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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2013 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
/*********************************************************************/
/* */
/* MODULE_NAME:ulog.c */
/* */
/* FUNCTION:ulog */
/* */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
/* mpexp.c mplog.c mpa.c */
/* ulog.tbl */
/* */
/* An ultimate log routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of log(x). */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include "endian.h"
#include <dla.h>
#include "mpa.h"
#include "MathLib.h"
#include <math_private.h>
#ifndef SECTION
# define SECTION
#endif
void __mplog (mp_no *, mp_no *, int);
/*********************************************************************/
/* An ultimate log routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of log(x). */
/*********************************************************************/
double
SECTION
__ieee754_log (double x)
{
#define M 4
static const int pr[M] = {8, 10, 18, 32};
int i, j, n, ux, dx, p;
double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb,
t1, t2, t7, t8, t, ra, rb, ww,
a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c;
#ifndef DLA_FMS
double t3, t4, t5, t6;
#endif
number num;
mp_no mpx, mpy, mpy1, mpy2, mperr;
#include "ulog.tbl"
#include "ulog.h"
/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
num.d = x;
ux = num.i[HIGH_HALF];
dx = num.i[LOW_HALF];
n = 0;
if (__builtin_expect (ux < 0x00100000, 0))
{
if (__builtin_expect (((ux & 0x7fffffff) | dx) == 0, 0))
return MHALF / 0.0; /* return -INF */
if (__builtin_expect (ux < 0, 0))
return (x - x) / 0.0; /* return NaN */
n -= 54;
x *= two54.d; /* scale x */
num.d = x;
}
if (__builtin_expect (ux >= 0x7ff00000, 0))
return x + x; /* INF or NaN */
/* Regular values of x */
w = x - ONE;
if (__builtin_expect (ABS (w) > U03, 1))
goto case_03;
/*--- Stage I, the case abs(x-1) < 0.03 */
t8 = MHALF * w;
EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
EADD (w, a, b, bb);
/* Evaluate polynomial II */
polII = b7.d + w * b8.d;
polII = b6.d + w * polII;
polII = b5.d + w * polII;
polII = b4.d + w * polII;
polII = b3.d + w * polII;
polII = b2.d + w * polII;
polII = b1.d + w * polII;
polII = b0.d + w * polII;
polII *= w * w * w;
c = (aa + bb) + polII;
/* End stage I, case abs(x-1) < 0.03 */
if ((y = b + (c + b * E2)) == b + (c - b * E2))
return y;
/*--- Stage II, the case abs(x-1) < 0.03 */
a = d19.d + w * d20.d;
a = d18.d + w * a;
a = d17.d + w * a;
a = d16.d + w * a;
a = d15.d + w * a;
a = d14.d + w * a;
a = d13.d + w * a;
a = d12.d + w * a;
a = d11.d + w * a;
EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5);
ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2);
MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (w, 0, s3, ss3, b, bb, t1, t2);
/* End stage II, case abs(x-1) < 0.03 */
if ((y = b + (bb + b * E4)) == b + (bb - b * E4))
return y;
goto stage_n;
/*--- Stage I, the case abs(x-1) > 0.03 */
case_03:
/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
n += (num.i[HIGH_HALF] >> 20) - 1023;
num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
if (num.d > SQRT_2)
{
num.d *= HALF;
n++;
}
u = num.d;
dbl_n = (double) n;
/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
num.d += h1.d;
i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
num.d = u * Iu[i].d + h2.d;
j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
/* Compute w=(u-ui*vj)/(ui*vj) */
p0 = (ONE + (i - 75) * DEL_U) * (ONE + (j - 180) * DEL_V);
q = u - p0;
r0 = Iu[i].d * Iv[j].d;
w = q * r0;
/* Evaluate polynomial I */
polI = w + (a2.d + a3.d * w) * w * w;
/* Add up everything */
nln2a = dbl_n * LN2A;
luai = Lu[i][0].d;
lubi = Lu[i][1].d;
lvaj = Lv[j][0].d;
lvbj = Lv[j][1].d;
EADD (luai, lvaj, sij, ssij);
EADD (nln2a, sij, A, ttij);
B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
B = polI + B0;
/* End stage I, case abs(x-1) >= 0.03 */
if ((y = A + (B + E1)) == A + (B - E1))
return y;
/*--- Stage II, the case abs(x-1) > 0.03 */
/* Improve the accuracy of r0 */
EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5);
t = r0 * ((ONE - sa) - sb);
EADD (r0, t, ra, rb);
/* Compute w */
MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8);
EADD (A, B0, a0, aa0);
/* Evaluate polynomial III */
s1 = (c3.d + (c4.d + c5.d * w) * w) * w;
EADD (c2.d, s1, s2, ss2);
MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2);
ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2);
/* End stage II, case abs(x-1) >= 0.03 */
if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3))
return y;
/* Final stages. Use multi-precision arithmetic. */
stage_n:
for (i = 0; i < M; i++)
{
p = pr[i];
__dbl_mp (x, &mpx, p);
__dbl_mp (y, &mpy, p);
__mplog (&mpx, &mpy, p);
__dbl_mp (e[i].d, &mperr, p);
__add (&mpy, &mperr, &mpy1, p);
__sub (&mpy, &mperr, &mpy2, p);
__mp_dbl (&mpy1, &y1, p);
__mp_dbl (&mpy2, &y2, p);
if (y1 == y2)
return y1;
}
return y1;
}
#ifndef __ieee754_log
strong_alias (__ieee754_log, __log_finite)
#endif
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