[Python-checkins] r60700 - in python/branches/trunk-math: Lib/test/cmath.ctest Lib/test/test_cmath.py Lib/test/test_math.py Modules/cmathmodule.c
mark.dickinson
python-checkins at python.org
Sat Feb 9 22:27:14 CET 2008
Author: mark.dickinson
Date: Sat Feb 9 22:27:13 2008
New Revision: 60700
Modified:
python/branches/trunk-math/Lib/test/cmath.ctest
python/branches/trunk-math/Lib/test/test_cmath.py
python/branches/trunk-math/Lib/test/test_math.py
python/branches/trunk-math/Modules/cmathmodule.c
Log:
Add C99 special value handling to the following cmath functions: acos,
asin, atan, acosh, asinh, atanh, log, sqrt, exp, cos, sin, tan, cosh,
sinh, tanh. These functions should now give the C99 Annex G specified
return values, raise ValueError on divide-by-zero or invalid
floating-point exceptions, and raise OverflowError on the overflow
floating-point exception.
Augment tests to include special values, and expand testcase syntax to
include flags.
Modified: python/branches/trunk-math/Lib/test/cmath.ctest
==============================================================================
--- python/branches/trunk-math/Lib/test/cmath.ctest (original)
+++ python/branches/trunk-math/Lib/test/cmath.ctest Sat Feb 9 22:27:13 2008
@@ -1,21 +1,38 @@
-- Testcases for functions in cmath.
---
+--
-- Each line takes the form:
---
--- <testid> <function> <input_value> -> <output_value>
---
+--
+-- <testid> <function> <input_value> -> <output_value> <flags>
+--
-- where:
+--
-- <testid> is a short name identifying the test,
+--
-- <function> is the function to be tested (exp, cos, asinh, ...),
+--
-- <input_value> is a pair of floats separated by whitespace
-- representing real and imaginary parts of a complex number, and
--- <output_value> is the expected (ideal) output value, again
+--
+-- <output_value> is the expected (ideal) output value, again
-- represented as a pair of floats.
---
+--
+-- <flags> is a list of the floating-point flags required by C99
+--
+-- The possible flags are:
+--
+-- divide-by-zero : raised when a finite input gives a
+-- mathematically infinite result.
+--
+-- overflow : raised when a finite input gives a finite result whose
+-- real or imaginary part is too large to fit in the usual range
+-- of an IEEE 754 double.
+--
+-- invalid : raised for invalid inputs.
+--
-- Lines beginning with '--' (like this one) start a comment, and are
-- ignored. Blank lines, or lines containing only whitespace, are also
-- ignored.
---
+
--------------------------
-- acos: Inverse cosine --
@@ -149,6 +166,46 @@
acos0230 acos -4.9406564584124654e-324 0.0 -> 1.5707963267948966 -0.0
acos0231 acos -1.7107517052899003e-318 -0.0 -> 1.5707963267948966 0.0
+-- special values
+acos1000 acos 0.0 0.0 -> 1.5707963267948966 -0.0
+acos1001 acos 0.0 -0.0 -> 1.5707963267948966 0.0
+acos1002 acos -0.0 0.0 -> 1.5707963267948966 -0.0
+acos1003 acos -0.0 -0.0 -> 1.5707963267948966 0.0
+acos1004 acos 0.0 nan -> 1.5707963267948966 nan
+acos1005 acos -0.0 nan -> 1.5707963267948966 nan
+acos1006 acos -2.3 inf -> 1.5707963267948966 -inf
+acos1007 acos -0.0 inf -> 1.5707963267948966 -inf
+acos1008 acos 0.0 inf -> 1.5707963267948966 -inf
+acos1009 acos 2.3 inf -> 1.5707963267948966 -inf
+acos1010 acos -2.3 nan -> nan nan
+acos1011 acos 2.3 nan -> nan nan
+acos1012 acos -inf 2.3 -> 3.1415926535897931 -inf
+acos1013 acos -inf 0.0 -> 3.1415926535897931 -inf
+acos1014 acos inf 2.3 -> 0.0 -inf
+acos1015 acos inf 0.0 -> 0.0 -inf
+acos1016 acos -inf inf -> 2.3561944901923448 -inf
+acos1017 acos inf inf -> 0.78539816339744828 -inf
+acos1018 acos inf nan -> nan inf
+acos1019 acos -inf nan -> nan inf
+acos1020 acos nan 0.0 -> nan nan
+acos1021 acos nan 2.3 -> nan nan
+acos1022 acos nan inf -> nan -inf
+acos1023 acos nan nan -> nan nan
+acos1024 acos -2.3 -inf -> 1.5707963267948966 inf
+acos1025 acos -0.0 -inf -> 1.5707963267948966 inf
+acos1026 acos 0.0 -inf -> 1.5707963267948966 inf
+acos1027 acos 2.3 -inf -> 1.5707963267948966 inf
+acos1028 acos -inf -2.3 -> 3.1415926535897931 inf
+acos1029 acos -inf -0.0 -> 3.1415926535897931 inf
+acos1030 acos inf -2.3 -> 0.0 inf
+acos1031 acos inf -0.0 -> 0.0 inf
+acos1032 acos -inf -inf -> 2.3561944901923448 inf
+acos1033 acos inf -inf -> 0.78539816339744828 inf
+acos1034 acos nan -0.0 -> nan nan
+acos1035 acos nan -2.3 -> nan nan
+acos1036 acos nan -inf -> nan inf
+
+
--------------------------------------
-- acosh: Inverse hyperbolic cosine --
--------------------------------------
@@ -281,6 +338,46 @@
acosh0230 acosh -3.7450175954766488e-320 0.0 -> 0.0 1.5707963267948966
acosh0231 acosh -8.4250563080885801e-311 -0.0 -> 0.0 -1.5707963267948966
+-- special values
+acosh1000 acosh 0.0 0.0 -> 0.0 1.5707963267948966
+acosh1001 acosh -0.0 0.0 -> 0.0 1.5707963267948966
+acosh1002 acosh 0.0 inf -> inf 1.5707963267948966
+acosh1003 acosh 2.3 inf -> inf 1.5707963267948966
+acosh1004 acosh -0.0 inf -> inf 1.5707963267948966
+acosh1005 acosh -2.3 inf -> inf 1.5707963267948966
+acosh1006 acosh 0.0 nan -> nan nan
+acosh1007 acosh 2.3 nan -> nan nan
+acosh1008 acosh -0.0 nan -> nan nan
+acosh1009 acosh -2.3 nan -> nan nan
+acosh1010 acosh -inf 0.0 -> inf 3.1415926535897931
+acosh1011 acosh -inf 2.3 -> inf 3.1415926535897931
+acosh1012 acosh inf 0.0 -> inf 0.0
+acosh1013 acosh inf 2.3 -> inf 0.0
+acosh1014 acosh -inf inf -> inf 2.3561944901923448
+acosh1015 acosh inf inf -> inf 0.78539816339744828
+acosh1016 acosh inf nan -> inf nan
+acosh1017 acosh -inf nan -> inf nan
+acosh1018 acosh nan 0.0 -> nan nan
+acosh1019 acosh nan 2.3 -> nan nan
+acosh1020 acosh nan inf -> inf nan
+acosh1021 acosh nan nan -> nan nan
+acosh1022 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1023 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1024 acosh 0.0 -inf -> inf -1.5707963267948966
+acosh1025 acosh 2.3 -inf -> inf -1.5707963267948966
+acosh1026 acosh -0.0 -inf -> inf -1.5707963267948966
+acosh1027 acosh -2.3 -inf -> inf -1.5707963267948966
+acosh1028 acosh -inf -0.0 -> inf -3.1415926535897931
+acosh1029 acosh -inf -2.3 -> inf -3.1415926535897931
+acosh1030 acosh inf -0.0 -> inf -0.0
+acosh1031 acosh inf -2.3 -> inf -0.0
+acosh1032 acosh -inf -inf -> inf -2.3561944901923448
