Issue #26040: Improve test_math and test_cmath coverage and rigour. Thanks Jeff Allen.

1 files changed, 141 insertions, 0 deletions

diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt
index 9b08653..dd7e458 100644
--- a/Lib/test/cmath_testcases.txt
+++ b/Lib/test/cmath_testcases.txt
@@ -53,6 +53,12 @@
 -- MPFR homepage at http://www.mpfr.org for more information about the
 -- MPFR project.
 
+-- A minority of the test cases were generated with the help of
+-- mpmath 0.19 at 100 bit accuracy (http://mpmath.org) to improve
+-- coverage of real functions with real-valued arguments. These are
+-- used in test.test_math.MathTests.test_testfile, as well as in
+-- test_cmath.
+
 
 --------------------------
 -- acos: Inverse cosine --
@@ -848,6 +854,18 @@ atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.553381029
 atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875
 atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692
 
+-- Additional real values (mpmath)
+atan0400 atan 1.7976931348623157e+308 0.0 -> 1.5707963267948966192 0.0
+atan0401 atan -1.7976931348623157e+308 0.0 -> -1.5707963267948966192 0.0
+atan0402 atan 1e-17 0.0 -> 1.0000000000000000715e-17 0.0
+atan0403 atan -1e-17 0.0 -> -1.0000000000000000715e-17 0.0
+atan0404 atan 0.0001 0.0 -> 0.000099999999666666673459 0.0
+atan0405 atan -0.0001 0.0 -> -0.000099999999666666673459 0.0
+atan0406 atan 0.999999999999999 0.0 -> 0.78539816339744781002 0.0
+atan0407 atan 1.000000000000001 0.0 -> 0.78539816339744886473 0.0
+atan0408 atan 14.101419947171719 0.0 -> 1.4999999999999999969 0.0
+atan0409 atan 1255.7655915007897 0.0 -> 1.5700000000000000622 0.0
+
 -- special values
 atan1000 atan -0.0 0.0 -> -0.0 0.0
 atan1001 atan nan 0.0 -> nan 0.0
@@ -1514,6 +1532,11 @@ sqrt0131 sqrt -1.5477066694467245e-310 -0.0 -> 0.0 -1.2440685951533077e-155
 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
 
+-- Additional real values (mpmath)
+sqrt0150 sqrt 1.7976931348623157e+308 0.0 -> 1.3407807929942596355e+154 0.0
+sqrt0151 sqrt 2.2250738585072014e-308 0.0 -> 1.4916681462400413487e-154 0.0
+sqrt0152 sqrt 5e-324 0.0 -> 2.2227587494850774834e-162 0.0
+
 -- special values
 sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0
 sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0
@@ -1616,6 +1639,20 @@ 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
 
+-- Additional real values (mpmath)
+exp0070 exp 1e-08 0.0 -> 1.00000001000000005 0.0
+exp0071 exp 0.0003 0.0 -> 1.0003000450045003375 0.0
+exp0072 exp 0.2 0.0 -> 1.2214027581601698475 0.0
+exp0073 exp 1.0 0.0 -> 2.7182818284590452354 0.0
+exp0074 exp -1e-08 0.0 -> 0.99999999000000005 0.0
+exp0075 exp -0.0003 0.0 -> 0.99970004499550033751 0.0
+exp0076 exp -1.0 0.0 -> 0.3678794411714423216 0.0
+exp0077 exp 2.220446049250313e-16 0.0 -> 1.000000000000000222 0.0
+exp0078 exp -1.1102230246251565e-16 0.0 -> 0.99999999999999988898 0.0
+exp0079 exp 2.302585092994046 0.0 -> 10.000000000000002171 0.0
+exp0080 exp -2.302585092994046 0.0 -> 0.099999999999999978292 0.0
+exp0081 exp 709.7827 0.0 -> 1.7976699566638014654e+308 0.0
+
 -- special values
 exp1000 exp 0.0 0.0 -> 1.0 0.0
 exp1001 exp -0.0 0.0 -> 1.0 0.0
@@ -1708,6 +1745,23 @@ cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.129026
 cosh0030 cosh 710.5 2.3519999999999999 -> -1.2967465239355998e+308 1.3076707908857333e+308
 cosh0031 cosh -710.5 0.69999999999999996 -> 1.4085466381392499e+308 -1.1864024666450239e+308
 
