373232979066e-01,
+2.659635484971379413391259265375e-01,
+2.778684510034563061863500329234e-01,
+2.896332925830426768788930555257e-01,
+3.012613305781617810128755382338e-01,
+3.127557100038968883862465596883e-01,
+3.241194686542119760906707604350e-01,
+3.353555419211378302571795798142e-01,
+3.464667673462085809184621884258e-01,
+3.574558889218037742260094901409e-01,
+3.683255611587076530482301540504e-01,
+3.790783529349694583908533456310e-01,
+3.897167511400252133704636040035e-01,
+4.002431641270127069293251019951e-01,
+4.106599249852683859343062031758e-01,
+4.209692946441296361288671615068e-01,
+4.311734648183713408591724789556e-01,
+4.412745608048752294894964416613e-01,
+4.512746441394585851446923830790e-01,
+4.611757151221701663679999255979e-01,
+4.709797152187910125468978560564e-01,
+4.806885293457519076766184554480e-01,
+4.903039880451938381503461596457e-01,
+4.998278695564493298213314152470e-01,
+5.092619017898079468040749192283e-01,
+5.186077642080456321529769963648e-01,
+5.278670896208423851138922177783e-01,
+5.370414658968836545667292441538e-01,
+5.461324375981356503823972092312e-01,
+5.551415075405015927154803595159e-01,
+5.640701382848029660713842900902e-01,
+5.729197535617855090927567266263e-01,
+5.816917396346224825206107537254e-01,
+5.903874466021763746419167081236e-01,
+5.990081896460833993816000244617e-01,
+6.075552502245417955010851527911e-01,
+6.160298772155140196475659281967e-01,
+6.244332880118935010425387440547e-01,
+6.327666695710378295457864685036e-01,
+6.410311794209312910556013344054e-01,
+6.492279466251098188908399699053e-01,
+6.573580727083600301418900232459e-01,
+6.654226325450904489500926100067e-01,
+6.734226752121667202979603888010e-01,
+6.813592248079030689480715595681e-01,
+6.892332812388089803249143378146e-01,
};
/* INDENT ON */

static double
large_gam(double x) {
        double ss, zz, z, t1, t2, w, y, u;
        unsigned lx;
        int k, ix, j, m;

        ix = __HI(x);
        lx = __LO(x);
        m = (ix >> 20) - 0x3ff;                 /* exponent of x, range:3-5 */
        ix = (ix & 0x000fffff) | 0x3ff00000;    /* y = scale x to [1,2] */
        __HI(y) = ix;
        __LO(y) = lx;
        __HI(z) = (ix & 0xffffc000) | 0x2000;   /* z[j]=1+j/64+1/128 */
        __LO(z) = 0;
        j = (ix >> 14) & 0x3f;
        t1 = y + z;
        t2 = y - z;
        u = t2 / t1;
        ss = T1[m - 3] + T2[j] + u * (two + A1 * (u * u));
                                                        /* ss = log(x)-1 */
        /*
         * compute ww = (x-.5)*(log(x)-1) + .5*(log(2pi)-1) + 1/x*(P(1/x^2)))
         * where ss = log(x) - 1
         */
        z = one / x;
        zz = z * z;
        w = ((x - half) * ss + hln2pi) + z * (GP0 + zz * GP1 + (zz * zz) * GP2);
        k = (int) (w * invln2_32 + half);

        /* compute the exponential of w */
        j = k & 0x1f;
        m = k >> 5;
        z = w - (double) k *ln2_32;
        zz = S[j] * (one + z + (z * z) * (Et1 + z * Et2));
        __HI(zz) += m << 20;
        return (zz);
}
/* INDENT OFF */
/*
 * kpsin(x)= sin(pi*x)/pi
 *                 3        5        7        9
 *      = x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x
 */
static const double ks[] = {
-1.64493404985645811354476665052005342839447790544e+0000,
+8.11740794458351064092797249069438269367389272270e-0001,
-1.90703144603551216933075809162889536878854055202e-0001,
+2.55742333994264563281155312271481108635575331201e-0002,
};
/* INDENT ON */

static double
kpsin(double x) {
        double z;

        z = x * x;
        return (x + (x * z) * ((ks[0] + z * ks[1]) + (z * z) * (ks[2] + z *
                ks[3])));
}

/* INDENT OFF */
/*
 * kpcos(x)= cos(pi*x)/pi
 *                     2        4        6
 *      = kc[0]+kc[1]*x +kc[2]*x +kc[3]*x
 */
static const double kc[] = {
+3.18309886183790671537767526745028724068919291480e-0001,
-1.57079581447762568199467875065854538626594937791e+0000,
+1.29183528092558692844073004029568674027807393862e+0000,
-4.20232949771307685981015914425195471602739075537e-0001,
};
/* INDENT ON */

static double
kpcos(double x) {
        double z;

        z = x * x;
        return (kc[0] + z * (kc[1] + z * kc[2] + (z * z) * kc[3]));
}

/* INDENT OFF */
static const double
t0z1 = 0.134861805732790769689793935774652917006,
t0z2 = 0.461632144968362341262659542325721328468,
t0z3 = 0.819773101100500601787868704921606996312;
        /* 1.134861805732790769689793935774652917006 */
/* INDENT ON */

