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Annotation of 43BSDReno/lib/libm/ieee/cabs.c, revision 1.1

1.1     ! root        1: /*
        !             2:  * Copyright (c) 1985 Regents of the University of California.
        !             3:  * All rights reserved.
        !             4:  *
        !             5:  * Redistribution and use in source and binary forms are permitted
        !             6:  * provided that: (1) source distributions retain this entire copyright
        !             7:  * notice and comment, and (2) distributions including binaries display
        !             8:  * the following acknowledgement:  ``This product includes software
        !             9:  * developed by the University of California, Berkeley and its contributors''
        !            10:  * in the documentation or other materials provided with the distribution
        !            11:  * and in all advertising materials mentioning features or use of this
        !            12:  * software. Neither the name of the University nor the names of its
        !            13:  * contributors may be used to endorse or promote products derived
        !            14:  * from this software without specific prior written permission.
        !            15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            18:  *
        !            19:  * All recipients should regard themselves as participants in an ongoing
        !            20:  * research project and hence should feel obligated to report their
        !            21:  * experiences (good or bad) with these elementary function codes, using
        !            22:  * the sendbug(8) program, to the authors.
        !            23:  */
        !            24: 
        !            25: #ifndef lint
        !            26: static char sccsid[] = "@(#)cabs.c     5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: /* HYPOT(X,Y)
        !            30:  * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
        !            31:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            32:  * CODED IN C BY K.C. NG, 11/28/84; 
        !            33:  * REVISED BY K.C. NG, 7/12/85.
        !            34:  *
        !            35:  * Required system supported functions :
        !            36:  *     copysign(x,y)
        !            37:  *     finite(x)
        !            38:  *     scalb(x,N)
        !            39:  *     sqrt(x)
        !            40:  *
        !            41:  * Method :
        !            42:  *     1. replace x by |x| and y by |y|, and swap x and
        !            43:  *        y if y > x (hence x is never smaller than y).
        !            44:  *     2. Hypot(x,y) is computed by:
        !            45:  *        Case I, x/y > 2
        !            46:  *             
        !            47:  *                                    y
        !            48:  *             hypot = x + -----------------------------
        !            49:  *                                         2
        !            50:  *                         sqrt ( 1 + [x/y]  )  +  x/y
        !            51:  *
        !            52:  *        Case II, x/y <= 2 
        !            53:  *                                                y
        !            54:  *             hypot = x + --------------------------------------------------
        !            55:  *                                                          2 
        !            56:  *                                                     [x/y]   -  2
        !            57:  *                        (sqrt(2)+1) + (x-y)/y + -----------------------------
        !            58:  *                                                               2
        !            59:  *                                               sqrt ( 1 + [x/y]  )  + sqrt(2)
        !            60:  *
        !            61:  *
        !            62:  *
        !            63:  * Special cases:
        !            64:  *     hypot(x,y) is INF if x or y is +INF or -INF; else
        !            65:  *     hypot(x,y) is NAN if x or y is NAN.
        !            66:  *
        !            67:  * Accuracy:
        !            68:  *     hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
        !            69:  *     in the last place). See Kahan's "Interval Arithmetic Options in the
        !            70:  *     Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
        !            71:  *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
        !            72:  *     code follows in comments.) In a test run with 500,000 random arguments
        !            73:  *     on a VAX, the maximum observed error was .959 ulps.
        !            74:  *
        !            75:  * Constants:
        !            76:  * The hexadecimal values are the intended ones for the following constants.
        !            77:  * The decimal values may be used, provided that the compiler will convert
        !            78:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            79:  * shown.
