github.com/afumu/libc@v0.0.6/musl/src/math/log10.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunSoft, 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   * Return the base 10 logarithm of x.  See log.c for most comments.
    14   *
    15   * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
    16   * as in log.c, then combine and scale in extra precision:
    17   *    log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
    18   */
    19  
    20  #include <math.h>
    21  #include <stdint.h>
    22  
    23  static const double
    24  ivln10hi  = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
    25  ivln10lo  = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
    26  log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
    27  log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
    28  Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
    29  Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
    30  Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
    31  Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
    32  Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
    33  Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
    34  Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
    35  
    36  double log10(double x)
    37  {
    38  	union {double f; uint64_t i;} u = {x};
    39  	double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
    40  	uint32_t hx;
    41  	int k;
    42  
    43  	hx = u.i>>32;
    44  	k = 0;
    45  	if (hx < 0x00100000 || hx>>31) {
    46  		if (u.i<<1 == 0)
    47  			return -1/(x*x);  /* log(+-0)=-inf */
    48  		if (hx>>31)
    49  			return (x-x)/0.0; /* log(-#) = NaN */
    50  		/* subnormal number, scale x up */
    51  		k -= 54;
    52  		x *= 0x1p54;
    53  		u.f = x;
    54  		hx = u.i>>32;
    55  	} else if (hx >= 0x7ff00000) {
    56  		return x;
    57  	} else if (hx == 0x3ff00000 && u.i<<32 == 0)
    58  		return 0;
    59  
    60  	/* reduce x into [sqrt(2)/2, sqrt(2)] */
    61  	hx += 0x3ff00000 - 0x3fe6a09e;
    62  	k += (int)(hx>>20) - 0x3ff;
    63  	hx = (hx&0x000fffff) + 0x3fe6a09e;
    64  	u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
    65  	x = u.f;
    66  
    67  	f = x - 1.0;
    68  	hfsq = 0.5*f*f;
    69  	s = f/(2.0+f);
    70  	z = s*s;
    71  	w = z*z;
    72  	t1 = w*(Lg2+w*(Lg4+w*Lg6));
    73  	t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
    74  	R = t2 + t1;
    75  
    76  	/* See log2.c for details. */
    77  	/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
    78  	hi = f - hfsq;
    79  	u.f = hi;
    80  	u.i &= (uint64_t)-1<<32;
    81  	hi = u.f;
    82  	lo = f - hi - hfsq + s*(hfsq+R);
    83  
    84  	/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
    85  	val_hi = hi*ivln10hi;
    86  	dk = k;
    87  	y = dk*log10_2hi;
    88  	val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
    89  
    90  	/*
    91  	 * Extra precision in for adding y is not strictly needed
    92  	 * since there is no very large cancellation near x = sqrt(2) or
    93  	 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
    94  	 * with some parallelism and it reduces the error for many args.
    95  	 */
    96  	w = y + val_hi;
    97  	val_lo += (y - w) + val_hi;
    98  	val_hi = w;
    99  
   100  	return val_lo + val_hi;
   101  }