/*
 * gamma(x+i) for 0 <= x < 1
 */
static double
gam_n(int i, double x) {
        double rr = 0.0L, yy;
        double z1, z2;

        /* compute yy = gamma(x+1) */
        if (x > 0.2845) {
                if (x > 0.6374)
                        yy = GT3(x - t0z3);
                else
                        yy = GT2(x - t0z2);
        } else
                yy = GT1(x - t0z1);

        /* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */
        switch (i) {
        case 0:         /* yy/x */
                rr = yy / x;
                break;
        case 1:         /* yy */
                rr = yy;
                break;
        case 2:         /* (x+1)*yy */
                rr = (x + one) * yy;
                break;
        case 3:         /* (x+2)*(x+1)*yy */
                rr = (x + one) * (x + two) * yy;
                break;

        case 4:         /* (x+1)*(x+3)*(x+2)*yy */
                rr = (x + one) * (x + two) * ((x + 3.0) * yy);
                break;
        case 5:         /* ((x+1)*(x+4)*(x+2)*(x+3))*yy */
                z1 = (x + two) * (x + 3.0) * yy;
                z2 = (x + one) * (x + 4.0);
                rr = z1 * z2;
                break;
        case 6:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5))*yy */
                z1 = (x + two) * (x + 3.0);
                z2 = (x + 5.0) * yy;
                rr = z1 * (z1 - two) * z2;
                break;
        case 7:         /* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5)*(x+6))*yy */
                z1 = (x + two) * (x + 3.0);
                z2 = (x + 5.0) * (x + 6.0) * yy;
                rr = z1 * (z1 - two) * z2;
                break;
        }
        return (rr);
}

float
tgammaf(float xf) {
        float zf;
        double ss, ww;
        double x, y, z;
        int i, j, k, ix, hx, xk;

        hx = *(int *) &xf;
        ix = hx & 0x7fffffff;

        x = (double) xf;
        if (ix < 0x33800000)
                return (1.0F / xf);     /* |x| < 2**-24 */

        if (ix >= 0x7f800000)
                return (xf * ((hx < 0)? 0.0F : xf)); /* +-Inf or NaN */

        if (hx > 0x420C290F)    /* x > 35.040096283... overflow */
                return (float)(x / tiny);

        if (hx >= 0x41000000)   /* x >= 8 */
                return ((float) large_gam(x));

        if (hx > 0) {           /* 0 < x < 8 */
                i = (int) xf;
                return ((float) gam_n(i, x - (double) i));
        }

        /* negative x */
        /* INDENT OFF */
        /*
         * compute xk =
         *      -2 ... x is an even int (-inf is considered even)
         *      -1 ... x is an odd int
         *      +0 ... x is not an int but chopped to an even int
         *      +1 ... x is not an int but chopped to an odd int
         */
        /* INDENT ON */
        xk = 0;
        if (ix >= 0x4b000000) {
                if (ix > 0x4b000000)
                        xk = -2;
                else
                        xk = -2 + (ix & 1);
        } else if (ix >= 0x3f800000) {
                k = (ix >> 23) - 0x7f;
                j = ix >> (23 - k);
                if ((j << (23 - k)) == ix)
                        xk = -2 + (j & 1);
                else
                        xk = j & 1;
        }
        if (xk < 0) {
                /* 0/0 invalid NaN, ideally gamma(-n)= (-1)**(n+1) * inf */
                zf = xf - xf;
                return (zf / zf);
        }

        /* negative underflow thresold */
        if (ix > 0x4224000B) {  /* x < -(41+11ulp) */
                if (xk == 0)
                        z = -tiny;
                else
                        z = tiny;
                return ((float)z);
        }

        /* INDENT OFF */
        /* now compute gamma(x) by  -1/((sin(pi*y)/pi)*gamma(1+y)), y = -x */
        /*
         * First compute ss = -sin(pi*y)/pi , so that
         * gamma(x) = 1/(ss*gamma(1+y))
         */
        /* INDENT ON */
        y = -x;
        j = (int) y;
        z = y - (double) j;
        if (z > 0.3183098861837906715377675)
                if (z > 0.6816901138162093284622325)
                        ss = kpsin(one - z);
                else
                        ss = kpcos(0.5 - z);
        else
                ss = kpsin(z);
        if (xk == 0)
                ss = -ss;

        /* Then compute ww = gamma(1+y)  */
        if (j < 7)
                ww = gam_n(j + 1, z);
        else
                ww = large_gam(y + one);

        /* return 1/(ss*ww) */
        return ((float) (one / (ww * ss)));
}