github.com/afumu/libc@v0.0.6/musl/src/math/lgammaf_r.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
     2  /*
     3   * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
     4   */
     5  /*
     6   * ====================================================
     7   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     8   *
     9   * Developed at SunPro, a Sun Microsystems, Inc. business.
    10   * Permission to use, copy, modify, and distribute this
    11   * software is freely granted, provided that this notice
    12   * is preserved.
    13   * ====================================================
    14   */
    15  
    16  #include "libm.h"
    17  
    18  static const float
    19  pi  =  3.1415927410e+00, /* 0x40490fdb */
    20  a0  =  7.7215664089e-02, /* 0x3d9e233f */
    21  a1  =  3.2246702909e-01, /* 0x3ea51a66 */
    22  a2  =  6.7352302372e-02, /* 0x3d89f001 */
    23  a3  =  2.0580807701e-02, /* 0x3ca89915 */
    24  a4  =  7.3855509982e-03, /* 0x3bf2027e */
    25  a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
    26  a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
    27  a7  =  5.1006977446e-04, /* 0x3a05b634 */
    28  a8  =  2.2086278477e-04, /* 0x39679767 */
    29  a9  =  1.0801156895e-04, /* 0x38e28445 */
    30  a10 =  2.5214456400e-05, /* 0x37d383a2 */
    31  a11 =  4.4864096708e-05, /* 0x383c2c75 */
    32  tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
    33  tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
    34  /* tt = -(tail of tf) */
    35  tt  =  6.6971006518e-09, /* 0x31e61c52 */
    36  t0  =  4.8383611441e-01, /* 0x3ef7b95e */
    37  t1  = -1.4758771658e-01, /* 0xbe17213c */
    38  t2  =  6.4624942839e-02, /* 0x3d845a15 */
    39  t3  = -3.2788541168e-02, /* 0xbd064d47 */
    40  t4  =  1.7970675603e-02, /* 0x3c93373d */
    41  t5  = -1.0314224288e-02, /* 0xbc28fcfe */
    42  t6  =  6.1005386524e-03, /* 0x3bc7e707 */
    43  t7  = -3.6845202558e-03, /* 0xbb7177fe */
    44  t8  =  2.2596477065e-03, /* 0x3b141699 */
    45  t9  = -1.4034647029e-03, /* 0xbab7f476 */
    46  t10 =  8.8108185446e-04, /* 0x3a66f867 */
    47  t11 = -5.3859531181e-04, /* 0xba0d3085 */
    48  t12 =  3.1563205994e-04, /* 0x39a57b6b */
    49  t13 = -3.1275415677e-04, /* 0xb9a3f927 */
    50  t14 =  3.3552918467e-04, /* 0x39afe9f7 */
    51  u0  = -7.7215664089e-02, /* 0xbd9e233f */
    52  u1  =  6.3282704353e-01, /* 0x3f2200f4 */
    53  u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
    54  u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
    55  u4  =  2.2896373272e-01, /* 0x3e6a7578 */
    56  u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
    57  v1  =  2.4559779167e+00, /* 0x401d2ebe */
    58  v2  =  2.1284897327e+00, /* 0x4008392d */
    59  v3  =  7.6928514242e-01, /* 0x3f44efdf */
    60  v4  =  1.0422264785e-01, /* 0x3dd572af */
    61  v5  =  3.2170924824e-03, /* 0x3b52d5db */
    62  s0  = -7.7215664089e-02, /* 0xbd9e233f */
    63  s1  =  2.1498242021e-01, /* 0x3e5c245a */
    64  s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
    65  s3  =  1.4635047317e-01, /* 0x3e15dce6 */
    66  s4  =  2.6642270386e-02, /* 0x3cda40e4 */
    67  s5  =  1.8402845599e-03, /* 0x3af135b4 */
    68  s6  =  3.1947532989e-05, /* 0x3805ff67 */
    69  r1  =  1.3920053244e+00, /* 0x3fb22d3b */
    70  r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
    71  r3  =  1.7193385959e-01, /* 0x3e300f6e */
    72  r4  =  1.8645919859e-02, /* 0x3c98bf54 */
    73  r5  =  7.7794247773e-04, /* 0x3a4beed6 */
    74  r6  =  7.3266842264e-06, /* 0x36f5d7bd */
    75  w0  =  4.1893854737e-01, /* 0x3ed67f1d */
    76  w1  =  8.3333335817e-02, /* 0x3daaaaab */
    77  w2  = -2.7777778450e-03, /* 0xbb360b61 */
    78  w3  =  7.9365057172e-04, /* 0x3a500cfd */
    79  w4  = -5.9518753551e-04, /* 0xba1c065c */
    80  w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
    81  w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
    82  
    83  /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
    84  static float sin_pi(float x)
    85  {
    86  	double_t y;
