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b_exp.c
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b_log.c
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b_tgamma.c
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mathimpl.h
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Editing: b_exp.c
/*- * SPDX-License-Identifier: BSD-3-Clause * * 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. 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. */ /* @(#)exp.c 8.1 (Berkeley) 6/4/93 */ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); /* EXP(X) * RETURN THE EXPONENTIAL OF X * 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, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. * * Required system supported functions: * scalb(x,n) * copysign(x,y) * finite(x) * * 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 exp(r) by * * exp(r) = 1 + r + r*R1/(2-R1), * where * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). * * 3. exp(x) = 2^k * exp(r) . * * Special cases: * exp(INF) is INF, exp(NaN) is NaN; * exp(-INF)= 0; * for finite argument, only exp(0)=1 is exact. * * Accuracy: * exp(x) returns the exponential of x nearly rounded. In a test run * with 1,156,000 random arguments on a VAX, the maximum observed * error was 0.869 ulps (units in the last place). */ #include "mathimpl.h" static const double p1 = 0x1.555555555553ep-3; static const double p2 = -0x1.6c16c16bebd93p-9; static const double p3 = 0x1.1566aaf25de2cp-14; static const double p4 = -0x1.bbd41c5d26bf1p-20; static const double p5 = 0x1.6376972bea4d0p-25; static const double ln2hi = 0x1.62e42fee00000p-1; static const double ln2lo = 0x1.a39ef35793c76p-33; static const double lnhuge = 0x1.6602b15b7ecf2p9; static const double lntiny = -0x1.77af8ebeae354p9; static const double invln2 = 0x1.71547652b82fep0; #if 0 double exp(x) double x; { double z,hi,lo,c; int k; #if !defined(vax)&&!defined(tahoe) if(x!=x) return(x); /* x is NaN */ #endif /* !defined(vax)&&!defined(tahoe) */ if( x <= lnhuge ) { if( x >= lntiny ) { /* argument reduction : x --> x - k*ln2 */ k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */ hi=x-k*ln2hi; x=hi-(lo=k*ln2lo); /* return 2^k*[1+x+x*c/(2+c)] */ z=x*x; c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k); } /* end of x > lntiny */ else /* exp(-big#) underflows to zero */ if(finite(x)) return(scalb(1.0,-5000)); /* exp(-INF) is zero */ else return(0.0); } /* end of x < lnhuge */ else /* exp(INF) is INF, exp(+big#) overflows to INF */ return( finite(x) ? scalb(1.0,5000) : x); } #endif /* returns exp(r = x + c) for |c| < |x| with no overlap. */ double __exp__D(x, c) double x, c; { double z,hi,lo; int k; if (x != x) /* x is NaN */ return(x); if ( x <= lnhuge ) { if ( x >= lntiny ) { /* argument reduction : x --> x - k*ln2 */ z = invln2*x; k = z + copysign(.5, x); /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ hi=(x-k*ln2hi); /* Exact. */ x= hi - (lo = k*ln2lo-c); /* return 2^k*[1+x+x*c/(2+c)] */ z=x*x; c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); c = (x*c)/(2.0-c); return scalb(1.+(hi-(lo - c)), k); } /* end of x > lntiny */ else /* exp(-big#) underflows to zero */ if(finite(x)) return(scalb(1.0,-5000)); /* exp(-INF) is zero */ else return(0.0); } /* end of x < lnhuge */ else /* exp(INF) is INF, exp(+big#) overflows to INF */ return( finite(x) ? scalb(1.0,5000) : x); }
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