Return to exp.c CVS log

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

Annotation of 43BSD/usr.lib/libm/exp.c, revision 1.1.1.1

1.1       root        1: /* 
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * 
                      4:  * Use and reproduction of this software are granted  in  accordance  with
                      5:  * the terms and conditions specified in  the  Berkeley  Software  License
                      6:  * Agreement (in particular, this entails acknowledgement of the programs'
                      7:  * source, and inclusion of this notice) with the additional understanding
                      8:  * that  all  recipients  should regard themselves as participants  in  an
                      9:  * ongoing  research  project and hence should  feel  obligated  to report
                     10:  * their  experiences (good or bad) with these elementary function  codes,
                     11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
                     12:  */
                     13: 
                     14: #ifndef lint
                     15: static char sccsid[] = "@(#)exp.c      4.3 (Berkeley) 8/21/85";
                     16: #endif not lint
                     17: 
                     18: /* EXP(X)
                     19:  * RETURN THE EXPONENTIAL OF X
                     20:  * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
                     21:  * CODED IN C BY K.C. NG, 1/19/85; 
                     22:  * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85.
                     23:  *
                     24:  * Required system supported functions:
                     25:  *     scalb(x,n)      
                     26:  *     copysign(x,y)   
                     27:  *     finite(x)
                     28:  *
                     29:  * Kernel function:
                     30:  *     exp__E(x,c)
                     31:  *
                     32:  * Method:
                     33:  *     1. Argument Reduction: given the input x, find r and integer k such 
                     34:  *        that
                     35:  *                        x = k*ln2 + r,  |r| <= 0.5*ln2 .  
                     36:  *        r will be represented as r := z+c for better accuracy.
                     37:  *
                     38:  *     2. Compute expm1(r)=exp(r)-1 by 
                     39:  *
                     40:  *                     expm1(r=z+c) := z + exp__E(z,r)
                     41:  *
                     42:  *     3. exp(x) = 2^k * ( expm1(r) + 1 ).
                     43:  *
                     44:  * Special cases:
                     45:  *     exp(INF) is INF, exp(NaN) is NaN;
                     46:  *     exp(-INF)=  0;
                     47:  *     for finite argument, only exp(0)=1 is exact.
                     48:  *
                     49:  * Accuracy:
                     50:  *     exp(x) returns the exponential of x nearly rounded. In a test run
                     51:  *     with 1,156,000 random arguments on a VAX, the maximum observed
                     52:  *     error was .768 ulps (units in the last place).
                     53:  *
                     54:  * Constants:
                     55:  * The hexadecimal values are the intended ones for the following constants.
                     56:  * The decimal values may be used, provided that the compiler will convert
                     57:  * from decimal to binary accurately enough to produce the hexadecimal values
                     58:  * shown.
                     59:  */
                     60: 
                     61: #ifdef VAX     /* VAX D format */
                     62: /* double static */
                     63: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
                     64: /* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
                     65: /* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 */
                     66: /* lntiny = -9.5654310917272452386E1     , Hex  2^  7   * -.BF4F01D72E33AF */
                     67: /* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */
                     68: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
                     69: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
                     70: static long    lnhugex[] = { 0xec1d43bd, 0x9010a73e};
                     71: static long    lntinyx[] = { 0x4f01c3bf, 0x33afd72e};
                     72: static long    invln2x[] = { 0xaa3b40b8, 0x17f1295c};
                     73: #define    ln2hi    (*(double*)ln2hix)
                     74: #define    ln2lo    (*(double*)ln2lox)
                     75: #define   lnhuge    (*(double*)lnhugex)
                     76: #define   lntiny    (*(double*)lntinyx)
                     77: #define   invln2    (*(double*)invln2x)
                     78: #else  /* IEEE double */
                     79: double static
                     80: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
                     81: ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
                     82: lnhuge =  7.1602103751842355450E2     , /*Hex  2^  9   *  1.6602B15B7ECF2 */
                     83: lntiny = -7.5137154372698068983E2     , /*Hex  2^  9   * -1.77AF8EBEAE354 */
                     84: invln2 =  1.4426950408889633870E0     ; /*Hex  2^  0   *  1.71547652B82FE */
                     85: #endif
                     86: 
                     87: double exp(x)
                     88: double x;
                     89: {
                     90:        double scalb(), copysign(), exp__E(), z,hi,lo,c;
                     91:        int k,finite();
                     92: 
                     93: #ifndef VAX
                     94:        if(x!=x) return(x);     /* x is NaN */
                     95: #endif
                     96:        if( x <= lnhuge ) {
                     97:                if( x >= lntiny ) {
                     98: 
                     99:                    /* argument reduction : x --> x - k*ln2 */
                    100: 
                    101:                        k=invln2*x+copysign(0.5,x);     /* k=NINT(x/ln2) */
                    102: 
                    103:                        /* express x-k*ln2 as z+c */
                    104:                        hi=x-k*ln2hi;
                    105:                        z=hi-(lo=k*ln2lo);
                    106:                        c=(hi-z)-lo;
                    107: 
                    108:                    /* return 2^k*[expm1(x) + 1]  */
                    109:                        z += exp__E(z,c);
                    110:                        return (scalb(z+1.0,k));  
                    111:                }
                    112:                /* end of x > lntiny */
                    113: 
                    114:                else 
                    115:                     /* exp(-big#) underflows to zero */
                    116:                     if(finite(x))  return(scalb(1.0,-5000));
                    117: 
                    118:                     /* exp(-INF) is zero */
                    119:                     else return(0.0);
                    120:        }
                    121:        /* end of x < lnhuge */
                    122: 
                    123:        else 
                    124:        /* exp(INF) is INF, exp(+big#) overflows to INF */
                    125:            return( finite(x) ?  scalb(1.0,5000)  : x);
                    126: }

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