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-rw-r--r--sysdeps/ieee754/dbl-64/e_pow.c481
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diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
deleted file mode 100644
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--- a/sysdeps/ieee754/dbl-64/e_pow.c
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@@ -1,481 +0,0 @@
-/*
- * 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: upow.c */
-/* */
-/* FUNCTIONS: upow */
-/* power1 */
-/* my_log2 */
-/* log1 */
-/* checkint */
-/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h */
-/* halfulp.c mpexp.c mplog.c slowexp.c slowpow.c mpa.c */
-/* uexp.c upow.c */
-/* root.tbl uexp.tbl upow.tbl */
-/* An ultimate power routine. Given two IEEE double machine numbers y,x */
-/* it computes the correctly rounded (to nearest) value of x^y. */
-/* Assumption: Machine arithmetic operations are performed in */
-/* round to nearest mode of IEEE 754 standard. */
-/* */
-/***************************************************************************/
-#include <math.h>
-#include "endian.h"
-#include "upow.h"
-#include <dla.h>
-#include "mydefs.h"
-#include "MathLib.h"
-#include "upow.tbl"
-#include <math_private.h>
-#include <fenv.h>
-
-#ifndef SECTION
-# define SECTION
-#endif
-
-static const double huge = 1.0e300, tiny = 1.0e-300;
-
-double __exp1 (double x, double xx, double error);
-static double log1 (double x, double *delta, double *error);
-static double my_log2 (double x, double *delta, double *error);
-double __slowpow (double x, double y, double z);
-static double power1 (double x, double y);
-static int checkint (double x);
-
-/* An ultimate power routine. Given two IEEE double machine numbers y, x it
- computes the correctly rounded (to nearest) value of X^y. */
-double
-SECTION
-__ieee754_pow (double x, double y)
-{
- double z, a, aa, error, t, a1, a2, y1, y2;
- mynumber u, v;
- int k;
- int4 qx, qy;
- v.x = y;
- u.x = x;
- if (v.i[LOW_HALF] == 0)
- { /* of y */
- qx = u.i[HIGH_HALF] & 0x7fffffff;
- /* Is x a NaN? */
- if ((((qx == 0x7ff00000) && (u.i[LOW_HALF] != 0)) || (qx > 0x7ff00000))
- && (y != 0 || issignaling (x)))
- return x + x;
- if (y == 1.0)
- return x;
- if (y == 2.0)
- return x * x;
- if (y == -1.0)
- return 1.0 / x;
- if (y == 0)
- return 1.0;
- }
- /* else */
- if (((u.i[HIGH_HALF] > 0 && u.i[HIGH_HALF] < 0x7ff00000) || /* x>0 and not x->0 */
- (u.i[HIGH_HALF] == 0 && u.i[LOW_HALF] != 0)) &&
- /* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
- (v.i[HIGH_HALF] & 0x7fffffff) < 0x4ff00000)
- { /* if y<-1 or y>1 */
- double retval;
-
- {
- SET_RESTORE_ROUND (FE_TONEAREST);
-
- /* Avoid internal underflow for tiny y. The exact value of y does
- not matter if |y| <= 2**-64. */
- if (fabs (y) < 0x1p-64)
- y = y < 0 ? -0x1p-64 : 0x1p-64;
- z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
- t = y * CN;
- y1 = t - (t - y);
- y2 = y - y1;
- t = z * CN;
- a1 = t - (t - z);
