Return to exp.c CVS log

Up to [CSRG BSD Unix] / 43BSDTahoe / usr.lib / libm

Annotation of 43BSDTahoe/usr.lib/libm/exp.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[] = "@(#)exp.c      5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* EXP(X)
        !            28:  * RETURN THE EXPONENTIAL OF X
        !            29:  * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
        !            30:  * CODED IN C BY K.C. NG, 1/19/85; 
        !            31:  * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
        !            32:  *
        !            33:  * Required system supported functions:
        !            34:  *     scalb(x,n)      
        !            35:  *     copysign(x,y)   
        !            36:  *     finite(x)
        !            37:  *
        !            38:  * Method:
        !            39:  *     1. Argument Reduction: given the input x, find r and integer k such 
        !            40:  *        that
        !            41:  *                        x = k*ln2 + r,  |r| <= 0.5*ln2 .  
        !            42:  *        r will be represented as r := z+c for better accuracy.
        !            43:  *
        !            44:  *     2. Compute exp(r) by 
        !            45:  *
        !            46:  *             exp(r) = 1 + r + r*R1/(2-R1),
        !            47:  *        where
        !            48:  *             R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
        !            49:  *
        !            50:  *     3. exp(x) = 2^k * exp(r) .
        !            51:  *
        !            52:  * Special cases:
        !            53:  *     exp(INF) is INF, exp(NaN) is NaN;
        !            54:  *     exp(-INF)=  0;
        !            55:  *     for finite argument, only exp(0)=1 is exact.
        !            56:  *
        !            57:  * Accuracy:
        !            58:  *     exp(x) returns the exponential of x nearly rounded. In a test run
        !            59:  *     with 1,156,000 random arguments on a VAX, the maximum observed
        !            60:  *     error was 0.869 ulps (units in the last place).
        !            61:  *
        !            62:  * Constants:
        !            63:  * The hexadecimal values are the intended ones for the following constants.
        !            64:  * The decimal values may be used, provided that the compiler will convert
        !            65:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            66:  * shown.
        !            67:  */
        !            68: 
        !            69: #if defined(vax)||defined(tahoe)       /* VAX D format */
        !            70: #ifdef vax
        !            71: #define _0x(A,B)       0x/**/A/**/B
        !            72: #else  /* vax */
        !            73: #define _0x(A,B)       0x/**/B/**/A
        !            74: #endif /* vax */
        !            75: /* static double */
        !            76: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
        !            77: /* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
        !            78: /* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 */
        !            79: /* lntiny = -9.5654310917272452386E1     , Hex  2^  7   * -.BF4F01D72E33AF */
        !            80: /* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */
        !            81: /* p1     =  1.6666666666666602251E-1    , Hex  2^-2    *  .AAAAAAAAAAA9F1 */
        !            82: /* p2     = -2.7777777777015591216E-3    , Hex  2^-8    * -.B60B60B5F5EC94 */
        !            83: /* p3     =  6.6137563214379341918E-5    , Hex  2^-13   *  .8AB355792EF15F */
        !            84: /* p4     = -1.6533902205465250480E-6    , Hex  2^-19   * -.DDEA0E2E935F84 */
        !            85: /* p5     =  4.1381367970572387085E-8    , Hex  2^-24   *  .B1BB4B95F52683 */
        !            86: static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
        !            87: static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
        !            88: static long    lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};
        !            89: static long    lntinyx[] = { _0x(4f01,c3bf), _0x(33af,d72e)};
        !            90: static long    invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
        !            91: static long        p1x[] = { _0x(aaaa,3f2a), _0x(a9f1,aaaa)};
        !            92: static long        p2x[] = { _0x(0b60,bc36), _0x(ec94,b5f5)};
        !            93: static long        p3x[] = { _0x(b355,398a), _0x(f15f,792e)};
        !            94: static long        p4x[] = { _0x(ea0e,b6dd), _0x(5f84,2e93)};
        !            95: static long        p5x[] = { _0x(bb4b,3431), _0x(2683,95f5)};
        !            96: #define    ln2hi    (*(double*)ln2hix)
        !            97: #define    ln2lo    (*(double*)ln2lox)
        !            98: #define   lnhuge    (*(double*)lnhugex)
        !            99: #define   lntiny    (*(double*)lntinyx)
        !           100: #define   invln2    (*(double*)invln2x)
        !           101: #define       p1    (*(double*)p1x)
        !           102: #define       p2    (*(double*)p2x)
        !           103: #define       p3    (*(double*)p3x)
        !           104: #define       p4    (*(double*)p4x)
        !           105: #define       p5    (*(double*)p5x)
        !           106: 
        !           107: #else  /* defined(vax)||defined(tahoe) */
        !           108: static double
        !           109: p1     =  1.6666666666666601904E-1    , /*Hex  2^-3    *  1.555555555553E */
        !           110: p2     = -2.7777777777015593384E-3    , /*Hex  2^-9    * -1.6C16C16BEBD93 */
        !           111: p3     =  6.6137563214379343612E-5    , /*Hex  2^-14   *  1.1566AAF25DE2C */
        !           112: p4     = -1.6533902205465251539E-6    , /*Hex  2^-20   * -1.BBD41C5D26BF1 */
        !           113: p5     =  4.1381367970572384604E-8    , /*Hex  2^-25   *  1.6376972BEA4D0 */
        !           114: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
        !           115: ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
        !           116: lnhuge =  7.1602103751842355450E2     , /*Hex  2^  9   *  1.6602B15B7ECF2 */
        !           117: lntiny = -7.5137154372698068983E2     , /*Hex  2^  9   * -1.77AF8EBEAE354 */
        !           118: invln2 =  1.4426950408889633870E0     ; /*Hex  2^  0   *  1.71547652B82FE */
        !           119: #endif /* defined(vax)||defined(tahoe) */
        !           120: 
        !           121: double exp(x)
        !           122: double x;
        !           123: {
        !           124:        double scalb(), copysign(), z,hi,lo,c;
        !           125:        int k,finite();
        !           126: 
        !           127: #if !defined(vax)&&!defined(tahoe)
        !           128:        if(x!=x) return(x);     /* x is NaN */
        !           129: #endif /* !defined(vax)&&!defined(tahoe) */
        !           130:        if( x <= lnhuge ) {
        !           131:                if( x >= lntiny ) {
        !           132: 
        !           133:                    /* argument reduction : x --> x - k*ln2 */
        !           134: 
        !           135:                        k=invln2*x+copysign(0.5,x);     /* k=NINT(x/ln2) */
        !           136: 
        !           137:                    /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
        !           138: 
        !           139:                        hi=x-k*ln2hi;
        !           140:                        x=hi-(lo=k*ln2lo);
        !           141: 
        !           142:                    /* return 2^k*[1+x+x*c/(2+c)]  */
        !           143:                        z=x*x;
        !           144:                        c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
        !           145:                        return  scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
        !           146: 
        !           147:                }
        !           148:                /* end of x > lntiny */
        !           149: 
        !           150:                else 
        !           151:                     /* exp(-big#) underflows to zero */
        !           152:                     if(finite(x))  return(scalb(1.0,-5000));
        !           153: 
        !           154:                     /* exp(-INF) is zero */
        !           155:                     else return(0.0);
        !           156:        }
        !           157:        /* end of x < lnhuge */
        !           158: 
        !           159:        else 
        !           160:        /* exp(INF) is INF, exp(+big#) overflows to INF */
        !           161:            return( finite(x) ?  scalb(1.0,5000)  : x);
        !           162: }

This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.