* Copyright (c) 1985 Regents of the University of California.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* 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
static char sccsid
[] = "@(#)log__L.c 5.6 (Berkeley) 10/9/90";
* RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
* 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.
* 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.
* Assuming no rounding error, the maximum magnitude of the approximation
* error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
* 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
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
)
#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) */