1/* $OpenBSD: eexp.c,v 1.1 2011/07/02 18:11:01 martynas Exp $ */ 2 3/* 4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5 * 6 * Permission to use, copy, modify, and distribute this software for any 7 * purpose with or without fee is hereby granted, provided that the above 8 * copyright notice and this permission notice appear in all copies. 9 * 10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17 */ 18 19/* xexp.c */ 20/* exponential function check routine */ 21/* by Stephen L. Moshier. */ 22 23 24#include "ehead.h" 25 26void eexp( x, y ) 27unsigned short *x, *y; 28{ 29unsigned short num[NE], den[NE], x2[NE]; 30long i; 31unsigned short sign, expchk; 32 33/* range reduction theory: x = i + f, 0<=f<1; 34 * e**x = e**i * e**f 35 * e**i = 2**(i/log 2). 36 * Let i/log2 = i1 + f1, 0<=f1<1. 37 * Then e**i = 2**i1 * 2**f1, so 38 * e**x = 2**i1 * e**(log 2 * f1) * e**f. 39 */ 40if( ecmp(x, ezero) == 0 ) 41 { 42 emov( eone, y ); 43 return; 44 } 45emov(x, x2); 46expchk = x2[NE-1]; 47sign = expchk & 0x8000; 48x2[NE-1] &= 0x7fff; 49 50/* Test for excessively large argument */ 51expchk &= 0x7fff; 52if( expchk > (EXONE + 15) ) 53 { 54 eclear( y ); 55 if( sign == 0 ) 56 einfin( y ); 57 return; 58 } 59 60eifrac( x2, &i, num ); /* x = i + f */ 61 62if( i != 0 ) 63 { 64 ltoe( &i, den ); /* floating point i */ 65 ediv( elog2, den, den ); /* i/log 2 */ 66 eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */ 67 emul( elog2, den, den ); /* log 2 * f1 */ 68 eadd( den, num, x2 ); /* log 2 * f1 + f */ 69 } 70 71/*x2[NE-1] -= 1;*/ 72eldexp( x2, -1L, x2 ); /* divide by 2 */ 73etanh( x2, x2 ); /* tanh( x/2 ) */ 74eadd( x2, eone, num ); /* 1 + tanh */ 75eneg( x2 ); 76eadd( x2, eone, den ); /* 1 - tanh */ 77ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */ 78 79/*y[NE-1] += i;*/ 80if( sign ) 81 { 82 ediv( y, eone, y ); 83 i = -i; 84 } 85eldexp( y, i, y ); /* multiply by 2**i */ 86} 87