    87  	int n;
    88  
    89  	/* spurious inexact if odd int */
    90  	x = 2*(x*0.5f - floorf(x*0.5f));  /* x mod 2.0 */
    91  
    92  	n = (int)(x*4);
    93  	n = (n+1)/2;
    94  	y = x - n*0.5f;
    95  	y *= 3.14159265358979323846;
    96  	switch (n) {
    97  	default: /* case 4: */
    98  	case 0: return __sindf(y);
    99  	case 1: return __cosdf(y);
   100  	case 2: return __sindf(-y);
   101  	case 3: return -__cosdf(y);
   102  	}
   103  }
   104  
   105  float __lgammaf_r(float x, int *signgamp)
   106  {
   107  	union {float f; uint32_t i;} u = {x};
   108  	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
   109  	uint32_t ix;
   110  	int i,sign;
   111  
   112  	/* purge off +-inf, NaN, +-0, tiny and negative arguments */
   113  	*signgamp = 1;
   114  	sign = u.i>>31;
   115  	ix = u.i & 0x7fffffff;
   116  	if (ix >= 0x7f800000)
   117  		return x*x;
   118  	if (ix < 0x35000000) {  /* |x| < 2**-21, return -log(|x|) */
   119  		if (sign) {
   120  			*signgamp = -1;
   121  			x = -x;
   122  		}
   123  		return -logf(x);
   124  	}
   125  	if (sign) {
   126  		x = -x;
   127  		t = sin_pi(x);
   128  		if (t == 0.0f) /* -integer */
   129  			return 1.0f/(x-x);
   130  		if (t > 0.0f)
   131  			*signgamp = -1;
   132  		else
   133  			t = -t;
   134  		nadj = logf(pi/(t*x));
   135  	}
   136  
   137  	/* purge off 1 and 2 */
   138  	if (ix == 0x3f800000 || ix == 0x40000000)
   139  		r = 0;
   140  	/* for x < 2.0 */
   141  	else if (ix < 0x40000000) {
   142  		if (ix <= 0x3f666666) {  /* lgamma(x) = lgamma(x+1)-log(x) */
   143  			r = -logf(x);
   144  			if (ix >= 0x3f3b4a20) {
   145  				y = 1.0f - x;
   146  				i = 0;
   147  			} else if (ix >= 0x3e6d3308) {
   148  				y = x - (tc-1.0f);
   149  				i = 1;
   150  			} else {
   151  				y = x;
   152  				i = 2;
   153  			}
   154  		} else {
   155  			r = 0.0f;
   156  			if (ix >= 0x3fdda618) {  /* [1.7316,2] */
   157  				y = 2.0f - x;
   158  				i = 0;
   159  			} else if (ix >= 0x3F9da620) {  /* [1.23,1.73] */
   160  				y = x - tc;
   161  				i = 1;
   162  			} else {
   163  				y = x - 1.0f;
   164  				i = 2;
   165  			}
   166  		}
   167  		switch(i) {
   168  		case 0:
   169  			z = y*y;
   170  			p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
   171  			p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
   172  			p = y*p1+p2;
   173  			r += p - 0.5f*y;
   174  			break;
   175  		case 1:
   176  			z = y*y;
   177  			w = z*y;
   178  			p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));    /* parallel comp */
   179  			p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
   180  			p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
   181  			p = z*p1-(tt-w*(p2+y*p3));
   182  			r += (tf + p);
   183  			break;
   184  		case 2:
   185  			p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
   186  			p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
   187  			r += -0.5f*y + p1/p2;
   188  		}
   189  	} else if (ix < 0x41000000) {  /* x < 8.0 */
   190  		i = (int)x;
   191  		y = x - (float)i;
   192  		p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
   193  		q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
   194  		r = 0.5f*y+p/q;
   195  		z = 1.0f;    /* lgamma(1+s) = log(s) + lgamma(s) */
   196  		switch (i) {
   197  		case 7: z *= y + 6.0f;  /* FALLTHRU */
   198  		case 6: z *= y + 5.0f;  /* FALLTHRU */
   199  		case 5: z *= y + 4.0f;  /* FALLTHRU */
   200  		case 4: z *= y + 3.0f;  /* FALLTHRU */
   201  		case 3: z *= y + 2.0f;  /* FALLTHRU */
   202  			r += logf(z);
   203  			break;
   204  		}
   205  	} else if (ix < 0x5c800000) {  /* 8.0 <= x < 2**58 */
   206  		t = logf(x);
   207  		z = 1.0f/x;
   208  		y = z*z;
   209  		w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
   210  		r = (x-0.5f)*(t-1.0f)+w;
   211  	} else                         /* 2**58 <= x <= inf */
   212  		r =  x*(logf(x)-1.0f);
   213  	if (sign)
   214  		r = nadj - r;
   215  	return r;
   216  }
   217  
   218  weak_alias(__lgammaf_r, lgammaf_r);