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Annotation of src/lib/libm/src/e_atan2.c, Revision 1.6

1.1       jtc         1: /* @(#)e_atan2.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:
                     13: #ifndef lint
1.6     ! jtc        14: static char rcsid[] = "$Id: e_atan2.c,v 1.5 1994/08/10 20:30:35 jtc Exp $";
1.3       jtc        15: #endif
1.1       jtc        16:
                     17: /* __ieee754_atan2(y,x)
                     18:  * Method :
                     19:  *     1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
                     20:  *     2. Reduce x to positive by (if x and y are unexceptional):
                     21:  *             ARG (x+iy) = arctan(y/x)           ... if x > 0,
                     22:  *             ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
                     23:  *
                     24:  * Special cases:
                     25:  *
                     26:  *     ATAN2((anything), NaN ) is NaN;
                     27:  *     ATAN2(NAN , (anything) ) is NaN;
                     28:  *     ATAN2(+-0, +(anything but NaN)) is +-0  ;
                     29:  *     ATAN2(+-0, -(anything but NaN)) is +-pi ;
                     30:  *     ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
                     31:  *     ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
                     32:  *     ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
                     33:  *     ATAN2(+-INF,+INF ) is +-pi/4 ;
                     34:  *     ATAN2(+-INF,-INF ) is +-3pi/4;
                     35:  *     ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
                     36:  *
                     37:  * Constants:
                     38:  * The hexadecimal values are the intended ones for the following
                     39:  * constants. The decimal values may be used, provided that the
                     40:  * compiler will convert from decimal to binary accurately enough
                     41:  * to produce the hexadecimal values shown.
                     42:  */
                     43:
1.5       jtc        44: #include "math.h"
                     45: #include "math_private.h"
1.1       jtc        46:
                     47: #ifdef __STDC__
                     48: static const double
                     49: #else
                     50: static double
                     51: #endif
                     52: tiny  = 1.0e-300,
                     53: zero  = 0.0,
                     54: pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
                     55: pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
                     56: pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
                     57: pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
                     58:
                     59: #ifdef __STDC__
                     60:        double __ieee754_atan2(double y, double x)
                     61: #else
                     62:        double __ieee754_atan2(y,x)
                     63:        double  y,x;
                     64: #endif
                     65: {
                     66:        double z;
1.6     ! jtc        67:        int32_t k,m,hx,hy,ix,iy;
        !            68:        u_int32_t lx,ly;
1.1       jtc        69:
1.5       jtc        70:        EXTRACT_WORDS(hx,lx,x);
                     71:        ix = hx&0x7fffffff;
                     72:        EXTRACT_WORDS(hy,ly,y);
                     73:        iy = hy&0x7fffffff;
1.1       jtc        74:        if(((ix|((lx|-lx)>>31))>0x7ff00000)||
                     75:           ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
                     76:           return x+y;
                     77:        if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
                     78:        m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
                     79:
                     80:     /* when y = 0 */
                     81:        if((iy|ly)==0) {
                     82:            switch(m) {
                     83:                case 0:
                     84:                case 1: return y;       /* atan(+-0,+anything)=+-0 */
                     85:                case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
                     86:                case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
                     87:            }
                     88:        }
                     89:     /* when x = 0 */
                     90:        if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
                     91:
                     92:     /* when x is INF */
                     93:        if(ix==0x7ff00000) {
                     94:            if(iy==0x7ff00000) {
                     95:                switch(m) {
                     96:                    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
                     97:                    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
                     98:                    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
                     99:                    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
                    100:                }
                    101:            } else {
                    102:                switch(m) {
                    103:                    case 0: return  zero  ;     /* atan(+...,+INF) */
                    104:                    case 1: return -zero  ;     /* atan(-...,+INF) */
                    105:                    case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
                    106:                    case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
                    107:                }
                    108:            }
                    109:        }
                    110:     /* when y is INF */
                    111:        if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
                    112:
                    113:     /* compute y/x */
                    114:        k = (iy-ix)>>20;
                    115:        if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
                    116:        else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
                    117:        else z=atan(fabs(y/x));         /* safe to do y/x */
                    118:        switch (m) {
                    119:            case 0: return       z  ;   /* atan(+,+) */
1.5       jtc       120:            case 1: {
1.6     ! jtc       121:                      u_int32_t zh;
1.5       jtc       122:                      GET_HIGH_WORD(zh,z);
                    123:                      SET_HIGH_WORD(z,zh ^ 0x80000000);
                    124:                    }
1.1       jtc       125:                    return       z  ;   /* atan(-,+) */
                    126:            case 2: return  pi-(z-pi_lo);/* atan(+,-) */
                    127:            default: /* case 3 */
                    128:                    return  (z-pi_lo)-pi;/* atan(-,-) */
                    129:        }
                    130: }