1 /* $NetBSD: n_log__L.c,v 1.5 2002/06/15 00:10:17 matt Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 #if 0 37 static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* log__L(Z) 42 * LOG(1+X) - 2S X 43 * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294... 44 * S 2 + X 45 * 46 * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS) 47 * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS 48 * CODED IN C BY K.C. NG, 1/19/85; 49 * REVISED BY K.C. Ng, 2/3/85, 4/16/85. 50 * 51 * Method : 52 * 1. Polynomial approximation: let s = x/(2+x). 53 * Based on log(1+x) = log(1+s) - log(1-s) 54 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., 55 * 56 * (log(1+x) - 2s)/s is computed by 57 * 58 * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...))) 59 * 60 * where z=s*s. (See the listing below for Lk's values.) The 61 * coefficients are obtained by a special Remez algorithm. 62 * 63 * Accuracy: 64 * Assuming no rounding error, the maximum magnitude of the approximation 65 * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63) 66 * for VAX D format. 67 * 68 * Constants: 69 * The hexadecimal values are the intended ones for the following constants. 70 * The decimal values may be used, provided that the compiler will convert 71 * from decimal to binary accurately enough to produce the hexadecimal values 72 * shown. 73 */ 74 75 #define _LIBM_STATIC 76 #include "mathimpl.h" 77 78 vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5) 79 vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684) 80 vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782) 81 vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C) 82 vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E) 83 vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D) 84 vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92) 85 vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000) 86 87 ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592) 88 ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24) 89 ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4) 90 ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6) 91 ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F) 92 ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B) 93 ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122) 94 95 #ifdef vccast 96 #define L1 vccast(L1) 97 #define L2 vccast(L2) 98 #define L3 vccast(L3) 99 #define L4 vccast(L4) 100 #define L5 vccast(L5) 101 #define L6 vccast(L6) 102 #define L7 vccast(L7) 103 #define L8 vccast(L8) 104 #endif 105 106 double 107 __log__L(double z) 108 { 109 #if defined(__vax__)||defined(tahoe) 110 return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8)))))))); 111 #else /* defined(__vax__)||defined(tahoe) */ 112 return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7))))))); 113 #endif /* defined(__vax__)||defined(tahoe) */ 114 } 115