1 /* $OpenBSD: elog.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 /* xlog.c */ 20 /* natural logarithm */ 21 /* by Stephen L. Moshier. */ 22 23 #include "mconf.h" 24 #include "ehead.h" 25 26 27 28 void elog( x, y ) 29 unsigned short *x, *y; 30 { 31 unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE]; 32 long ex; 33 int fex; 34 35 36 if( x[NE-1] & (unsigned short )0x8000 ) 37 { 38 eclear(y); 39 mtherr( "elog", DOMAIN ); 40 return; 41 } 42 if( ecmp( x, ezero ) == 0 ) 43 { 44 einfin( y ); 45 eneg(y); 46 mtherr( "elog", SING ); 47 return; 48 } 49 if( ecmp( x, eone ) == 0 ) 50 { 51 eclear( y ); 52 return; 53 } 54 55 /* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */ 56 efrexp( x, &fex, xx ); 57 /* 58 emov(x, xx ); 59 ex = xx[NX-1] & 0x7fff; 60 ex -= 0x3ffe; 61 xx[NX-1] = 0x3ffe; 62 */ 63 64 /* Adjust range to 1/sqrt(2), sqrt(2) */ 65 esqrt2[NE-1] -= 1; 66 if( ecmp( xx, esqrt2 ) < 0 ) 67 { 68 fex -= 1; 69 emul( xx, etwo, xx ); 70 } 71 esqrt2[NE-1] += 1; 72 73 esub( eone, xx, a ); 74 if( a[NE-1] == 0 ) 75 { 76 eclear( y ); 77 goto logdon; 78 } 79 eadd( eone, xx, b ); 80 ediv( b, a, y ); /* store (x-1)/(x+1) in y */ 81 82 emul( y, y, z ); 83 84 emov( eone, a ); 85 emov( eone, b ); 86 emov( eone, qj ); 87 do 88 { 89 eadd( etwo, qj, qj ); /* 2 * i + 1 */ 90 emul( z, a, a ); 91 ediv( qj, a, t ); 92 eadd( t, b, b ); 93 } 94 while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS ); 95 96 97 emul( b, y, y ); 98 emul( y, etwo, y ); 99 100 logdon: 101 102 /* now add log of 2**ex */ 103 if( fex != 0 ) 104 { 105 ex = fex; 106 ltoe( &ex, b ); 107 emul( elog2, b, b ); 108 eadd( b, y, y ); 109 } 110 } 111