github.com/afumu/libc@v0.0.6/musl/src/math/log10f.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunPro, a Sun Microsystems, Inc. business.
     7   * Permission to use, copy, modify, and distribute this
     8   * software is freely granted, provided that this notice
     9   * is preserved.
    10   * ====================================================
    11   */
    12  /*
    13   * See comments in log10.c.
    14   */
    15  
    16  #include <math.h>
    17  #include <stdint.h>
    18  
    19  static const float
    20  ivln10hi  =  4.3432617188e-01, /* 0x3ede6000 */
    21  ivln10lo  = -3.1689971365e-05, /* 0xb804ead9 */
    22  log10_2hi =  3.0102920532e-01, /* 0x3e9a2080 */
    23  log10_2lo =  7.9034151668e-07, /* 0x355427db */
    24  /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
    25  Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
    26  Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
    27  Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
    28  Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
    29  
    30  float log10f(float x)
    31  {
    32  	union {float f; uint32_t i;} u = {x};
    33  	float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo;
    34  	uint32_t ix;
    35  	int k;
    36  
    37  	ix = u.i;
    38  	k = 0;
    39  	if (ix < 0x00800000 || ix>>31) {  /* x < 2**-126  */
    40  		if (ix<<1 == 0)
    41  			return -1/(x*x);  /* log(+-0)=-inf */
    42  		if (ix>>31)
    43  			return (x-x)/0.0f; /* log(-#) = NaN */
    44  		/* subnormal number, scale up x */
    45  		k -= 25;
    46  		x *= 0x1p25f;
    47  		u.f = x;
    48  		ix = u.i;
    49  	} else if (ix >= 0x7f800000) {
    50  		return x;
    51  	} else if (ix == 0x3f800000)
    52  		return 0;
    53  
    54  	/* reduce x into [sqrt(2)/2, sqrt(2)] */
    55  	ix += 0x3f800000 - 0x3f3504f3;
    56  	k += (int)(ix>>23) - 0x7f;
    57  	ix = (ix&0x007fffff) + 0x3f3504f3;
    58  	u.i = ix;
    59  	x = u.f;
    60  
    61  	f = x - 1.0f;
    62  	s = f/(2.0f + f);
    63  	z = s*s;
    64  	w = z*z;
    65  	t1= w*(Lg2+w*Lg4);
    66  	t2= z*(Lg1+w*Lg3);
    67  	R = t2 + t1;
    68  	hfsq = 0.5f*f*f;
    69  
    70  	hi = f - hfsq;
    71  	u.f = hi;
    72  	u.i &= 0xfffff000;
    73  	hi = u.f;
    74  	lo = f - hi - hfsq + s*(hfsq+R);
    75  	dk = k;
    76  	return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi;
    77  }