+acosh1033 acosh inf -inf -> inf -0.78539816339744828
+acosh1034 acosh nan -0.0 -> nan nan
+acosh1035 acosh nan -2.3 -> nan nan
+acosh1036 acosh nan -inf -> inf nan
+
+
------------------------
-- asin: Inverse sine --
------------------------
@@ -399,6 +496,7 @@
asin0218 asin -5.2499000118824295 4.6655578977512214e+307 -> -1.1252459249113292e-307 709.1269781491103
asin0219 asin -5.9904782760833433 -4.7315689314781163e+307 -> -1.2660659419394637e-307 -709.14102757522312
+
------------------------------------
-- asinh: Inverse hyperbolic sine --
------------------------------------
@@ -531,15 +629,55 @@
asinh0230 asinh -4.9406564584124654e-324 0.0 -> -4.9406564584124654e-324 0.0
asinh0231 asinh -2.221137922799485e-308 -0.0 -> -2.2211379227994845e-308 -0.0
+-- special values
+asinh1000 asinh 0.0 0.0 -> 0.0 0.0
+asinh1001 asinh 0.0 -0.0 -> 0.0 -0.0
+asinh1002 asinh -0.0 0.0 -> -0.0 0.0
+asinh1003 asinh -0.0 -0.0 -> -0.0 -0.0
+asinh1004 asinh 0.0 inf -> inf 1.5707963267948966
+asinh1005 asinh 2.3 inf -> inf 1.5707963267948966
+asinh1006 asinh 0.0 nan -> nan nan
+asinh1007 asinh 2.3 nan -> nan nan
+asinh1008 asinh inf 0.0 -> inf 0.0
+asinh1009 asinh inf 2.3 -> inf 0.0
+asinh1010 asinh inf inf -> inf 0.78539816339744828
+asinh1011 asinh inf nan -> inf nan
+asinh1012 asinh nan 0.0 -> nan 0.0
+asinh1013 asinh nan 2.3 -> nan nan
+asinh1014 asinh nan inf -> inf nan
+asinh1015 asinh nan nan -> nan nan
+asinh1016 asinh 0.0 -inf -> inf -1.5707963267948966
+asinh1017 asinh 2.3 -inf -> inf -1.5707963267948966
+asinh1018 asinh inf -0.0 -> inf -0.0
+asinh1019 asinh inf -2.3 -> inf -0.0
+asinh1020 asinh inf -inf -> inf -0.78539816339744828
+asinh1021 asinh nan -0.0 -> nan -0.0
+asinh1022 asinh nan -2.3 -> nan nan
+asinh1023 asinh nan -inf -> inf nan
+asinh1024 asinh -0.0 -inf -> -inf -1.5707963267948966
+asinh1025 asinh -2.3 -inf -> -inf -1.5707963267948966
+asinh1026 asinh -0.0 nan -> nan nan
+asinh1027 asinh -2.3 nan -> nan nan
+asinh1028 asinh -inf -0.0 -> -inf -0.0
+asinh1029 asinh -inf -2.3 -> -inf -0.0
+asinh1030 asinh -inf -inf -> -inf -0.78539816339744828
+asinh1031 asinh -inf nan -> -inf nan
+asinh1032 asinh -0.0 inf -> -inf 1.5707963267948966
+asinh1033 asinh -2.3 inf -> -inf 1.5707963267948966
+asinh1034 asinh -inf 0.0 -> -inf 0.0
+asinh1035 asinh -inf 2.3 -> -inf 0.0
+asinh1036 asinh -inf inf -> -inf 0.78539816339744828
+
+
---------------------------
-- atan: Inverse tangent --
---------------------------
-- zeros
atan0000 atan 0.0 0.0 -> 0.0 0.0
-atan0001 atan 0.0 -0.0 -> 0.0 0.0
+atan0001 atan 0.0 -0.0 -> 0.0 -0.0
atan0002 atan -0.0 0.0 -> -0.0 0.0
-atan0003 atan -0.0 -0.0 -> -0.0 0.0
+atan0003 atan -0.0 -0.0 -> -0.0 -0.0
-- values along both sides of imaginary axis
atan0010 atan 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
@@ -631,9 +769,9 @@
atan0206 atan 0.0 -9.5155296715763696e+307 -> 1.5707963267948966 -1.050913648020118e-308
atan0207 atan -0.0 -1.5565700490496501e+308 -> -1.5707963267948966 -6.4243816114189071e-309
atan0208 atan 1.2956339389525244e+308 0.0 -> 1.5707963267948966 0.0
-atan0209 atan 1.4408126243772151e+308 -0.0 -> 1.5707963267948966 0.0
+atan0209 atan 1.4408126243772151e+308 -0.0 -> 1.5707963267948966 -0.0
atan0210 atan -1.0631786461936417e+308 0.0 -> -1.5707963267948966 0.0
-atan0211 atan -1.0516056964171069e+308 -0.0 -> -1.5707963267948966 0.0
+atan0211 atan -1.0516056964171069e+308 -0.0 -> -1.5707963267948966 -0.0
atan0212 atan 1.236162319603838e+308 4.6827953496242936 -> 1.5707963267948966 0.0
atan0213 atan 7.000516472897218e+307 -5.8631608017844163 -> 1.5707963267948966 -0.0
atan0214 atan -1.5053444003338508e+308 5.1199197268420313 -> -1.5707963267948966 0.0
@@ -650,6 +788,7 @@
atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875
atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692
+
---------------------------------------
-- atanh: Inverse hyperbolic tangent --
---------------------------------------
@@ -657,8 +796,8 @@
-- zeros
atanh0000 atanh 0.0 0.0 -> 0.0 0.0
atanh0001 atanh 0.0 -0.0 -> 0.0 -0.0
-atanh0002 atanh -0.0 0.0 -> 0.0 0.0
-atanh0003 atanh -0.0 -0.0 -> 0.0 -0.0
+atanh0002 atanh -0.0 0.0 -> -0.0 0.0
+atanh0003 atanh -0.0 -0.0 -> -0.0 -0.0
-- values along both sides of real axis
atanh0010 atanh -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
@@ -746,9 +885,9 @@
atanh0202 atanh -1.3435325735762247e+308 9.8947369259601547e+307 -> -4.8256680906589956e-309 1.5707963267948966
atanh0203 atanh -1.4359857522598942e+308 -9.4701204702391004e+307 -> -4.8531282262872645e-309 -1.5707963267948966
atanh0204 atanh 0.0 5.6614181068098497e+307 -> 0.0 1.5707963267948966
-atanh0205 atanh -0.0 6.9813212721450139e+307 -> 0.0 1.5707963267948966
+atanh0205 atanh -0.0 6.9813212721450139e+307 -> -0.0 1.5707963267948966
atanh0206 atanh 0.0 -7.4970613060311453e+307 -> 0.0 -1.5707963267948966
-atanh0207 atanh -0.0 -1.5280601880314068e+308 -> 0.0 -1.5707963267948966
+atanh0207 atanh -0.0 -1.5280601880314068e+308 -> -0.0 -1.5707963267948966
atanh0208 atanh 8.2219472336000745e+307 0.0 -> 1.2162568933954813e-308 1.5707963267948966
atanh0209 atanh 1.4811519617280899e+308 -0.0 -> 6.7515017083951325e-309 -1.5707963267948966
atanh0210 atanh -1.2282016263598785e+308 0.0 -> -8.1419856360537615e-309 1.5707963267948966
@@ -768,9 +907,9 @@
atanh0222 atanh -5.9656816081325078e-317 9.9692253555416263e-313 -> -5.9656816081325078e-317 9.9692253555416263e-313
atanh0223 atanh -6.5606671178400239e-313 -2.1680936406357335e-309 -> -6.5606671178400239e-313 -2.1680936406357335e-309
atanh0224 atanh 0.0 2.5230944401820779e-319 -> 0.0 2.5230944401820779e-319
-atanh0225 atanh -0.0 5.6066569490064658e-320 -> 0.0 5.6066569490064658e-320
+atanh0225 atanh -0.0 5.6066569490064658e-320 -> -0.0 5.6066569490064658e-320
atanh0226 atanh 0.0 -2.4222487249468377e-317 -> 0.0 -2.4222487249468377e-317
-atanh0227 atanh -0.0 -3.0861101089206037e-316 -> 0.0 -3.0861101089206037e-316
+atanh0227 atanh -0.0 -3.0861101089206037e-316 -> -0.0 -3.0861101089206037e-316
atanh0228 atanh 3.1219222884393986e-310 0.0 -> 3.1219222884393986e-310 0.0
atanh0229 atanh 9.8926337564976196e-309 -0.0 -> 9.8926337564976196e-309 -0.0
atanh0230 atanh -1.5462535092918154e-312 0.0 -> -1.5462535092918154e-312 0.0
