libs/musl/src/math/log10.c

   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 #include "libm.h"
  23
  24 static const double
  25 ivln10hi  = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
  26 ivln10lo  = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
  27 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  28 log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
  29 Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
  30 Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
  31 Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
  32 Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
  33 Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
  34 Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
  35 Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
  36
  37 double __cdecl log10(double x)
  38 {
  39         union {double f; uint64_t i;} u = {x};
  40         double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
  41         uint32_t hx;
  42         int k;
  43
  44         hx = u.i>>32;
  45         k = 0;
  46         if (hx < 0x00100000 || hx>>31) {
  47                 if (u.i<<1 == 0)
  48                         return math_error(_SING, "log10", x, 0, -1 / (x * x));
  49                 if ((u.i & ~(1ULL << 63)) > 0x7ff0000000000000ULL)
  50                         return x;
  51                 if (hx >> 31)
  52                         return math_error(_DOMAIN, "log10", x, 0, (x - x) / (x - x));
  53                 /* subnormal number, scale x up */
  54                 k -= 54;
  55                 x *= 0x1p54;
  56                 u.f = x;
  57                 hx = u.i>>32;
  58         } else if (hx >= 0x7ff00000) {
  59                 return x;
  60         } else if (hx == 0x3ff00000 && u.i<<32 == 0)
  61                 return 0;
  62
  63         /* reduce x into [sqrt(2)/2, sqrt(2)] */
  64         hx += 0x3ff00000 - 0x3fe6a09e;
  65         k += (int)(hx>>20) - 0x3ff;
  66         hx = (hx&0x000fffff) + 0x3fe6a09e;
  67         u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
  68         x = u.f;
  69
  70         f = x - 1.0;
  71         hfsq = 0.5*f*f;
  72         s = f/(2.0+f);
  73         z = s*s;
  74         w = z*z;
  75         t1 = w*(Lg2+w*(Lg4+w*Lg6));
  76         t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  77         R = t2 + t1;
  78
  79         /* See log2.c for details. */
  80         /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
  81         hi = f - hfsq;
  82         u.f = hi;
  83         u.i &= (uint64_t)-1<<32;
  84         hi = u.f;
  85         lo = f - hi - hfsq + s*(hfsq+R);
  86
  87         /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
  88         val_hi = hi*ivln10hi;
  89         dk = k;
  90         y = dk*log10_2hi;
  91         val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
  92
  93         /*
  94          * Extra precision in for adding y is not strictly needed
  95          * since there is no very large cancellation near x = sqrt(2) or
  96          * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
  97          * with some parallelism and it reduces the error for many args.
  98          */
  99         w = y + val_hi;
 100         val_lo += (y - w) + val_hi;
 101         val_hi = w;
 102
 103         return val_lo + val_hi;
 104 }