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Diffstat (limited to 'sysdeps/generic/log__L.c')
| -rw-r--r-- | sysdeps/generic/log__L.c | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/sysdeps/generic/log__L.c b/sysdeps/generic/log__L.c new file mode 100644 index 0000000000..c00158fa51 --- /dev/null +++ b/sysdeps/generic/log__L.c @@ -0,0 +1,110 @@ +/* + * 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[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* log__L(Z) + * LOG(1+X) - 2S X + * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294... + * S 2 + X + * + * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS) + * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. Ng, 2/3/85, 4/16/85. + * + * Method : + * 1. Polynomial approximation: let s = x/(2+x). + * Based on log(1+x) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * + * (log(1+x) - 2s)/s is computed by + * + * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...))) + * + * where z=s*s. (See the listing below for Lk's values.) The + * coefficients are obtained by a special Remez algorithm. + * + * Accuracy: + * Assuming no rounding error, the maximum magnitude of the approximation + * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63) + * for VAX D format. + * + * 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(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5) +vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684) +vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782) +vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C) +vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E) +vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D) +vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92) +vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000) + +ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592) +ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24) +ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4) +ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6) +ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F) +ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B) +ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122) + +#ifdef vccast +#define L1 vccast(L1) +#define L2 vccast(L2) +#define L3 vccast(L3) +#define L4 vccast(L4) +#define L5 vccast(L5) +#define L6 vccast(L6) +#define L7 vccast(L7) +#define L8 vccast(L8) +#endif + +double __log__L(z) +double z; +{ +#if defined(vax)||defined(tahoe) + return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8)))))))); +#else /* defined(vax)||defined(tahoe) */ + return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7))))))); +#endif /* defined(vax)||defined(tahoe) */ +} |