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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/dbl-64/e_log.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
downloadglibc-zack/build-layout-experiment.tar.gz
Prepare for radical source tree reorganization.zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
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+/*
+ * IBM Accurate Mathematical Library
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001-2017 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.h>
+#include <math_private.h>
+#include <stap-probe.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 (__glibc_unlikely (ux < 0x00100000))
+ {
+ if (__glibc_unlikely (((ux & 0x7fffffff) | dx) == 0))
+ return MHALF / 0.0; /* return -INF */
+ if (__glibc_unlikely (ux < 0))
+ return (x - x) / 0.0; /* return NaN */
+ n -= 54;
+ x *= two54.d; /* scale x */
+ num.d = x;
+ }
+ if (__glibc_unlikely (ux >= 0x7ff00000))
+ return x + x; /* INF or NaN */
+
+ /* Regular values of x */
+
+ w = x - 1;
+ if (__glibc_likely (fabs (w) > U03))
+ goto case_03;
+
+ /* log (1) is +0 in all rounding modes. */
+ if (w == 0.0)
+ return 0.0;
+
+ /*--- 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 = (1 + (i - 75) * DEL_U) * (1 + (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 * ((1 - 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)
+ {
+ LIBC_PROBE (slowlog, 3, &p, &x, &y1);
+ return y1;
+ }
+ }
+ LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1);
+ return y1;
+}
+
+#ifndef __ieee754_log
+strong_alias (__ieee754_log, __log_finite)
+#endif