@@ -783,6 +922,50 @@
atanh0303 atanh 1.0 -1e-165 -> 190.30984376228875 -0.78539816339744828
atanh0304 atanh -1.0 -9.8813129168249309e-324 -> -372.22003596069061 -0.78539816339744828
+-- special values
+atanh1000 atanh 0.0 0.0 -> 0.0 0.0
+atanh1001 atanh 0.0 nan -> 0.0 nan
+atanh1002 atanh 1.0 0.0 -> inf 0.0 divide-by-zero
+atanh1003 atanh 0.0 inf -> 0.0 1.5707963267948966
+atanh1004 atanh 2.3 inf -> 0.0 1.5707963267948966
+atanh1005 atanh 2.3 nan -> nan nan
+atanh1006 atanh inf 0.0 -> 0.0 1.5707963267948966
+atanh1007 atanh inf 2.3 -> 0.0 1.5707963267948966
+atanh1008 atanh inf inf -> 0.0 1.5707963267948966
+atanh1009 atanh inf nan -> 0.0 nan
+atanh1010 atanh nan 0.0 -> nan nan
+atanh1011 atanh nan 2.3 -> nan nan
+atanh1012 atanh nan inf -> 0.0 1.5707963267948966
+atanh1013 atanh nan nan -> nan nan
+atanh1014 atanh 0.0 -0.0 -> 0.0 -0.0
+atanh1015 atanh 1.0 -0.0 -> inf -0.0 divide-by-zero
+atanh1016 atanh 0.0 -inf -> 0.0 -1.5707963267948966
+atanh1017 atanh 2.3 -inf -> 0.0 -1.5707963267948966
+atanh1018 atanh inf -0.0 -> 0.0 -1.5707963267948966
+atanh1019 atanh inf -2.3 -> 0.0 -1.5707963267948966
+atanh1020 atanh inf -inf -> 0.0 -1.5707963267948966
+atanh1021 atanh nan -0.0 -> nan nan
+atanh1022 atanh nan -2.3 -> nan nan
+atanh1023 atanh nan -inf -> 0.0 -1.5707963267948966
+atanh1024 atanh -0.0 -0.0 -> -0.0 -0.0
+atanh1025 atanh -0.0 nan -> -0.0 nan
+atanh1026 atanh -1.0 -0.0 -> -inf -0.0 divide-by-zero
+atanh1027 atanh -0.0 -inf -> -0.0 -1.5707963267948966
+atanh1028 atanh -2.3 -inf -> -0.0 -1.5707963267948966
+atanh1029 atanh -2.3 nan -> nan nan
+atanh1030 atanh -inf -0.0 -> -0.0 -1.5707963267948966
+atanh1031 atanh -inf -2.3 -> -0.0 -1.5707963267948966
+atanh1032 atanh -inf -inf -> -0.0 -1.5707963267948966
+atanh1033 atanh -inf nan -> -0.0 nan
+atanh1034 atanh -0.0 0.0 -> -0.0 0.0
+atanh1035 atanh -1.0 0.0 -> -inf 0.0 divide-by-zero
+atanh1036 atanh -0.0 inf -> -0.0 1.5707963267948966
+atanh1037 atanh -2.3 inf -> -0.0 1.5707963267948966
+atanh1038 atanh -inf 0.0 -> -0.0 1.5707963267948966
+atanh1039 atanh -inf 2.3 -> -0.0 1.5707963267948966
+atanh1040 atanh -inf inf -> -0.0 1.5707963267948966
+
+
----------------------------
-- log: Natural logarithm --
----------------------------
@@ -911,6 +1094,46 @@
log0200 log -0.59999999999999998 0.80000000000000004 -> 2.2204460492503132e-17 2.2142974355881808
log0201 log 0.79999999999999993 0.60000000000000009 -> 6.1629758220391547e-33 0.64350110879328448
+-- special values
+log1000 log -0.0 0.0 -> -inf 3.1415926535897931 divide-by-zero
+log1001 log 0.0 0.0 -> -inf 0.0 divide-by-zero
+log1002 log 0.0 inf -> inf 1.5707963267948966
+log1003 log 2.3 inf -> inf 1.5707963267948966
+log1004 log -0.0 inf -> inf 1.5707963267948966
+log1005 log -2.3 inf -> inf 1.5707963267948966
+log1006 log 0.0 nan -> nan nan
+log1007 log 2.3 nan -> nan nan
+log1008 log -0.0 nan -> nan nan
+log1009 log -2.3 nan -> nan nan
+log1010 log -inf 0.0 -> inf 3.1415926535897931
+log1011 log -inf 2.3 -> inf 3.1415926535897931
+log1012 log inf 0.0 -> inf 0.0
+log1013 log inf 2.3 -> inf 0.0
+log1014 log -inf inf -> inf 2.3561944901923448
+log1015 log inf inf -> inf 0.78539816339744828
+log1016 log inf nan -> inf nan
+log1017 log -inf nan -> inf nan
+log1018 log nan 0.0 -> nan nan
+log1019 log nan 2.3 -> nan nan
+log1020 log nan inf -> inf nan
+log1021 log nan nan -> nan nan
+log1022 log -0.0 -0.0 -> -inf -3.1415926535897931 divide-by-zero
+log1023 log 0.0 -0.0 -> -inf -0.0 divide-by-zero
+log1024 log 0.0 -inf -> inf -1.5707963267948966
+log1025 log 2.3 -inf -> inf -1.5707963267948966
+log1026 log -0.0 -inf -> inf -1.5707963267948966
+log1027 log -2.3 -inf -> inf -1.5707963267948966
+log1028 log -inf -0.0 -> inf -3.1415926535897931
+log1029 log -inf -2.3 -> inf -3.1415926535897931
+log1030 log inf -0.0 -> inf -0.0
+log1031 log inf -2.3 -> inf -0.0
+log1032 log -inf -inf -> inf -2.3561944901923448
+log1033 log inf -inf -> inf -0.78539816339744828
+log1034 log nan -0.0 -> nan nan
+log1035 log nan -2.3 -> nan nan
+log1036 log nan -inf -> inf nan
+
+
-----------------------
-- sqrt: Square root --
-----------------------
@@ -1019,14 +1242,55 @@
sqrt0140 sqrt 1.6999999999999999e+308 -1.6999999999999999e+308 -> 1.4325088230154573e+154 -5.9336458271212207e+153
sqrt0141 sqrt -1.797e+308 -9.9999999999999999e+306 -> 3.7284476432057307e+152 -1.3410406899802901e+154
--- For exp, cosh, sinh, tanh we limit tests to arguments whose
+-- special values
+sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0
+sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0
+sqrt1002 sqrt 0.0 inf -> inf inf
+sqrt1003 sqrt 2.3 inf -> inf inf
+sqrt1004 sqrt inf inf -> inf inf
+sqrt1005 sqrt -0.0 inf -> inf inf
+sqrt1006 sqrt -2.3 inf -> inf inf
+sqrt1007 sqrt -inf inf -> inf inf
+sqrt1008 sqrt nan inf -> inf inf
+sqrt1009 sqrt 0.0 nan -> nan nan
+sqrt1010 sqrt 2.3 nan -> nan nan
+sqrt1011 sqrt -0.0 nan -> nan nan
+sqrt1012 sqrt -2.3 nan -> nan nan
+sqrt1013 sqrt -inf 0.0 -> 0.0 inf
+sqrt1014 sqrt -inf 2.3 -> 0.0 inf
+sqrt1015 sqrt inf 0.0 -> inf 0.0
+sqrt1016 sqrt inf 2.3 -> inf 0.0
+sqrt1017 sqrt -inf nan -> nan inf
+sqrt1018 sqrt inf nan -> inf nan
+sqrt1019 sqrt nan 0.0 -> nan nan
+sqrt1020 sqrt nan 2.3 -> nan nan
+sqrt1021 sqrt nan nan -> nan nan
+sqrt1022 sqrt 0.0 -0.0 -> 0.0 -0.0
+sqrt1023 sqrt -0.0 -0.0 -> 0.0 -0.0
+sqrt1024 sqrt 0.0 -inf -> inf -inf
+sqrt1025 sqrt 2.3 -inf -> inf -inf
+sqrt1026 sqrt inf -inf -> inf -inf
+sqrt1027 sqrt -0.0 -inf -> inf -inf
+sqrt1028 sqrt -2.3 -inf -> inf -inf
+sqrt1029 sqrt -inf -inf -> inf -inf
+sqrt1030 sqrt nan -inf -> inf -inf
+sqrt1031 sqrt -inf -0.0 -> 0.0 -inf
+sqrt1032 sqrt -inf -2.3 -> 0.0 -inf
+sqrt1033 sqrt inf -0.0 -> inf -0.0
+sqrt1034 sqrt inf -2.3 -> inf -0.0
+sqrt1035 sqrt nan -0.0 -> nan nan
+sqrt1036 sqrt nan -2.3 -> nan nan
+
+
+-- For exp, cosh, sinh, tanh we limit tests to arguments whose
-- imaginary part is less than 10 in absolute value: most math
--- libraries have poor accuracy for (real) sine and cosine for
--- large arguments, and the accuracy of these complex functions
+-- libraries have poor accuracy for (real) sine and cosine for
+-- large arguments, and the accuracy of these complex functions
-- suffer correspondingly.
