| /* Test of exp2*() function family. |
| Copyright (C) 2012-2020 Free Software Foundation, Inc. |
| |
| This program is free software: you can redistribute it and/or modify |
| it under the terms of the GNU General Public License as published by |
| the Free Software Foundation; either version 3 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 General Public License for more details. |
| |
| You should have received a copy of the GNU General Public License |
| along with this program. If not, see <https://www.gnu.org/licenses/>. */ |
| |
| static void |
| test_function (void) |
| { |
| int i; |
| int j; |
| const DOUBLE TWO_MANT_DIG = |
| /* Assume MANT_DIG <= 5 * 31. |
| Use the identity |
| n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */ |
| (DOUBLE) (1U << ((MANT_DIG - 1) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5)) |
| * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5)); |
| |
| /* Integral arguments. */ |
| { |
| DOUBLE x = L_(0.0); |
| DOUBLE y = EXP2 (x); |
| ASSERT (y == L_(1.0)); |
| } |
| /* <https://sourceware.org/bugzilla/show_bug.cgi?id=13824> */ |
| #if !(defined __linux__ && (defined __sparc__ || defined __powerpc__)) |
| { |
| int e; |
| DOUBLE x; |
| DOUBLE y; |
| for (e = 0, x = L_(0.0), y = L_(1.0); |
| e <= MAX_EXP - 1; |
| e++, x = x + L_(1.0), y = y * L_(2.0)) |
| { |
| /* Invariant: x = e, y = 2^e. */ |
| DOUBLE z = EXP2 (x); |
| ASSERT (z == y); |
| } |
| } |
| { |
| int e; |
| DOUBLE x; |
| DOUBLE y; |
| for (e = 0, x = L_(0.0), y = L_(1.0); |
| e >= MIN_EXP - 1; |
| e--, x = x - L_(1.0), y = y * L_(0.5)) |
| { |
| /* Invariant: x = e, y = 2^e. */ |
| DOUBLE z = EXP2 (x); |
| ASSERT (z == y); |
| } |
| } |
| #endif |
| |
| /* Randomized tests. */ |
| { |
| /* Error bound, in ulps. */ |
| const DOUBLE err_bound = |
| (sizeof (DOUBLE) > sizeof (double) ? |
| #if defined __i386__ && defined __FreeBSD__ |
| /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of |
| precision in the compiler but 64 bits of precision at runtime. See |
| <https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>. |
| The compiler has truncated all 'long double' literals in exp2l.c to |
| 53 bits of precision. */ |
| L_(1350.0) |
| #else |
| L_(3.0) |
| #endif |
| : L_(3.0)); |
| |
| for (i = 0; i < SIZEOF (RANDOM); i++) |
| { |
| DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */ |
| DOUBLE y = EXP2 (x); |
| DOUBLE z = EXP2 (- x); |
| DOUBLE err = y * z - L_(1.0); |
| ASSERT (y > L_(0.0)); |
| ASSERT (z > L_(0.0)); |
| ASSERT (err > - err_bound / TWO_MANT_DIG |
| && err < err_bound / TWO_MANT_DIG); |
| } |
| } |
| |
| { |
| /* Error bound, in ulps. */ |
| const DOUBLE err_bound = |
| (sizeof (DOUBLE) > sizeof (double) ? |
| #if defined __i386__ && defined __FreeBSD__ |
| L_(2300.0) |
| #else |
| L_(29.0) |
| #endif |
| : L_(11.0)); |
| |
| for (i = 0; i < SIZEOF (RANDOM) / 5; i++) |
| for (j = 0; j < SIZEOF (RANDOM) / 5; j++) |
| { |
| DOUBLE x = L_(32.0) * RANDOM[i] - L_(16.0); /* -16.0 <= x <= 16.0 */ |
| DOUBLE y = L_(32.0) * RANDOM[j] - L_(16.0); /* -16.0 <= y <= 16.0 */ |
| DOUBLE z = - x - y; |
| /* Approximately x + y + z = 0. */ |
| DOUBLE err = EXP2 (x) * EXP2 (y) * EXP2 (z) - L_(1.0); |
| ASSERT (err > - err_bound / TWO_MANT_DIG |
| && err < err_bound / TWO_MANT_DIG); |
| } |
| } |
| } |
| |
| volatile DOUBLE x; |
| DOUBLE y; |