/* erf_lgamma.c -- float version of er_lgamma.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */

#define _ADD_UNDER_R_TO_FUNCS

#include "fdlibm.h"

static const float two23 = 8.3886080000e+06, /* 0x4b000000 */
    half = 5.0000000000e-01, /* 0x3f000000 */
    one = 1.0000000000e+00, /* 0x3f800000 */
    pi = 3.1415927410e+00, /* 0x40490fdb */
    a0 = 7.7215664089e-02, /* 0x3d9e233f */
    a1 = 3.2246702909e-01, /* 0x3ea51a66 */
    a2 = 6.7352302372e-02, /* 0x3d89f001 */
    a3 = 2.0580807701e-02, /* 0x3ca89915 */
    a4 = 7.3855509982e-03, /* 0x3bf2027e */
    a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
    a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
    a7 = 5.1006977446e-04, /* 0x3a05b634 */
    a8 = 2.2086278477e-04, /* 0x39679767 */
    a9 = 1.0801156895e-04, /* 0x38e28445 */
    a10 = 2.5214456400e-05, /* 0x37d383a2 */
    a11 = 4.4864096708e-05, /* 0x383c2c75 */
    tc = 1.4616321325e+00, /* 0x3fbb16c3 */
    tf = -1.2148628384e-01, /* 0xbdf8cdcd */
    /* tt = -(tail of tf) */
    tt = 6.6971006518e-09, /* 0x31e61c52 */
    t0 = 4.8383611441e-01, /* 0x3ef7b95e */
    t1 = -1.4758771658e-01, /* 0xbe17213c */
    t2 = 6.4624942839e-02, /* 0x3d845a15 */
    t3 = -3.2788541168e-02, /* 0xbd064d47 */
    t4 = 1.7970675603e-02, /* 0x3c93373d */
    t5 = -1.0314224288e-02, /* 0xbc28fcfe */
    t6 = 6.1005386524e-03, /* 0x3bc7e707 */
    t7 = -3.6845202558e-03, /* 0xbb7177fe */
    t8 = 2.2596477065e-03, /* 0x3b141699 */
    t9 = -1.4034647029e-03, /* 0xbab7f476 */
    t10 = 8.8108185446e-04, /* 0x3a66f867 */
    t11 = -5.3859531181e-04, /* 0xba0d3085 */
    t12 = 3.1563205994e-04, /* 0x39a57b6b */
    t13 = -3.1275415677e-04, /* 0xb9a3f927 */
    t14 = 3.3552918467e-04, /* 0x39afe9f7 */
    u0 = -7.7215664089e-02, /* 0xbd9e233f */
    u1 = 6.3282704353e-01, /* 0x3f2200f4 */
    u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
    u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
    u4 = 2.2896373272e-01, /* 0x3e6a7578 */
    u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
    v1 = 2.4559779167e+00, /* 0x401d2ebe */
    v2 = 2.1284897327e+00, /* 0x4008392d */
    v3 = 7.6928514242e-01, /* 0x3f44efdf */
    v4 = 1.0422264785e-01, /* 0x3dd572af */
    v5 = 3.2170924824e-03, /* 0x3b52d5db */
    s0 = -7.7215664089e-02, /* 0xbd9e233f */
    s1 = 2.1498242021e-01, /* 0x3e5c245a */
    s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
    s3 = 1.4635047317e-01, /* 0x3e15dce6 */
    s4 = 2.6642270386e-02, /* 0x3cda40e4 */
    s5 = 1.8402845599e-03, /* 0x3af135b4 */
    s6 = 3.1947532989e-05, /* 0x3805ff67 */
    r1 = 1.3920053244e+00, /* 0x3fb22d3b */
    r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
    r3 = 1.7193385959e-01, /* 0x3e300f6e */
    r4 = 1.8645919859e-02, /* 0x3c98bf54 */
    r5 = 7.7794247773e-04, /* 0x3a4beed6 */
    r6 = 7.3266842264e-06, /* 0x36f5d7bd */
    w0 = 4.1893854737e-01, /* 0x3ed67f1d */
    w1 = 8.3333335817e-02, /* 0x3daaaaab */
    w2 = -2.7777778450e-03, /* 0xbb360b61 */
    w3 = 7.9365057172e-04, /* 0x3a500cfd */
    w4 = -5.9518753551e-04, /* 0xba1c065c */
    w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
    w6 = -1.6309292987e-03; /* 0xbad5c4e8 */

static const float zero = 0.0000000000e+00;

static float
sin_pif(float x)
{
    float y, z;
    __int32_t n, ix;

    GET_FLOAT_WORD(ix, x);
    ix &= 0x7fffffff;

    if (ix < 0x3e800000)
        return __kernel_sinf(pi * x, zero, 0);
    y = -x; /* x is assume negative */