- a2 = (z - a1) + aa;
- a = y1 * a1;
- aa = y2 * a1 + y * a2;
- a1 = a + aa;
- a2 = (a - a1) + aa;
- error = error * fabs (y);
- t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
- retval = (t > 0) ? t : power1 (x, y);
- }
-
- if (isinf (retval))
- retval = huge * huge;
- else if (retval == 0)
- retval = tiny * tiny;
- else
- math_check_force_underflow_nonneg (retval);
- return retval;
- }
-
- if (x == 0)
- {
- if (((v.i[HIGH_HALF] & 0x7fffffff) == 0x7ff00000 && v.i[LOW_HALF] != 0)
- || (v.i[HIGH_HALF] & 0x7fffffff) > 0x7ff00000) /* NaN */
- return y + y;
- if (fabs (y) > 1.0e20)
- return (y > 0) ? 0 : 1.0 / 0.0;
- k = checkint (y);
- if (k == -1)
- return y < 0 ? 1.0 / x : x;
- else
- return y < 0 ? 1.0 / 0.0 : 0.0; /* return 0 */
- }
-
- qx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
- qy = v.i[HIGH_HALF] & 0x7fffffff; /* no sign */
-
- if (qx >= 0x7ff00000 && (qx > 0x7ff00000 || u.i[LOW_HALF] != 0)) /* NaN */
- return x + y;
- if (qy >= 0x7ff00000 && (qy > 0x7ff00000 || v.i[LOW_HALF] != 0)) /* NaN */
- return x == 1.0 && !issignaling (y) ? 1.0 : y + y;
-
- /* if x<0 */
- if (u.i[HIGH_HALF] < 0)
- {
- k = checkint (y);
- if (k == 0)
- {
- if (qy == 0x7ff00000)
- {
- if (x == -1.0)
- return 1.0;
- else if (x > -1.0)
- return v.i[HIGH_HALF] < 0 ? INF.x : 0.0;
- else
- return v.i[HIGH_HALF] < 0 ? 0.0 : INF.x;
- }
- else if (qx == 0x7ff00000)
- return y < 0 ? 0.0 : INF.x;
- return (x - x) / (x - x); /* y not integer and x<0 */
- }
- else if (qx == 0x7ff00000)
- {
- if (k < 0)
- return y < 0 ? nZERO.x : nINF.x;
- else
- return y < 0 ? 0.0 : INF.x;
- }
- /* if y even or odd */
- if (k == 1)
- return __ieee754_pow (-x, y);
- else
- {
- double retval;
- {
- SET_RESTORE_ROUND (FE_TONEAREST);
- retval = -__ieee754_pow (-x, y);
- }
- if (isinf (retval))
- retval = -huge * huge;
- else if (retval == 0)
- retval = -tiny * tiny;
- return retval;
- }
- }
- /* x>0 */
-
- if (qx == 0x7ff00000) /* x= 2^-0x3ff */
- return y > 0 ? x : 0;
-
- if (qy > 0x45f00000 && qy < 0x7ff00000)
- {
- if (x == 1.0)
- return 1.0;
- if (y > 0)
- return (x > 1.0) ? huge * huge : tiny * tiny;
- if (y < 0)
- return (x < 1.0) ? huge * huge : tiny * tiny;
- }
-
- if (x == 1.0)
- return 1.0;
- if (y > 0)
- return (x > 1.0) ? INF.x : 0;
- if (y < 0)
- return (x < 1.0) ? INF.x : 0;
- return 0; /* unreachable, to make the compiler happy */
-}
-
-#ifndef __ieee754_pow
-strong_alias (__ieee754_pow, __pow_finite)
-#endif
-
-/* Compute x^y using more accurate but more slow log routine. */
-static double
-SECTION
-power1 (double x, double y)
-{
- double z, a, aa, error, t, a1, a2, y1, y2;
- z = my_log2 (x, &aa, &error);
- t = y * CN;
- y1 = t - (t - y);
- y2 = y - y1;
- t = z * CN;
- a1 = t - (t - z);
- a2 = z - a1;
- a = y * z;
- aa = ((y1 * a1 - a) + y1 * a2 + y2 * a1) + y2 * a2 + aa * y;
- a1 = a + aa;
- a2 = (a - a1) + aa;
- error = error * fabs (y);
- t = __exp1 (a1, a2, 1.9e16 * error);
- return (t >= 0) ? t : __slowpow (x, y, z);
