sysdeps/libm-ieee754/e_acos.c

   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 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
  13    for performance improvement on pipelined processors.
  14  */
  15
  16 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: e_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
  18 #endif
  19
  20 /* __ieee754_acos(x)
  21  * Method :
  22  *      acos(x)  = pi/2 - asin(x)
  23  *      acos(-x) = pi/2 + asin(x)
  24  * For |x|<=0.5
  25  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  26  * For x>0.5
  27  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  28  *              = 2asin(sqrt((1-x)/2))
  29  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  30  *              = 2f + (2c + 2s*z*R(z))
  31  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  32  *     for f so that f+c ~ sqrt(z).
  33  * For x<-0.5
  34  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  35  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  36  *
  37  * Special cases:
  38  *      if x is NaN, return x itself;
  39  *      if |x|>1, return NaN with invalid signal.
  40  *
  41  * Function needed: __ieee754_sqrt
  42  */
  43
  44 #include "math.h"
  45 #include "math_private.h"
  46 #define one qS[0]
  47
  48 #ifdef __STDC__
  49 static const double
  50 #else
  51 static double
  52 #endif
  53 pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
  54 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
  55 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
  56 pS[] =  {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
  57  -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
  58   2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
  59  -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
  60   7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
  61   3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */
  62 qS[] ={1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
  63   2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
  64  -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
  65   7.70381505559019352791e-02}; /* 0x3FB3B8C5, 0xB12E9282 */
  66
  67 #ifdef __STDC__
  68         double __ieee754_acos(double x)
  69 #else
  70         double __ieee754_acos(x)
  71         double x;
  72 #endif
  73 {
  74         double z,p,q,r,w,s,c,df,p1,p2,p3,q1,q2,z2,z4,z6;
  75         int32_t hx,ix;
  76         GET_HIGH_WORD(hx,x);
  77         ix = hx&0x7fffffff;
  78         if(ix>=0x3ff00000) {    /* |x| >= 1 */
  79             u_int32_t lx;
  80             GET_LOW_WORD(lx,x);
  81             if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
  82                 if(hx>0) return 0.0;            /* acos(1) = 0  */
  83                 else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
  84             }
  85             return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
  86         }
  87         if(ix<0x3fe00000) {     /* |x| < 0.5 */
  88             if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
  89             z = x*x;
  90 #ifdef DO_NOT_USE_THIS
  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 #else
  94             p1 = z*pS[0]; z2=z*z;
  95             p2 = pS[1]+z*pS[2]; z4=z2*z2;
  96             p3 = pS[3]+z*pS[4]; z6=z4*z2;
  97             q1 = one+z*qS[1];
  98             q2 = qS[2]+z*qS[3];
  99             p = p1 + z2*p2 + z4*p3 + z6*pS[5];
 100             q = q1 + z2*q2 + z4*qS[4];
 101 #endif
 102             r = p/q;
 103             return pio2_hi - (x - (pio2_lo-x*r));
 104         } else  if (hx<0) {             /* x < -0.5 */
 105             z = (one+x)*0.5;
 106 #ifdef DO_NOT_USE_THIS
 107             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
 108             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
 109 #else
 110             p1 = z*pS[0]; z2=z*z;
 111             p2 = pS[1]+z*pS[2]; z4=z2*z2;
 112             p3 = pS[3]+z*pS[4]; z6=z4*z2;
 113             q1 = one+z*qS[1];
 114             q2 = qS[2]+z*qS[3];
 115             p = p1 + z2*p2 + z4*p3 + z6*pS[5];
 116             q = q1 + z2*q2 + z4*qS[4];
 117 #endif
 118             s = __ieee754_sqrt(z);
 119             r = p/q;
 120             w = r*s-pio2_lo;
 121             return pi - 2.0*(s+w);
 122         } else {                        /* x > 0.5 */
 123             z = (one-x)*0.5;
 124             s = __ieee754_sqrt(z);
 125             df = s;
 126             SET_LOW_WORD(df,0);
 127             c  = (z-df*df)/(s+df);
 128 #ifdef DO_NOT_USE_THIS
 129             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
 130             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
 131 #else
 132             p1 = z*pS[0]; z2=z*z;
 133             p2 = pS[1]+z*pS[2]; z4=z2*z2;
 134             p3 = pS[3]+z*pS[4]; z6=z4*z2;
 135             q1 = one+z*qS[1];
 136             q2 = qS[2]+z*qS[3];
 137             p = p1 + z2*p2 + z4*p3 + z6*pS[5];
 138             q = q1 + z2*q2 + z4*qS[4];
 139 #endif
 140             r = p/q;
 141             w = r*s+c;
 142             return 2.0*(df+w);
 143         }
 144 }