e_acos.c 3.4 KB

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  1. /* @(#)e_acos.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_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
  14. #endif
  15. /* __ieee754_acos(x)
  16. * Method :
  17. * acos(x) = pi/2 - asin(x)
  18. * acos(-x) = pi/2 + asin(x)
  19. * For |x|<=0.5
  20. * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
  21. * For x>0.5
  22. * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  23. * = 2asin(sqrt((1-x)/2))
  24. * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
  25. * = 2f + (2c + 2s*z*R(z))
  26. * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  27. * for f so that f+c ~ sqrt(z).
  28. * For x<-0.5
  29. * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  30. * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  31. *
  32. * Special cases:
  33. * if x is NaN, return x itself;
  34. * if |x|>1, return NaN with invalid signal.
  35. *
  36. * Function needed: __ieee754_sqrt
  37. */
  38. #include "math.h"
  39. #include "math_private.h"
  40. #ifdef __STDC__
  41. static const double
  42. #else
  43. static double
  44. #endif
  45. one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  46. pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  47. pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
  48. pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
  49. pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
  50. pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  51. pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
  52. pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  53. pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  54. pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
  55. qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  56. qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
  57. qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  58. qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
  59. #ifdef __STDC__
  60. double __ieee754_acos(double x)
  61. #else
  62. double __ieee754_acos(x)
  63. double x;
  64. #endif
  65. {
  66. double z,p,q,r,w,s,c,df;
  67. int32_t hx,ix;
  68. GET_HIGH_WORD(hx,x);
  69. ix = hx&0x7fffffff;
  70. if(ix>=0x3ff00000) { /* |x| >= 1 */
  71. u_int32_t lx;
  72. GET_LOW_WORD(lx,x);
  73. if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
  74. if(hx>0) return 0.0; /* acos(1) = 0 */
  75. else return pi+2.0*pio2_lo; /* acos(-1)= pi */
  76. }
  77. return (x-x)/(x-x); /* acos(|x|>1) is NaN */
  78. }
  79. if(ix<0x3fe00000) { /* |x| < 0.5 */
  80. if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
  81. z = x*x;
  82. p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  83. q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  84. r = p/q;
  85. return pio2_hi - (x - (pio2_lo-x*r));
  86. } else if (hx<0) { /* x < -0.5 */
  87. z = (one+x)*0.5;
  88. p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  89. q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  90. s = __ieee754_sqrt(z);
  91. r = p/q;
  92. w = r*s-pio2_lo;
  93. return pi - 2.0*(s+w);
  94. } else { /* x > 0.5 */
  95. z = (one-x)*0.5;
  96. s = __ieee754_sqrt(z);
  97. df = s;
  98. SET_LOW_WORD(df,0);
  99. c = (z-df*df)/(s+df);
  100. p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  101. q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  102. r = p/q;
  103. w = r*s+c;
  104. return 2.0*(df+w);
  105. }
  106. }