diff options
Diffstat (limited to 'Lib')
| -rw-r--r-- | Lib/test/cmath_testcases.txt | 2355 | ||||
| -rw-r--r-- | Lib/test/ieee754.txt | 183 | ||||
| -rwxr-xr-x | Lib/test/test_cmath.py | 338 | ||||
| -rw-r--r-- | Lib/test/test_float.py | 21 | ||||
| -rw-r--r-- | Lib/test/test_math.py | 241 |
5 files changed, 3106 insertions, 32 deletions
diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt new file mode 100644 index 0000000..2fabebf --- /dev/null +++ b/Lib/test/cmath_testcases.txt @@ -0,0 +1,2355 @@ +-- Testcases for functions in cmath. +-- +-- Each line takes the form: +-- +-- <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 +-- 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. +-- +-- ignore-real-sign : indicates that the sign of the real part of +-- the result is unspecified; if the real part of the result is +-- given as inf, then both -inf and inf should be accepted as +-- correct. +-- +-- ignore-imag-sign : indicates that the sign of the imaginary part +-- of the result is unspecified. +-- +-- Flags may appear in any order. +-- +-- 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 -- +-------------------------- + +-- zeros +acos0000 acos 0.0 0.0 -> 1.5707963267948966 -0.0 +acos0001 acos 0.0 -0.0 -> 1.5707963267948966 0.0 +acos0002 acos -0.0 0.0 -> 1.5707963267948966 -0.0 +acos0003 acos -0.0 -0.0 -> 1.5707963267948966 0.0 + +-- branch points: +/-1 +acos0010 acos 1.0 0.0 -> 0.0 -0.0 +acos0011 acos 1.0 -0.0 -> 0.0 0.0 +acos0012 acos -1.0 0.0 -> 3.1415926535897931 -0.0 +acos0013 acos -1.0 -0.0 -> 3.1415926535897931 0.0 + +-- values along both sides of real axis +acos0020 acos -9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0 +acos0021 acos -9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0 +acos0022 acos -1e-305 0.0 -> 1.5707963267948966 -0.0 +acos0023 acos -1e-305 -0.0 -> 1.5707963267948966 0.0 +acos0024 acos -1e-150 0.0 -> 1.5707963267948966 -0.0 +acos0025 acos -1e-150 -0.0 -> 1.5707963267948966 0.0 +acos0026 acos -9.9999999999999998e-17 0.0 -> 1.5707963267948968 -0.0 +acos0027 acos -9.9999999999999998e-17 -0.0 -> 1.5707963267948968 0.0 +acos0028 acos -0.001 0.0 -> 1.5717963269615634 -0.0 +acos0029 acos -0.001 -0.0 -> 1.5717963269615634 0.0 +acos0030 acos -0.57899999999999996 0.0 -> 2.1882979816120667 -0.0 +acos0031 acos -0.57899999999999996 -0.0 -> 2.1882979816120667 0.0 +acos0032 acos -0.99999999999999989 0.0 -> 3.1415926386886319 -0.0 +acos0033 acos -0.99999999999999989 -0.0 -> 3.1415926386886319 0.0 +acos0034 acos -1.0000000000000002 0.0 -> 3.1415926535897931 -2.1073424255447014e-08 +acos0035 acos -1.0000000000000002 -0.0 -> 3.1415926535897931 2.1073424255447014e-08 +acos0036 acos -1.0009999999999999 0.0 -> 3.1415926535897931 -0.044717633608306849 +acos0037 acos -1.0009999999999999 -0.0 -> 3.1415926535897931 0.044717633608306849 +acos0038 acos -2.0 0.0 -> 3.1415926535897931 -1.3169578969248168 +acos0039 acos -2.0 -0.0 -> 3.1415926535897931 1.3169578969248168 +acos0040 acos -23.0 0.0 -> 3.1415926535897931 -3.8281684713331012 +acos0041 acos -23.0 -0.0 -> 3.1415926535897931 3.8281684713331012 +acos0042 acos -10000000000000000.0 0.0 -> 3.1415926535897931 -37.534508668464674 +acos0043 acos -10000000000000000.0 -0.0 -> 3.1415926535897931 37.534508668464674 +acos0044 acos -9.9999999999999998e+149 0.0 -> 3.1415926535897931 -346.08091112966679 +acos0045 acos -9.9999999999999998e+149 -0.0 -> 3.1415926535897931 346.08091112966679 +acos0046 acos -1.0000000000000001e+299 0.0 -> 3.1415926535897931 -689.16608998577965 +acos0047 acos -1.0000000000000001e+299 -0.0 -> 3.1415926535897931 689.16608998577965 +acos0048 acos 9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0 +acos0049 acos 9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0 +acos0050 acos 1e-305 0.0 -> 1.5707963267948966 -0.0 +acos0051 acos 1e-305 -0.0 -> 1.5707963267948966 0.0 +acos0052 acos 1e-150 0.0 -> 1.5707963267948966 -0.0 +acos0053 acos 1e-150 -0.0 -> 1.5707963267948966 0.0 +acos0054 acos 9.9999999999999998e-17 0.0 -> 1.5707963267948966 -0.0 +acos0055 acos 9.9999999999999998e-17 -0.0 -> 1.5707963267948966 0.0 +acos0056 acos 0.001 0.0 -> 1.56979632662823 -0.0 +acos0057 acos 0.001 -0.0 -> 1.56979632662823 0.0 +acos0058 acos 0.57899999999999996 0.0 -> 0.95329467197772655 -0.0 +acos0059 acos 0.57899999999999996 -0.0 -> 0.95329467197772655 0.0 +acos0060 acos 0.99999999999999989 0.0 -> 1.4901161193847656e-08 -0.0 +acos0061 acos 0.99999999999999989 -0.0 -> 1.4901161193847656e-08 0.0 +acos0062 acos 1.0000000000000002 0.0 -> 0.0 -2.1073424255447014e-08 +acos0063 acos 1.0000000000000002 -0.0 -> 0.0 2.1073424255447014e-08 +acos0064 acos 1.0009999999999999 0.0 -> 0.0 -0.044717633608306849 +acos0065 acos 1.0009999999999999 -0.0 -> 0.0 0.044717633608306849 +acos0066 acos 2.0 0.0 -> 0.0 -1.3169578969248168 +acos0067 acos 2.0 -0.0 -> 0.0 1.3169578969248168 +acos0068 acos 23.0 0.0 -> 0.0 -3.8281684713331012 +acos0069 acos 23.0 -0.0 -> 0.0 3.8281684713331012 +acos0070 acos 10000000000000000.0 0.0 -> 0.0 -37.534508668464674 +acos0071 acos 10000000000000000.0 -0.0 -> 0.0 37.534508668464674 +acos0072 acos 9.9999999999999998e+149 0.0 -> 0.0 -346.08091112966679 +acos0073 acos 9.9999999999999998e+149 -0.0 -> 0.0 346.08091112966679 +acos0074 acos 1.0000000000000001e+299 0.0 -> 0.0 -689.16608998577965 +acos0075 acos 1.0000000000000001e+299 -0.0 -> 0.0 689.16608998577965 + +-- random inputs +acos0100 acos -3.3307113324596682 -10.732007530863266 -> 1.8706085694482339 3.113986806554613 +acos0101 acos -2863.952991743291 -2681013315.2571239 -> 1.5707973950301699 22.402607843274758 +acos0102 acos -0.33072639793220088 -0.85055464658253055 -> 1.8219426895922601 0.79250166729311966 +acos0103 acos -2.5722325842097802 -12.703940809821574 -> 1.7699942413107408 3.2565170156527325 +acos0104 acos -42.495233785459583 -0.54039320751337161 -> 3.1288732573153304 4.4424815519735601 +acos0105 acos -1.1363818625856401 9641.1325498630376 -> 1.5709141948820049 -9.8669410553254284 +acos0106 acos -2.4398426824157866e-11 0.33002051890266165 -> 1.570796326818066 -0.32430578041578667 +acos0107 acos -1.3521340428186552 2.9369737912076772 -> 1.9849059192339338 -1.8822893674117942 +acos0108 acos -1.827364706477915 1.0355459232147557 -> 2.5732246307960032 -1.4090688267854969 +acos0109 acos -0.25978373706403546 10.09712669185833 -> 1.5963940386378306 -3.0081673050196063 +acos0110 acos 0.33561778471072551 -4587350.6823999118 -> 1.5707962536333251 16.031960402579539 +acos0111 acos 0.49133444610998445 -0.8071422362990015 -> 1.1908761712801788 0.78573345813187867 +acos0112 acos 0.42196734507823974 -2.4812965431745115 -> 1.414091186100692 1.651707260988172 +acos0113 acos 2.961426210100655 -219.03295695248664 -> 1.5572768319822778 6.0824659885827304 +acos0114 acos 2.886209063652641 -20.38011207220606 -> 1.4302765252297889 3.718201853147642 +acos0115 acos 0.4180568075276509 1.4833433990823484 -> 1.3393834558303042 -1.2079847758301576 +acos0116 acos 52.376111405924718 0.013930429001941001 -> 0.00026601761804024188 -4.6515066691204714 +acos0117 acos 41637948387.625969 1.563418292894041 -> 3.7547918507883548e-11 -25.145424989809381 +acos0118 acos 0.061226659122249526 0.8447234394615154 -> 1.5240280306367315 -0.76791798971140812 +acos0119 acos 2.4480466420442959e+26 0.18002339201384662 -> 7.353756620564798e-28 -61.455650015996376 + +-- values near infinity +acos0200 acos 1.6206860518683021e+308 1.0308426226285283e+308 -> 0.56650826093826223 -710.54206874241561 +acos0201 acos 1.2067735875070062e+308 -1.3429173724390276e+308 -> 0.83874369390864889 710.48017794027498 +acos0202 acos -7.4130145132549047e+307 1.1759130543927645e+308 -> 2.1332729346478536 -710.21871115698752 +acos0203 acos -8.6329426442257249e+307 -1.2316282952184133e+308 -> 2.1821511032444838 710.29752145697148 +acos0204 acos 0.0 1.4289713855849746e+308 -> 1.5707963267948966 -710.24631069738996 +acos0205 acos -0.0 1.3153524545987432e+308 -> 1.5707963267948966 -710.1634604787539 +acos0206 acos 0.0 -9.6229037669269321e+307 -> 1.5707963267948966 709.85091679573691 +acos0207 acos -0.0 -4.9783616421107088e+307 -> 1.5707963267948966 709.19187157911233 +acos0208 acos 1.3937541925739389e+308 0.0 -> 0.0 -710.22135678707264 +acos0209 acos 9.1362388967371536e+307 -0.0 -> 0.0 709.79901953124613 +acos0210 acos -1.3457361220697436e+308 0.0 -> 3.1415926535897931 -710.18629698871848 +acos0211 acos -5.4699090056144284e+307 -0.0 -> 3.1415926535897931 709.28603271085649 +acos0212 acos 1.5880716932358901e+308 5.5638401252339929 -> 3.503519487773873e-308 -710.35187633140583 +acos0213 acos 1.2497211663463164e+308 -3.0456477717911024 -> 2.4370618453197486e-308 710.11227628223412 +acos0214 acos -9.9016224006029528e+307 4.9570427340789056 -> 3.1415926535897931 -709.87946935229468 +acos0215 acos -1.5854071066874139e+308 -4.4233577741497783 -> 