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glibc/sysdeps/generic/expm1.c
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/* | |
* 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); | |
} | |
#undef expm1 | |
weak_alias (__expm1, expm1) |