log10.c raw

   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  }
 102