3.1415926535897931 710.35019704672004 +acos0216 acos 9.3674623083647628 1.5209559051877979e+308 -> 1.5707963267948966 -710.30869484491086 +acos0217 acos 8.1773832021784383 -6.6093445795000056e+307 -> 1.5707963267948966 709.4752552227792 +acos0218 acos -3.1845935000665104 1.5768856396650893e+308 -> 1.5707963267948966 -710.34480761042687 +acos0219 acos -1.0577303880953903 -6.4574626815735613e+307 -> 1.5707963267948966 709.45200719662046 + +-- values near 0 +acos0220 acos 1.8566986970714045e-320 3.1867234156760402e-321 -> 1.5707963267948966 -3.1867234156760402e-321 +acos0221 acos 7.9050503334599447e-323 -8.8931816251424378e-323 -> 1.5707963267948966 8.8931816251424378e-323 +acos0222 acos -4.4465908125712189e-323 2.4654065097222727e-311 -> 1.5707963267948966 -2.4654065097222727e-311 +acos0223 acos -6.1016916408192619e-311 -2.4703282292062327e-323 -> 1.5707963267948966 2.4703282292062327e-323 +acos0224 acos 0.0 3.4305783621842729e-311 -> 1.5707963267948966 -3.4305783621842729e-311 +acos0225 acos -0.0 1.6117409498633145e-319 -> 1.5707963267948966 -1.6117409498633145e-319 +acos0226 acos 0.0 -4.9900630229965901e-322 -> 1.5707963267948966 4.9900630229965901e-322 +acos0227 acos -0.0 -4.4889279210592818e-311 -> 1.5707963267948966 4.4889279210592818e-311 +acos0228 acos 5.3297678681477214e-312 0.0 -> 1.5707963267948966 -0.0 +acos0229 acos 6.2073425897211614e-313 -0.0 -> 1.5707963267948966 0.0 +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 ignore-imag-sign +acos1019 acos -inf nan -> nan inf ignore-imag-sign +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 -- +-------------------------------------- + +-- zeros +acosh0000 acosh 0.0 0.0 -> 0.0 1.5707963267948966 +acosh0001 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966 +acosh0002 acosh -0.0 0.0 -> 0.0 1.5707963267948966 +acosh0003 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966 + +-- branch points: +/-1 +acosh0010 acosh 1.0 0.0 -> 0.0 0.0 +acosh0011 acosh 1.0 -0.0 -> 0.0 -0.0 +acosh0012 acosh -1.0 0.0 -> 0.0 3.1415926535897931 +acosh0013 acosh -1.0 -0.0 -> 0.0 -3.1415926535897931 + +-- values along both sides of real axis +acosh0020 acosh -9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966 +acosh0021 acosh -9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966 +acosh0022 acosh -1e-305 0.0 -> 0.0 1.5707963267948966 +acosh0023 acosh -1e-305 -0.0 -> 0.0 -1.5707963267948966 +acosh0024 acosh -1e-150 0.0 -> 0.0 1.5707963267948966 +acosh0025 acosh -1e-150 -0.0 -> 0.0 -1.5707963267948966 +acosh0026 acosh -9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948968 +acosh0027 acosh -9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948968 +acosh0028 acosh -0.001 0.0 -> 0.0 1.5717963269615634 +acosh0029 acosh -0.001 -0.0 -> 0.0 -1.5717963269615634 +acosh0030 acosh -0.57899999999999996 0.0 -> 0.0 2.1882979816120667 +acosh0031 acosh -0.57899999999999996 -0.0 -> 0.0 -2.1882979816120667 +acosh0032 acosh -0.99999999999999989 0.0 -> 0.0 3.1415926386886319 +acosh0033 acosh -0.99999999999999989 -0.0 -> 0.0 -3.1415926386886319 +acosh0034 acosh -1.0000000000000002 0.0 -> 2.1073424255447014e-08 3.1415926535897931 +acosh0035 acosh -1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -3.1415926535897931 +acosh0036 acosh -1.0009999999999999 0.0 -> 0.044717633608306849 3.1415926535897931 +acosh0037 acosh -1.0009999999999999 -0.0 -> 0.044717633608306849 -3.1415926535897931 +acosh0038 acosh -2.0 0.0 -> 1.3169578969248168 3.1415926535897931 +acosh0039 acosh -2.0 -0.0 -> 1.3169578969248168 -3.1415926535897931 +acosh0040 acosh -23.0 0.0 -> 3.8281684713331012 3.1415926535897931 +acosh0041 acosh -23.0 -0.0 -> 3.8281684713331012 -3.1415926535897931 +acosh0042 acosh -10000000000000000.0 0.0 -> 37.534508668464674 3.1415926535897931 +acosh0043 acosh -10000000000000000.0 -0.0 -> 37.534508668464674 -3.1415926535897931 +acosh0044 acosh -9.9999999999999998e+149 0.0 -> 346.08091112966679 3.1415926535897931 +acosh0045 acosh -9.9999999999999998e+149 -0.0 -> 346.08091112966679 -3.1415926535897931 +acosh0046 acosh -1.0000000000000001e+299 0.0 -> 689.16608998577965 3.1415926535897931 +acosh0047 acosh -1.0000000000000001e+299 -0.0 -> 689.16608998577965 -3.1415926535897931 +acosh0048 acosh 9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966 +acosh0049 acosh 9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966 +acosh0050 acosh 1e-305 0.0 -> 0.0 1.5707963267948966 +acosh0051 acosh 1e-305 -0.0 -> 0.0 -1.5707963267948966 +acosh0052 acosh 1e-150 0.0 -> 0.0 1.5707963267948966 +acosh0053 acosh 1e-150 -0.0 -> 0.0 -1.5707963267948966 +acosh0054 acosh 9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948966 +acosh0055 acosh 9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948966 +acosh0056 acosh 0.001 0.0 -> 0.0 1.56979632662823 +acosh0057 acosh 0.001 -0.0 -> 0.0 -1.56979632662823 +acosh0058 acosh 0.57899999999999996 0.0 -> 0.0 0.95329467197772655 +acosh0059 acosh 0.57899999999999996 -0.0 -> 0.0 -0.95329467197772655 +acosh0060 acosh 0.99999999999999989 0.0 -> 0.0 1.4901161193847656e-08 +acosh0061 acosh 0.99999999999999989 -0.0 -> 0.0 -1.4901161193847656e-08 +acosh0062 acosh 1.0000000000000002 0.0 -> 2.1073424255447014e-08 0.0 +acosh0063 acosh 1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -0.0 +acosh0064 acosh 1.0009999999999999 0.0 -> 0.044717633608306849 0.0 +acosh0065 acosh 1.0009999999999999 -0.0 -> 0.044717633608306849 -0.0 +acosh0066 acosh 2.0 0.0 -> 1.3169578969248168 0.0 +acosh0067 acosh 2.0 -0.0 -> 1.3169578969248168 -0.0 +acosh0068 acosh 23.0 0.0 -> 3.8281684713331012 0.0 +acosh0069 acosh 23.0 -0.0 -> 3.8281684713331012 -0.0 +acosh0070 acosh 10000000000000000.0 0.0 -> 37.534508668464674 0.0 +acosh0071 acosh 10000000000000000.0 -0.0 -> 37.534508668464674 -0.0 +acosh0072 acosh 9.9999999999999998e+149 0.0 -> 346.08091112966679 0.0 +acosh0073 acosh 9.9999999999999998e+149 -0.0 -> 346.08091112966679 -0.0 +acosh0074 acosh 1.0000000000000001e+299 0.0 -> 689.16608998577965 0.0 +acosh0075 acosh 1.0000000000000001e+299 -0.0 -> 689.16608998577965 -0.0 + +-- random inputs +acosh0100 acosh -1.4328589581250843 -1.8370347775558309 -> 1.5526962646549587 -2.190250168435786 +acosh0101 acosh -0.31075819156220957 -1.0772555786839297 -> 0.95139168286193709 -1.7812228089636479 +acosh0102 acosh -1.9044776578070453 -20.485370158932124 -> 3.7177411088932359 -1.6633888745861227 +acosh0103 acosh -0.075642506000858742 -21965976320.873051 -> 24.505907742881991 -1.5707963267983402 +acosh0104 acosh -1.6162271181056307 -3.0369343458696099 -> 1.9407057262861227 -2.0429549461750209 +acosh0105 acosh -0.3103780280298063 0.00018054880018078987 -> 0.00018992877058761416 1.886386995096728 +acosh0106 acosh -9159468751.5897655 5.8014747664273649 -> 23.631201197959193 3.1415926529564078 +acosh0107 acosh -0.037739157550933884 0.21841357493510705 -> 0.21685844960602488 1.6076735133449402 +acosh0108 acosh -8225991.0508394297 0.28318543008913644 -> 16.615956520420287 3.1415926191641019 +acosh0109 acosh -35.620070502302639 0.31303237005015 -> 4.2658980006943965 3.1328013255541873 +acosh0110 acosh 96.729939906820917 -0.029345228372365334 -> 5.2650434775863548 -0.00030338895866972843 +acosh0111 acosh 0.59656024007966491 -2.0412294654163978 -> 1.4923002024287835 -1.312568421900338 +acosh0112 acosh 109.29384112677828 -0.00015454863061533812 -> 5.3871662961545477 -1.4141245154061214e-06 +acosh0113 acosh 8.6705651969361597 -3.6723631649787465 -> 2.9336180958363545 -0.40267362031872861 +acosh0114 acosh 1.8101646445052686 -0.012345132721855478 -> 1.1997148566285769 -0.0081813912760150265 +acosh0115 acosh 52.56897195025288 0.001113916065985443 -> 4.6551827622264135 2.1193445872040307e-05 +acosh0116 acosh 0.28336786164214739 355643992457.40485 -> 27.290343226816528 1.5707963267940999 +acosh0117 acosh 0.73876621291911437 2.8828594541104322e-20 -> 4.2774820978159067e-20 0.73955845836827927 +acosh0118 acosh 0.025865471781718878 37125746064318.492 -> 31.938478989418012 1.5707963267948959 +acosh0119 acosh 2.2047353511780132 0.074712248143489271 -> 1.4286403248698021 0.037997904971626598 + +-- values near infinity +acosh0200 acosh 8.1548592876467785e+307 9.0943779335951128e+307 -> 710.08944620800605 0.83981165425478954 +acosh0201 acosh 1.4237229680972531e+308 -1.0336966617874858e+308 -> 710.4543331094759 -0.6279972876348755 +acosh0202 acosh -1.5014526899738939e+308 1.5670700378448792e+308 -> 710.66420706795464 2.3348137299106697 +acosh0203 acosh -1.0939040375213928e+308 -1.0416960351127978e+308 -> 710.30182863115886 -2.380636147787027 +acosh0204 acosh 0.0 1.476062433559588e+308 -> 710.27873384716929 1.5707963267948966 +acosh0205 acosh -0.0 6.2077210326221094e+307 -> 709.41256457484769 1.5707963267948966 +acosh0206 acosh 0.0 -1.5621899909968308e+308 -> 710.33544449990734 -1.5707963267948966 +acosh0207 acosh -0.0 -8.3556624833839122e+307 -> 709.70971018048317 -1.5707963267948966 +acosh0208 acosh 1.3067079752499342e+308 0.0 -> 710.15686680107228 0.0 +acosh0209 acosh 1.5653640340214026e+308 -0.0 -> 710.33747422926706 -0.0 +acosh0210 acosh -6.9011375992290636e+307 0.0 -> 709.51845699719922 3.1415926535897931 +acosh0211 acosh -9.9539576809926973e+307 -0.0 -> 709.88474095870185 -3.1415926535897931 +acosh0212 acosh 7.6449598518914925e+307 9.5706540768268358 -> 709.62081731754802 1.2518906916769345e-307 +acosh0213 acosh 5.4325410972602197e+307 -7.8064807816522706 -> 709.279177727925 -1.4369851312471974e-307 +acosh0214 acosh -1.1523626112360465e+308 7.0617510038869336 -> 710.03117010216909 3.1415926535897931 +acosh0215 acosh -1.1685027786862599e+308 -5.1568558357925625 -> 710.04507907571417 -3.1415926535897931 +acosh0216 acosh 3.0236370339788721 1.7503248720096417e+308 -> 710.44915723458064 1.5707963267948966 +acosh0217 acosh 6.6108007926031149 -9.1469968225806149e+307 -> 709.80019633903328 -1.5707963267948966 +acosh0218 acosh -5.1096262905623959 6.4484926785412395e+307 -> 709.45061713997973 1.5707963267948966 +acosh0219 acosh -2.8080920608735846 -1.7716118836519368e+308 -> 710.46124562363445 -1.5707963267948966 + +-- values near 0 +acosh0220 acosh 4.5560530326699304e-317 7.3048989121436657e-318 -> 7.3048989121436657e-318 1.5707963267948966 +acosh0221 acosh 4.8754274133585331e-314 -9.8469794897684199e-315 -> 9.8469794897684199e-315 -1.5707963267948966 +acosh0222 acosh -4.6748876009960097e-312 9.7900342887557606e-318 -> 9.7900342887557606e-318 1.5707963267948966 +acosh0223 acosh -4.3136871538399236e-320 -4.9406564584124654e-323 -> 4.9406564584124654e-323 -1.5707963267948966 +acosh0224 acosh 0.0 4.3431013866496774e-314 -> 4.3431013866496774e-314 1.5707963267948966 +acosh0225 acosh -0.0 6.0147334335829184e-317 -> 6.0147334335829184e-317 1.5707963267948966 +acosh0226 acosh 0.0 -1.2880291387081297e-320 -> 1.2880291387081297e-320 -1.5707963267948966 +acosh0227 acosh -0.0 -1.4401563976534621e-317 -> 1.4401563976534621e-317 -1.5707963267948966 +acosh0228 acosh 1.3689680570863091e-313 0.0 -> 0.0 1.5707963267948966 +acosh0229 acosh 1.5304346893494371e-312 -0.0 -> 0.0 -1.5707963267948966 +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 -- +------------------------ + +-- zeros +asin0000 asin 0.0 0.0 -> 0.0 0.0 +asin0001 asin 0.0 -0.0 -> 0.0 -0.0 +asin0002 asin -0.0 0.0 -> -0.0 0.0 +asin0003 asin -0.0 -0.0 -> -0.0 -0.0 + +-- branch points: +/-1 +asin0010 asin 1.0 0.0 -> 1.5707963267948966 0.0 +asin0011 asin 1.0 -0.0 -> 1.5707963267948966 -0.0 +asin0012 asin -1.0 0.0 -> -1.5707963267948966 0.0 +asin0013 asin -1.0 -0.0 -> -1.5707963267948966 -0.0 + +-- values along both sides of real axis +asin0020 asin -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0 +asin0021 asin -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0 +asin0022 asin -1e-305 0.0 -> -1e-305 0.0 +asin0023 asin -1e-305 -0.0 -> -1e-305 -0.0 +asin0024 asin -1e-150 0.0 -> -1e-150 0.0 +asin0025 asin -1e-150 -0.0 -> -1e-150 -0.0 +asin0026 asin -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0 +asin0027 asin -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0 +asin0028 asin -0.001 0.0 -> -0.0010000001666667416 0.0 +asin0029 asin -0.001 -0.0 -> -0.0010000001666667416 -0.0 +asin0030 asin -0.57899999999999996 0.0 -> -0.61750165481717001 0.0 +asin0031 asin -0.57899999999999996 -0.0 -> -0.61750165481717001 -0.0 +asin0032 asin -0.99999999999999989 0.0 -> -1.5707963118937354 0.0 +asin0033 asin -0.99999999999999989 -0.0 -> -1.5707963118937354 -0.0 +asin0034 asin -1.0000000000000002 0.0 -> -1.5707963267948966 2.1073424255447014e-08 +asin0035 asin -1.0000000000000002 -0.0 -> -1.5707963267948966 -2.1073424255447014e-08 +asin0036 asin -1.0009999999999999 0.0 -> -1.5707963267948966 0.044717633608306849 +asin0037 asin -1.0009999999999999 -0.0 -> -1.5707963267948966 -0.044717633608306849 +asin0038 asin -2.0 0.0 -> -1.5707963267948966 1.3169578969248168 +asin0039 asin -2.0 -0.0 -> -1.5707963267948966 -1.3169578969248168 +asin0040 asin -23.0 0.0 -> -1.5707963267948966 3.8281684713331012 +asin0041 asin -23.0 -0.0 -> -1.5707963267948966 -3.8281684713331012 +asin0042 asin -10000000000000000.0 0.0 -> -1.5707963267948966 37.534508668464674 +asin0043 asin -10000000000000000.0 -0.0 -> -1.5707963267948966 -37.534508668464674 +asin0044 asin -9.9999999999999998e+149 0.0 -> -1.5707963267948966 346.08091112966679 +asin0045 asin -9.9999999999999998e+149 -0.0 -> -1.5707963267948966 -346.08091112966679 +asin0046 asin -1.0000000000000001e+299 0.0 -> -1.5707963267948966 689.16608998577965 +asin0047 asin -1.0000000000000001e+299 -0.0 -> -1.5707963267948966 -689.16608998577965 +asin0048 asin 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0 +asin0049 asin 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0 +asin0050 asin 1e-305 0.0 -> 1e-305 0.0 +asin0051 asin 1e-305 -0.0 -> 1e-305 -0.0 +asin0052 asin 1e-150 0.0 -> 1e-150 0.0 +asin0053 asin 1e-150 -0.0 -> 1e-150 -0.0 +asin0054 asin 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0 +asin0055 asin 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0 +asin0056 asin 0.001 0.0 -> 0.0010000001666667416 0.0 +asin0057 asin 0.001 -0.0 -> 0.0010000001666667416 -0.0 +asin0058 asin 0.57899999999999996 0.0 -> 0.61750165481717001 0.0 +asin0059 asin 0.57899999999999996 -0.0 -> 0.61750165481717001 -0.0 +asin0060 asin 0.99999999999999989 0.0 -> 1.5707963118937354 0.0 +asin0061 asin 0.99999999999999989 -0.0 -> 1.5707963118937354 -0.0 +asin0062 asin 1.0000000000000002 0.0 -> 1.5707963267948966 2.1073424255447014e-08 +asin0063 asin 1.0000000000000002 -0.0 -> 1.5707963267948966 -2.1073424255447014e-08 +asin0064 asin 1.0009999999999999 0.0 -> 1.5707963267948966 0.044717633608306849 +asin0065 asin 1.0009999999999999 -0.0 -> 1.5707963267948966 -0.044717633608306849 +asin0066 asin 2.0 0.0 -> 1.5707963267948966 1.3169578969248168 +asin0067 asin 2.0 -0.0 -> 1.5707963267948966 -1.3169578969248168 +asin0068 asin 23.0 0.0 -> 1.5707963267948966 3.8281684713331012 +asin0069 asin 23.0 -0.0 -> 1.5707963267948966 -3.8281684713331012 +asin0070 asin 10000000000000000.0 0.0 -> 1.5707963267948966 37.534508668464674 +asin0071 asin 10000000000000000.0 -0.0 -> 1.5707963267948966 -37.534508668464674 +asin0072 asin 9.9999999999999998e+149 0.0 -> 1.5707963267948966 346.08091112966679 +asin0073 asin 9.9999999999999998e+149 -0.0 -> 1.5707963267948966 -346.08091112966679 +asin0074 asin 1.0000000000000001e+299 0.0 -> 1.5707963267948966 689.16608998577965 +asin0075 asin 1.0000000000000001e+299 -0.0 -> 1.5707963267948966 -689.16608998577965 + +-- random inputs +asin0100 asin -1.5979555835086083 -0.15003009814595247 -> -1.4515369557405788 -1.0544476399790823 +asin0101 asin -0.57488225895317679 -9.6080397838952743e-13 -> -0.61246024460412851 -1.174238005400403e-12 +asin0102 asin -3.6508087930516249 -0.36027527093220152 -> -1.4685890605305874 -1.9742273007152038 +asin0103 asin -1.5238659792326819 -1.1360813516996364 -> -0.86080051691147275 -1.3223742205689195 +asin0104 asin -1592.0639045555306 -0.72362427935018236 -> -1.5703418071175179 -8.0659336918729228 +asin0105 asin -0.19835471371312019 4.2131508416697709 -> -0.045777831019935149 2.1461732751933171 +asin0106 asin -1.918471054430213 0.40603305079779234 -> -1.3301396585791556 1.30263642314981 +asin0107 asin -254495.01623373642 0.71084414434470822 -> -1.5707935336394359 13.140183712762321 +asin0108 asin -0.31315882715691157 3.9647994288429866 -> -0.076450403840916004 2.0889762138713457 +asin0109 asin -0.90017064284720816 1.2530659485907105 -> -0.53466509741943447 1.1702811557577 +asin0110 asin 2.1615181696571075 -0.14058647488229523 -> 1.4976166323896871 -1.4085811039334604 +asin0111 asin 1.2104749210707795 -0.85732484485298999 -> 0.83913071588343924 -1.0681719250525901 +asin0112 asin 1.7059733185128891 -0.84032966373156581 -> 1.0510900815816229 -1.2967979791361652 +asin0113 asin 9.9137085017290687 -1.4608383970250893 -> 1.4237704820128891 -2.995414677560686 +asin0114 asin 117.12344751041495 -5453908091.5334015 -> 2.1475141411392012e-08 -23.112745450217066 +asin0115 asin 0.081041187798029227 0.067054349860173196 -> 0.080946786856771813 0.067223991060639698 +asin0116 asin 46.635472322049949 2.3835190718056678 -> 1.5197194940010779 4.5366989600972083 +asin0117 asin 3907.0687961127105 19.144021886390181 -> 1.5658965233083235 8.9637018715924217 +asin0118 asin 1.0889312322308273 509.01577883554768 -> 0.0021392803817829316 6.9256294494524706 +asin0119 asin 0.10851518277509224 1.5612510908217476 -> 0.058491014243902621 1.2297075725621327 + +-- values near infinity +asin0200 asin 1.5230241998821499e+308 5.5707228994084525e+307 -> 1.2201446370892068 710.37283486535966 +asin0201 asin 8.1334317698672204e+307 -9.2249425197872451e+307 -> 0.72259991284020042 -710.0962453049026 +asin0202 asin -9.9138506659241768e+307 6.701544526434995e+307 -> -0.97637511742194594 710.06887486671371 +asin0203 asin -1.4141298868173842e+308 -5.401505134514191e+307 -> -1.2059319055160587 -710.30396478954628 +asin0204 asin 0.0 9.1618092977897431e+307 -> 0.0 709.80181441050593 +asin0205 asin -0.0 6.8064342551939755e+307 -> -0.0 709.50463910853489 +asin0206 asin 0.0 -6.4997516454798215e+307 -> 0.0 -709.45853469751592 +asin0207 asin -0.0 -1.6767449053345242e+308 -> -0.0 -710.4062101803022 +asin0208 asin 5.4242749957378916e+307 0.0 -> 1.5707963267948966 709.27765497888902 +asin0209 asin 9.5342145121164749e+307 -0.0 -> 1.5707963267948966 -709.84165758595907 +asin0210 asin -7.0445698006201847e+307 0.0 -> -1.5707963267948966 709.53902780872136 +asin0211 asin -1.0016025569769706e+308 -0.0 -> -1.5707963267948966 -709.89095709697881 +asin0212 asin 1.6552203778877204e+308 0.48761543336249491 -> 1.5707963267948966 710.39328998153474 +asin0213 asin 1.2485712830384869e+308 -4.3489311161278899 -> 1.5707963267948966 -710.1113557467786 +asin0214 asin -1.5117842813353125e+308 5.123452666102434 -> -1.5707963267948966 710.30264641923031 +asin0215 asin -1.3167634313008016e+308 -0.52939679793528982 -> -1.5707963267948966 -710.16453260239768 +asin0216 asin 0.80843929176985907 1.0150851827767876e+308 -> 7.9642507396113875e-309 709.90432835561637 +asin0217 asin 8.2544809829680901 -1.7423548140539474e+308 -> 4.7375430746865733e-308 -710.44459336242164 +asin0218 asin -5.2499000118824295 4.6655578977512214e+307 -> -1.1252459249113292e-307 709.1269781491103 +asin0219 asin -5.9904782760833433 -4.7315689314781163e+307 -> -1.2660659419394637e-307 -709.14102757522312 + +-- special values +asin1000 asin -0.0 0.0 -> -0.0 0.0 +asin1001 asin 0.0 0.0 -> 0.0 0.0 +asin1002 asin -0.0 -0.0 -> -0.0 -0.0 +asin1003 asin 0.0 -0.0 -> 0.0 -0.0 +asin1004 asin -inf 0.0 -> -1.5707963267948966 inf +asin1005 asin -inf 2.2999999999999998 -> -1.5707963267948966 inf +asin1006 asin nan 0.0 -> nan nan +asin1007 asin nan 2.2999999999999998 -> nan nan +asin1008 asin -0.0 inf -> -0.0 inf +asin1009 asin -2.2999999999999998 inf -> -0.0 inf +asin1010 asin -inf inf -> -0.78539816339744828 inf +asin1011 asin nan inf -> nan inf +asin1012 asin -0.0 nan -> -0.0 nan +asin1013 asin -2.2999999999999998 nan -> nan nan +asin1014 asin -inf nan -> nan inf ignore-imag-sign +asin1015 asin nan nan -> nan nan +asin1016 asin inf 0.0 -> 1.5707963267948966 inf +asin1017 asin inf 2.2999999999999998 -> 1.5707963267948966 inf +asin1018 asin 0.0 inf -> 0.0 inf +asin1019 asin 2.2999999999999998 inf -> 0.0 inf +asin1020 asin inf inf -> 0.78539816339744828 inf +asin1021 asin 0.0 nan -> 0.0 nan +asin1022 asin 2.2999999999999998 nan -> nan nan +asin1023 asin inf nan -> nan inf ignore-imag-sign +asin1024 asin inf -0.0 -> 1.5707963267948966 -inf +asin1025 asin inf -2.2999999999999998 -> 1.5707963267948966 -inf +asin1026 asin nan -0.0 -> nan nan +asin1027 asin nan -2.2999999999999998 -> nan nan +asin1028 asin 0.0 -inf -> 0.0 -inf +asin1029 asin 2.2999999999999998 -inf -> 0.0 -inf +asin1030 asin inf -inf -> 0.78539816339744828 -inf +asin1031 asin nan -inf -> nan -inf +asin1032 asin -inf -0.0 -> -1.5707963267948966 -inf +asin1033 asin -inf -2.2999999999999998 -> -1.5707963267948966 -inf +asin1034 asin -0.0 -inf -> -0.0 -inf +asin1035 asin -2.2999999999999998 -inf -> -0.0 -inf +asin1036 asin -inf -inf -> -0.78539816339744828 -inf + + +------------------------------------ +-- asinh: Inverse hyperbolic sine -- +------------------------------------ + +-- zeros +asinh0000 asinh 0.0 0.0 -> 0.0 0.0 +asinh0001 asinh 0.0 -0.0 -> 0.0 -0.0 +asinh0002 asinh -0.0 0.0 -> -0.0 0.0 +asinh0003 asinh -0.0 -0.0 -> -0.0 -0.0 + +-- branch points: +/-i +asinh0010 asinh 0.0 1.0 -> 0.0 1.5707963267948966 +asinh0011 asinh 0.0 -1.0 -> 0.0 -1.5707963267948966 +asinh0012 asinh -0.0 1.0 -> -0.0 1.5707963267948966 +asinh0013 asinh -0.0 -1.0 -> -0.0 -1.5707963267948966 + +-- values along both sides of imaginary axis +asinh0020 asinh 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324 +asinh0021 asinh -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324 +asinh0022 asinh 0.0 -1e-305 -> 0.0 -1e-305 +asinh0023 asinh -0.0 -1e-305 -> -0.0 -1e-305 +asinh0024 asinh 0.0 -1e-150 -> 0.0 -1e-150 +asinh0025 asinh -0.0 -1e-150 -> -0.0 -1e-150 +asinh0026 asinh 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17 +asinh0027 asinh -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17 +asinh0028 asinh 0.0 -0.001 -> 0.0 -0.0010000001666667416 +asinh0029 asinh -0.0 -0.001 -> -0.0 -0.0010000001666667416 +asinh0030 asinh 0.0 -0.57899999999999996 -> 0.0 -0.61750165481717001 +asinh0031 asinh -0.0 -0.57899999999999996 -> -0.0 -0.61750165481717001 +asinh0032 asinh 0.0 -0.99999999999999989 -> 0.0 -1.5707963118937354 +asinh0033 asinh -0.0 -0.99999999999999989 -> -0.0 -1.5707963118937354 +asinh0034 asinh 0.0 -1.0000000000000002 -> 2.1073424255447014e-08 -1.5707963267948966 +asinh0035 asinh -0.0 -1.0000000000000002 -> -2.1073424255447014e-08 -1.5707963267948966 +asinh0036 asinh 0.0 -1.0009999999999999 -> 0.044717633608306849 -1.5707963267948966 +asinh0037 asinh -0.0 -1.0009999999999999 -> -0.044717633608306849 -1.5707963267948966 +asinh0038 asinh 0.0 -2.0 -> 1.3169578969248168 -1.5707963267948966 +asinh0039 asinh -0.0 -2.0 -> -1.3169578969248168 -1.5707963267948966 +asinh0040 asinh 0.0 -20.0 -> 3.6882538673612966 -1.5707963267948966 +asinh0041 asinh -0.0 -20.0 -> -3.6882538673612966 -1.5707963267948966 +asinh0042 asinh 0.0 -10000000000000000.0 -> 37.534508668464674 -1.5707963267948966 +asinh0043 asinh -0.0 -10000000000000000.0 -> -37.534508668464674 -1.5707963267948966 +asinh0044 asinh 0.0 -9.9999999999999998e+149 -> 346.08091112966679 -1.5707963267948966 +asinh0045 asinh -0.0 -9.9999999999999998e+149 -> -346.08091112966679 -1.5707963267948966 +asinh0046 asinh 0.0 -1.0000000000000001e+299 -> 689.16608998577965 -1.5707963267948966 +asinh0047 asinh -0.0 -1.0000000000000001e+299 -> -689.16608998577965 -1.5707963267948966 +asinh0048 asinh 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324 +asinh0049 asinh -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324 +asinh0050 asinh 0.0 1e-305 -> 0.0 1e-305 +asinh0051 asinh -0.0 1e-305 -> -0.0 1e-305 +asinh0052 asinh 0.0 1e-150 -> 0.0 1e-150 +asinh0053 asinh -0.0 1e-150 -> -0.0 1e-150 +asinh0054 asinh 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17 +asinh0055 asinh -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17 +asinh0056 asinh 0.0 0.001 -> 0.0 0.0010000001666667416 +asinh0057 asinh -0.0 0.001 -> -0.0 0.0010000001666667416 +asinh0058 asinh 0.0 0.57899999999999996 -> 0.0 0.61750165481717001 +asinh0059 asinh -0.0 0.57899999999999996 -> -0.0 0.61750165481717001 +asinh0060 asinh 0.0 0.99999999999999989 -> 0.0 1.5707963118937354 +asinh0061 asinh -0.0 0.99999999999999989 -> -0.0 1.5707963118937354 +asinh0062 asinh 0.0 1.0000000000000002 -> 2.1073424255447014e-08 1.5707963267948966 +asinh0063 asinh -0.0 1.0000000000000002 -> -2.1073424255447014e-08 1.5707963267948966 +asinh0064 asinh 0.0 1.0009999999999999 -> 0.044717633608306849 1.5707963267948966 +asinh0065 asinh -0.0 1.0009999999999999 -> -0.044717633608306849 1.5707963267948966 +asinh0066 asinh 0.0 2.0 -> 1.3169578969248168 1.5707963267948966 +asinh0067 asinh -0.0 2.0 -> -1.3169578969248168 1.5707963267948966 +asinh0068 asinh 0.0 20.0 -> 3.6882538673612966 1.5707963267948966 +asinh0069 asinh -0.0 20.0 -> -3.6882538673612966 1.5707963267948966 +asinh0070 asinh 0.0 10000000000000000.0 -> 37.534508668464674 1.5707963267948966 +asinh0071 asinh -0.0 10000000000000000.0 -> -37.534508668464674 1.5707963267948966 +asinh0072 asinh 0.0 9.9999999999999998e+149 -> 346.08091112966679 1.5707963267948966 +asinh0073 asinh -0.0 9.9999999999999998e+149 -> -346.08091112966679 1.5707963267948966 +asinh0074 asinh 0.0 1.0000000000000001e+299 -> 689.16608998577965 1.5707963267948966 +asinh0075 asinh -0.0 1.0000000000000001e+299 -> -689.16608998577965 1.5707963267948966 + +-- random inputs +asinh0100 asinh -0.5946402853710423 -0.044506548910000145 -> -0.56459775392653022 -0.038256221441536356 +asinh0101 asinh -0.19353958046180916 -0.017489624793193454 -> -0.19237926804196651 -0.017171741895336792 +asinh0102 asinh -0.033117585138955893 -8.5256414015933757 -> -2.8327758348650969 -1.5668848791092411 +asinh0103 asinh -1.5184043184035716 -0.73491245339073275 -> -1.2715891419764005 -0.39204624408542355 +asinh0104 asinh -0.60716120271208818 -0.28900743958436542 -> -0.59119299421187232 -0.24745931678118135 +asinh0105 asinh -0.0237177865112429 2.8832601052166313 -> -1.7205820772413236 1.5620261702963094 +asinh0106 asinh -2.3906812342743979 2.6349216848574013 -> -1.9609636249445124 0.8142142660574706 +asinh0107 asinh -0.0027605019787620517 