---
--- Similarly, for cos, sin and tan we limit tests to arguments
--- with relatively small real part.
+--
+-- Similarly, for cos, sin and tan we limit tests to arguments
+-- with relatively small real part.
+
-------------------------------
-- exp: Exponential function --
@@ -1064,9 +1328,77 @@
exp0030 exp 710.0 0.78500000000000003 -> 1.5803016909637158e+308 1.5790437551806911e+308
exp0031 exp 710.0 -0.78500000000000003 -> 1.5803016909637158e+308 -1.5790437551806911e+308
--- values for which exp(x) underflows
+-- values for which exp(x) is subnormal, or underflows to 0
exp0040 exp -735.0 0.78500000000000003 -> 4.3976783136329355e-320 4.3942198541120468e-320
exp0041 exp -735.0 -2.3559999999999999 -> -4.3952079854037293e-320 -4.396690182341253e-320
+exp0042 exp -745.0 0.0 -> 4.9406564584124654e-324 0.0
+exp0043 exp -745.0 0.7 -> 0.0 0.0
+exp0044 exp -745.0 2.1 -> -0.0 0.0
+exp0045 exp -745.0 3.7 -> -0.0 -0.0
+exp0046 exp -745.0 5.3 -> 0.0 -0.0
+
+-- values for which exp(z) overflows
+exp0050 exp 710.0 0.0 -> inf 0.0 overflow
+exp0051 exp 711.0 0.7 -> inf inf overflow
+exp0052 exp 710.0 1.5 -> 1.5802653829857376e+307 inf overflow
+exp0053 exp 710.0 1.6 -> -6.5231579995501372e+306 inf overflow
+exp0054 exp 710.0 2.8 -> -inf 7.4836177417448528e+307 overflow
+
+-- special values
+exp1000 exp 0.0 0.0 -> 1.0 0.0
+exp1001 exp -0.0 0.0 -> 1.0 0.0
+exp1002 exp 0.0 inf -> nan nan invalid
+exp1003 exp 2.3 inf -> nan nan invalid
+exp1004 exp -0.0 inf -> nan nan invalid
+exp1005 exp -2.3 inf -> nan nan invalid
+exp1006 exp 0.0 nan -> nan nan
+exp1007 exp 2.3 nan -> nan nan
+exp1008 exp -0.0 nan -> nan nan
+exp1009 exp -2.3 nan -> nan nan
+exp1010 exp -inf 0.0 -> 0.0 0.0
+exp1011 exp -inf 1.4 -> 0.0 0.0
+exp1012 exp -inf 2.8 -> -0.0 0.0
+exp1013 exp -inf 4.2 -> -0.0 -0.0
+exp1014 exp -inf 5.6 -> 0.0 -0.0
+exp1015 exp -inf 7.0 -> 0.0 0.0
+exp1016 exp inf 0.0 -> inf 0.0
+exp1017 exp inf 1.4 -> inf inf
+exp1018 exp inf 2.8 -> -inf inf
+exp1019 exp inf 4.2 -> -inf -inf
+exp1020 exp inf 5.6 -> inf -inf
+exp1021 exp inf 7.0 -> inf inf
+exp1022 exp -inf inf -> 0.0 0.0
+exp1023 exp inf inf -> inf nan invalid
+exp1024 exp -inf nan -> 0.0 0.0
+exp1025 exp inf nan -> inf nan
+exp1026 exp nan 0.0 -> nan 0.0
+exp1027 exp nan 2.3 -> nan nan
+exp1028 exp nan inf -> nan nan
+exp1029 exp nan nan -> nan nan
+exp1030 exp 0.0 -0.0 -> 1.0 -0.0
+exp1031 exp -0.0 -0.0 -> 1.0 -0.0
+exp1032 exp 0.0 -inf -> nan nan invalid
+exp1033 exp 2.3 -inf -> nan nan invalid
+exp1034 exp -0.0 -inf -> nan nan invalid
+exp1035 exp -2.3 -inf -> nan nan invalid
+exp1036 exp -inf -0.0 -> 0.0 -0.0
+exp1037 exp -inf -1.4 -> 0.0 -0.0
+exp1038 exp -inf -2.8 -> -0.0 -0.0
+exp1039 exp -inf -4.2 -> -0.0 0.0
+exp1040 exp -inf -5.6 -> 0.0 0.0
+exp1041 exp -inf -7.0 -> 0.0 -0.0
+exp1042 exp inf -0.0 -> inf -0.0
+exp1043 exp inf -1.4 -> inf -inf
+exp1044 exp inf -2.8 -> -inf -inf
+exp1045 exp inf -4.2 -> -inf inf
+exp1046 exp inf -5.6 -> inf inf
+exp1047 exp inf -7.0 -> inf -inf
+exp1048 exp -inf -inf -> 0.0 0.0
+exp1049 exp inf -inf -> inf nan invalid
+exp1050 exp nan -0.0 -> nan -0.0
+exp1051 exp nan -2.3 -> nan nan
+exp1052 exp nan -inf -> nan nan
+
-----------------------------
-- cosh: Hyperbolic Cosine --
@@ -1104,6 +1436,62 @@
cosh0030 cosh 710.5 2.3519999999999999 -> -1.2967465239355998e+308 1.3076707908857333e+308
cosh0031 cosh -710.5 0.69999999999999996 -> 1.4085466381392499e+308 -1.1864024666450239e+308
+-- special values
+cosh1000 cosh 0.0 0.0 -> 1.0 0.0
+cosh1001 cosh 0.0 inf -> nan 0.0 invalid
+cosh1002 cosh 0.0 nan -> nan 0.0
+cosh1003 cosh 2.3 inf -> nan nan invalid
+cosh1004 cosh 2.3 nan -> nan nan
+cosh1005 cosh inf 0.0 -> inf 0.0
+cosh1006 cosh inf 1.4 -> inf inf
+cosh1007 cosh inf 2.8 -> -inf inf
+cosh1008 cosh inf 4.2 -> -inf -inf
+cosh1009 cosh inf 5.6 -> inf -inf
+cosh1010 cosh inf 7.0 -> inf inf
+cosh1011 cosh inf inf -> inf nan invalid
+cosh1012 cosh inf nan -> inf nan
+cosh1013 cosh nan 0.0 -> nan 0.0
+cosh1014 cosh nan 2.3 -> nan nan
+cosh1015 cosh nan inf -> nan nan
+cosh1016 cosh nan nan -> nan nan
+cosh1017 cosh 0.0 -0.0 -> 1.0 -0.0
+cosh1018 cosh 0.0 -inf -> nan 0.0 invalid
+cosh1019 cosh 2.3 -inf -> nan nan invalid
+cosh1020 cosh inf -0.0 -> inf -0.0
+cosh1021 cosh inf -1.4 -> inf -inf
+cosh1022 cosh inf -2.8 -> -inf -inf
+cosh1023 cosh inf -4.2 -> -inf inf
+cosh1024 cosh inf -5.6 -> inf inf
+cosh1025 cosh inf -7.0 -> inf -inf
+cosh1026 cosh inf -inf -> inf nan invalid
+cosh1027 cosh nan -0.0 -> nan 0.0
+cosh1028 cosh nan -2.3 -> nan nan
+cosh1029 cosh nan -inf -> nan nan
+cosh1030 cosh -0.0 -0.0 -> 1.0 0.0
+cosh1031 cosh -0.0 -inf -> nan 0.0 invalid
+cosh1032 cosh -0.0 nan -> nan 0.0
+cosh1033 cosh -2.3 -inf -> nan nan invalid
+cosh1034 cosh -2.3 nan -> nan nan
+cosh1035 cosh -inf -0.0 -> inf 0.0
+cosh1036 cosh -inf -1.4 -> inf inf
+cosh1037 cosh -inf -2.8 -> -inf inf
+cosh1038 cosh -inf -4.2 -> -inf -inf
+cosh1039 cosh -inf -5.6 -> inf -inf
+cosh1040 cosh -inf -7.0 -> inf inf
+cosh1041 cosh -inf -inf -> inf nan invalid
+cosh1042 cosh -inf nan -> inf nan
+cosh1043 cosh -0.0 0.0 -> 1.0 -0.0
+cosh1044 cosh -0.0 inf -> nan 0.0 invalid
+cosh1045 cosh -2.3 inf -> nan nan invalid
+cosh1046 cosh -inf 0.0 -> inf -0.0
+cosh1047 cosh -inf 1.4 -> inf -inf
+cosh1048 cosh -inf 2.8 -> -inf -inf
+cosh1049 cosh -inf 4.2 -> -inf inf
+cosh1050 cosh -inf 5.6 -> inf inf
+cosh1051 cosh -inf 7.0 -> inf -inf
+cosh1052 cosh -inf inf -> inf nan invalid