    /*
     * argument reduction, make sure inexact flag not raised if input
     * is an integer
     */
    z = floorf(y);
    if (z != y) { /* inexact anyway */
        y *= (float)0.5;
        y = (float)2.0 * (y - floorf(y)); /* y = |x| mod 2.0 */
        n = (__int32_t)(y * (float)4.0);
    } else {
        if (ix >= 0x4b800000) {
            y = zero;
            n = 0; /* y must be even */
        } else {
            if (ix < 0x4b000000)
                z = y + two23; /* exact */
            GET_FLOAT_WORD(n, z);
            n &= 1;
            y = n;
            n <<= 2;
        }
    }
    switch (n) {
    case 0:
        y = __kernel_sinf(pi * y, zero, 0);
        break;
    case 1:
    case 2:
        y = __kernel_cosf(pi * ((float)0.5 - y), zero);
        break;
    case 3:
    case 4:
        y = __kernel_sinf(pi * (one - y), zero, 0);
        break;
    case 5:
    case 6:
        y = -__kernel_cosf(pi * (y - (float)1.5), zero);
        break;
    default:
        y = __kernel_sinf(pi * (y - (float)2.0), zero, 0);
        break;
    }
    return -y;
}

float
__math_lgammaf_r(float x, int *signgamp, int *divzero)
{
    float t, y, z, nadj = 0.0, p, p1, p2, p3, q, r, w;
    __int32_t i, hx, ix;

    GET_FLOAT_WORD(hx, x);

    /* purge off +-inf, NaN, +-0, and negative arguments */
    *signgamp = 1;
    ix = hx & 0x7fffffff;
    if (ix >= 0x7f800000)
        return fabsf(x+x);
    if (ix == 0) {
        if (hx < 0)
            *signgamp = -1;
        *divzero = 1;
        return __math_divzerof(0);
    }
    if (ix < 0x1c800000) { /* |x|<2**-70, return -log(|x|) */
        if (hx < 0) {
            *signgamp = -1;
            return -logf(-x);
        } else
            return -logf(x);
    }
    if (hx < 0) {
        if (ix >= 0x4b000000) { /* |x|>=2**23, must be -integer */
            *divzero = 1;
            return __math_divzerof(0);
        }
        t = sin_pif(x);
        if (t == zero) {
            *divzero = 1;
            return __math_divzerof(0);
        }
        nadj = logf(pi / fabsf(t * x));
        if (t < zero)
            *signgamp = -1;
        x = -x;
    }

    /* purge off 1 and 2 */
    if (ix == 0x3f800000 || ix == 0x40000000)
        r = 0;
    /* for x < 2.0 */
    else if (ix < 0x40000000) {
        if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
            r = -logf(x);
            if (ix >= 0x3f3b4a20) {
                y = one - x;
                i = 0;
            } else if (ix >= 0x3e6d3308) {
                y = x - (tc - one);
                i = 1;
            } else {
                y = x;
                i = 2;
            }
        } else {
            r = zero;
            if (ix >= 0x3fdda618) {
                y = (float)2.0 - x;
                i = 0;
            } /* [1.7316,2] */
            else if (ix >= 0x3F9da620) {
                y = x - tc;
                i = 1;
            } /* [1.23,1.73] */
            else {
                y = x - one;
                i = 2;
            }
        }
        switch (i) {
        case 0:
            z = y * y;
            p1 = a0 + z * (a2 + z * (a4 + z * (a6 + z * (a8 + z * a10))));
            p2 = z * (a1 + z * (a3 + z * (a5 + z * (a7 + z * (a9 + z * a11)))));
            p = y * p1 + p2;
            r += (p - (float)0.5 * y);
            break;
        case 1:
            z = y * y;
            w = z * y;
            p1 = t0 +
                 w * (t3 + w * (t6 + w * (t9 + w * t12))); /* parallel comp */
            p2 = t1 + w * (t4 + w * (t7 + w * (t10 + w * t13)));
            p3 = t2 + w * (t5 + w * (t8 + w * (t11 + w * t14)));
            p = z * p1 - (tt - w * (p2 + y * p3));
            r += (tf + p);
            break;
        case 2:
            p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * u5)))));
            p2 = one + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5))));
            r += (-(float)0.5 * y + p1 / p2);
        }
    } else if (ix < 0x41000000) { /* x < 8.0 */
        i = (__int32_t)x;
        y = x - (float)i;
        p = y * (s0 +
                 y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
        q = one + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6)))));
        r = half * y + p / q;
        z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
        switch (i) {
        case 7:
            z *= (y + (float)6.0); /* FALLTHRU */
        case 6:
            z *= (y + (float)5.0); /* FALLTHRU */
        case 5:
            z *= (y + (float)4.0); /* FALLTHRU */
        case 4:
            z *= (y + (float)3.0); /* FALLTHRU */
        case 3:
            z *= (y + (float)2.0); /* FALLTHRU */
            r += logf(z);
            break;
        }
        /* 8.0 <= x < 2**58 */
    } else if (ix < 0x5c800000) {
        t = logf(x);
        z = one / x;
        y = z * z;
        w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6)))));
        r = (x - half) * (t - one) + w;
    } else
        /* 2**58 <= x <= inf */
        r = x * (logf(x) - one);
    if (hx < 0)
        r = nadj - r;
    return check_oflowf(r);
}

float
lgammaf_r(float x, int *signgamp)
{
    int divzero = 0;
    return __math_lgammaf_r(x, signgamp, &divzero);
}

_MATH_ALIAS_f_fI(lgamma)