-}
-
-/* Compute log(x) (x is left argument). The result is the returned double + the
- parameter DELTA. The result is bounded by ERROR. */
-static double
-SECTION
-log1 (double x, double *delta, double *error)
-{
- unsigned int i, j;
- int m;
- double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
- mynumber u, v;
-#ifdef BIG_ENDI
- mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
-#else
-# ifdef LITTLE_ENDI
- mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
-# endif
-#endif
-
- u.x = x;
- m = u.i[HIGH_HALF];
- *error = 0;
- *delta = 0;
- if (m < 0x00100000) /* 1<x<2^-1007 */
- {
- x = x * t52.x;
- add = -52.0;
- u.x = x;
- m = u.i[HIGH_HALF];
- }
-
- if ((m & 0x000fffff) < 0x0006a09e)
- {
- u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
- two52.i[LOW_HALF] = (m >> 20);
- }
- else
- {
- u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
- two52.i[LOW_HALF] = (m >> 20) + 1;
- }
-
- v.x = u.x + bigu.x;
- uu = v.x - bigu.x;
- i = (v.i[LOW_HALF] & 0x000003ff) << 2;
- if (two52.i[LOW_HALF] == 1023) /* nx = 0 */
- {
- if (i > 1192 && i < 1208) /* |x-1| < 1.5*2**-10 */
- {
- t = x - 1.0;
- t1 = (t + 5.0e6) - 5.0e6;
- t2 = t - t1;
- e1 = t - 0.5 * t1 * t1;
- e2 = (t * t * t * (r3 + t * (r4 + t * (r5 + t * (r6 + t
- * (r7 + t * r8)))))
- - 0.5 * t2 * (t + t1));
- res = e1 + e2;
- *error = 1.0e-21 * fabs (t);
- *delta = (e1 - res) + e2;
- return res;
- } /* |x-1| < 1.5*2**-10 */
- else
- {
- v.x = u.x * (ui.x[i] + ui.x[i + 1]) + bigv.x;
- vv = v.x - bigv.x;
- j = v.i[LOW_HALF] & 0x0007ffff;
- j = j + j + j;
- eps = u.x - uu * vv;
- e1 = eps * ui.x[i];
- e2 = eps * (ui.x[i + 1] + vj.x[j] * (ui.x[i] + ui.x[i + 1]));
- e = e1 + e2;
- e2 = ((e1 - e) + e2);
- t = ui.x[i + 2] + vj.x[j + 1];
- t1 = t + e;
- t2 = ((((t - t1) + e) + (ui.x[i + 3] + vj.x[j + 2])) + e2 + e * e
- * (p2 + e * (p3 + e * p4)));
- res = t1 + t2;
- *error = 1.0e-24;
- *delta = (t1 - res) + t2;
- return res;
- }
- } /* nx = 0 */
- else /* nx != 0 */
- {
- eps = u.x - uu;
- nx = (two52.x - two52e.x) + add;
- e1 = eps * ui.x[i];
- e2 = eps * ui.x[i + 1];
- e = e1 + e2;
- e2 = (e1 - e) + e2;
- t = nx * ln2a.x + ui.x[i + 2];
- t1 = t + e;
- t2 = ((((t - t1) + e) + nx * ln2b.x + ui.x[i + 3] + e2) + e * e
- * (q2 + e * (q3 + e * (q4 + e * (q5 + e * q6)))));
- res = t1 + t2;
- *error = 1.0e-21;
- *delta = (t1 - res) + t2;
- return res;
- } /* nx != 0 */
-}
-
-/* Slower but more accurate routine of log. The returned result is double +
- DELTA. The result is bounded by ERROR. */
-static double
-SECTION
-my_log2 (double x, double *delta, double *error)
-{
- unsigned int i, j;
- int m;
- double uu, vv, eps, nx, e, e1, e2, t, t1, t2, res, add = 0;
- double ou1, ou2, lu1, lu2, ov, lv1, lv2, a, a1, a2;
- double y, yy, z, zz, j1, j2, j7, j8;
-#ifndef DLA_FMS
- double j3, j4, j5, j6;
-#endif
- mynumber u, v;
-#ifdef BIG_ENDI
- mynumber /**/ two52 = {{0x43300000, 0x00000000}}; /* 2**52 */
-#else
-# ifdef LITTLE_ENDI
