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Annotation of 43BSDTahoe/usr.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 the above copyright notice and this paragraph are
        !             7:  * duplicated in all such forms and that any documentation,
        !             8:  * advertising materials, and other materials related to such
        !             9:  * distribution and use acknowledge that the software was developed
        !            10:  * by the University of California, Berkeley.  The name of the
        !            11:  * University may not be used to endorse or promote products derived
        !            12:  * from this software without specific prior written permission.
        !            13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            16:  *
        !            17:  * All recipients should regard themselves as participants in an ongoing
        !            18:  * research project and hence should feel obligated to report their
        !            19:  * experiences (good or bad) with these elementary function codes, using
        !            20:  * the sendbug(8) program, to the authors.
        !            21:  */
        !            22: 
        !            23: #ifndef lint
        !            24: static char sccsid[] = "@(#)cabs.c     5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* HYPOT(X,Y)
        !            28:  * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
        !            29:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            30:  * CODED IN C BY K.C. NG, 11/28/84; 
        !            31:  * REVISED BY K.C. NG, 7/12/85.
        !            32:  *
        !            33:  * Required system supported functions :
        !            34:  *     copysign(x,y)
        !            35:  *     finite(x)
        !            36:  *     scalb(x,N)
        !            37:  *     sqrt(x)
        !            38:  *
        !            39:  * Method :
        !            40:  *     1. replace x by |x| and y by |y|, and swap x and
        !            41:  *        y if y > x (hence x is never smaller than y).
        !            42:  *     2. Hypot(x,y) is computed by:
        !            43:  *        Case I, x/y > 2
        !            44:  *             
        !            45:  *                                    y
        !            46:  *             hypot = x + -----------------------------
        !            47:  *                                         2
        !            48:  *                         sqrt ( 1 + [x/y]  )  +  x/y
        !            49:  *
        !            50:  *        Case II, x/y <= 2 
        !            51:  *                                                y
        !            52:  *             hypot = x + --------------------------------------------------
        !            53:  *                                                          2 
        !            54:  *                                                     [x/y]   -  2
        !            55:  *                        (sqrt(2)+1) + (x-y)/y + -----------------------------
        !            56:  *                                                               2
        !            57:  *                                               sqrt ( 1 + [x/y]  )  + sqrt(2)
        !            58:  *
        !            59:  *
        !            60:  *
        !            61:  * Special cases:
        !            62:  *     hypot(x,y) is INF if x or y is +INF or -INF; else
        !            63:  *     hypot(x,y) is NAN if x or y is NAN.
        !            64:  *
        !            65:  * Accuracy:
        !            66:  *     hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
        !            67:  *     in the last place). See Kahan's "Interval Arithmetic Options in the
        !            68:  *     Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
        !            69:  *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
        !            70:  *     code follows in comments.) In a test run with 500,000 random arguments
        !            71:  *     on a VAX, the maximum observed error was .959 ulps.
        !            72:  *
        !            73:  * Constants:
        !            74:  * The hexadecimal values are the intended ones for the following constants.
        !            75:  * The decimal values may be used, provided that the compiler will convert
        !            76:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            77:  * shown.
        !            78:  */
        !            79: 
        !            80: #if defined(vax)||defined(tahoe)       /* VAX D format */
        !            81: #ifdef vax
        !            82: #define _0x(A,B)       0x/**/A/**/B
        !            83: #else  /* vax */
        !            84: #define _0x(A,B)       0x/**/B/**/A
        !            85: #endif /* vax */
        !            86: /* static double */
        !            87: /* r2p1hi =  2.4142135623730950345E0     , Hex  2^  2   *  .9A827999FCEF32 */
        !            88: /* r2p1lo =  1.4349369327986523769E-17   , Hex  2^-55   *  .84597D89B3754B */
        !            89: /* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
        !            90: static long    r2p1hix[] = { _0x(8279,411a), _0x(ef32,99fc)};
        !            91: static long    r2p1lox[] = { _0x(597d,2484), _0x(754b,89b3)};
        !            92: static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
        !            93: #define   r2p1hi    (*(double*)r2p1hix)
        !            94: #define   r2p1lo    (*(double*)r2p1lox)
        !            95: #define    sqrt2    (*(double*)sqrt2x)
        !            96: #else  /* defined(vax)||defined(tahoe) */
        !            97: static double
        !            98: r2p1hi =  2.4142135623730949234E0     , /*Hex  2^1     *  1.3504F333F9DE6 */
        !            99: r2p1lo =  1.2537167179050217666E-16   , /*Hex  2^-53   *  1.21165F626CDD5 */
        !           100: sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
        !           101: #endif /* defined(vax)||defined(tahoe) */
        !           102: 
        !           103: double
        !           104: hypot(x,y)
        !           105: double x, y;
        !           106: {
        !           107:        static double zero=0, one=1, 
