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Diffstat (limited to 'lib/libm/common_source/expm1.c')
| -rw-r--r-- | lib/libm/common_source/expm1.c | 167 |
1 files changed, 167 insertions, 0 deletions
diff --git a/lib/libm/common_source/expm1.c b/lib/libm/common_source/expm1.c new file mode 100644 index 000000000000..760d2bed677d --- /dev/null +++ b/lib/libm/common_source/expm1.c @@ -0,0 +1,167 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* EXPM1(X) + * RETURN THE EXPONENTIAL OF X MINUS ONE + * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * finite(x) + * + * Kernel function: + * exp__E(x,c) + * + * Method: + * 1. Argument Reduction: given the input x, find r and integer k such + * that + * x = k*ln2 + r, |r| <= 0.5*ln2 . + * r will be represented as r := z+c for better accuracy. + * + * 2. Compute EXPM1(r)=exp(r)-1 by + * + * EXPM1(r=z+c) := z + exp__E(z,c) + * + * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ). + * + * Remarks: + * 1. When k=1 and z < -0.25, we use the following formula for + * better accuracy: + * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) ) + * 2. To avoid rounding error in 1-2^-k where k is large, we use + * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 } + * when k>56. + * + * Special cases: + * EXPM1(INF) is INF, EXPM1(NaN) is NaN; + * EXPM1(-INF)= -1; + * for finite argument, only EXPM1(0)=0 is exact. + * + * Accuracy: + * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with + * 1,166,000 random arguments on a VAX, the maximum observed error was + * .872 ulps (units of the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) +vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) +vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) +ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) +ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#define lnhuge vccast(lnhuge) +#define invln2 vccast(invln2) +#endif + +double expm1(x) +double x; +{ + const static double one=1.0, half=1.0/2.0; + double z,hi,lo,c; + int k; +#if defined(vax)||defined(tahoe) + static prec=56; +#else /* defined(vax)||defined(tahoe) */ + static prec=53; +#endif /* defined(vax)||defined(tahoe) */ + +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + + if( x <= lnhuge ) { + if( x >= -40.0 ) { + + /* argument reduction : x - k*ln2 */ + k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */ + hi=x-k*ln2hi ; + z=hi-(lo=k*ln2lo); + c=(hi-z)-lo; + + if(k==0) return(z+__exp__E(z,c)); + if(k==1) + if(z< -0.25) + {x=z+half;x +=__exp__E(z,c); return(x+x);} + else + {z+=__exp__E(z,c); x=half+z; return(x+x);} + /* end of k=1 */ + + else { + if(k<=prec) + { x=one-scalb(one,-k); z += __exp__E(z,c);} + else if(k<100) + { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;} + else + { x = __exp__E(z,c)+z; z=one;} + + return (scalb(x+z,k)); + } + } + /* end of x > lnunfl */ + + else + /* expm1(-big#) rounded to -1 (inexact) */ + if(finite(x)) + { ln2hi+ln2lo; return(-one);} + + /* expm1(-INF) is -1 */ + else return(-one); + } + /* end of x < lnhuge */ + + else + /* expm1(INF) is INF, expm1(+big#) overflows to INF */ + return( finite(x) ? scalb(one,5000) : x); +} |