+
+
---------------------------
-- sinh: Hyperbolic Sine --
---------------------------
@@ -1140,6 +1528,62 @@
sinh0030 sinh 710.5 -2.3999999999999999 -> -1.3579970564885919e+308 -1.24394470907798e+308
sinh0031 sinh -710.5 0.80000000000000004 -> -1.2830671601735164e+308 1.3210954193997678e+308
+-- special values
+sinh1000 sinh 0.0 0.0 -> 0.0 0.0
+sinh1000 sinh 0.0 inf -> 0.0 nan invalid
+sinh1000 sinh 0.0 nan -> 0.0 nan
+sinh1000 sinh 2.3 inf -> nan nan invalid
+sinh1000 sinh 2.3 nan -> nan nan
+sinh1000 sinh inf 0.0 -> inf 0.0
+sinh1000 sinh inf 1.4 -> inf inf
+sinh1000 sinh inf 2.8 -> -inf inf
+sinh1000 sinh inf 4.2 -> -inf -inf
+sinh1000 sinh inf 5.6 -> inf -inf
+sinh1000 sinh inf 7.0 -> inf inf
+sinh1000 sinh inf inf -> inf nan invalid
+sinh1000 sinh inf nan -> inf nan
+sinh1000 sinh nan 0.0 -> nan 0.0
+sinh1000 sinh nan 2.3 -> nan nan
+sinh1000 sinh nan inf -> nan nan
+sinh1000 sinh nan nan -> nan nan
+sinh1000 sinh 0.0 -0.0 -> 0.0 -0.0
+sinh1000 sinh 0.0 -inf -> 0.0 nan invalid
+sinh1000 sinh 2.3 -inf -> nan nan invalid
+sinh1000 sinh inf -0.0 -> inf -0.0
+sinh1000 sinh inf -1.4 -> inf -inf
+sinh1000 sinh inf -2.8 -> -inf -inf
+sinh1000 sinh inf -4.2 -> -inf inf
+sinh1000 sinh inf -5.6 -> inf inf
+sinh1000 sinh inf -7.0 -> inf -inf
+sinh1000 sinh inf -inf -> inf nan invalid
+sinh1000 sinh nan -0.0 -> nan -0.0
+sinh1000 sinh nan -2.3 -> nan nan
+sinh1000 sinh nan -inf -> nan nan
+sinh1000 sinh -0.0 -0.0 -> -0.0 -0.0
+sinh1000 sinh -0.0 -inf -> 0.0 nan invalid
+sinh1000 sinh -0.0 nan -> 0.0 nan
+sinh1000 sinh -2.3 -inf -> nan nan invalid
+sinh1000 sinh -2.3 nan -> nan nan
+sinh1000 sinh -inf -0.0 -> -inf -0.0
+sinh1000 sinh -inf -1.4 -> -inf -inf
+sinh1000 sinh -inf -2.8 -> inf -inf
+sinh1000 sinh -inf -4.2 -> inf inf
+sinh1000 sinh -inf -5.6 -> -inf inf
+sinh1000 sinh -inf -7.0 -> -inf -inf
+sinh1000 sinh -inf -inf -> inf nan invalid
+sinh1000 sinh -inf nan -> inf nan
+sinh1000 sinh -0.0 0.0 -> -0.0 0.0
+sinh1000 sinh -0.0 inf -> 0.0 nan invalid
+sinh1000 sinh -2.3 inf -> nan nan invalid
+sinh1000 sinh -inf 0.0 -> -inf 0.0
+sinh1000 sinh -inf 1.4 -> -inf inf
+sinh1000 sinh -inf 2.8 -> inf inf
+sinh1000 sinh -inf 4.2 -> inf -inf
+sinh1000 sinh -inf 5.6 -> -inf -inf
+sinh1000 sinh -inf 7.0 -> -inf inf
+sinh1000 sinh -inf inf -> inf nan invalid
+
+
------------------------------
-- tanh: Hyperbolic Tangent --
------------------------------
@@ -1178,6 +1622,62 @@
tanh0032 tanh 1000 -2.3199999999999998 -> 1.0 0.0
tanh0033 tanh -1.0000000000000001e+300 -9.6699999999999999 -> -1.0 -0.0
+--special values
+tanh1000 tanh 0.0 0.0 -> 0.0 0.0
+tanh1001 tanh 0.0 inf -> nan nan invalid
+tanh1002 tanh 2.3 inf -> nan nan invalid
+tanh1003 tanh 0.0 nan -> nan nan
+tanh1004 tanh 2.3 nan -> nan nan
+tanh1005 tanh inf 0.0 -> 1.0 0.0
+tanh1006 tanh inf 0.7 -> 1.0 0.0
+tanh1007 tanh inf 1.4 -> 1.0 0.0
+tanh1008 tanh inf 2.1 -> 1.0 -0.0
+tanh1009 tanh inf 2.8 -> 1.0 -0.0
+tanh1010 tanh inf 3.5 -> 1.0 0.0
+tanh1011 tanh inf inf -> 1.0 0.0
+tanh1012 tanh inf nan -> 1.0 0.0
+tanh1013 tanh nan 0.0 -> nan 0.0
+tanh1014 tanh nan 2.3 -> nan nan
+tanh1015 tanh nan inf -> nan nan
+tanh1016 tanh nan nan -> nan nan
+tanh1017 tanh 0.0 -0.0 -> 0.0 -0.0
+tanh1018 tanh 0.0 -inf -> nan nan invalid
+tanh1019 tanh 2.3 -inf -> nan nan invalid
+tanh1020 tanh inf -0.0 -> 1.0 -0.0
+tanh1021 tanh inf -0.7 -> 1.0 -0.0
+tanh1022 tanh inf -1.4 -> 1.0 -0.0
+tanh1023 tanh inf -2.1 -> 1.0 0.0
+tanh1024 tanh inf -2.8 -> 1.0 0.0
+tanh1025 tanh inf -3.5 -> 1.0 -0.0
+tanh1026 tanh inf -inf -> 1.0 0.0
+tanh1027 tanh nan -0.0 -> nan -0.0
+tanh1028 tanh nan -2.3 -> nan nan
+tanh1029 tanh nan -inf -> nan nan
+tanh1030 tanh -0.0 -0.0 -> -0.0 -0.0
+tanh1031 tanh -0.0 -inf -> nan nan invalid
+tanh1032 tanh -2.3 -inf -> nan nan invalid
+tanh1033 tanh -0.0 nan -> nan nan
+tanh1034 tanh -2.3 nan -> nan nan
+tanh1035 tanh -inf -0.0 -> -1.0 -0.0
+tanh1036 tanh -inf -0.7 -> -1.0 -0.0
+tanh1037 tanh -inf -1.4 -> -1.0 -0.0
+tanh1038 tanh -inf -2.1 -> -1.0 0.0
+tanh1039 tanh -inf -2.8 -> -1.0 0.0
+tanh1040 tanh -inf -3.5 -> -1.0 -0.0
+tanh1041 tanh -inf -inf -> -1.0 0.0
+tanh1042 tanh -inf nan -> -1.0 0.0
+tanh1043 tanh -0.0 0.0 -> -0.0 0.0
+tanh1044 tanh -0.0 inf -> nan nan invalid
+tanh1045 tanh -2.3 inf -> nan nan invalid
+tanh1046 tanh -inf 0.0 -> -1.0 0.0
+tanh1047 tanh -inf 0.7 -> -1.0 0.0
+tanh1048 tanh -inf 1.4 -> -1.0 0.0
+tanh1049 tanh -inf 2.1 -> -1.0 -0.0
+tanh1050 tanh -inf 2.8 -> -1.0 -0.0
+tanh1051 tanh -inf 3.5 -> -1.0 0.0
+tanh1052 tanh -inf inf -> -1.0 0.0
+
+
-----------------
-- cos: Cosine --
-----------------
@@ -1210,6 +1710,7 @@
cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582
cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477
+
---------------
-- sin: Sine --
---------------
@@ -1242,6 +1743,7 @@
sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852
sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62
+
------------------
-- tan: Tangent --
------------------
Modified: python/branches/trunk-math/Lib/test/test_cmath.py
==============================================================================
--- python/branches/trunk-math/Lib/test/test_cmath.py (original)
+++ python/branches/trunk-math/Lib/test/test_cmath.py Sat Feb 9 22:27:13 2008
@@ -27,6 +27,23 @@
def rAssertAlmostEqual(self, a, b, rel_eps = 2e-15, abs_eps = 5e-323):
"""Check that two floating-point numbers are almost equal."""
