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  1.  
  2. /* @(#)e_log10.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  */
  13.  
  14. /* __ieee754_log10(x)
  15.  * Return the base 10 logarithm of x
  16.  *
  17.  * Method :
  18.  *      Let log10_2hi = leading 40 bits of log10(2) and
  19.  *          log10_2lo = log10(2) - log10_2hi,
  20.  *          ivln10   = 1/log(10) rounded.
  21.  *      Then
  22.  *              n = ilogb(x),
  23.  *              if(n<0)  n = n+1;
  24.  *              x = scalbn(x,-n);
  25.  *              log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  26.  *
  27.  * Note 1:
  28.  *      To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  29.  *      mode must set to Round-to-Nearest.
  30.  * Note 2:
  31.  *      [1/log(10)] rounded to 53 bits has error  .198   ulps;
  32.  *      log10 is monotonic at all binary break points.
  33.  *
  34.  * Special cases:
  35.  *      log10(x) is NaN with signal if x < 0;
  36.  *      log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  37.  *      log10(NaN) is that NaN with no signal;
  38.  *      log10(10**N) = N  for N=0,1,...,22.
  39.  *
  40.  * Constants:
  41.  * The hexadecimal values are the intended ones for the following constants.
  42.  * The decimal values may be used, provided that the compiler will convert
  43.  * from decimal to binary accurately enough to produce the hexadecimal values
  44.  * shown.
  45.  */
  46.  
  47. #include "fdlibm.h"
  48.  
  49. #ifndef _DOUBLE_IS_32BITS
  50.  
  51. #ifdef __STDC__
  52. static const double
  53. #else
  54. static double
  55. #endif
  56. two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  57. ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  58. log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  59. log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  60.  
  61. #ifdef __STDC__
  62. static const double zero   =  0.0;
  63. #else
  64. static double zero   =  0.0;
  65. #endif
  66.  
  67. #ifdef __STDC__
  68.         double __ieee754_log10(double x)
  69. #else
  70.         double __ieee754_log10(x)
  71.         double x;
  72. #endif
  73. {
  74.         double y,z;
  75.         __int32_t i,k,hx;
  76.         __uint32_t lx;
  77.  
  78.         EXTRACT_WORDS(hx,lx,x);
  79.  
  80.         k=0;
  81.         if (hx < 0x00100000) {                  /* x < 2**-1022  */
  82.             if (((hx&0x7fffffff)|lx)==0)
  83.                 return -two54/zero;             /* log(+-0)=-inf */
  84.             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
  85.             k -= 54; x *= two54; /* subnormal number, scale up x */
  86.             GET_HIGH_WORD(hx,x);
  87.         }
  88.         if (hx >= 0x7ff00000) return x+x;
  89.         k += (hx>>20)-1023;
  90.         i  = ((__uint32_t)k&0x80000000)>>31;
  91.         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  92.         y  = (double)(k+i);
  93.         SET_HIGH_WORD(x,hx);
  94.         z  = y*log10_2lo + ivln10*__ieee754_log(x);
  95.         return  z+y*log10_2hi;
  96. }
  97.  
  98. #endif /* defined(_DOUBLE_IS_32BITS) */
  99.