        !            80:  */
        !            81: #include "mathimpl.h"
        !            82: 
        !            83: vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
        !            84: vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
        !            85: vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)
        !            86: 
        !            87: ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
        !            88: ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
        !            89: ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)
        !            90: 
        !            91: #ifdef vccast
        !            92: #define        r2p1hi  vccast(r2p1hi)
        !            93: #define        r2p1lo  vccast(r2p1lo)
        !            94: #define        sqrt2   vccast(sqrt2)
        !            95: #endif
        !            96: 
        !            97: double
        !            98: hypot(x,y)
        !            99: double x, y;
        !           100: {
        !           101:        static const double zero=0, one=1, 
        !           102:                      small=1.0E-18;    /* fl(1+small)==1 */
        !           103:        static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
        !           104:        double t,r;
        !           105:        int exp;
        !           106: 
        !           107:        if(finite(x))
        !           108:            if(finite(y))
        !           109:            {   
        !           110:                x=copysign(x,one);
        !           111:                y=copysign(y,one);
        !           112:                if(y > x) 
        !           113:                    { t=x; x=y; y=t; }
        !           114:                if(x == zero) return(zero);
        !           115:                if(y == zero) return(x);
        !           116:                exp= logb(x);
        !           117:                if(exp-(int)logb(y) > ibig )    
        !           118:                        /* raise inexact flag and return |x| */
        !           119:                   { one+small; return(x); }
        !           120: 
        !           121:            /* start computing sqrt(x^2 + y^2) */
        !           122:                r=x-y;
        !           123:                if(r>y) {       /* x/y > 2 */
        !           124:                    r=x/y;
        !           125:                    r=r+sqrt(one+r*r); }
        !           126:                else {          /* 1 <= x/y <= 2 */
        !           127:                    r/=y; t=r*(r+2.0);
        !           128:                    r+=t/(sqrt2+sqrt(2.0+t));
        !           129:                    r+=r2p1lo; r+=r2p1hi; }
        !           130: 
        !           131:                r=y/r;
        !           132:                return(x+r);
        !           133: 
        !           134:            }
        !           135: 
        !           136:            else if(y==y)          /* y is +-INF */
        !           137:                     return(copysign(y,one));
        !           138:            else 
        !           139:                     return(y);    /* y is NaN and x is finite */
        !           140: 
        !           141:        else if(x==x)              /* x is +-INF */
        !           142:                 return (copysign(x,one));
        !           143:        else if(finite(y))
        !           144:                 return(x);                /* x is NaN, y is finite */
        !           145: #if !defined(vax)&&!defined(tahoe)
        !           146:        else if(y!=y) return(y);  /* x and y is NaN */
        !           147: #endif /* !defined(vax)&&!defined(tahoe) */
        !           148:        else return(copysign(y,one));   /* y is INF */
        !           149: }
        !           150: 
        !           151: /* CABS(Z)
        !           152:  * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
        !           153:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !           154:  * CODED IN C BY K.C. NG, 11/28/84.
        !           155:  * REVISED BY K.C. NG, 7/12/85.
        !           156:  *
        !           157:  * Required kernel function :
        !           158:  *     hypot(x,y)
        !           159:  *
        !           160:  * Method :
        !           161:  *     cabs(z) = hypot(x,y) .
        !           162:  */
        !           163: 
        !           164: double
        !           165: cabs(z)
        !           166: struct { double x, y;} z;
        !           167: {
        !           168:        return hypot(z.x,z.y);
        !           169: }
        !           170: 
        !           171: double
        !           172: z_abs(z)
        !           173: struct { double x,y;} *z;
        !           174: {
        !           175:        return hypot(z->x,z->y);
        !           176: }
        !           177: 
        !           178: /* A faster but less accurate version of cabs(x,y) */
        !           179: #if 0
        !           180: double hypot(x,y)
        !           181: double x, y;
        !           182: {
        !           183:        static const double zero=0, one=1;
        !           184:                      small=1.0E-18;    /* fl(1+small)==1 */
        !           185:        static const ibig=30;   /* fl(1+2**(2*ibig))==1 */
        !           186:        double temp;
        !           187:        int exp;
        !           188: 
        !           189:        if(finite(x))
        !           190:            if(finite(y))
        !           191:            {   
        !           192:                x=copysign(x,one);
        !           193:                y=copysign(y,one);
        !           194:                if(y > x) 
        !           195:                    { temp=x; x=y; y=temp; }
        !           196:                if(x == zero) return(zero);
        !           197:                if(y == zero) return(x);
        !           198:                exp= logb(x);
        !           199:                x=scalb(x,-exp);
        !           200:                if(exp-(int)logb(y) > ibig ) 
        !           201:                        /* raise inexact flag and return |x| */
        !           202:                   { one+small; return(scalb(x,exp)); }
        !           203:                else y=scalb(y,-exp);
        !           204:                return(scalb(sqrt(x*x+y*y),exp));
        !           205:            }
        !           206: 
        !           207:            else if(y==y)          /* y is +-INF */
        !           208:                     return(copysign(y,one));
        !           209:            else 
        !           210:                     return(y);    /* y is NaN and x is finite */
        !           211: 
        !           212:        else if(x==x)              /* x is +-INF */
        !           213:                 return (copysign(x,one));
        !           214:        else if(finite(y))
        !           215:                 return(x);                /* x is NaN, y is finite */
        !           216:        else if(y!=y) return(y);        /* x and y is NaN */
        !           217:        else return(copysign(y,one));   /* y is INF */
        !           218: }
        !           219: #endif

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