+ # special values testing
+ if math.isnan(a):
+ if math.isnan(b):
+ return
+ self.fail("%s should be nan" % repr(b))
+
+ if math.isinf(a):
+ if a == b:
+ return
+ self.fail("finite result where infinity excpected: "
+ "expected %s, got %s" % (repr(a), repr(b)))
+
+ if not a and not b:
+ if math.atan2(a, -1.) != math.atan2(b, -1.):
+ self.fail("zero has wrong sign: expected %s, got %s" %
+ (repr(a), repr(b)))
+
# test passes if either the absolute error or the relative
# error is sufficiently small. The defaults amount to an
# error of between 9 ulps and 19 ulps on an IEEE-754 compliant
@@ -213,12 +230,19 @@
def test_specific_values(self):
if not float.__getformat__("double").startswith("IEEE"):
return
- for id, fn, ar, ai, er, ei in parse_testfile(test_file):
+ for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
arg = complex(ar, ai)
expected = complex(er, ei)
function = getattr(cmath, fn)
- actual = function(arg)
+ if 'divide-by-zero' in flags or 'invalid' in flags:
+ self.assertRaises(ValueError, function, arg)
+ continue
+
+ if 'overflow' in flags:
+ self.assertRaises(OverflowError, function, arg)
+ continue
+ actual = function(arg)
if fn=='log':
# for the real part of the log function, we allow an
# absolute error of up to 2e-15.
Modified: python/branches/trunk-math/Lib/test/test_math.py
==============================================================================
--- python/branches/trunk-math/Lib/test/test_math.py (original)
+++ python/branches/trunk-math/Lib/test/test_math.py Sat Feb 9 22:27:13 2008
@@ -34,11 +34,14 @@
lhs, rhs = line.split('->')
id, fn, arg_real, arg_imag = lhs.split()
- exp_real, exp_imag = rhs.split()
+ rhs_pieces = rhs.split()
+ exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
+ flags = rhs_pieces[2:]
yield (id, fn,
float(arg_real), float(arg_imag),
- float(exp_real), float(exp_imag)
+ float(exp_real), float(exp_imag),
+ flags
)
class MathTests(unittest.TestCase):
@@ -515,9 +518,10 @@
def test_testfile(self):
if not float.__getformat__("double").startswith("IEEE"):
return
- for id, fn, ar, ai, er, ei in parse_testfile(test_file):
- # Skip if either input or result is complex
- if ai != 0. or ei != 0.:
+ for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+ # Skip if either the input or result is complex, or if
+ # flags is nonempty
+ if ai != 0. or ei != 0. or flags:
continue
func = getattr(math, fn)
result = func(ar)
Modified: python/branches/trunk-math/Modules/cmathmodule.c
==============================================================================
--- python/branches/trunk-math/Modules/cmathmodule.c (original)
+++ python/branches/trunk-math/Modules/cmathmodule.c Sat Feb 9 22:27:13 2008
@@ -58,7 +58,7 @@
ST_NAN, /* 6, Not a Number */
};
-static enum special_types
+static enum special_types
special_type(double d)
{
if (Py_IS_FINITE(d)) {
@@ -85,28 +85,25 @@
#define SPECIAL_VALUE(z, table) \
if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) { \
- double *special_value = table[special_type((z).real)] \
- [special_type((z).imag)]; \
- r.real = special_value[0]; \
- r.imag = special_value[1]; \
- return r; \
+ errno = 0; \
+ return table[special_type((z).real)] \
+ [special_type((z).imag)]; \
}
#define P Py_MATH_PI
#define I Py_HUGE_VAL
#define N Py_NAN
-#define U -1.345e26 /* unlikely value, used as placeholder */
/* First, the C functions that do the real work */
-static double acos_special_values[7][7][2] = {
- {{.75*P, I}, {P, I}, {P, I}, {P, -I}, {P, -I}, {.75*P, -I}, {N, I}},
- {{.5*P, I}, {U, U}, {U, U}, {U, U}, {U, U}, {.5*P, -I}, {N, N}},
- {{.5*P, I}, {U, U}, {U, U}, {U, U}, {U, U}, {.5*P, -I}, {.25*P, N}},
- {{.5*P, I}, {U, U}, {U, U}, {U, U}, {U, U}, {.5*P, -I}, {.25*P, N}},
- {{.5*P, I}, {U, U}, {U, U}, {U, U}, {U, U}, {.5*P, -I}, {N, N}},
- {{.25*P, I}, {0, I}, {0, I}, {0, -I}, {0, -I}, {.25*P, -I}, {N, I}},
- {{N, I}, {N, N}, {N, N}, {N, N}, {N, N}, {N, N}, {N, N}}
+static Py_complex acos_special_values[7][7] = {
+ {{.75*P,I},{P,I}, {P,I}, {P,-I}, {P, -I}, {.75*P,-I},{N,I}},
+ {{.5*P,I}, {}, {}, {}, {}, {.5*P,-I}, {N,N}},
+ {{.5*P,I}, {}, {.5*P,0.},{.5*P,-0.},{}, {.5*P,-I}, {.5*P,N}},
+ {{.5*P,I}, {}, {.5*P,0.},{.5*P,-0.},{}, {.5*P,-I}, {.5*P,N}},
+ {{.5*P,I}, {}, {}, {}, {}, {.5*P,-I}, {N,N}},
+ {{.25*P,I},{0.,I},{0.,I}, {0.,-I}, {0.,-I}, {.25*P,-I},{N,I}},
+ {{N,I}, {N,N}, {N,N}, {N,N}, {N,N}, {N,-I}, {N,N}}
};
static Py_complex
@@ -122,9 +119,11 @@
/* split into cases to make sure that the branch cut has the
correct continuity on systems with unsigned zeros */
if (z.real < 0.) {
- r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) + M_LN2*2., z.imag);
+ r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
+ M_LN2*2., z.imag);
} else {
- r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) + M_LN2*2., -z.imag);
+ r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
+ M_LN2*2., -z.imag);
}
} else {
s1.real = 1.-z.real;
@@ -136,6 +135,7 @@
r.real = 2.*atan2(s1.real, s2.real);
r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
}
+ errno = 0;
return r;
}
@@ -145,11 +145,23 @@
"Return the arc cosine of x.");
+static Py_complex acosh_special_values[7][7] = {
+ {{I,-.75*P},{I,-P}, {I,-P}, {I,P}, {I,P}, {I,.75*P},{I,N}},
+ {{I,-.5*P}, {}, {}, {}, {}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {0.,-.5*P},{0.,.5*P},{}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {0.,-.5*P},{0.,.5*P},{}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {}, {}, {}, {I,.5*P}, {N,N}},
+ {{I,-.25*P},{I,-0.},{I,-0.}, {I,0.}, {I,0.},{I,.25*P},{I,N}},
+ {{I,N}, {N,N}, {N,N}, {N,N}, {N,N}, {I,N}, {N,N}}
+};
+
static Py_complex
c_acosh(Py_complex z)
{
Py_complex s1, s2, r;
+ SPECIAL_VALUE(z, acosh_special_values);
+
if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
/* avoid unnecessary overflow for large arguments */
r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
@@ -164,6 +176,7 @@
r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
r.imag = 2.*atan2(s1.imag, s2.real);
}
+ errno = 0;
return r;
}
@@ -192,16 +205,30 @@
"Return the arc sine of x.");
+static Py_complex asinh_special_values[7][7] = {
+ {{-I,-.25*P},{-I,-0.},{-I,-0.}, {-I,0.}, {-I,0.},{-I,.25*P},{-I,N}},
+ {{-I,-.5*P}, {}, {}, {}, {}, {-I,.5*P}, {N,N}},
+ {{-I,-.5*P}, {}, {-0.,-0.},{-0.,0.},{}, {-I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {0.,-0.}, {0.,0.}, {}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {}, {}, {}, {I,.5*P}, {N,N}},
+ {{I,-.25*P}, {I,-0.}, {I,-0.}, {I,0.}, {I,0.}, {I,.25*P}, {I,N}},
+ {{I,N}, {N,N}, {N,-0.}, {N,0.}, {N,N}, {I,N}, {N,N}}
