nsz Git - musl/blob - src/math/acos.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, 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 /* acos(x)
  13  * Method :
  14  *      acos(x)  = pi/2 - asin(x)
  15  *      acos(-x) = pi/2 + asin(x)
  16  * For |x|<=0.5
  17  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  18  * For x>0.5
  19  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  20  *              = 2asin(sqrt((1-x)/2))
  21  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  22  *              = 2f + (2c + 2s*z*R(z))
  23  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  24  *     for f so that f+c ~ sqrt(z).
  25  * For x<-0.5
  26  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  27  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  28  *
  29  * Special cases:
  30  *      if x is NaN, return x itself;
  31  *      if |x|>1, return NaN with invalid signal.
  32  *
  33  * Function needed: sqrt
  34  */
  35
  36 #include "libm.h"
  37
  38 static const double
  39 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  40 pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  41 pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
  42 static const volatile double
  43 pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
  44 static const double
  45 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
  46 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  47 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
  48 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  49 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  50 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
  51 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  52 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
  53 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  54 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
  55
  56 double acos(double x)
  57 {
  58         double z,p,q,r,w,s,c,df;
  59         int32_t hx,ix;
  60
  61         GET_HIGH_WORD(hx, x);
  62         ix = hx & 0x7fffffff;
  63         if (ix >= 0x3ff00000) {  /* |x| >= 1 */
  64                 uint32_t lx;
  65
  66                 GET_LOW_WORD(lx,x);
  67                 if ((ix-0x3ff00000 | lx) == 0) {  /* |x|==1 */
  68                         if (hx > 0) return 0.0;  /* acos(1) = 0  */
  69                         return pi + 2.0*pio2_lo; /* acos(-1)= pi */
  70                 }
  71                 return (x-x)/(x-x);  /* acos(|x|>1) is NaN */
  72         }
  73         if (ix < 0x3fe00000) {   /* |x| < 0.5 */
  74                 if (ix <= 0x3c600000)  /* |x| < 2**-57 */
  75                         return pio2_hi + pio2_lo;
  76                 z = x*x;
  77                 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  78                 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  79                 r = p/q;
  80                 return pio2_hi - (x - (pio2_lo-x*r));
  81         } else if (hx < 0) {     /* x < -0.5 */
  82                 z = (one+x)*0.5;
  83                 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  84                 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  85                 s = sqrt(z);
  86                 r = p/q;
  87                 w = r*s-pio2_lo;
  88                 return pi - 2.0*(s+w);
  89         } else {                 /* x > 0.5 */
  90                 z = (one-x)*0.5;
  91                 s = sqrt(z);
  92                 df = s;
  93                 SET_LOW_WORD(df,0);
  94                 c  = (z-df*df)/(s+df);
  95                 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
  96                 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  97                 r = p/q;
  98                 w = r*s+c;
  99                 return 2.0*(df+w);
 100         }
 101 }