/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.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.
 * ====================================================
 */

#include "libm.h"
#include "libc.h"

static const float 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 */

/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
static float sin_pi(float x) {
  double_t y;
  int n;

  /* spurious inexact if odd int */
  x = 2 * (x * 0.5f - floorf(x * 0.5f)); /* x mod 2.0 */

  n = (int)(x * 4);
  n = (n + 1) / 2;
  y = x - n * 0.5f;
  y *= 3.14159265358979323846;
  switch (n) {
    default: /* case 4: */
    case 0:
      return __sindf(y);
    case 1:
      return __cosdf(y);
    case 2:
      return __sindf(-y);
    case 3:
      return -__cosdf(y);
  }
}

float __lgammaf_r(float x, int* signgamp) {
  union {
    float f;
    uint32_t i;
  } u = {x};
  float t, y, z, nadj, p, p1, p2, p3, q, r, w;
  uint32_t ix;
  int i, sign;

  /* purge off +-inf, NaN, +-0, tiny and negative arguments */
  *signgamp = 1;
  sign = u.i >> 31;
  ix = u.i & 0x7fffffff;
  if (ix >= 0x7f800000)
    return x * x;
  if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
    if (sign) {
      *signgamp = -1;
      x = -x;
    }
    return -logf(x);
  }
  if (sign) {
    x = -x;
    t = sin_pi(x);
    if (t == 0.0f) /* -integer */
      return 1.0f / (x - x);
    if (t > 0.0f)
      *signgamp = -1;
    else
      t = -t;
    nadj = logf(pi / (t * 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 = 1.0f - x;
        i = 0;
      } else if (ix >= 0x3e6d3308) {
        y = x - (tc - 1.0f);
        i = 1;
      } else {
        y = x;
        i = 2;
      }
    } else {
      r = 0.0f;
      if (ix >= 0x3fdda618) { /* [1.7316,2] */
        y = 2.0f - x;
        i = 0;
      } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
        y = x - tc;
        i = 1;
      } else {
        y = x - 1.0f;
        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 - 0.5f * 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 = 1.0f + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5))));
        r += -0.5f * y + p1 / p2;
    }
  } else if (ix < 0x41000000) { /* x < 8.0 */
    i = (int)x;
    y = x - (float)i;
    p = y *
        (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
    q = 1.0f + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6)))));
    r = 0.5f * y + p / q;
    z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
    switch (i) {
      case 7:
        z *= y + 6.0f; /* FALLTHRU */
      case 6:
        z *= y + 5.0f; /* FALLTHRU */
      case 5:
        z *= y + 4.0f; /* FALLTHRU */
      case 4:
        z *= y + 3.0f; /* FALLTHRU */
      case 3:
        z *= y + 2.0f; /* FALLTHRU */
        r += logf(z);
        break;
    }
  } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
    t = logf(x);
    z = 1.0f / x;
    y = z * z;
    w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6)))));
    r = (x - 0.5f) * (t - 1.0f) + w;
  } else /* 2**58 <= x <= inf */
    r = x * (logf(x) - 1.0f);
  if (sign)
    r = nadj - r;
  return r;
}

weak_alias(__lgammaf_r, lgammaf_r);