183.85588476550555 -> -5.9072920005445066 1.5707813120847871 +asinh0108 asinh -0.99083661164404713 0.028006797051617648 -> -0.8750185251283995 0.019894099615994653 +asinh0109 asinh -3.0362951937986393 0.86377266758504867 -> -1.8636030714685221 0.26475058859950168 +asinh0110 asinh 0.34438464536152769 -0.71603790174885029 -> 0.43985415690734164 -0.71015037409294324 +asinh0111 asinh 4.4925124413876256 -60604595352.871613 -> 25.520783738612078 -1.5707963267207683 +asinh0112 asinh 2.3213991428170337 -7.5459667007307258 -> 2.7560464993451643 -1.270073210856117 +asinh0113 asinh 0.21291939741682028 -1.2720428814784408 -> 0.77275088137338266 -1.3182099250896895 +asinh0114 asinh 6.6447359379455957 -0.97196191666946996 -> 2.602830695139672 -0.14368247412319965 +asinh0115 asinh 7.1326256655083746 2.1516360452706857 -> 2.7051146374367212 0.29051701669727581 +asinh0116 asinh 0.18846550905063442 3.4705348585339832 -> 1.917697875799296 1.514155593347924 +asinh0117 asinh 0.19065075303281598 0.26216814548222012 -> 0.19603050785932474 0.26013422809614117 +asinh0118 asinh 2.0242004665739719 0.70510281647495787 -> 1.4970366212896002 0.30526007200481453 +asinh0119 asinh 37.336596461576057 717.29157391678234 -> 7.269981997945294 1.5187910219576033 + +-- values near infinity +asinh0200 asinh 1.0760517500874541e+308 1.1497786241240167e+308 -> 710.34346055651815 0.81850936961793475 +asinh0201 asinh 1.1784839328845529e+308 -1.6478429586716638e+308 -> 710.59536255783678 -0.94996311735607697 +asinh0202 asinh -4.8777682248909193e+307 1.4103736217538474e+308 -> -710.28970147376992 1.2378239519096443 +asinh0203 asinh -1.2832478903233108e+308 -1.5732392613155698e+308 -> -710.59750164290745 -0.88657181439322452 +asinh0204 asinh 0.0 6.8431383856345372e+307 -> 709.51001718444604 1.5707963267948966 +asinh0205 asinh -0.0 8.601822432238051e+307 -> -709.73874482126689 1.5707963267948966 +asinh0206 asinh 0.0 -5.5698396067303782e+307 -> 709.30413698733742 -1.5707963267948966 +asinh0207 asinh -0.0 -7.1507777734621804e+307 -> -709.55399186002705 -1.5707963267948966 +asinh0208 asinh 1.6025136110019349e+308 0.0 -> 710.3609292261076 0.0 +asinh0209 asinh 1.3927819858239114e+308 -0.0 -> 710.22065899832899 -0.0 +asinh0210 asinh -6.0442994056210995e+307 0.0 -> -709.38588631057621 0.0 +asinh0211 asinh -1.2775271979042634e+308 -0.0 -> -710.13428215553972 -0.0 +asinh0212 asinh 1.0687496260268489e+308 1.0255615699476961 -> 709.95584521407841 9.5959010882679093e-309 +asinh0213 asinh 1.0050967333370962e+308 -0.87668970117333433 -> 709.89443961168183 -8.7224410556242882e-309 +asinh0214 asinh -5.7161452814862392e+307 8.2377808413450122 -> -709.33006540611166 1.4411426644501116e-307 +asinh0215 asinh -8.2009040727653315e+307 -6.407409526654976 -> -709.69101513070109 -7.8130526461510088e-308 +asinh0216 asinh 6.4239368496483982 1.6365990821551427e+308 -> 710.38197618101287 1.5707963267948966 +asinh0217 asinh 5.4729111423315882 -1.1227237438144211e+308 -> 710.00511346983546 -1.5707963267948966 +asinh0218 asinh -8.3455818297412723 1.443172020182019e+308 -> -710.25619930551818 1.5707963267948966 +asinh0219 asinh -2.6049726230372441 -1.7952291144022702e+308 -> -710.47448847685644 -1.5707963267948966 + +-- values near 0 +asinh0220 asinh 1.2940113339664088e-314 6.9169190417774516e-323 -> 1.2940113339664088e-314 6.9169190417774516e-323 +asinh0221 asinh 2.3848478863874649e-315 -3.1907655025717717e-310 -> 2.3848478863874649e-315 -3.1907655025717717e-310 +asinh0222 asinh -3.0097643679641622e-316 4.6936236354918422e-322 -> -3.0097643679641622e-316 4.6936236354918422e-322 +asinh0223 asinh -1.787997087755751e-308 -8.5619622834902341e-310 -> -1.787997087755751e-308 -8.5619622834902341e-310 +asinh0224 asinh 0.0 1.2491433448427325e-314 -> 0.0 1.2491433448427325e-314 +asinh0225 asinh -0.0 2.5024072154538062e-308 -> -0.0 2.5024072154538062e-308 +asinh0226 asinh 0.0 -2.9643938750474793e-323 -> 0.0 -2.9643938750474793e-323 +asinh0227 asinh -0.0 -2.9396905927554169e-320 -> -0.0 -2.9396905927554169e-320 +asinh0228 asinh 5.64042930029359e-317 0.0 -> 5.64042930029359e-317 0.0 +asinh0229 asinh 3.3833911866596068e-318 -0.0 -> 3.3833911866596068e-318 -0.0 +asinh0230 asinh -4.9406564584124654e-324 0.0 -> -4.9406564584124654e-324 0.0 +asinh0231 asinh -2.2211379227994845e-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 ignore-real-sign +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 ignore-real-sign +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 +atan0002 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 +atan0011 atan -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324 +atan0012 atan 0.0 -1e-305 -> 0.0 -1e-305 +atan0013 atan -0.0 -1e-305 -> -0.0 -1e-305 +atan0014 atan 0.0 -1e-150 -> 0.0 -1e-150 +atan0015 atan -0.0 -1e-150 -> -0.0 -1e-150 +atan0016 atan 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17 +atan0017 atan -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17 +atan0018 atan 0.0 -0.001 -> 0.0 -0.0010000003333335333 +atan0019 atan -0.0 -0.001 -> -0.0 -0.0010000003333335333 +atan0020 atan 0.0 -0.57899999999999996 -> 0.0 -0.6609570902866303 +atan0021 atan -0.0 -0.57899999999999996 -> -0.0 -0.6609570902866303 +atan0022 atan 0.0 -0.99999999999999989 -> 0.0 -18.714973875118524 +atan0023 atan -0.0 -0.99999999999999989 -> -0.0 -18.714973875118524 +atan0024 atan 0.0 -1.0000000000000002 -> 1.5707963267948966 -18.36840028483855 +atan0025 atan -0.0 -1.0000000000000002 -> -1.5707963267948966 -18.36840028483855 +atan0026 atan 0.0 -1.0009999999999999 -> 1.5707963267948966 -3.8007011672919218 +atan0027 atan -0.0 -1.0009999999999999 -> -1.5707963267948966 -3.8007011672919218 +atan0028 atan 0.0 -2.0 -> 1.5707963267948966 -0.54930614433405489 +atan0029 atan -0.0 -2.0 -> -1.5707963267948966 -0.54930614433405489 +atan0030 atan 0.0 -20.0 -> 1.5707963267948966 -0.050041729278491265 +atan0031 atan -0.0 -20.0 -> -1.5707963267948966 -0.050041729278491265 +atan0032 atan 0.0 -10000000000000000.0 -> 1.5707963267948966 -9.9999999999999998e-17 +atan0033 atan -0.0 -10000000000000000.0 -> -1.5707963267948966 -9.9999999999999998e-17 +atan0034 atan 0.0 -9.9999999999999998e+149 -> 1.5707963267948966 -1e-150 +atan0035 atan -0.0 -9.9999999999999998e+149 -> -1.5707963267948966 -1e-150 +atan0036 atan 0.0 -1.0000000000000001e+299 -> 1.5707963267948966 -9.9999999999999999e-300 +atan0037 atan -0.0 -1.0000000000000001e+299 -> -1.5707963267948966 -9.9999999999999999e-300 +atan0038 atan 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324 +atan0039 atan -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324 +atan0040 atan 0.0 1e-305 -> 0.0 1e-305 +atan0041 atan -0.0 1e-305 -> -0.0 1e-305 +atan0042 atan 0.0 1e-150 -> 0.0 1e-150 +atan0043 atan -0.0 1e-150 -> -0.0 1e-150 +atan0044 atan 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17 +atan0045 atan -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17 +atan0046 atan 0.0 0.001 -> 0.0 0.0010000003333335333 +atan0047 atan -0.0 0.001 -> -0.0 0.0010000003333335333 +atan0048 atan 0.0 0.57899999999999996 -> 0.0 0.6609570902866303 +atan0049 atan -0.0 0.57899999999999996 -> -0.0 0.6609570902866303 +atan0050 atan 0.0 0.99999999999999989 -> 0.0 18.714973875118524 +atan0051 atan -0.0 0.99999999999999989 -> -0.0 18.714973875118524 +atan0052 atan 0.0 1.0000000000000002 -> 1.5707963267948966 18.36840028483855 +atan0053 atan -0.0 1.0000000000000002 -> -1.5707963267948966 18.36840028483855 +atan0054 atan 0.0 1.0009999999999999 -> 1.5707963267948966 3.8007011672919218 +atan0055 atan -0.0 1.0009999999999999 -> -1.5707963267948966 3.8007011672919218 +atan0056 atan 0.0 2.0 -> 1.5707963267948966 0.54930614433405489 +atan0057 atan -0.0 2.0 -> -1.5707963267948966 0.54930614433405489 +atan0058 atan 0.0 20.0 -> 1.5707963267948966 0.050041729278491265 +atan0059 atan -0.0 20.0 -> -1.5707963267948966 0.050041729278491265 +atan0060 atan 0.0 10000000000000000.0 -> 1.5707963267948966 9.9999999999999998e-17 +atan0061 atan -0.0 10000000000000000.0 -> -1.5707963267948966 9.9999999999999998e-17 +atan0062 atan 0.0 9.9999999999999998e+149 -> 1.5707963267948966 1e-150 +atan0063 atan -0.0 9.9999999999999998e+149 -> -1.5707963267948966 1e-150 +atan0064 atan 0.0 1.0000000000000001e+299 -> 1.5707963267948966 9.9999999999999999e-300 +atan0065 atan -0.0 1.0000000000000001e+299 -> -1.5707963267948966 9.9999999999999999e-300 + +-- random inputs +atan0100 atan -0.32538873661060214 -1.5530461550412578 -> -1.3682728427554227 -0.69451401598762041 +atan0101 atan -0.45863393495197929 -4799.1747094903594 -> -1.5707963068820623 -0.00020836916050636145 +atan0102 atan -8.3006999685976162 -2.6788890251790938 -> -1.4619862771810199 -0.034811669653327826 +atan0103 atan -1.8836307682985314 -1.1441976638861771 -> -1.1839984370871612 -0.20630956157312796 +atan0104 atan -0.00063230482407491669 -4.9312520961829485 -> -1.5707692093223147 -0.20563867743008304 +atan0105 atan -0.84278137150065946 179012.37493146997 -> -1.5707963267685969 5.5862059836425272e-06 +atan0106 atan -0.95487853984049287 14.311334539886177 -> -1.5661322859434561 0.069676024526232005 +atan0107 atan -1.3513252539663239 6.0500727021632198e-08 -> -0.93371676315220975 2.140800269742656e-08 +atan0108 atan -0.20566254458595795 0.11933771944159823 -> -0.20556463711174916 0.11493405387141732 +atan0109 atan -0.58563718795408559 0.64438965423212868 -> -0.68361089300233124 0.46759762751800249 +atan0110 atan 48.479267751948292 -78.386382460112543 -> 1.5650888770910523 -0.0092276811373297584 +atan0111 atan 1.0575373914056061 -0.75988012377296987 -> 0.94430886722043594 -0.31915698126703118 +atan0112 atan 4444810.4314677203 -0.56553404593942558 -> 1.5707961018134231 -2.8625446437701909e-14 +atan0113 atan 0.010101405082520009 -0.032932668550282478 -> 0.01011202676646334 -0.032941214776834996 +atan0114 atan 1.5353585300154911 -2.1947099346796519 -> 1.3400310739206394 -0.29996003607449045 +atan0115 atan 0.21869457055670882 9.9915684254007093 -> 1.5685846078876444 0.1003716881759439 +atan0116 atan 0.17783290150246836 0.064334689863650957 -> 0.17668728064286277 0.062435808728873846 +atan0117 atan 15.757474087615918 383.57262142534 -> 1.5706894060369621 0.0026026817278826603 +atan0118 atan 10.587017408533317 0.21720238081843438 -> 1.4766594681336236 0.0019199097383010061 +atan0119 atan 0.86026078678781204 0.1230148609359502 -> 0.7147259322534929 0.070551221954286605 + +-- values near infinity +atan0200 atan 7.8764397011195798e+307 8.1647921137746308e+307 -> 1.5707963267948966 6.3439446939604493e-309 +atan0201 atan 1.5873698696131487e+308 -1.0780367422960641e+308 -> 1.5707963267948966 -2.9279309368530781e-309 +atan0202 atan -1.5844551864825834e+308 1.0290657809098675e+308 -> -1.5707963267948966 2.8829614736961417e-309 +atan0203 atan -1.3168792562524032e+308 -9.088432341614825e+307 -> -1.5707963267948966 -3.5499373057390056e-309 +atan0204 atan 0.0 1.0360465742258337e+308 -> 1.5707963267948966 9.6520757355646018e-309 +atan0205 atan -0.0 1.0045063210373196e+308 -> -1.5707963267948966 9.955138947929503e-309 +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 +atan0210 atan -1.0631786461936417e+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 +atan0215 atan -1.399172518147259e+308 -3.5687766472913673 -> -1.5707963267948966 -0.0 +atan0216 atan 8.1252833070803021 6.2782953917343822e+307 -> 1.5707963267948966 1.5927890256908564e-308 +atan0217 atan 2.8034285947515167 -1.3378049775753878e+308 -> 1.5707963267948966 -7.4749310756219562e-309 +atan0218 atan -1.4073509988974953 1.6776381785968355e+308 -> -1.5707963267948966 5.9607608646364569e-309 +atan0219 atan -2.7135551527592119 -1.281567445525738e+308 -> -1.5707963267948966 -7.8029447727565326e-309 + +-- imaginary part = +/-1, real part tiny +atan0300 atan -1e-150 -1.0 -> -0.78539816339744828 -173.04045556483339 +atan0301 atan 1e-155 1.0 -> 0.78539816339744828 178.79691829731851 +atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.55338102980363 +atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875 +atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692 + +-- special values +atan1000 atan -0.0 0.0 -> -0.0 0.0 +atan1001 atan nan 0.0 -> nan 0.0 +atan1002 atan -0.0 1.0 -> -0.0 inf divide-by-zero +atan1003 atan -inf 0.0 -> -1.5707963267948966 0.0 +atan1004 atan -inf 2.2999999999999998 -> -1.5707963267948966 0.0 +atan1005 atan nan 2.2999999999999998 -> nan nan +atan1006 atan -0.0 inf -> -1.5707963267948966 0.0 +atan1007 atan -2.2999999999999998 inf -> -1.5707963267948966 0.0 +atan1008 atan -inf inf -> -1.5707963267948966 0.0 +atan1009 atan nan inf -> nan 0.0 +atan1010 atan -0.0 nan -> nan nan +atan1011 atan -2.2999999999999998 nan -> nan nan +atan1012 atan -inf nan -> -1.5707963267948966 0.0 ignore-imag-sign +atan1013 atan nan nan -> nan nan +atan1014 atan 0.0 0.0 -> 0.0 0.0 +atan1015 atan 0.0 1.0 -> 0.0 inf divide-by-zero +atan1016 atan inf 0.0 -> 1.5707963267948966 0.0 +atan1017 atan inf 2.2999999999999998 -> 1.5707963267948966 0.0 +atan1018 atan 0.0 inf -> 1.5707963267948966 0.0 +atan1019 atan 2.2999999999999998 inf -> 1.5707963267948966 0.0 +atan1020 atan inf inf -> 1.5707963267948966 0.0 +atan1021 atan 0.0 nan -> nan nan +atan1022 atan 2.2999999999999998 nan -> nan nan +atan1023 atan inf nan -> 1.5707963267948966 0.0 ignore-imag-sign +atan1024 atan 0.0 -0.0 -> 0.0 -0.0 +atan1025 atan nan -0.0 -> nan -0.0 +atan1026 atan 0.0 -1.0 -> 0.0 -inf divide-by-zero +atan1027 atan inf -0.0 -> 1.5707963267948966 -0.0 +atan1028 atan inf -2.2999999999999998 -> 1.5707963267948966 -0.0 +atan1029 atan nan -2.2999999999999998 -> nan nan +atan1030 atan 0.0 -inf -> 1.5707963267948966 -0.0 +atan1031 atan 2.2999999999999998 -inf -> 1.5707963267948966 -0.0 +atan1032 atan inf -inf -> 1.5707963267948966 -0.0 +atan1033 atan nan -inf -> nan -0.0 +atan1034 atan -0.0 -0.0 -> -0.0 -0.0 +atan1035 atan -0.0 -1.0 -> -0.0 -inf divide-by-zero +atan1036 atan -inf -0.0 -> -1.5707963267948966 -0.0 +atan1037 atan -inf -2.2999999999999998 -> -1.5707963267948966 -0.0 +atan1038 atan -0.0 -inf -> -1.5707963267948966 -0.0 +atan1039 atan -2.2999999999999998 -inf -> -1.5707963267948966 -0.0 +atan1040 atan -inf -inf -> -1.5707963267948966 -0.0 + + +--------------------------------------- +-- atanh: Inverse hyperbolic tangent -- +--------------------------------------- + +-- 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 + +-- values along both sides of real axis +atanh0010 atanh -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0 +atanh0011 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0 +atanh0012 atanh -1e-305 0.0 -> -1e-305 0.0 +atanh0013 atanh -1e-305 -0.0 -> -1e-305 -0.0 +atanh0014 atanh -1e-150 0.0 -> -1e-150 0.0 +atanh0015 atanh -1e-150 -0.0 -> -1e-150 -0.0 +atanh0016 atanh -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0 +atanh0017 atanh -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0 +atanh0018 atanh -0.001 0.0 -> -0.0010000003333335333 0.0 +atanh0019 atanh -0.001 -0.0 -> -0.0010000003333335333 -0.0 +atanh0020 atanh -0.57899999999999996 0.0 -> -0.6609570902866303 0.0 +atanh0021 atanh -0.57899999999999996 -0.0 -> -0.6609570902866303 -0.0 +atanh0022 atanh -0.99999999999999989 0.0 -> -18.714973875118524 0.0 +atanh0023 atanh -0.99999999999999989 -0.0 -> -18.714973875118524 -0.0 +atanh0024 atanh -1.0000000000000002 0.0 -> -18.36840028483855 1.5707963267948966 +atanh0025 atanh -1.0000000000000002 -0.0 -> -18.36840028483855 -1.5707963267948966 +atanh0026 atanh -1.0009999999999999 0.0 -> -3.8007011672919218 1.5707963267948966 +atanh0027 atanh -1.0009999999999999 -0.0 -> -3.8007011672919218 -1.5707963267948966 +atanh0028 atanh -2.0 0.0 -> -0.54930614433405489 1.5707963267948966 +atanh0029 atanh -2.0 -0.0 -> -0.54930614433405489 -1.5707963267948966 +atanh0030 atanh -23.0 0.0 -> -0.043505688494814884 1.5707963267948966 +atanh0031 atanh -23.0 -0.0 -> -0.043505688494814884 -1.5707963267948966 +atanh0032 atanh -10000000000000000.0 0.0 -> -9.9999999999999998e-17 1.5707963267948966 +atanh0033 atanh -10000000000000000.0 -0.0 -> -9.9999999999999998e-17 -1.5707963267948966 +atanh0034 atanh -9.9999999999999998e+149 0.0 -> -1e-150 1.5707963267948966 +atanh0035 atanh -9.9999999999999998e+149 -0.0 -> -1e-150 -1.5707963267948966 +atanh0036 atanh -1.0000000000000001e+299 0.0 -> -9.9999999999999999e-300 1.5707963267948966 +atanh0037 atanh -1.0000000000000001e+299 -0.0 -> -9.9999999999999999e-300 -1.5707963267948966 +atanh0038 atanh 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0 +atanh0039 atanh 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0 +atanh0040 atanh 1e-305 0.0 -> 1e-305 0.0 +atanh0041 atanh 1e-305 -0.0 -> 1e-305 -0.0 +atanh0042 atanh 1e-150 0.0 -> 1e-150 0.0 +atanh0043 atanh 1e-150 -0.0 -> 1e-150 -0.0 +atanh0044 atanh 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0 +atanh0045 atanh 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0 +atanh0046 atanh 0.001 0.0 -> 0.0010000003333335333 0.0 +atanh0047 atanh 0.001 -0.0 -> 0.0010000003333335333 -0.0 +atanh0048 atanh 0.57899999999999996 0.0 -> 0.6609570902866303 0.0 +atanh0049 atanh 0.57899999999999996 -0.0 -> 0.6609570902866303 -0.0 +atanh0050 atanh 0.99999999999999989 0.0 -> 18.714973875118524 0.0 +atanh0051 atanh 0.99999999999999989 -0.0 -> 18.714973875118524 -0.0 +atanh0052 atanh 1.0000000000000002 0.0 -> 18.36840028483855 1.5707963267948966 +atanh0053 atanh 1.0000000000000002 -0.0 -> 18.36840028483855 -1.5707963267948966 +atanh0054 atanh 1.0009999999999999 0.0 -> 3.8007011672919218 1.5707963267948966 +atanh0055 atanh 1.0009999999999999 -0.0 -> 3.8007011672919218 -1.5707963267948966 +atanh0056 atanh 2.0 0.0 -> 0.54930614433405489 1.5707963267948966 +atanh0057 