log1pf.c 2.9 KB

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  1. /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
  2. /*
  3. * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
  4. */
  5. /*
  6. * ====================================================
  7. * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  8. *
  9. * Developed at SunPro, a Sun Microsystems, Inc. business.
  10. * Permission to use, copy, modify, and distribute this
  11. * software is freely granted, provided that this notice
  12. * is preserved.
  13. * ====================================================
  14. */
  15. #include "libm.h"
  16. static const float
  17. ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
  18. ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
  19. two25 = 3.355443200e+07, /* 0x4c000000 */
  20. Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  21. Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  22. Lp3 = 2.8571429849e-01, /* 3E924925 */
  23. Lp4 = 2.2222198546e-01, /* 3E638E29 */
  24. Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  25. Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  26. Lp7 = 1.4798198640e-01; /* 3E178897 */
  27. float log1pf(float x)
  28. {
  29. float hfsq,f,c,s,z,R,u;
  30. int32_t k,hx,hu,ax;
  31. GET_FLOAT_WORD(hx, x);
  32. ax = hx & 0x7fffffff;
  33. k = 1;
  34. if (hx < 0x3ed413d0) { /* 1+x < sqrt(2)+ */
  35. if (ax >= 0x3f800000) { /* x <= -1.0 */
  36. if (x == -1.0f)
  37. return -two25/0.0f; /* log1p(-1)=+inf */
  38. return (x-x)/(x-x); /* log1p(x<-1)=NaN */
  39. }
  40. if (ax < 0x38000000) { /* |x| < 2**-15 */
  41. /* if 0x1p-126 <= |x| < 0x1p-24, avoid raising underflow */
  42. if (ax < 0x33800000 && ax >= 0x00800000)
  43. return x;
  44. #if FLT_EVAL_METHOD != 0
  45. FORCE_EVAL(x*x);
  46. #endif
  47. return x - x*x*0.5f;
  48. }
  49. if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  50. k = 0;
  51. f = x;
  52. hu = 1;
  53. }
  54. }
  55. if (hx >= 0x7f800000)
  56. return x+x;
  57. if (k != 0) {
  58. if (hx < 0x5a000000) {
  59. u = 1 + x;
  60. GET_FLOAT_WORD(hu, u);
  61. k = (hu>>23) - 127;
  62. /* correction term */
  63. c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
  64. c /= u;
  65. } else {
  66. u = x;
  67. GET_FLOAT_WORD(hu,u);
  68. k = (hu>>23) - 127;
  69. c = 0;
  70. }
  71. hu &= 0x007fffff;
  72. /*
  73. * The approximation to sqrt(2) used in thresholds is not
  74. * critical. However, the ones used above must give less
  75. * strict bounds than the one here so that the k==0 case is
  76. * never reached from here, since here we have committed to
  77. * using the correction term but don't use it if k==0.
  78. */
  79. if (hu < 0x3504f4) { /* u < sqrt(2) */
  80. SET_FLOAT_WORD(u, hu|0x3f800000); /* normalize u */
  81. } else {
  82. k += 1;
  83. SET_FLOAT_WORD(u, hu|0x3f000000); /* normalize u/2 */
  84. hu = (0x00800000-hu)>>2;
  85. }
  86. f = u - 1.0f;
  87. }
  88. hfsq = 0.5f * f * f;
  89. if (hu == 0) { /* |f| < 2**-20 */
  90. if (f == 0.0f) {
  91. if (k == 0)
  92. return 0.0f;
  93. c += k*ln2_lo;
  94. return k*ln2_hi+c;
  95. }
  96. R = hfsq*(1.0f - 0.66666666666666666f * f);
  97. if (k == 0)
  98. return f - R;
  99. return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
  100. }
  101. s = f/(2.0f + f);
  102. z = s*s;
  103. R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
  104. if (k == 0)
  105. return f - (hfsq-s*(hfsq+R));
  106. return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
  107. }