| /* Test of fmod*() 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 DOUBLE |
| my_ldexp (DOUBLE x, int d) |
| { |
| for (; d > 0; d--) |
| x *= L_(2.0); |
| for (; d < 0; d++) |
| x *= L_(0.5); |
| return x; |
| } |
| |
| 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)); |
| |
| /* Randomized tests. */ |
| for (i = 0; i < SIZEOF (RANDOM) / 5; i++) |
| for (j = 0; j < SIZEOF (RANDOM) / 5; j++) |
| { |
| DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */ |
| DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */ |
| if (y > L_(0.0)) |
| { |
| DOUBLE z = FMOD (x, y); |
| ASSERT (z >= L_(0.0)); |
| ASSERT (z < y); |
| z -= x - (int) (x / y) * y; |
| ASSERT (/* The common case. */ |
| (z > - L_(16.0) / TWO_MANT_DIG |
| && z < L_(16.0) / TWO_MANT_DIG) |
| || /* rounding error: x / y computed too large */ |
| (z > y - L_(16.0) / TWO_MANT_DIG |
| && z < y + L_(16.0) / TWO_MANT_DIG) |
| || /* rounding error: x / y computed too small */ |
| (z > - y - L_(16.0) / TWO_MANT_DIG |
| && z < - y + L_(16.0) / TWO_MANT_DIG)); |
| } |
| } |
| |
| for (i = 0; i < SIZEOF (RANDOM) / 5; i++) |
| for (j = 0; j < SIZEOF (RANDOM) / 5; j++) |
| { |
| DOUBLE x = L_(1.0e9) * RANDOM[i]; /* 0.0 <= x <= 10^9 */ |
| DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */ |
| if (y > L_(0.0)) |
| { |
| DOUBLE z = FMOD (x, y); |
| DOUBLE r; |
| ASSERT (z >= L_(0.0)); |
| ASSERT (z < y); |
| { |
| /* Determine the quotient x / y in two steps, because it |
| may be > 2^31. */ |
| int q1 = (int) (x / y / L_(65536.0)); |
| int q2 = (int) ((x - q1 * L_(65536.0) * y) / y); |
| DOUBLE q = (DOUBLE) q1 * L_(65536.0) + (DOUBLE) q2; |
| r = x - q * y; |
| } |
| /* The absolute error of z can be up to 1e9/2^MANT_DIG. |
| The absolute error of r can also be up to 1e9/2^MANT_DIG. |
| Therefore the error of z - r can be twice as large. */ |
| z -= r; |
| ASSERT (/* The common case. */ |
| (z > - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG |
| && z < L_(2.0) * L_(1.0e9) / TWO_MANT_DIG) |
| || /* rounding error: x / y computed too large */ |
| (z > y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG |
| && z < y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG) |
| || /* rounding error: x / y computed too small */ |
| (z > - y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG |
| && z < - y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)); |
| } |
| } |
| |
| { |
| int large_exp = (MAX_EXP - 1 < 1000 ? MAX_EXP - 1 : 1000); |
| DOUBLE large = my_ldexp (L_(1.0), large_exp); /* = 2^large_exp */ |
| for (i = 0; i < SIZEOF (RANDOM) / 10; i++) |
| for (j = 0; j < SIZEOF (RANDOM) / 10; j++) |
| { |
| DOUBLE x = large * RANDOM[i]; /* 0.0 <= x <= 2^large_exp */ |
| DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */ |
| if (y > L_(0.0)) |
| { |
| DOUBLE z = FMOD (x, y); |
| /* Regardless how large the rounding errors are, the result |
| must be >= 0, < y. */ |
| ASSERT (z >= L_(0.0)); |
| ASSERT (z < y); |
| } |
| } |
| } |
| } |
| |
| volatile DOUBLE x; |
| volatile DOUBLE y; |
| DOUBLE z; |