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263 lines
8.1 KiB
C
263 lines
8.1 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) 2001-2015 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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/* mpexp.c mplog.c mpa.c */
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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 correctly 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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#include <stap-probe.h>
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#ifndef SECTION
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# define SECTION
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#endif
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void __mplog (mp_no *, mp_no *, int);
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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 correctly 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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#define M 4
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static const int pr[M] = { 8, 10, 18, 32 };
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int i, j, n, ux, dx, p;
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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, y, y1, y2, polI, polII, sa, sb,
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t1, t2, t7, t8, t, ra, rb, ww,
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a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c;
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#ifndef DLA_FMS
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double t3, t4, t5, t6;
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#endif
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number num;
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mp_no mpx, mpy, mpy1, mpy2, mperr;
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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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/*--- Stage I, 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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/* End stage I, case abs(x-1) < 0.03 */
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if ((y = b + (c + b * E2)) == b + (c - b * E2))
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return y;
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/*--- Stage II, the case abs(x-1) < 0.03 */
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a = d19.d + w * d20.d;
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a = d18.d + w * a;
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a = d17.d + w * a;
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a = d16.d + w * a;
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a = d15.d + w * a;
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a = d14.d + w * a;
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a = d13.d + w * a;
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a = d12.d + w * a;
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a = d11.d + w * a;
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EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5);
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ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (w, 0, s3, ss3, b, bb, t1, t2);
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/* End stage II, case abs(x-1) < 0.03 */
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if ((y = b + (bb + b * E4)) == b + (bb - b * E4))
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return y;
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goto stage_n;
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/*--- Stage I, 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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/* End stage I, case abs(x-1) >= 0.03 */
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if ((y = A + (B + E1)) == A + (B - E1))
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return y;
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/*--- Stage II, the case abs(x-1) > 0.03 */
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/* Improve the accuracy of r0 */
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EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5);
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t = r0 * ((1 - sa) - sb);
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EADD (r0, t, ra, rb);
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/* Compute w */
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MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8);
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EADD (A, B0, a0, aa0);
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/* Evaluate polynomial III */
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s1 = (c3.d + (c4.d + c5.d * w) * w) * w;
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EADD (c2.d, s1, s2, ss2);
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MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2);
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ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2);
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/* End stage II, case abs(x-1) >= 0.03 */
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if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3))
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return y;
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/* Final stages. Use multi-precision arithmetic. */
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stage_n:
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for (i = 0; i < M; i++)
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{
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p = pr[i];
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__dbl_mp (x, &mpx, p);
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__dbl_mp (y, &mpy, p);
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__mplog (&mpx, &mpy, p);
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__dbl_mp (e[i].d, &mperr, p);
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__add (&mpy, &mperr, &mpy1, p);
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__sub (&mpy, &mperr, &mpy2, p);
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__mp_dbl (&mpy1, &y1, p);
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__mp_dbl (&mpy2, &y2, p);
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if (y1 == y2)
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{
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LIBC_PROBE (slowlog, 3, &p, &x, &y1);
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return y1;
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}
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}
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LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1);
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return y1;
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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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