atanh 2.0 -0.0 -> 0.54930614433405489 -1.5707963267948966 +atanh0058 atanh 23.0 0.0 -> 0.043505688494814884 1.5707963267948966 +atanh0059 atanh 23.0 -0.0 -> 0.043505688494814884 -1.5707963267948966 +atanh0060 atanh 10000000000000000.0 0.0 -> 9.9999999999999998e-17 1.5707963267948966 +atanh0061 atanh 10000000000000000.0 -0.0 -> 9.9999999999999998e-17 -1.5707963267948966 +atanh0062 atanh 9.9999999999999998e+149 0.0 -> 1e-150 1.5707963267948966 +atanh0063 atanh 9.9999999999999998e+149 -0.0 -> 1e-150 -1.5707963267948966 +atanh0064 atanh 1.0000000000000001e+299 0.0 -> 9.9999999999999999e-300 1.5707963267948966 +atanh0065 atanh 1.0000000000000001e+299 -0.0 -> 9.9999999999999999e-300 -1.5707963267948966 + +-- random inputs +atanh0100 atanh -0.54460925980633501 -0.54038050126721027 -> -0.41984265808446974 -0.60354153938352828 +atanh0101 atanh -1.6934614269829051 -0.48807386108113621 -> -0.58592769102243281 -1.3537837470975898 +atanh0102 atanh -1.3467293985501207 -0.47868354895395876 -> -0.69961624370709985 -1.1994450156570076 +atanh0103 atanh -5.6142232418984888 -544551613.39307702 -> -1.8932657550925744e-17 -1.5707963249585235 +atanh0104 atanh -0.011841460381263651 -3.259978899823385 -> -0.0010183936547405188 -1.2731614020743838 +atanh0105 atanh -0.0073345736950029532 0.35821949670922248 -> -0.0065004869024682466 0.34399359971920895 +atanh0106 atanh -13.866782244320014 0.9541129545860273 -> -0.071896852055058899 1.5658322704631409 +atanh0107 atanh -708.59964982780775 21.984802159266675 -> -0.0014098779074189741 1.5707525842838959 +atanh0108 atanh -30.916832076030602 1.3691897138829843 -> -0.032292682045743676 1.5693652094847115 +atanh0109 atanh -0.57461806339861754 0.29534797443913063 -> -0.56467464472482765 0.39615612824172625 +atanh0110 atanh 0.40089246737415685 -1.632285984300659 -> 0.1063832707890608 -1.0402821335326482 +atanh0111 atanh 2119.6167688262176 -1.5383653437377242e+17 -> 8.9565008518382049e-32 -1.5707963267948966 +atanh0112 atanh 756.86017850941641 -6.6064087133223817 -> 0.0013211481136820046 -1.5707847948702234 +atanh0113 atanh 4.0490617718041602 -2.5784456791040652e-12 -> 0.25218425538553618 -1.5707963267947291 +atanh0114 atanh 10.589254957173523 -0.13956391149624509 -> 0.094700890282197664 -1.5695407140217623 +atanh0115 atanh 1.0171187553160499 0.70766113465354019 -> 0.55260251975367791 0.96619711116641682 +atanh0116 atanh 0.031645502527750849 0.067319983726544394 -> 0.031513018344086742 0.067285437670549036 +atanh0117 atanh 0.13670177624994517 0.43240089361857947 -> 0.11538933151017253 0.41392008145336212 +atanh0118 atanh 0.64173899243596688 2.9008577686695256 -> 0.065680142424134405 1.2518535724053921 +atanh0119 atanh 0.19313813528025942 38.799619150741869 -> 0.00012820765917366644 1.5450292202823612 + +-- values near infinity +atanh0200 atanh 5.3242646831347954e+307 1.3740396080084153e+308 -> 2.4519253616695576e-309 1.5707963267948966 +atanh0201 atanh 1.158701641241358e+308 -6.5579268873375853e+307 -> 6.5365375267795098e-309 -1.5707963267948966 +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 +atanh0206 atanh 0.0 -7.4970613060311453e+307 -> 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 +atanh0211 atanh -1.0616427760154426e+308 -0.0 -> -9.4193642399489563e-309 -1.5707963267948966 +atanh0212 atanh 1.2971536510180682e+308 5.2847948452333293 -> 7.7091869510998328e-309 1.5707963267948966 +atanh0213 atanh 1.1849860977411851e+308 -7.9781906447459949 -> 8.4389175696339014e-309 -1.5707963267948966 +atanh0214 atanh -1.4029969422586635e+308 0.93891986543663375 -> -7.127599283218073e-309 1.5707963267948966 +atanh0215 atanh -4.7508098912248211e+307 -8.2702421247039908 -> -2.1049042645278043e-308 -1.5707963267948966 +atanh0216 atanh 8.2680742115769998 8.1153898410918065e+307 -> 0.0 1.5707963267948966 +atanh0217 atanh 1.2575325146218885 -1.4746679147661649e+308 -> 0.0 -1.5707963267948966 +atanh0218 atanh -2.4618803682310899 1.3781522717005568e+308 -> -0.0 1.5707963267948966 +atanh0219 atanh -4.0952386694788112 -1.231083376353703e+308 -> -0.0 -1.5707963267948966 + +-- values near 0 +atanh0220 atanh 3.8017563659811628e-314 2.6635484239074319e-312 -> 3.8017563659811628e-314 2.6635484239074319e-312 +atanh0221 atanh 1.7391110733611878e-321 -4.3547800672541419e-313 -> 1.7391110733611878e-321 -4.3547800672541419e-313 +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 +atanh0226 atanh 0.0 -2.4222487249468377e-317 -> 0.0 -2.4222487249468377e-317 +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 +atanh0231 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0 + +-- real part = +/-1, imaginary part tiny +atanh0300 atanh 1.0 1e-153 -> 176.49433320432448 0.78539816339744828 +atanh0301 atanh 1.0 9.9999999999999997e-155 -> 177.64562575082149 0.78539816339744828 +atanh0302 atanh -1.0 1e-161 -> -185.70467357630065 0.78539816339744828 +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 ignore-real-sign +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 ignore-real-sign +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 -- +---------------------------- + +log0000 log 1.0 0.0 -> 0.0 0.0 +log0001 log 1.0 -0.0 -> 0.0 -0.0 +log0002 log -1.0 0.0 -> 0.0 3.1415926535897931 +log0003 log -1.0 -0.0 -> 0.0 -3.1415926535897931 +-- values along both sides of real axis +log0010 log -9.8813129168249309e-324 0.0 -> -743.74692474082133 3.1415926535897931 +log0011 log -9.8813129168249309e-324 -0.0 -> -743.74692474082133 -3.1415926535897931 +log0012 log -1e-305 0.0 -> -702.28845336318398 3.1415926535897931 +log0013 log -1e-305 -0.0 -> -702.28845336318398 -3.1415926535897931 +log0014 log -1e-150 0.0 -> -345.38776394910684 3.1415926535897931 +log0015 log -1e-150 -0.0 -> -345.38776394910684 -3.1415926535897931 +log0016 log -9.9999999999999998e-17 0.0 -> -36.841361487904734 3.1415926535897931 +log0017 log -9.9999999999999998e-17 -0.0 -> -36.841361487904734 -3.1415926535897931 +log0018 log -0.001 0.0 -> -6.9077552789821368 3.1415926535897931 +log0019 log -0.001 -0.0 -> -6.9077552789821368 -3.1415926535897931 +log0020 log -0.57899999999999996 0.0 -> -0.54645280140914188 3.1415926535897931 +log0021 log -0.57899999999999996 -0.0 -> -0.54645280140914188 -3.1415926535897931 +log0022 log -0.99999999999999989 0.0 -> -1.1102230246251565e-16 3.1415926535897931 +log0023 log -0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -3.1415926535897931 +log0024 log -1.0000000000000002 0.0 -> 2.2204460492503128e-16 3.1415926535897931 +log0025 log -1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -3.1415926535897931 +log0026 log -1.0009999999999999 0.0 -> 0.00099950033308342321 3.1415926535897931 +log0027 log -1.0009999999999999 -0.0 -> 0.00099950033308342321 -3.1415926535897931 +log0028 log -2.0 0.0 -> 0.69314718055994529 3.1415926535897931 +log0029 log -2.0 -0.0 -> 0.69314718055994529 -3.1415926535897931 +log0030 log -23.0 0.0 -> 3.1354942159291497 3.1415926535897931 +log0031 log -23.0 -0.0 -> 3.1354942159291497 -3.1415926535897931 +log0032 log -10000000000000000.0 0.0 -> 36.841361487904734 3.1415926535897931 +log0033 log -10000000000000000.0 -0.0 -> 36.841361487904734 -3.1415926535897931 +log0034 log -9.9999999999999998e+149 0.0 -> 345.38776394910684 3.1415926535897931 +log0035 log -9.9999999999999998e+149 -0.0 -> 345.38776394910684 -3.1415926535897931 +log0036 log -1.0000000000000001e+299 0.0 -> 688.47294280521965 3.1415926535897931 +log0037 log -1.0000000000000001e+299 -0.0 -> 688.47294280521965 -3.1415926535897931 +log0038 log 9.8813129168249309e-324 0.0 -> -743.74692474082133 0.0 +log0039 log 9.8813129168249309e-324 -0.0 -> -743.74692474082133 -0.0 +log0040 log 1e-305 0.0 -> -702.28845336318398 0.0 +log0041 log 1e-305 -0.0 -> -702.28845336318398 -0.0 +log0042 log 1e-150 0.0 -> -345.38776394910684 0.0 +log0043 log 1e-150 -0.0 -> -345.38776394910684 -0.0 +log0044 log 9.9999999999999998e-17 0.0 -> -36.841361487904734 0.0 +log0045 log 9.9999999999999998e-17 -0.0 -> -36.841361487904734 -0.0 +log0046 log 0.001 0.0 -> -6.9077552789821368 0.0 +log0047 log 0.001 -0.0 -> -6.9077552789821368 -0.0 +log0048 log 0.57899999999999996 0.0 -> -0.54645280140914188 0.0 +log0049 log 0.57899999999999996 -0.0 -> -0.54645280140914188 -0.0 +log0050 log 0.99999999999999989 0.0 -> -1.1102230246251565e-16 0.0 +log0051 log 0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -0.0 +log0052 log 1.0000000000000002 0.0 -> 2.2204460492503128e-16 0.0 +log0053 log 1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -0.0 +log0054 log 1.0009999999999999 0.0 -> 0.00099950033308342321 0.0 +log0055 log 1.0009999999999999 -0.0 -> 0.00099950033308342321 -0.0 +log0056 log 2.0 0.0 -> 0.69314718055994529 0.0 +log0057 log 2.0 -0.0 -> 0.69314718055994529 -0.0 +log0058 log 23.0 0.0 -> 3.1354942159291497 0.0 +log0059 log 23.0 -0.0 -> 3.1354942159291497 -0.0 +log0060 log 