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Annotation of src/lib/libm/src/e_acos.c, Revision 1.7

1.1       jtc         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:  */
1.3       jtc        12:
1.7     ! jtc        13: #if defined(LIBM_SCCS) && !defined(lint)
        !            14: static char rcsid[] = "$Id: e_acos.c,v 1.6 1994/08/18 23:04:51 jtc Exp $";
1.3       jtc        15: #endif
1.1       jtc        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:
1.5       jtc        41: #include "math.h"
                     42: #include "math_private.h"
1.1       jtc        43:
                     44: #ifdef __STDC__
                     45: static const double
                     46: #else
                     47: static double
                     48: #endif
                     49: one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
                     50: pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
                     51: pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
                     52: pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
                     53: pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
                     54: pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
                     55: pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
                     56: pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
                     57: pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
                     58: pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
                     59: qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
                     60: qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
                     61: qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
                     62: qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
                     63:
                     64: #ifdef __STDC__
                     65:        double __ieee754_acos(double x)
                     66: #else
                     67:        double __ieee754_acos(x)
                     68:        double x;
                     69: #endif
                     70: {
                     71:        double z,p,q,r,w,s,c,df;
1.6       jtc        72:        int32_t hx,ix;
1.5       jtc        73:        GET_HIGH_WORD(hx,x);
1.1       jtc        74:        ix = hx&0x7fffffff;
                     75:        if(ix>=0x3ff00000) {    /* |x| >= 1 */
1.6       jtc        76:            u_int32_t lx;
1.5       jtc        77:            GET_LOW_WORD(lx,x);
                     78:            if(((ix-0x3ff00000)|lx)==0) {       /* |x|==1 */
1.1       jtc        79:                if(hx>0) return 0.0;            /* acos(1) = 0  */
                     80:                else return pi+2.0*pio2_lo;     /* acos(-1)= pi */
                     81:            }
                     82:            return (x-x)/(x-x);         /* acos(|x|>1) is NaN */
                     83:        }
                     84:        if(ix<0x3fe00000) {     /* |x| < 0.5 */
                     85:            if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
                     86:            z = x*x;
                     87:            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
                     88:            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
                     89:            r = p/q;
                     90:            return pio2_hi - (x - (pio2_lo-x*r));
                     91:        } else  if (hx<0) {             /* x < -0.5 */
                     92:            z = (one+x)*0.5;
                     93:            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
                     94:            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
                     95:            s = sqrt(z);
                     96:            r = p/q;
                     97:            w = r*s-pio2_lo;
                     98:            return pi - 2.0*(s+w);
                     99:        } else {                        /* x > 0.5 */
                    100:            z = (one-x)*0.5;
                    101:            s = sqrt(z);
                    102:            df = s;
1.5       jtc       103:            SET_LOW_WORD(df,0);
1.1       jtc       104:            c  = (z-df*df)/(s+df);
                    105:            p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
                    106:            q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
                    107:            r = p/q;
                    108:            w = r*s+c;
                    109:            return 2.0*(df+w);
                    110:        }
                    111: }

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