- mynumber /**/ two52 = {{0x00000000, 0x43300000}}; /* 2**52 */
-# endif
-#endif
-
- u.x = x;
- m = u.i[HIGH_HALF];
- *error = 0;
- *delta = 0;
- add = 0;
- if (m < 0x00100000)
- { /* x < 2^-1022 */
- x = x * t52.x;
- add = -52.0;
- u.x = x;
- m = u.i[HIGH_HALF];
- }
-
- if ((m & 0x000fffff) < 0x0006a09e)
- {
- u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3ff00000;
- two52.i[LOW_HALF] = (m >> 20);
- }
- else
- {
- u.i[HIGH_HALF] = (m & 0x000fffff) | 0x3fe00000;
- two52.i[LOW_HALF] = (m >> 20) + 1;
- }
-
- v.x = u.x + bigu.x;
- uu = v.x - bigu.x;
- i = (v.i[LOW_HALF] & 0x000003ff) << 2;
- /*------------------------------------- |x-1| < 2**-11------------------------------- */
- if ((two52.i[LOW_HALF] == 1023) && (i == 1200))
- {
- t = x - 1.0;
- EMULV (t, s3, y, yy, j1, j2, j3, j4, j5);
- ADD2 (-0.5, 0, y, yy, z, zz, j1, j2);
- MUL2 (t, 0, z, zz, y, yy, j1, j2, j3, j4, j5, j6, j7, j8);
- MUL2 (t, 0, y, yy, z, zz, j1, j2, j3, j4, j5, j6, j7, j8);
-
- e1 = t + z;
- e2 = ((((t - e1) + z) + zz) + t * t * t
- * (ss3 + t * (s4 + t * (s5 + t * (s6 + t * (s7 + t * s8))))));
- res = e1 + e2;
- *error = 1.0e-25 * fabs (t);
- *delta = (e1 - res) + e2;
- return res;
- }
- /*----------------------------- |x-1| > 2**-11 -------------------------- */
- else
- { /*Computing log(x) according to log table */
- nx = (two52.x - two52e.x) + add;
- ou1 = ui.x[i];
- ou2 = ui.x[i + 1];
- lu1 = ui.x[i + 2];
- lu2 = ui.x[i + 3];
- v.x = u.x * (ou1 + ou2) + bigv.x;
- vv = v.x - bigv.x;
- j = v.i[LOW_HALF] & 0x0007ffff;
- j = j + j + j;
- eps = u.x - uu * vv;
- ov = vj.x[j];
- lv1 = vj.x[j + 1];
- lv2 = vj.x[j + 2];
- a = (ou1 + ou2) * (1.0 + ov);
- a1 = (a + 1.0e10) - 1.0e10;
- a2 = a * (1.0 - a1 * uu * vv);
- e1 = eps * a1;
- e2 = eps * a2;
- e = e1 + e2;
- e2 = (e1 - e) + e2;
- t = nx * ln2a.x + lu1 + lv1;
- t1 = t + e;
- t2 = ((((t - t1) + e) + (lu2 + lv2 + nx * ln2b.x + e2)) + e * e
- * (p2 + e * (p3 + e * p4)));
- res = t1 + t2;
- *error = 1.0e-27;
- *delta = (t1 - res) + t2;
- return res;
- }
-}
-
-/* This function receives a double x and checks if it is an integer. If not,
- it returns 0, else it returns 1 if even or -1 if odd. */
-static int
-SECTION
-checkint (double x)
-{
- union
- {
- int4 i[2];
- double x;
- } u;
- int k, m, n;
- u.x = x;
- m = u.i[HIGH_HALF] & 0x7fffffff; /* no sign */
- if (m >= 0x7ff00000)
- return 0; /* x is +/-inf or NaN */
- if (m >= 0x43400000)
- return 1; /* |x| >= 2**53 */
- if (m < 0x40000000)
- return 0; /* |x| < 2, can not be 0 or 1 */
- n = u.i[LOW_HALF];
- k = (m >> 20) - 1023; /* 1 <= k <= 52 */
- if (k == 52)
- return (n & 1) ? -1 : 1; /* odd or even */
- if (k > 20)
- {
- if (n << (k - 20) != 0)
- return 0; /* if not integer */
- return (n << (k - 21) != 0) ? -1 : 1;
- }
- if (n)
- return 0; /*if not integer */
- if (k == 20)
- return (m & 1) ? -1 : 1;
- if (m << (k + 12) != 0)
- return 0;
- return (m << (k + 11) != 0) ? -1 : 1;
-}
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