+-- Additional real values (mpmath)
+cosh0050 cosh 1e-150 0.0 -> 1.0 0.0
+cosh0051 cosh 1e-18 0.0 -> 1.0 0.0
+cosh0052 cosh 1e-09 0.0 -> 1.0000000000000000005 0.0
+cosh0053 cosh 0.0003 0.0 -> 1.0000000450000003375 0.0
+cosh0054 cosh 0.2 0.0 -> 1.0200667556190758485 0.0
+cosh0055 cosh 1.0 0.0 -> 1.5430806348152437785 0.0
+cosh0056 cosh -1e-18 0.0 -> 1.0 -0.0
+cosh0057 cosh -0.0003 0.0 -> 1.0000000450000003375 -0.0
+cosh0058 cosh -1.0 0.0 -> 1.5430806348152437785 -0.0
+cosh0059 cosh 1.3169578969248168 0.0 -> 2.0000000000000001504 0.0
+cosh0060 cosh -1.3169578969248168 0.0 -> 2.0000000000000001504 -0.0
+cosh0061 cosh 17.328679513998633 0.0 -> 16777216.000000021938 0.0
+cosh0062 cosh 18.714973875118524 0.0 -> 67108864.000000043662 0.0
+cosh0063 cosh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0
+cosh0064 cosh -709.7827 0.0 -> 8.9883497833190073272e+307 -0.0
+
 -- special values
 cosh1000 cosh 0.0 0.0 -> 1.0 0.0
 cosh1001 cosh 0.0 inf -> nan 0.0        invalid ignore-imag-sign
@@ -1800,6 +1854,24 @@ sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0
 sinh0030 sinh 710.5 -2.3999999999999999 -> -1.3579970564885919e+308 -1.24394470907798e+308
 sinh0031 sinh -710.5 0.80000000000000004 -> -1.2830671601735164e+308 1.3210954193997678e+308
 
+-- Additional real values (mpmath)
+sinh0050 sinh 1e-100 0.0 -> 1.00000000000000002e-100 0.0
+sinh0051 sinh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0
+sinh0052 sinh 1e-16 0.0 -> 9.999999999999999791e-17 0.0
+sinh0053 sinh 3.7e-08 0.0 -> 3.7000000000000008885e-8 0.0
+sinh0054 sinh 0.001 0.0 -> 0.0010000001666666750208 0.0
+sinh0055 sinh 0.2 0.0 -> 0.20133600254109399895 0.0
+sinh0056 sinh 1.0 0.0 -> 1.1752011936438014569 0.0
+sinh0057 sinh -3.7e-08 0.0 -> -3.7000000000000008885e-8 0.0
+sinh0058 sinh -0.001 0.0 -> -0.0010000001666666750208 0.0
+sinh0059 sinh -1.0 0.0 -> -1.1752011936438014569 0.0
+sinh0060 sinh 1.4436354751788103 0.0 -> 1.9999999999999999078 0.0
+sinh0061 sinh -1.4436354751788103 0.0 -> -1.9999999999999999078 0.0
+sinh0062 sinh 17.328679513998633 0.0 -> 16777215.999999992136 0.0
+sinh0063 sinh 18.714973875118524 0.0 -> 67108864.000000036211 0.0
+sinh0064 sinh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0
+sinh0065 sinh -709.7827 0.0 -> -8.9883497833190073272e+307 0.0
+
 -- special values
 sinh1000 sinh 0.0 0.0 -> 0.0 0.0
 sinh1001 sinh 0.0 inf -> 0.0 nan        invalid ignore-real-sign
@@ -1897,6 +1969,24 @@ tanh0031 tanh -711 7.4000000000000004 -> -1.0 0.0
 tanh0032 tanh 1000 -2.3199999999999998 -> 1.0 0.0
 tanh0033 tanh -1.0000000000000001e+300 -9.6699999999999999 -> -1.0 -0.0
 
+-- Additional real values (mpmath)
+tanh0050 tanh 1e-100 0.0 -> 1.00000000000000002e-100 0.0
+tanh0051 tanh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0
+tanh0052 tanh 1e-16 0.0 -> 9.999999999999999791e-17 0.0
+tanh0053 tanh 3.7e-08 0.0 -> 3.6999999999999983559e-8 0.0
+tanh0054 tanh 0.001 0.0 -> 0.00099999966666680002076 0.0
+tanh0055 tanh 0.2 0.0 -> 0.19737532022490401141 0.0
+tanh0056 tanh 1.0 0.0 -> 0.76159415595576488812 0.0
+tanh0057 tanh -3.7e-08 0.0 -> -3.6999999999999983559e-8 0.0
+tanh0058 tanh -0.001 0.0 -> -0.00099999966666680002076 0.0
+tanh0059 tanh -1.0 0.0 -> -0.76159415595576488812 0.0
+tanh0060 tanh 0.5493061443340549 0.0 -> 0.50000000000000003402 0.0
+tanh0061 tanh -0.5493061443340549 0.0 -> -0.50000000000000003402 0.0
+tanh0062 tanh 17.328679513998633 0.0 -> 0.99999999999999822364 0.0
+tanh0063 tanh 18.714973875118524 0.0 -> 0.99999999999999988898 0.0
+tanh0064 tanh 711 0.0 -> 1.0 0.0
+tanh0065 tanh 1.797e+308 0.0 -> 1.0 0.0
+
 --special values
 tanh1000 tanh 0.0 0.0 -> 0.0 0.0
 tanh1001 tanh 0.0 inf -> nan nan        invalid
@@ -1985,6 +2075,22 @@ cos0021 cos 4.8048375263775256 0.0062248852898515658 -> 0.092318702015846243 0.0
 cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582
 cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477
 
