168 lines
5.3 KiB
C
168 lines
5.3 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2018 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/*********************************************************************/
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/* */
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/* MODULE_NAME:ulog.c */
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/* */
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/* FUNCTION:ulog */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
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/* ulog.tbl */
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/* */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the rounded (to nearest) value of log(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include "endian.h"
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#include <dla.h>
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#include "mpa.h"
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#include "MathLib.h"
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#include <math.h>
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#include <math_private.h>
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#ifndef SECTION
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# define SECTION
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#endif
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the rounded (to nearest) value of log(x). */
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/*********************************************************************/
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double
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SECTION
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__ieee754_log (double x)
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{
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int i, j, n, ux, dx;
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double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
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sij, ssij, ttij, A, B, B0, polI, polII, t8, a, aa, b, bb, c;
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#ifndef DLA_FMS
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double t1, t2, t3, t4, t5;
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#endif
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number num;
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#include "ulog.tbl"
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#include "ulog.h"
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/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
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num.d = x;
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ux = num.i[HIGH_HALF];
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dx = num.i[LOW_HALF];
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n = 0;
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if (__glibc_unlikely (ux < 0x00100000))
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{
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if (__glibc_unlikely (((ux & 0x7fffffff) | dx) == 0))
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return MHALF / 0.0; /* return -INF */
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if (__glibc_unlikely (ux < 0))
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return (x - x) / 0.0; /* return NaN */
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n -= 54;
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x *= two54.d; /* scale x */
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num.d = x;
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}
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if (__glibc_unlikely (ux >= 0x7ff00000))
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return x + x; /* INF or NaN */
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/* Regular values of x */
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w = x - 1;
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if (__glibc_likely (fabs (w) > U03))
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goto case_03;
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/* log (1) is +0 in all rounding modes. */
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if (w == 0.0)
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return 0.0;
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/*--- The case abs(x-1) < 0.03 */
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t8 = MHALF * w;
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EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
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EADD (w, a, b, bb);
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/* Evaluate polynomial II */
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polII = b7.d + w * b8.d;
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polII = b6.d + w * polII;
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polII = b5.d + w * polII;
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polII = b4.d + w * polII;
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polII = b3.d + w * polII;
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polII = b2.d + w * polII;
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polII = b1.d + w * polII;
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polII = b0.d + w * polII;
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polII *= w * w * w;
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c = (aa + bb) + polII;
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/* Here b contains the high part of the result, and c the low part.
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Maximum error is b * 2.334e-19, so accuracy is >61 bits.
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Therefore max ULP error of b + c is ~0.502. */
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return b + c;
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/*--- The case abs(x-1) > 0.03 */
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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n += (num.i[HIGH_HALF] >> 20) - 1023;
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num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
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if (num.d > SQRT_2)
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{
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num.d *= HALF;
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n++;
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}
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u = num.d;
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dbl_n = (double) n;
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/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
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num.d += h1.d;
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i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
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/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
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num.d = u * Iu[i].d + h2.d;
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j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
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/* Compute w=(u-ui*vj)/(ui*vj) */
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p0 = (1 + (i - 75) * DEL_U) * (1 + (j - 180) * DEL_V);
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q = u - p0;
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r0 = Iu[i].d * Iv[j].d;
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w = q * r0;
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/* Evaluate polynomial I */
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polI = w + (a2.d + a3.d * w) * w * w;
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/* Add up everything */
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nln2a = dbl_n * LN2A;
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luai = Lu[i][0].d;
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lubi = Lu[i][1].d;
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lvaj = Lv[j][0].d;
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lvbj = Lv[j][1].d;
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EADD (luai, lvaj, sij, ssij);
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EADD (nln2a, sij, A, ttij);
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B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
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B = polI + B0;
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/* Here A contains the high part of the result, and B the low part.
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Maximum abs error is 6.095e-21 and min log (x) is 0.0295 since x > 1.03.
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Therefore max ULP error of A + B is ~0.502. */
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return A + B;
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}
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#ifndef __ieee754_log
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strong_alias (__ieee754_log, __log_finite)
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#endif
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