Expm1Tests.java revision 809
* under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. * This code 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 * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, * CA 95054 USA or visit www.sun.com if you need additional information or * @bug 4851638 4900189 4939441 * @summary Tests for {Math, StrictMath}.expm1 * @author Joseph D. Darcy * The Taylor expansion of expxm1(x) = exp(x) -1 is * 1 + x/1! + x^2/2! + x^3/3| + ... -1 = * x + x^2/2! + x^3/3 + ... * Therefore, for small values of x, expxm1 ~= x. * For large values of x, expxm1(x) ~= exp(x) * For large negative x, expxm1(x) ~= -1. // For |x| < 2^-54 expm1(x) ~= x // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) // overflows for x > ~= 709.8 // Use a 2-ulp error threshold to account for errors in the // exp implementation; the increments of d in the loop will be for(
double d =
37.5; d <=
709.5; d +=
1.0) {
// For x > 710, expm1(x) should be infinity // By monotonicity, once the limit is reached, the // implemenation should return the limit for all smaller // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; // The greatest such y is ln(2^-53) ~= -36.7368005696771. for(
double d = -
36.75; d >= -
127.75; d -=
1.0) {
// Test for monotonicity failures near multiples of log(2). // Test two numbers before and two numbers after each chosen // {nextDown(nextDown(pc)), // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) for(
int i = -
50; i <=
50; i++) {