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  1.  
  2. /* @(#)e_acos.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_acos(x)
  15.  * Method :                  
  16.  *      acos(x)  = pi/2 - asin(x)
  17.  *      acos(-x) = pi/2 + asin(x)
  18.  * For |x|<=0.5
  19.  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  20.  * For x>0.5
  21.  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  22.  *              = 2asin(sqrt((1-x)/2))  
  23.  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  24.  *              = 2f + (2c + 2s*z*R(z))
  25.  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  26.  *     for f so that f+c ~ sqrt(z).
  27.  * For x<-0.5
  28.  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  29.  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  30.  *
  31.  * Special cases:
  32.  *      if x is NaN, return x itself;
  33.  *      if |x|>1, return NaN with invalid signal.
  34.  *
  35.  * Function needed: sqrt
  36.  */
  37.  
  38. #include "fdlibm.h"
  39.  
  40. #ifndef _DOUBLE_IS_32BITS
  41.  
  42. #ifdef __STDC__
  43. static const double
  44. #else
  45. static double
  46. #endif
  47. one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  48. pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  49. pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
  50. pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
  51. pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
  52. pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  53. pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
  54. pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  55. pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  56. pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
  57. qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  58. qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
  59. qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  60. qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
  61.  
  62. #ifdef __STDC__
  63.         double __ieee754_acos(double x)
  64. #else
  65.         double __ieee754_acos(x)
  66.         double x;
  67. #endif
  68. {
  69.         double z,p,q,r,w,s,c,df;
  70.         __int32_t hx,ix;
  71.         GET_HIGH_WORD(hx,x);
  72.         ix = hx&0x7fffffff;
  73.         if(ix>=0x3ff00000) {    /* |x| >= 1 */
  74.             __uint32_t lx;
  75.             GET_LOW_WORD(lx,x);
  76.             if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
  77.                 if(hx>0) return 0.0;            /* acos(1) = 0  */
  78.                 else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
  79.             }
  80.             return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
  81.         }
  82.         if(ix<0x3fe00000) {     /* |x| < 0.5 */
  83.             if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
  84.             z = x*x;
  85.             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  86.             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  87.             r = p/q;
  88.             return pio2_hi - (x - (pio2_lo-x*r));
  89.         } else  if (hx<0) {             /* x < -0.5 */
  90.             z = (one+x)*0.5;
  91.             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  92.             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  93.             s = __ieee754_sqrt(z);
  94.             r = p/q;
  95.             w = r*s-pio2_lo;
  96.             return pi - 2.0*(s+w);
  97.         } else {                        /* x > 0.5 */
  98.             z = (one-x)*0.5;
  99.             s = __ieee754_sqrt(z);
  100.             df = s;
  101.             SET_LOW_WORD(df,0);
  102.             c  = (z-df*df)/(s+df);
  103.             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  104.             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  105.             r = p/q;
  106.             w = r*s+c;
  107.             return 2.0*(df+w);
  108.         }
  109. }
  110.  
  111. #endif /* defined(_DOUBLE_IS_32BITS) */
  112.