Merged revisions 76861 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r76861 | mark.dickinson | 2009-12-16 20:13:40 +0000 (Wed, 16 Dec 2009) | 3 lines

  Issue #3366: Add expm1 function to math module.  Thanks Eric Smith for
  testing on Windows.
........

Lib/test/math_testcases.txt

@@ -249,3 +249,73 @@ gam0132 gamma -4503599627370495.5 -> 0.0
 -- thanks to loss of accuracy in 1-x
 gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88
 gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214
+
+-----------------------------------------------------------
+-- expm1: exp(x) - 1, without precision loss for small x --
+-----------------------------------------------------------
+
+-- special values
+expm10000 expm1 0.0 -> 0.0
+expm10001 expm1 -0.0 -> -0.0
+expm10002 expm1 inf -> inf
+expm10003 expm1 -inf -> -1.0
+expm10004 expm1 nan -> nan
+
+-- expm1(x) ~ x for tiny x
+expm10010 expm1 5e-324 -> 5e-324
+expm10011 expm1 1e-320 -> 1e-320
+expm10012 expm1 1e-300 -> 1e-300
+expm10013 expm1 1e-150 -> 1e-150
+expm10014 expm1 1e-20 -> 1e-20
+
+expm10020 expm1 -5e-324 -> -5e-324
+expm10021 expm1 -1e-320 -> -1e-320
+expm10022 expm1 -1e-300 -> -1e-300
+expm10023 expm1 -1e-150 -> -1e-150
+expm10024 expm1 -1e-20 -> -1e-20
+
+-- moderate sized values, where direct evaluation runs into trouble
+expm10100 expm1 1e-10 -> 1.0000000000500000e-10
+expm10101 expm1 -9.9999999999999995e-08 -> -9.9999995000000163e-8
+expm10102 expm1 3.0000000000000001e-05 -> 3.0000450004500034e-5
+expm10103 expm1 -0.0070000000000000001 -> -0.0069755570667648951
+expm10104 expm1 -0.071499208740094633 -> -0.069002985744820250
+expm10105 expm1 -0.063296004180116799 -> -0.061334416373633009
+expm10106 expm1 0.02390954035597756 -> 0.024197665143819942
+expm10107 expm1 0.085637352649044901 -> 0.089411184580357767
+expm10108 expm1 0.5966174947411006 -> 0.81596588596501485
+expm10109 expm1 0.30247206212075139 -> 0.35319987035848677
+expm10110 expm1 0.74574727375889516 -> 1.1080161116737459
+expm10111 expm1 0.97767512926555711 -> 1.6582689207372185
+expm10112 expm1 0.8450154566787712 -> 1.3280137976535897
+expm10113 expm1 -0.13979260323125264 -> -0.13046144381396060
+expm10114 expm1 -0.52899322039643271 -> -0.41080213643695923
+expm10115 expm1 -0.74083261478900631 -> -0.52328317124797097
+expm10116 expm1 -0.93847766984546055 -> -0.60877704724085946
+expm10117 expm1 10.0 -> 22025.465794806718
+expm10118 expm1 27.0 -> 532048240600.79865
+expm10119 expm1 123 -> 2.6195173187490626e+53
+expm10120 expm1 -12.0 -> -0.99999385578764666
+expm10121 expm1 -35.100000000000001 -> -0.99999999999999944
+
+-- extreme negative values
+expm10201 expm1 -37.0 -> -0.99999999999999989
+expm10200 expm1 -38.0 -> -1.0
+expm10210 expm1 -710.0 -> -1.0
+-- the formula expm1(x) = 2 * sinh(x/2) * exp(x/2) doesn't work so
+-- well when exp(x/2) is subnormal or underflows to zero; check we're
+-- not using it!
+expm10211 expm1 -1420.0 -> -1.0
+expm10212 expm1 -1450.0 -> -1.0
+expm10213 expm1 -1500.0 -> -1.0
+expm10214 expm1 -1e50 -> -1.0
+expm10215 expm1 -1.79e308 -> -1.0
+
+-- extreme positive values
+expm10300 expm1 300 -> 1.9424263952412558e+130
+expm10301 expm1 700 -> 1.0142320547350045e+304
+expm10302 expm1 709.78271289328393 -> 1.7976931346824240e+308
+expm10303 expm1 709.78271289348402 -> inf overflow
+expm10304 expm1 1000 -> inf overflow
+expm10305 expm1 1e50 -> inf overflow
+expm10306 expm1 1.79e308 -> inf overflow

Lib/test/test_math.py

@@ -984,17 +984,16 @@ class MathTests(unittest.TestCase):
                 if math.isnan(expected) and math.isnan(got):
                     continue
                 if not math.isnan(expected) and not math.isnan(got):
-                    # we use different closeness criteria for
-                    # different functions.
-                    if fn == 'gamma':
-                        accuracy_failure = ulps_check(expected, got, 20)
-                    elif fn == 'lgamma':
+                    if fn == 'lgamma':
+                        # we use a weaker accuracy test for lgamma;
+                        # lgamma only achieves an absolute error of
+                        # a few multiples of the machine accuracy, in
+                        # general.
                         accuracy_failure = acc_check(expected, got,
                                                   rel_err = 5e-15,
                                                   abs_err = 5e-15)
                     else:
-                        raise ValueError("don't know how to check accuracy "
-                                         "for this function")
+                        accuracy_failure = ulps_check(expected, got, 20)
                     if accuracy_failure is None:
                         continue