+-- Additional real values (mpmath)
+cos0050 cos 1e-150 0.0 -> 1.0 -0.0
+cos0051 cos 1e-18 0.0 -> 1.0 -0.0
+cos0052 cos 1e-09 0.0 -> 0.9999999999999999995 -0.0
+cos0053 cos 0.0003 0.0 -> 0.9999999550000003375 -0.0
+cos0054 cos 0.2 0.0 -> 0.98006657784124162892 -0.0
+cos0055 cos 1.0 0.0 -> 0.5403023058681397174 -0.0
+cos0056 cos -1e-18 0.0 -> 1.0 0.0
+cos0057 cos -0.0003 0.0 -> 0.9999999550000003375 0.0
+cos0058 cos -1.0 0.0 -> 0.5403023058681397174 0.0
+cos0059 cos 1.0471975511965976 0.0 -> 0.50000000000000009945 -0.0
+cos0060 cos 2.5707963267948966 0.0 -> -0.84147098480789647357 -0.0
+cos0061 cos -2.5707963267948966 0.0 -> -0.84147098480789647357 0.0
+cos0062 cos 7.225663103256523 0.0 -> 0.58778525229247407559 -0.0
+cos0063 cos -8.79645943005142 0.0 -> -0.80901699437494722255 0.0
+
 -- special values
 cos1000 cos -0.0 0.0 -> 1.0 0.0
 cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
@@ -2073,6 +2179,22 @@ sin0021 sin 1.4342727387492671 0.81361889790284347 -> 1.3370960060947923 0.12336
 sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852
 sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62
 
+-- Additional real values (mpmath)
+sin0050 sin 1e-100 0.0 -> 1.00000000000000002e-100 0.0
+sin0051 sin 3.7e-08 0.0 -> 3.6999999999999992001e-8 0.0
+sin0052 sin 0.001 0.0 -> 0.00099999983333334168748 0.0
+sin0053 sin 0.2 0.0 -> 0.19866933079506122634 0.0
+sin0054 sin 1.0 0.0 -> 0.84147098480789650665 0.0
+sin0055 sin -3.7e-08 0.0 -> -3.6999999999999992001e-8 0.0
+sin0056 sin -0.001 0.0 -> -0.00099999983333334168748 0.0
+sin0057 sin -1.0 0.0 -> -0.84147098480789650665 0.0
+sin0058 sin 0.5235987755982989 0.0 -> 0.50000000000000004642 0.0
+sin0059 sin -0.5235987755982989 0.0 -> -0.50000000000000004642 0.0
+sin0060 sin 2.6179938779914944 0.0 -> 0.49999999999999996018 -0.0
+sin0061 sin -2.6179938779914944 0.0 -> -0.49999999999999996018 -0.0
+sin0062 sin 7.225663103256523 0.0 -> 0.80901699437494673648 0.0
+sin0063 sin -8.79645943005142 0.0 -> -0.58778525229247340658 -0.0
+
 -- special values
 sin1000 sin -0.0 0.0 -> -0.0 0.0
 sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
@@ -2161,6 +2283,25 @@ tan0021 tan 1.7809617968443272 1.5052381702853379 -> -0.044066222118946903 1.093
 tan0022 tan 1.1615313900880577 1.7956298728647107 -> 0.041793186826390362 1.0375339546034792
 tan0023 tan 0.067014779477908945 5.8517361577457097 -> 2.2088639754800034e-06 0.9999836182420061
 
+-- Additional real values (mpmath)
+tan0050 tan 1e-100 0.0 -> 1.00000000000000002e-100 0.0
+tan0051 tan 3.7e-08 0.0 -> 3.7000000000000017328e-8 0.0
+tan0052 tan 0.001 0.0 -> 0.0010000003333334666875 0.0
+tan0053 tan 0.2 0.0 -> 0.20271003550867249488 0.0
+tan0054 tan 1.0 0.0 -> 1.5574077246549022305 0.0
+tan0055 tan -3.7e-08 0.0 -> -3.7000000000000017328e-8 0.0
+tan0056 tan -0.001 0.0 -> -0.0010000003333334666875 0.0
+tan0057 tan -1.0 0.0 -> -1.5574077246549022305 0.0
+tan0058 tan 0.4636476090008061 0.0 -> 0.49999999999999997163 0.0
+tan0059 tan -0.4636476090008061 0.0 -> -0.49999999999999997163 0.0
+tan0060 tan 1.1071487177940904 0.0 -> 1.9999999999999995298 0.0
+tan0061 tan -1.1071487177940904 0.0 -> -1.9999999999999995298 0.0
+tan0062 tan 1.5 0.0 -> 14.101419947171719388 0.0
+tan0063 tan 1.57 0.0 -> 1255.7655915007896475 0.0
+tan0064 tan 1.5707963267948961 0.0 -> 1978937966095219.0538 0.0
+tan0065 tan 7.225663103256523 0.0 -> 1.3763819204711701522 0.0
+tan0066 tan -8.79645943005142 0.0 -> 0.7265425280053614098 0.0
+
 -- special values
 tan1000 tan -0.0 0.0 -> -0.0 0.0
 tan1001 tan -inf 0.0 -> nan nan invalid