+};
+
static Py_complex
c_asinh(Py_complex z)
{
Py_complex s1, s2, r;
+ SPECIAL_VALUE(z, asinh_special_values);
+
if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
if (z.imag >= 0.) {
- r.real = copysign(log(hypot(z.real/2., z.imag/2.)) + M_LN2*2., z.real);
+ r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
+ M_LN2*2., z.real);
} else {
- r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) + M_LN2*2., -z.real);
+ r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
+ M_LN2*2., -z.real);
}
r.imag = atan2(z.imag, fabs(z.real));
} else {
@@ -214,6 +241,7 @@
r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
}
+ errno = 0;
return r;
}
@@ -242,12 +270,24 @@
"Return the arc tangent of x.");
+static Py_complex atanh_special_values[7][7] = {
+ {{-0.,-.5*P},{-0.,-.5*P},{-0.,-.5*P},{-0.,.5*P},{-0.,.5*P},{-0.,.5*P},{-0.,N}},
+ {{-0.,-.5*P},{}, {}, {}, {}, {-0.,.5*P},{N,N}},
+ {{-0.,-.5*P},{}, {-0.,-0.}, {-0.,0.}, {}, {-0.,.5*P},{-0.,N}},
+ {{0.,-.5*P}, {}, {0.,-0.}, {0.,0.}, {}, {0.,.5*P}, {0.,N}},
+ {{0.,-.5*P}, {}, {}, {}, {}, {0.,.5*P}, {N,N}},
+ {{0.,-.5*P}, {0.,-.5*P}, {0.,-.5*P}, {0.,.5*P}, {0.,.5*P}, {0.,.5*P}, {0.,N}},
+ {{0.,-.5*P}, {N,N}, {N,N}, {N,N}, {N,N}, {0.,.5*P}, {N,N}}
+};
+
static Py_complex
c_atanh(Py_complex z)
{
Py_complex r;
double ay, h;
+ SPECIAL_VALUE(z, atanh_special_values);
+
/* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
if (z.real < 0.) {
return c_neg(c_atanh(c_neg(z)));
@@ -255,7 +295,7 @@
ay = fabs(z.imag);
if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
- /*
+ /*
if abs(z) is large then we use the approximation
atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
of z.imag)
@@ -267,17 +307,22 @@
ensure that the branch cut has the correct continuity on
systems that don't support signed zeros */
r.imag = -copysign(Py_MATH_PI/2., -z.imag);
+ errno = 0;
} else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
/* C99 standard says: atanh(1+/-0.) should be inf +/- 0i */
- r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
if (ay == 0.) {
+ r.real = I;
r.imag = z.imag;
+ errno = EDOM;
} else {
+ r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
r.imag = copysign(atan2(2., -ay)/2, z.imag);
+ errno = 0;
}
} else {
r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
+ errno = 0;
}
return r;
}
@@ -305,12 +350,49 @@
"Return the cosine of x.");
+/* cosh(infinity + i*y) needs to be dealt with specially */
+static Py_complex cosh_special_values[7][7] = {
+ {{I,N}, {}, {I,0.}, {I,-0.}, {}, {I,N}, {I,N}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{N,0.},{}, {1.,0.}, {1.,-0.},{}, {N,0.},{N,0.}},
+ {{N,0.},{}, {1.,-0.},{1.,0.}, {}, {N,0.},{N,0.}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{I,N}, {}, {I,-0.}, {I,0.}, {}, {I,N}, {I,N}},
+ {{N,N}, {N,N},{N,0.}, {N,0.}, {N,N},{N,N}, {N,N}}
+};
+
static Py_complex
c_cosh(Py_complex z)
{
Py_complex r;
double x_minus_one;
+ /* special treatment for cosh(+/-inf + iy) if y is not a NaN */
+ if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+ if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
+ (z.imag != 0.)) {
+ if (z.real > 0) {
+ r.real = copysign(I, cos(z.imag));
+ r.imag = copysign(I, sin(z.imag));
+ }
+ else {
+ r.real = copysign(I, cos(z.imag));
+ r.imag = -copysign(I, sin(z.imag));
+ }
+ }
+ else {
+ r = cosh_special_values[special_type(z.real)]
+ [special_type(z.imag)];
+ }
+ /* need to set errno = EDOM if y is +/- infinity and x is not
+ a NaN */
+ if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
+ errno = EDOM;
+ else
+ errno = 0;
+ return r;
+ }
+
if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
/* deal correctly with cases where cosh(z.real) overflows but
cosh(z) does not. */
@@ -321,6 +403,11 @@
r.real = cos(z.imag) * cosh(z.real);
r.imag = sin(z.imag) * sinh(z.real);
}
+ /* detect overflow, and set errno accordingly */
+ if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+ errno = ERANGE;
+ else
+ errno = 0;
return r;
}
@@ -330,12 +417,51 @@
"Return the hyperbolic cosine of x.");
+/* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
+ finite y */
+static Py_complex exp_special_values[7][7] = {
+ {{0.,0.},{}, {0.,-0.},{0.,0.},{}, {0.,0.},{0.,0.}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{N,N}, {}, {1.,-0.},{1.,0.},{}, {N,N}, {N,N}},
+ {{N,N}, {}, {1.,-0.},{1.,0.},{}, {N,N}, {N,N}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{I,N}, {}, {I,-0.}, {I,0.}, {}, {I,N}, {I,N}},
+ {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
+};
+
static Py_complex
c_exp(Py_complex z)
{
Py_complex r;
double l;
+ if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+ if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+ && (z.imag != 0.)) {
+ if (z.real > 0) {
+ r.real = copysign(I, cos(z.imag));
+ r.imag = copysign(I, sin(z.imag));
+ }
+ else {
+ r.real = copysign(0., cos(z.imag));
+ r.imag = copysign(0., sin(z.imag));
+ }
+ }
+ else {
+ r = exp_special_values[special_type(z.real)]
+ [special_type(z.imag)];
+ }
+ /* need to set errno = EDOM if y is +/- infinity and x is not
+ a NaN and not -infinity */
+ if (Py_IS_INFINITY(z.imag) &&
+ (Py_IS_FINITE(z.real) ||
+ (Py_IS_INFINITY(z.real) && z.real > 0)))
+ errno = EDOM;
+ else
+ errno = 0;
+ return r;
+ }
+
if (z.real > CM_LOG_LARGE_DOUBLE) {
l = exp(z.real-1.);
r.real = l*cos(z.imag)*Py_MATH_E;
@@ -345,6 +471,11 @@
r.real = l*cos(z.imag);
r.imag = l*sin(z.imag);
}
+ /* detect overflow, and set errno accordingly */
+ if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+ errno = ERANGE;
+ else
+ errno = 0;
return r;
}
@@ -354,6 +485,16 @@
"Return the exponential value e**x.");
+static Py_complex log_special_values[7][7] = {
+ {{I,-.75*P},{I,-P}, {I,-P}, {I,P}, {I,P}, {I,.75*P},{I,N}},
+ {{I,-.5*P}, {}, {}, {}, {}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {-I,-P}, {-I,P}, {}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {-I,-0.},{-I,0.},{}, {I,.5*P}, {N,N}},
+ {{I,-.5*P}, {}, {}, {}, {}, {I,.5*P}, {N,N}},
+ {{I,-.25*P},{I,-0.},{I,-0.}, {I,0.}, {I,0.},{I,.25*P},{I,N}},
+ {{I,N}, {N,N}, {N,N}, {N,N}, {N,N}, {I,N}, {N,N}}
+};
+
static Py_complex
c_log(Py_complex z)
{
@@ -388,14 +529,26 @@
Py_complex r;
double ax, ay, am, an, h;
+ SPECIAL_VALUE(z, log_special_values);
+
ax = fabs(z.real);
ay = fabs(z.imag);
if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) {
r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
- } else if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
- /* catch cases where hypot(ax, ay) is subnormal */
