Line data    Source code

       1             : 
       2             : /* @(#)e_acos.c 1.3 95/01/18 */
       3             : /*
       4             :  * ====================================================
       5             :  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       6             :  *
       7             :  * Developed at SunSoft, 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             : //#include <sys/cdefs.h>
      15             : //__FBSDID("$FreeBSD$");
      16             : 
      17             : /* __ieee754_acos(x)
      18             :  * Method :                  
      19             :  *      acos(x)  = pi/2 - asin(x)
      20             :  *      acos(-x) = pi/2 + asin(x)
      21             :  * For |x|<=0.5
      22             :  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
      23             :  * For x>0.5
      24             :  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
      25             :  *              = 2asin(sqrt((1-x)/2))  
      26             :  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
      27             :  *              = 2f + (2c + 2s*z*R(z))
      28             :  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
      29             :  *     for f so that f+c ~ sqrt(z).
      30             :  * For x<-0.5
      31             :  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
      32             :  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
      33             :  *
      34             :  * Special cases:
      35             :  *      if x is NaN, return x itself;
      36             :  *      if |x|>1, return NaN with invalid signal.
      37             :  *
      38             :  * Function needed: sqrt
      39             :  */
      40             : 
      41             : #include <float.h>
      42             : 
      43             : #include "math_private.h"
      44             : 
      45             : static const double
      46             : one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
      47             : pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
      48             : pio2_hi =  1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
      49             : static volatile double
      50             : pio2_lo =  6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
      51             : static const double
      52             : pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
      53             : pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
      54             : pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
      55             : pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
      56             : pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
      57             : pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
      58             : qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
      59             : qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
      60             : qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
      61             : qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
      62             : 
      63             : double
      64           0 : __ieee754_acos(double x)
      65             : {
      66             :         double z,p,q,r,w,s,c,df;
      67             :         int32_t hx,ix;
      68           0 :         GET_HIGH_WORD(hx,x);
      69           0 :         ix = hx&0x7fffffff;
      70           0 :         if(ix>=0x3ff00000) { /* |x| >= 1 */
      71             :             u_int32_t lx;
      72           0 :             GET_LOW_WORD(lx,x);
      73           0 :             if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
      74           0 :                 if(hx>0) return 0.0;         /* acos(1) = 0  */
      75           0 :                 else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
      76             :             }
      77           0 :             return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
      78             :         }
      79           0 :         if(ix<0x3fe00000) {  /* |x| < 0.5 */
      80           0 :             if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
      81           0 :             z = x*x;
      82           0 :             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
      83           0 :             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
      84           0 :             r = p/q;
      85           0 :             return pio2_hi - (x - (pio2_lo-x*r));
      86           0 :         } else  if (hx<0) {          /* x < -0.5 */
      87           0 :             z = (one+x)*0.5;
      88           0 :             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
      89           0 :             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
      90           0 :             s = sqrt(z);
      91           0 :             r = p/q;
      92           0 :             w = r*s-pio2_lo;
      93           0 :             return pi - 2.0*(s+w);
      94             :         } else {                        /* x > 0.5 */
      95           0 :             z = (one-x)*0.5;
      96           0 :             s = sqrt(z);
      97           0 :             df = s;
      98           0 :             SET_LOW_WORD(df,0);
      99           0 :             c  = (z-df*df)/(s+df);
     100           0 :             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
     101           0 :             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
     102           0 :             r = p/q;
     103           0 :             w = r*s+c;
     104           0 :             return 2.0*(df+w);
     105             :         }
     106             : }