e_log10.c 2.8 KB

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  1. /* @(#)e_log10.c 5.1 93/09/24 */
  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. #if defined(LIBM_SCCS) && !defined(lint)
  13. static char rcsid[] = "$NetBSD: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
  14. #endif
  15. /* __ieee754_log10(x)
  16. * Return the base 10 logarithm of x
  17. *
  18. * Method :
  19. * Let log10_2hi = leading 40 bits of log10(2) and
  20. * log10_2lo = log10(2) - log10_2hi,
  21. * ivln10 = 1/log(10) rounded.
  22. * Then
  23. * n = ilogb(x),
  24. * if(n<0) n = n+1;
  25. * x = scalbn(x,-n);
  26. * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
  27. *
  28. * Note 1:
  29. * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
  30. * mode must set to Round-to-Nearest.
  31. * Note 2:
  32. * [1/log(10)] rounded to 53 bits has error .198 ulps;
  33. * log10 is monotonic at all binary break points.
  34. *
  35. * Special cases:
  36. * log10(x) is NaN with signal if x < 0;
  37. * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
  38. * log10(NaN) is that NaN with no signal;
  39. * log10(10**N) = N for N=0,1,...,22.
  40. *
  41. * Constants:
  42. * The hexadecimal values are the intended ones for the following constants.
  43. * The decimal values may be used, provided that the compiler will convert
  44. * from decimal to binary accurately enough to produce the hexadecimal values
  45. * shown.
  46. */
  47. #include "math.h"
  48. #include "math_private.h"
  49. #ifdef __STDC__
  50. static const double
  51. #else
  52. static double
  53. #endif
  54. two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
  55. ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
  56. log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  57. log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
  58. #ifdef __STDC__
  59. static const double zero = 0.0;
  60. #else
  61. static double zero = 0.0;
  62. #endif
  63. #ifdef __STDC__
  64. double __ieee754_log10(double x)
  65. #else
  66. double __ieee754_log10(x)
  67. double x;
  68. #endif
  69. {
  70. double y,z;
  71. int32_t i,k,hx;
  72. u_int32_t lx;
  73. EXTRACT_WORDS(hx,lx,x);
  74. k=0;
  75. if (hx < 0x00100000) { /* x < 2**-1022 */
  76. if (((hx&0x7fffffff)|lx)==0)
  77. return -two54/zero; /* log(+-0)=-inf */
  78. if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
  79. k -= 54; x *= two54; /* subnormal number, scale up x */
  80. GET_HIGH_WORD(hx,x);
  81. }
  82. if (hx >= 0x7ff00000) return x+x;
  83. k += (hx>>20)-1023;
  84. i = ((u_int32_t)k&0x80000000)>>31;
  85. hx = (hx&0x000fffff)|((0x3ff-i)<<20);
  86. y = (double)(k+i);
  87. SET_HIGH_WORD(x,hx);
  88. z = y*log10_2lo + ivln10*__ieee754_log(x);
  89. return z+y*log10_2hi;
  90. }