- r.real = log(hypot(ldexp(ax, DBL_MANT_DIG), ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
+ } else if (ax < DBL_MIN && ay < DBL_MIN) {
+ if (ax > 0. || ay > 0.) {
+ /* catch cases where hypot(ax, ay) is subnormal */
+ r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
+ ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
+ }
+ else {
+ /* log(+/-0. +/- 0i) */
+ r.real = -I;
+ r.imag = atan2(z.imag, z.real);
+ errno = EDOM;
+ return r;
+ }
} else {
h = hypot(ax, ay);
if (0.71 <= h && h <= 1.73) {
@@ -407,6 +560,7 @@
}
}
r.imag = atan2(z.imag, z.real);
+ errno = 0;
return r;
}
@@ -415,10 +569,13 @@
c_log10(Py_complex z)
{
Py_complex r;
+ int errno_save;
r = c_log(z);
+ errno_save = errno; /* just in case the divisions affect errno */
r.real = r.real / M_LN10;
r.imag = r.imag / M_LN10;
+ errno = errno_save;
return r;
}
@@ -447,12 +604,50 @@
"Return the sine of x.");
+/* sinh(infinity + i*y) needs to be dealt with specially */
+static Py_complex sinh_special_values[7][7] = {
+ {{I,N}, {}, {-I,-0.}, {-I,0.}, {}, {I,N}, {I,N}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{0.,N},{}, {-0.,-0.},{-0.,0.},{}, {0.,N},{0.,N}},
+ {{0.,N},{}, {0.,-0.}, {0.,0.}, {}, {0.,N},{0.,N}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{I,N}, {}, {I,-0.}, {I,0.}, {}, {I,N}, {I,N}},
+ {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
+};
+
static Py_complex
c_sinh(Py_complex z)
{
Py_complex r;
double x_minus_one;
+ /* special treatment for sinh(+/-inf + iy) if y is finite and
+ nonzero */
+ if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+ if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+ && (z.imag != 0.)) {
+ if (z.real > 0) {
+ r.real = copysign(I, cos(z.imag));
+ r.imag = copysign(I, sin(z.imag));
+ }
+ else {
+ r.real = -copysign(I, cos(z.imag));
+ r.imag = copysign(I, sin(z.imag));
+ }
+ }
+ else {
+ r = sinh_special_values[special_type(z.real)]
+ [special_type(z.imag)];
+ }
+ /* need to set errno = EDOM if y is +/- infinity and x is not
+ a NaN */
+ if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
+ errno = EDOM;
+ else
+ errno = 0;
+ return r;
+ }
+
if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
x_minus_one = z.real - copysign(1., z.real);
r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
@@ -461,6 +656,11 @@
r.real = cos(z.imag) * sinh(z.real);
r.imag = sin(z.imag) * cosh(z.real);
}
+ /* detect overflow, and set errno accordingly */
+ if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+ errno = ERANGE;
+ else
+ errno = 0;
return r;
}
@@ -471,6 +671,16 @@
"Return the hyperbolic sine of x.");
+static Py_complex sqrt_special_values[7][7] = {
+ {{I,-I},{0.,-I},{0.,-I}, {0.,I}, {0.,I},{I,I},{N,I}},
+ {{I,-I},{}, {}, {}, {}, {I,I},{N,N}},
+ {{I,-I},{}, {0.,-0.},{0.,0.},{}, {I,I},{N,N}},
+ {{I,-I},{}, {0.,-0.},{0.,0.},{}, {I,I},{N,N}},
+ {{I,-I},{}, {}, {}, {}, {I,I},{N,N}},
+ {{I,-I},{I,-0.},{I,-0.}, {I,0.}, {I,0.},{I,I},{I,N}},
+ {{I,-I},{N,N}, {N,N}, {N,N}, {N,N}, {I,I},{N,N}}
+};
+
static Py_complex
c_sqrt(Py_complex z)
{
@@ -505,6 +715,8 @@
double s,d;
double ax, ay;
+ SPECIAL_VALUE(z, sqrt_special_values);
+
if (z.real == 0. && z.imag == 0.) {
r.real = 0.;
r.imag = z.imag;
@@ -517,7 +729,8 @@
if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
/* here we catch cases where hypot(ax, ay) is subnormal */
ax = ldexp(ax, CM_SCALE_UP);
- s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))), CM_SCALE_DOWN);
+ s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
+ CM_SCALE_DOWN);
} else {
ax /= 8.;
s = 2.*sqrt(ax + hypot(ax, ay/8.));
@@ -531,6 +744,7 @@
r.real = d;
r.imag = copysign(s, z.imag);
}
+ errno = 0;
return r;
}
@@ -559,6 +773,17 @@
"Return the tangent of x.");
+/* tanh(infinity + i*y) needs to be dealt with specially */
+static Py_complex tanh_special_values[7][7] = {
+ {{-1.,0.},{}, {-1.,-0.},{-1.,0.},{}, {-1.,0.},{-1.,0.}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{N,N}, {}, {-0.,-0.},{-0.,0.},{}, {N,N}, {N,N}},
+ {{N,N}, {}, {0.,-0.}, {0.,0.}, {}, {N,N}, {N,N}},
+ {{N,N}, {}, {}, {}, {}, {N,N}, {N,N}},
+ {{1.,0.}, {}, {1.,-0.}, {1.,0.}, {}, {1.,0.}, {1.,0.}},
+ {{N,N}, {N,N},{N,-0.}, {N,0.}, {N,N},{N,N}, {N,N}}
+};
+
static Py_complex
c_tanh(Py_complex z)
{
@@ -577,9 +802,39 @@
Py_complex r;
double tx, ty, cx, txty, denom;
+ /* special treatment for tanh(+/-inf + iy) if y is finite and
+ nonzero */
+ if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+ if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+ && (z.imag != 0.)) {
+ if (z.real > 0) {
+ r.real = 1.0;
+ r.imag = copysign(0.,
+ 2.*sin(z.imag)*cos(z.imag));
+ }
+ else {
+ r.real = -1.0;
+ r.imag = copysign(0.,
+ 2.*sin(z.imag)*cos(z.imag));
+ }
+ }
+ else {
+ r = tanh_special_values[special_type(z.real)]
+ [special_type(z.imag)];
+ }
+ /* need to set errno = EDOM if z.imag is +/-infinity and
+ z.real is finite */
+ if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
+ errno = EDOM;
+ else
+ errno = 0;
+ return r;
+ }
+
+ /* danger of overflow in 2.*z.imag !*/
if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
r.real = copysign(1., z.real);
- r.imag = 2.*sin(2.*z.imag)*exp(-2.*fabs(z.real));
+ r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real));
} else {
tx = tanh(z.real);
ty = tan(z.imag);
@@ -589,6 +844,7 @@
r.real = tx*(1.+ty*ty)/denom;
r.imag = ((ty/denom)*cx)*cx;
}
+ errno = 0;
return r;
}
@@ -597,6 +853,7 @@
"\n"
"Return the hyperbolic tangent of x.");
+
static PyObject *
cmath_log(PyObject *self, PyObject *args)
{
@@ -612,7 +869,6 @@
if (PyTuple_GET_SIZE(args) == 2)
x = c_quot(x, c_log(y));
PyFPE_END_PROTECT(x)
- Py_ADJUST_ERANGE2(x.real, x.imag);
if (errno != 0)
return math_error();
return PyComplex_FromCComplex(x);
@@ -640,18 +896,24 @@
static PyObject *
math_1(PyObject *args, Py_complex (*func)(Py_complex))
{
- Py_complex x;
+ Py_complex x,r ;
if (!PyArg_ParseTuple(args, "D", &x))
return NULL;
errno = 0;
- PyFPE_START_PROTECT("complex function", return 0)
- x = (*func)(x);
- PyFPE_END_PROTECT(x)
- Py_ADJUST_ERANGE2(x.real, x.imag);
- if (errno != 0)
- return math_error();
- else
- return PyComplex_FromCComplex(x);
+ PyFPE_START_PROTECT("complex function", return 0);
+ r = (*func)(x);
+ PyFPE_END_PROTECT(r);
+ if (errno == EDOM) {
+ PyErr_SetString(PyExc_ValueError, "math domain error");
+ return NULL;
+ }
+ else if (errno == ERANGE) {
+ PyErr_SetString(PyExc_OverflowError, "math range error");
+ return NULL;
+ }
+ else {
+ return PyComplex_FromCComplex(r);
+ }
}
#define FUNC1(stubname, func) \
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