83e4fa69d9
hypotf() functions for vax. Play the namespace and weak alias game for functions used internally by the complex functions. Should fix the vax build of libm.
216 lines
6.7 KiB
C
216 lines
6.7 KiB
C
/* $NetBSD: n_exp.c,v 1.8 2008/03/20 16:41:26 mhitch Exp $ */
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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#if 0
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static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
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#endif
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#endif /* not lint */
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/* EXP(X)
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* RETURN THE EXPONENTIAL OF X
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* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
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* CODED IN C BY K.C. NG, 1/19/85;
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* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
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*
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* Required system supported functions:
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* scalb(x,n)
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* copysign(x,y)
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* finite(x)
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*
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* Method:
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* 1. Argument Reduction: given the input x, find r and integer k such
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* that
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* x = k*ln2 + r, |r| <= 0.5*ln2 .
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* r will be represented as r := z+c for better accuracy.
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*
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* 2. Compute exp(r) by
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*
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* exp(r) = 1 + r + r*R1/(2-R1),
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* where
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* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
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*
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* 3. exp(x) = 2^k * exp(r) .
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*
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* Special cases:
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* exp(INF) is INF, exp(NaN) is NaN;
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* exp(-INF)= 0;
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* for finite argument, only exp(0)=1 is exact.
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*
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* Accuracy:
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* exp(x) returns the exponential of x nearly rounded. In a test run
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* with 1,156,000 random arguments on a VAX, the maximum observed
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* error was 0.869 ulps (units in the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#define _LIBM_STATIC
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#include "../src/namespace.h"
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#include "mathimpl.h"
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#ifdef __weak_alias
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__weak_alias(exp, _exp);
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__weak_alias(expf, _expf);
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#endif
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vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
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vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
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vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
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vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
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vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
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vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
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vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
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vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
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vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
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vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
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#ifdef vccast
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#define ln2hi vccast(ln2hi)
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#define ln2lo vccast(ln2lo)
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#define lnhuge vccast(lnhuge)
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#define lntiny vccast(lntiny)
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#define invln2 vccast(invln2)
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#define p1 vccast(p1)
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#define p2 vccast(p2)
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#define p3 vccast(p3)
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#define p4 vccast(p4)
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#define p5 vccast(p5)
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#endif
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ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
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ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
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ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
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ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
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ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
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ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
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ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
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ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
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ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
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ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
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double
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exp(double x)
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{
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double z,hi,lo,c;
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int k;
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#if !defined(__vax__)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(__vax__)&&!defined(tahoe) */
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if( x <= lnhuge ) {
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if( x >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
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/* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=x-k*ln2hi;
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x=hi-(lo=k*ln2lo);
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/* return 2^k*[1+x+x*c/(2+c)] */
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z=x*x;
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c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
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return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
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}
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/* end of x > lntiny */
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else
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/* exp(-big#) underflows to zero */
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if(finite(x)) return(scalb(1.0,-5000));
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/* exp(-INF) is zero */
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else return(0.0);
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}
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/* end of x < lnhuge */
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else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return( finite(x) ? scalb(1.0,5000) : x);
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}
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float
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expf(float x)
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{
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return(exp((double)x));
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}
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/* returns exp(r = x + c) for |c| < |x| with no overlap. */
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double
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__exp__D(double x, double c)
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{
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double z,hi,lo;
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int k;
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#if !defined(__vax__)&&!defined(tahoe)
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if (x!=x) return(x); /* x is NaN */
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#endif /* !defined(__vax__)&&!defined(tahoe) */
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if ( x <= lnhuge ) {
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if ( x >= lntiny ) {
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/* argument reduction : x --> x - k*ln2 */
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z = invln2*x;
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k = z + copysign(.5, x);
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/* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
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hi=(x-k*ln2hi); /* Exact. */
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x= hi - (lo = k*ln2lo-c);
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/* return 2^k*[1+x+x*c/(2+c)] */
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z=x*x;
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c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
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c = (x*c)/(2.0-c);
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return scalb(1.+(hi-(lo - c)), k);
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}
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/* end of x > lntiny */
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else
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/* exp(-big#) underflows to zero */
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if(finite(x)) return(scalb(1.0,-5000));
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/* exp(-INF) is zero */
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else return(0.0);
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}
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/* end of x < lnhuge */
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else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return( finite(x) ? scalb(1.0,5000) : x);
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}
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