| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001-2014 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> |
| #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 (__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 - 1; |
| 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 = (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 |
