gonzui

    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: 
   13: /* acos(x)
   14:  * Method :                  
   15:  *      acos(x)  = pi/2 - asin(x)
   16:  *      acos(-x) = pi/2 + asin(x)
   17:  * For |x|<=0.5
   18:  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))  (see asin.c)
   19:  * For x>0.5
   20:  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
   21:  *              = 2asin(sqrt((1-x)/2))  
   22:  *              = 2s + 2s*z*R(z)    ...z=(1-x)/2, s=sqrt(z)
   23:  *              = 2f + (2c + 2s*z*R(z))
   24:  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
   25:  *     for f so that f+c ~ sqrt(z).
   26:  * For x<-0.5
   27:  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
   28:  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
   29:  *
   30:  * Special cases:
   31:  *      if x is NaN, return x itself;
   32:  *      if |x|>1, return NaN with invalid signal.
   33:  *
   34:  * Function needed: sqrt
   35:  */
   36: 
   37: /* LINTLIBRARY */
   38: 
   39: #include <sys/cdefs.h>
   40: #include <float.h>
   41: #include <math.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: pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
   50: pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
   51: pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
   52: pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
   53: pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
   54: pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
   55: pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
   56: qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
   57: qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
   58: qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
   59: qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
   60: 
   61: double
   62: acos(double x)
   63: {
   64:         double z,p,q,r,w,s,c,df;
   65:         int32_t hx,ix;
   66:         GET_HIGH_WORD(hx,x);
   67:         ix = hx&0x7fffffff;
   68:         if(ix>=0x3ff00000) {   /* |x| >= 1 */
   69:             u_int32_t lx;
   70:             GET_LOW_WORD(lx,x);
   71:             if(((ix-0x3ff00000)|lx)==0) {      /* |x|==1 */
   72:                 if(hx>0) return 0.0;          /* acos(1) = 0  */
   73:                 else return pi+2.0*pio2_lo;   /* acos(-1)= pi */
   74:             }
   75:             return (x-x)/(x-x);                /* acos(|x|>1) is NaN */
   76:         }
   77:         if(ix<0x3fe00000) {    /* |x| < 0.5 */
   78:             if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
   79:             z = x*x;
   80:             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
   81:             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
   82:             r = p/q;
   83:             return pio2_hi - (x - (pio2_lo-x*r));
   84:         } else  if (hx<0) {            /* x < -0.5 */
   85:             z = (one+x)*0.5;
   86:             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
   87:             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
   88:             s = sqrt(z);
   89:             r = p/q;
   90:             w = r*s-pio2_lo;
   91:             return pi - 2.0*(s+w);
   92:         } else {                       /* x > 0.5 */
   93:             z = (one-x)*0.5;
   94:             s = sqrt(z);
   95:             df = s;
   96:             SET_LOW_WORD(df,0);
   97:             c  = (z-df*df)/(s+df);
   98:             p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
   99:             q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
  100:             r = p/q;
  101:             w = r*s+c;
  102:             return 2.0*(df+w);
  103:         }
  104: }
  105: 
  106: #if     LDBL_MANT_DIG == 53
  107: #ifdef  lint
  108: /* PROTOLIB1 */
  109: long double acosl(long double);
  110: #else   /* lint */
  111: __weak_alias(acosl, acos);
  112: #endif  /* lint */
  113: #endif  /* LDBL_MANT_DIG == 53 */