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Annotation of 43BSDTahoe/usr.lib/libm/log.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[] = "@(#)log.c      5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* LOG(X)
        !            28:  * RETURN THE LOGARITHM OF x 
        !            29:  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
        !            30:  * CODED IN C BY K.C. NG, 1/19/85;
        !            31:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 3/24/85, 4/16/85.
        !            32:  *
        !            33:  * Required system supported functions:
        !            34:  *     scalb(x,n)
        !            35:  *     copysign(x,y)
        !            36:  *     logb(x) 
        !            37:  *     finite(x)
        !            38:  *
        !            39:  * Required kernel function:
        !            40:  *     log__L(z) 
        !            41:  *
        !            42:  * Method :
        !            43:  *     1. Argument Reduction: find k and f such that 
        !            44:  *                     x = 2^k * (1+f), 
        !            45:  *        where  sqrt(2)/2 < 1+f < sqrt(2) .
        !            46:  *
        !            47:  *     2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
        !            48:  *              = 2s + 2/3 s**3 + 2/5 s**5 + .....,
        !            49:  *        log(1+f) is computed by
        !            50:  *
        !            51:  *                     log(1+f) = 2s + s*log__L(s*s)
        !            52:  *        where
        !            53:  *             log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
        !            54:  *
        !            55:  *        See log__L() for the values of the coefficients.
        !            56:  *
        !            57:  *     3. Finally,  log(x) = k*ln2 + log(1+f).  (Here n*ln2 will be stored
        !            58:  *        in two floating point number: n*ln2hi + n*ln2lo, n*ln2hi is exact
        !            59:  *        since the last 20 bits of ln2hi is 0.)
        !            60:  *
        !            61:  * Special cases:
        !            62:  *     log(x) is NaN with signal if x < 0 (including -INF) ; 
        !            63:  *     log(+INF) is +INF; log(0) is -INF with signal;
        !            64:  *     log(NaN) is that NaN with no signal.
        !            65:  *
        !            66:  * Accuracy:
        !            67:  *     log(x) returns the exact log(x) nearly rounded. In a test run with
        !            68:  *     1,536,000 random arguments on a VAX, the maximum observed error was
        !            69:  *     .826 ulps (units in the last place).
        !            70:  *
        !            71:  * Constants:
        !            72:  * The hexadecimal values are the intended ones for the following constants.
        !            73:  * The decimal values may be used, provided that the compiler will convert
        !            74:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            75:  * shown.
        !            76:  */
        !            77: 
        !            78: #if defined(vax)||defined(tahoe)       /* VAX D format */
        !            79: #include <errno.h>
        !            80: #ifdef vax
        !            81: #define _0x(A,B)       0x/**/A/**/B
        !            82: #else  /* vax */
        !            83: #define _0x(A,B)       0x/**/B/**/A
        !            84: #endif /* vax */
        !            85: /* static double */
        !            86: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
        !            87: /* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
        !            88: /* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
        !            89: static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
        !            90: static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
        !            91: static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
        !            92: #define    ln2hi    (*(double*)ln2hix)
        !            93: #define    ln2lo    (*(double*)ln2lox)
        !            94: #define    sqrt2    (*(double*)sqrt2x)
        !            95: #else  /* defined(vax)||defined(tahoe) */
        !            96: static double
        !            97: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
        !            98: ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
        !            99: sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
        !           100: #endif /* defined(vax)||defined(tahoe) */
        !           101: 
        !           102: double log(x)
        !           103: double x;
        !           104: {
        !           105:        static double zero=0.0, negone= -1.0, half=1.0/2.0;
        !           106:        double logb(),scalb(),copysign(),log__L(),s,z,t;
        !           107:        int k,n,finite();
        !           108: 
        !           109: #if !defined(vax)&&!defined(tahoe)
        !           110:        if(x!=x) return(x);     /* x is NaN */
        !           111: #endif /* !defined(vax)&&!defined(tahoe) */
        !           112:        if(finite(x)) {
        !           113:           if( x > zero ) {
        !           114: 
        !           115:           /* argument reduction */
        !           116:              k=logb(x);   x=scalb(x,-k);
        !           117:              if(k == -1022) /* subnormal no. */
        !           118:                   {n=logb(x); x=scalb(x,-n); k+=n;} 
        !           119:              if(x >= sqrt2 ) {k += 1; x *= half;}
        !           120:              x += negone ;
        !           121: 
        !           122:           /* compute log(1+x)  */
        !           123:               s=x/(2+x); t=x*x*half;
        !           124:              z=k*ln2lo+s*(t+log__L(s*s));
        !           125:              x += (z - t) ;
        !           126: 
        !           127:              return(k*ln2hi+x);
        !           128:           }
        !           129:        /* end of if (x > zero) */
        !           130: 
        !           131:           else {
        !           132: #if defined(vax)||defined(tahoe)
        !           133:                extern double infnan();
        !           134:                if ( x == zero )
        !           135:                    return (infnan(-ERANGE));   /* -INF */
        !           136:                else
        !           137:                    return (infnan(EDOM));      /* NaN */
        !           138: #else  /* defined(vax)||defined(tahoe) */
        !           139:                /* zero argument, return -INF with signal */
        !           140:                if ( x == zero )
        !           141:                    return( negone/zero );
        !           142: 
        !           143:                /* negative argument, return NaN with signal */
        !           144:                else 
        !           145:                    return ( zero / zero );
        !           146: #endif /* defined(vax)||defined(tahoe) */
        !           147:            }
        !           148:        }
        !           149:     /* end of if (finite(x)) */
        !           150:     /* NOTREACHED if defined(vax)||defined(tahoe) */
        !           151: 
        !           152:     /* log(-INF) is NaN with signal */
        !           153:        else if (x<0) 
        !           154:            return(zero/zero);      
        !           155: 
        !           156:     /* log(+INF) is +INF */
        !           157:        else return(x);      
        !           158: 
        !           159: }

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