        !           108:                      small=1.0E-18;    /* fl(1+small)==1 */
        !           109:        static ibig=30; /* fl(1+2**(2*ibig))==1 */
        !           110:        double copysign(),scalb(),logb(),sqrt(),t,r;
        !           111:        int finite(), exp;
        !           112: 
        !           113:        if(finite(x))
        !           114:            if(finite(y))
        !           115:            {   
        !           116:                x=copysign(x,one);
        !           117:                y=copysign(y,one);
        !           118:                if(y > x) 
        !           119:                    { t=x; x=y; y=t; }
        !           120:                if(x == zero) return(zero);
        !           121:                if(y == zero) return(x);
        !           122:                exp= logb(x);
        !           123:                if(exp-(int)logb(y) > ibig )    
        !           124:                        /* raise inexact flag and return |x| */
        !           125:                   { one+small; return(x); }
        !           126: 
        !           127:            /* start computing sqrt(x^2 + y^2) */
        !           128:                r=x-y;
        !           129:                if(r>y) {       /* x/y > 2 */
        !           130:                    r=x/y;
        !           131:                    r=r+sqrt(one+r*r); }
        !           132:                else {          /* 1 <= x/y <= 2 */
        !           133:                    r/=y; t=r*(r+2.0);
        !           134:                    r+=t/(sqrt2+sqrt(2.0+t));
        !           135:                    r+=r2p1lo; r+=r2p1hi; }
        !           136: 
        !           137:                r=y/r;
        !           138:                return(x+r);
        !           139: 
        !           140:            }
        !           141: 
        !           142:            else if(y==y)          /* y is +-INF */
        !           143:                     return(copysign(y,one));
        !           144:            else 
        !           145:                     return(y);    /* y is NaN and x is finite */
        !           146: 
        !           147:        else if(x==x)              /* x is +-INF */
        !           148:                 return (copysign(x,one));
        !           149:        else if(finite(y))
        !           150:                 return(x);                /* x is NaN, y is finite */
        !           151: #if !defined(vax)&&!defined(tahoe)
        !           152:        else if(y!=y) return(y);  /* x and y is NaN */
        !           153: #endif /* !defined(vax)&&!defined(tahoe) */
        !           154:        else return(copysign(y,one));   /* y is INF */
        !           155: }
        !           156: 
        !           157: /* CABS(Z)
        !           158:  * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
        !           159:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !           160:  * CODED IN C BY K.C. NG, 11/28/84.
        !           161:  * REVISED BY K.C. NG, 7/12/85.
        !           162:  *
        !           163:  * Required kernel function :
        !           164:  *     hypot(x,y)
        !           165:  *
        !           166:  * Method :
        !           167:  *     cabs(z) = hypot(x,y) .
        !           168:  */
        !           169: 
        !           170: double
        !           171: cabs(z)
        !           172: struct { double x, y;} z;
        !           173: {
        !           174:        return hypot(z.x,z.y);
        !           175: }
        !           176: 
        !           177: double
        !           178: z_abs(z)
        !           179: struct { double x,y;} *z;
        !           180: {
        !           181:        return hypot(z->x,z->y);
        !           182: }
        !           183: 
        !           184: /* A faster but less accurate version of cabs(x,y) */
        !           185: #if 0
        !           186: double hypot(x,y)
        !           187: double x, y;
        !           188: {
        !           189:        static double zero=0, one=1;
        !           190:                      small=1.0E-18;    /* fl(1+small)==1 */
        !           191:        static ibig=30; /* fl(1+2**(2*ibig))==1 */
        !           192:        double copysign(),scalb(),logb(),sqrt(),temp;
        !           193:        int finite(), exp;
        !           194: 
        !           195:        if(finite(x))
        !           196:            if(finite(y))
        !           197:            {   
        !           198:                x=copysign(x,one);
        !           199:                y=copysign(y,one);
        !           200:                if(y > x) 
        !           201:                    { temp=x; x=y; y=temp; }
        !           202:                if(x == zero) return(zero);
        !           203:                if(y == zero) return(x);
        !           204:                exp= logb(x);
        !           205:                x=scalb(x,-exp);
        !           206:                if(exp-(int)logb(y) > ibig ) 
        !           207:                        /* raise inexact flag and return |x| */
        !           208:                   { one+small; return(scalb(x,exp)); }
        !           209:                else y=scalb(y,-exp);
        !           210:                return(scalb(sqrt(x*x+y*y),exp));
        !           211:            }
        !           212: 
        !           213:            else if(y==y)          /* y is +-INF */
        !           214:                     return(copysign(y,one));
        !           215:            else 
        !           216:                     return(y);    /* y is NaN and x is finite */
        !           217: 
        !           218:        else if(x==x)              /* x is +-INF */
        !           219:                 return (copysign(x,one));
        !           220:        else if(finite(y))
        !           221:                 return(x);                /* x is NaN, y is finite */
        !           222:        else if(y!=y) return(y);        /* x and y is NaN */
        !           223:        else return(copysign(y,one));   /* y is INF */
        !           224: }
        !           225: #endif

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