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Annotation of 43BSDReno/lib/libm/common_source/expm1.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[] = "@(#)expm1.c    5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: /* EXPM1(X)
        !            30:  * RETURN THE EXPONENTIAL OF X MINUS ONE
        !            31:  * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
        !            32:  * CODED IN C BY K.C. NG, 1/19/85; 
        !            33:  * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
        !            34:  *
        !            35:  * Required system supported functions:
        !            36:  *     scalb(x,n)      
        !            37:  *     copysign(x,y)   
        !            38:  *     finite(x)
        !            39:  *
        !            40:  * Kernel function:
        !            41:  *     exp__E(x,c)
        !            42:  *
        !            43:  * Method:
        !            44:  *     1. Argument Reduction: given the input x, find r and integer k such 
        !            45:  *        that
        !            46:  *                        x = k*ln2 + r,  |r| <= 0.5*ln2 .  
        !            47:  *        r will be represented as r := z+c for better accuracy.
        !            48:  *
        !            49:  *     2. Compute EXPM1(r)=exp(r)-1 by 
        !            50:  *
        !            51:  *                     EXPM1(r=z+c) := z + exp__E(z,c)
        !            52:  *
        !            53:  *     3. EXPM1(x) =  2^k * ( EXPM1(r) + 1-2^-k ).
        !            54:  *
        !            55:  *     Remarks: 
        !            56:  *        1. When k=1 and z < -0.25, we use the following formula for
        !            57:  *           better accuracy:
        !            58:  *                     EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
        !            59:  *        2. To avoid rounding error in 1-2^-k where k is large, we use
        !            60:  *                     EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
        !            61:  *           when k>56. 
        !            62:  *
        !            63:  * Special cases:
        !            64:  *     EXPM1(INF) is INF, EXPM1(NaN) is NaN;
        !            65:  *     EXPM1(-INF)= -1;
        !            66:  *     for finite argument, only EXPM1(0)=0 is exact.
        !            67:  *
        !            68:  * Accuracy:
        !            69:  *     EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
        !            70:  *     1,166,000 random arguments on a VAX, the maximum observed error was
        !            71:  *     .872 ulps (units of the last place).
        !            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: #include "mathimpl.h"
        !            81: 
        !            82: vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
        !            83: vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
        !            84: vc(lnhuge, 9.4961163736712506989E1   ,ec1d,43bd,9010,a73e,   7, .BDEC1DA73E9010)
        !            85: vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)
        !            86: 
        !            87: ic(ln2hi,  6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
        !            88: ic(ln2lo,  1.9082149292705877000E-10, -33, 1.A39EF35793C76)
        !            89: ic(lnhuge, 7.1602103751842355450E2,     9, 1.6602B15B7ECF2)
        !            90: ic(invln2, 1.4426950408889633870E0,     0, 1.71547652B82FE)
        !            91: 
        !            92: #ifdef vccast
        !            93: #define        ln2hi   vccast(ln2hi)
        !            94: #define        ln2lo   vccast(ln2lo)
        !            95: #define        lnhuge  vccast(lnhuge)
        !            96: #define        invln2  vccast(invln2)
        !            97: #endif
        !            98: 
        !            99: double expm1(x)
        !           100: double x;
        !           101: {
        !           102:        const static double one=1.0, half=1.0/2.0; 
        !           103:        double  z,hi,lo,c;
        !           104:        int k;
        !           105: #if defined(vax)||defined(tahoe)
        !           106:        static prec=56;
        !           107: #else  /* defined(vax)||defined(tahoe) */
        !           108:        static prec=53;
        !           109: #endif /* defined(vax)||defined(tahoe) */
        !           110: 
        !           111: #if !defined(vax)&&!defined(tahoe)
        !           112:        if(x!=x) return(x);     /* x is NaN */
        !           113: #endif /* !defined(vax)&&!defined(tahoe) */
        !           114: 
        !           115:        if( x <= lnhuge ) {
        !           116:                if( x >= -40.0 ) {
        !           117: 
        !           118:                    /* argument reduction : x - k*ln2 */
        !           119:                        k= invln2 *x+copysign(0.5,x);   /* k=NINT(x/ln2) */
        !           120:                        hi=x-k*ln2hi ; 
        !           121:                        z=hi-(lo=k*ln2lo);
        !           122:                        c=(hi-z)-lo;
        !           123: 
        !           124:                        if(k==0) return(z+exp__E(z,c));
        !           125:                        if(k==1)
        !           126:                            if(z< -0.25) 
        !           127:                                {x=z+half;x +=exp__E(z,c); return(x+x);}
        !           128:                            else
        !           129:                                {z+=exp__E(z,c); x=half+z; return(x+x);}
        !           130:                    /* end of k=1 */
        !           131: 
        !           132:                        else {
        !           133:                            if(k<=prec)
        !           134:                              { x=one-scalb(one,-k); z += exp__E(z,c);}
        !           135:                            else if(k<100)
        !           136:                              { x = exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
        !           137:                            else 
        !           138:                              { x = exp__E(z,c)+z; z=one;}
        !           139: 
        !           140:                            return (scalb(x+z,k));  
        !           141:                        }
        !           142:                }
        !           143:                /* end of x > lnunfl */
        !           144: 
        !           145:                else 
        !           146:                     /* expm1(-big#) rounded to -1 (inexact) */
        !           147:                     if(finite(x))  
        !           148:                         { ln2hi+ln2lo; return(-one);}
        !           149: 
        !           150:                     /* expm1(-INF) is -1 */
        !           151:                     else return(-one);
        !           152:        }
        !           153:        /* end of x < lnhuge */
        !           154: 
        !           155:        else 
        !           156:        /*  expm1(INF) is INF, expm1(+big#) overflows to INF */
        !           157:            return( finite(x) ?  scalb(one,5000) : x);
        !           158: }

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