10000000000000000.0 0.0 -> 36.841361487904734 0.0 +log0061 log 10000000000000000.0 -0.0 -> 36.841361487904734 -0.0 +log0062 log 9.9999999999999998e+149 0.0 -> 345.38776394910684 0.0 +log0063 log 9.9999999999999998e+149 -0.0 -> 345.38776394910684 -0.0 +log0064 log 1.0000000000000001e+299 0.0 -> 688.47294280521965 0.0 +log0065 log 1.0000000000000001e+299 -0.0 -> 688.47294280521965 -0.0 + +-- random inputs +log0066 log -1.9830454945186191e-16 -2.0334448025673346 -> 0.70973130194329803 -1.5707963267948968 +log0067 log -0.96745853024741857 -0.84995816228299692 -> 0.25292811398722387 -2.4207570438536905 +log0068 log -0.1603644313948418 -0.2929942111041835 -> -1.0965857872427374 -2.0715870859971419 +log0069 log -0.15917913168438699 -0.25238799251132177 -> -1.2093477313249901 -2.1334784232033863 +log0070 log -0.68907818535078802 -3.0693105853476346 -> 1.1460398629184565 -1.7916403813913211 +log0071 log -17.268133447565589 6.8165120014604756 -> 2.9212694465974836 2.7656245081603164 +log0072 log -1.7153894479690328 26.434055372802636 -> 3.2767542953718003 1.6355986276341734 +log0073 log -8.0456794648936578e-06 0.19722758057570208 -> -1.6233969848296075 1.5708371206810101 +log0074 log -2.4306442691323173 0.6846919750700996 -> 0.92633592001969589 2.8670160576718331 +log0075 log -3.5488049250888194 0.45324040643185254 -> 1.2747008374256426 3.0145640007885111 +log0076 log 0.18418516851510189 -0.26062518836212617 -> -1.1421287121940344 -0.95558440841183434 +log0077 log 2.7124837795638399 -13.148769067133387 -> 2.5971659975706802 -1.3673583045209439 +log0078 log 3.6521275476169149e-13 -3.7820543023170673e-05 -> -10.182658136741569 -1.5707963171384316 +log0079 log 5.0877545813862239 -1.2834978326786852 -> 1.6576856213076328 -0.24711583497738485 +log0080 log 0.26477986808461512 -0.67659001194187429 -> -0.31944085207999973 -1.197773671987121 +log0081 log 0.0014754261398071962 5.3514691608205442 -> 1.6773711707153829 1.5705206219261802 +log0082 log 0.29667334462157885 0.00020056045042584795 -> -1.2151233667079588 0.00067603114168689204 +log0083 log 0.82104233671099425 3.9005387130133102 -> 1.3827918965299593 1.3633304701848363 +log0084 log 0.27268135358180667 124.42088110945804 -> 4.8236724223559229 1.5686047258789015 +log0085 log 0.0026286959168267485 0.47795808180573013 -> -0.73821712137809126 1.5652965360960087 + +-- values near infinity +log0100 log 1.0512025744003172e+308 7.2621669750664611e+307 -> 709.44123967814494 0.60455434048332968 +log0101 log 5.5344249034372126e+307 -1.2155859158431275e+308 -> 709.48562300345679 -1.143553056717973 +log0102 log -1.3155575403469408e+308 1.1610793541663864e+308 -> 709.75847809546428 2.41848796504974 +log0103 log -1.632366720973235e+308 -1.54299446211448e+308 -> 710.00545236515586 -2.3843326028455087 +log0104 log 0.0 5.9449276692327712e+307 -> 708.67616191258526 1.5707963267948966 +log0105 log -0.0 1.1201850459025692e+308 -> 709.30970253338171 1.5707963267948966 +log0106 log 0.0 -1.6214225933466528e+308 -> 709.6795125501086 -1.5707963267948966 +log0107 log -0.0 -1.7453269791591058e+308 -> 709.75315056087379 -1.5707963267948966 +log0108 log 1.440860577601428e+308 0.0 -> 709.56144920058262 0.0 +log0109 log 1.391515176148282e+308 -0.0 -> 709.52660185041327 -0.0 +log0110 log -1.201354401295296e+308 0.0 -> 709.37965823023956 3.1415926535897931 +log0111 log -1.6704337825976804e+308 -0.0 -> 709.70929198492399 -3.1415926535897931 +log0112 log 7.2276974655190223e+307 7.94879711369164 -> 708.87154406512104 1.0997689307850458e-307 +log0113 log 1.1207859593716076e+308 -6.1956200868221147 -> 709.31023883080104 -5.5279244310803286e-308 +log0114 log -4.6678933874471045e+307 9.947107893220382 -> 708.43433142431388 3.1415926535897931 +log0115 log -1.5108012453950142e+308 -5.3117197179375619 -> 709.60884877835008 -3.1415926535897931 +log0116 log 7.4903750871504435 1.5320703776626352e+308 -> 709.62282865085137 1.5707963267948966 +log0117 log 5.9760325525654778 -8.0149473997349123e+307 -> 708.97493177248396 -1.5707963267948966 +log0118 log -7.880194206386629 1.7861845814767441e+308 -> 709.77629046837137 1.5707963267948966 +log0119 log -9.886438993852865 -6.19235781080747e+307 -> 708.71693946977302 -1.5707963267948966 + +-- values near 0 +log0120 log 2.2996867579227779e-308 6.7861840770939125e-312 -> -708.36343567717392 0.00029509166223339815 +log0121 log 6.9169190417774516e-323 -9.0414013188948118e-322 -> -739.22766796468386 -1.4944423210001669 +log0122 log -1.5378064962914011e-316 1.8243628389354635e-310 -> -713.20014803142965 1.5707971697228842 +log0123 log -2.3319898483706837e-321 -2.2358763941866371e-313 -> -719.9045008332522 -1.570796337224766 +log0124 log 0.0 3.872770101081121e-315 -> -723.96033425374401 1.5707963267948966 +log0125 log -0.0 9.6342800939043076e-322 -> -739.16707236281752 1.5707963267948966 +log0126 log 0.0 -2.266099393427834e-308 -> -708.37814861757965 -1.5707963267948966 +log0127 log -0.0 -2.1184695673766626e-315 -> -724.56361036731812 -1.5707963267948966 +log0128 log 1.1363509854348671e-322 0.0 -> -741.30457770545206 0.0 +log0129 log 3.5572726500569751e-322 -0.0 -> -740.16340580236522 -0.0 +log0130 log -2.3696071074040593e-310 0.0 -> -712.93865466421641 3.1415926535897931 +log0131 log -2.813283897266934e-317 -0.0 -> -728.88512203138862 -3.1415926535897931 + +-- values near the unit circle +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 + + +------------------------------ +-- log10: Logarithm base 10 -- +------------------------------ + +logt0000 log10 1.0 0.0 -> 0.0 0.0 +logt0001 log10 1.0 -0.0 -> 0.0 -0.0 +logt0002 log10 -1.0 0.0 -> 0.0 1.3643763538418414 +logt0003 log10 -1.0 -0.0 -> 0.0 -1.3643763538418414 +-- values along both sides of real axis +logt0010 log10 -9.8813129168249309e-324 0.0 -> -323.0051853474518 1.3643763538418414 +logt0011 log10 -9.8813129168249309e-324 -0.0 -> -323.0051853474518 -1.3643763538418414 +logt0012 log10 -1e-305 0.0 -> -305.0 1.3643763538418414 +logt0013 log10 -1e-305 -0.0 -> -305.0 -1.3643763538418414 +logt0014 log10 -1e-150 0.0 -> -150.0 1.3643763538418414 +logt0015 log10 -1e-150 -0.0 -> -150.0 -1.3643763538418414 +logt0016 log10 -9.9999999999999998e-17 0.0 -> -16.0 1.3643763538418414 +logt0017 log10 -9.9999999999999998e-17 -0.0 -> -16.0 -1.3643763538418414 +logt0018 log10 -0.001 0.0 -> -3.0 1.3643763538418414 +logt0019 log10 -0.001 -0.0 -> -3.0 -1.3643763538418414 +logt0020 log10 -0.57899999999999996 0.0 -> -0.23732143627256383 1.3643763538418414 +logt0021 log10 -0.57899999999999996 -0.0 -> -0.23732143627256383 -1.3643763538418414 +logt0022 log10 -0.99999999999999989 0.0 -> -4.821637332766436e-17 1.3643763538418414 +logt0023 log10 -0.99999999999999989 -0.0 -> -4.821637332766436e-17 -1.3643763538418414 +logt0024 log10 -1.0000000000000002 0.0 -> 9.6432746655328696e-17 1.3643763538418414 +logt0025 log10 -1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -1.3643763538418414 +logt0026 log10 -1.0009999999999999 0.0 -> 0.0004340774793185929 1.3643763538418414 +logt0027 log10 -1.0009999999999999 -0.0 -> 0.0004340774793185929 -1.3643763538418414 +logt0028 log10 -2.0 0.0 -> 0.3010299956639812 1.3643763538418414 +logt0029 log10 -2.0 -0.0 -> 0.3010299956639812 -1.3643763538418414 +logt0030 log10 -23.0 0.0 -> 1.3617278360175928 1.3643763538418414 +logt0031 log10 -23.0 -0.0 -> 1.3617278360175928 -1.3643763538418414 +logt0032 log10 -10000000000000000.0 0.0 -> 16.0 1.3643763538418414 +logt0033 log10 -10000000000000000.0 -0.0 -> 16.0 -1.3643763538418414 +logt0034 log10 -9.9999999999999998e+149 0.0 -> 150.0 1.3643763538418414 +logt0035 log10 -9.9999999999999998e+149 -0.0 -> 150.0 -1.3643763538418414 +logt0036 log10 -1.0000000000000001e+299 0.0 -> 299.0 1.3643763538418414 +logt0037 log10 -1.0000000000000001e+299 -0.0 -> 299.0 -1.3643763538418414 +logt0038 log10 9.8813129168249309e-324 0.0 -> -323.0051853474518 0.0 +logt0039 log10 9.8813129168249309e-324 -0.0 -> -323.0051853474518 -0.0 +logt0040 log10 1e-305 0.0 -> -305.0 0.0 +logt0041 log10 1e-305 -0.0 -> -305.0 -0.0 +logt0042 log10 1e-150 0.0 -> -150.0 0.0 +logt0043 log10 1e-150 -0.0 -> -150.0 -0.0 +logt0044 log10 9.9999999999999998e-17 0.0 -> -16.0 0.0 +logt0045 log10 9.9999999999999998e-17 -0.0 -> -16.0 -0.0 +logt0046 log10 0.001 0.0 -> -3.0 0.0 +logt0047 log10 0.001 -0.0 -> -3.0 -0.0 +logt0048 log10 0.57899999999999996 0.0 -> -0.23732143627256383 0.0 +logt0049 log10 0.57899999999999996 -0.0 -> -0.23732143627256383 -0.0 +logt0050 log10 0.99999999999999989 0.0 -> -4.821637332766436e-17 0.0 +logt0051 log10 0.99999999999999989 -0.0 -> -4.821637332766436e-17 -0.0 +logt0052 log10 1.0000000000000002 0.0 -> 9.6432746655328696e-17 0.0 +logt0053 log10 1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -0.0 +logt0054 log10 1.0009999999999999 0.0 -> 0.0004340774793185929 0.0 +logt0055 log10 1.0009999999999999 -0.0 -> 0.0004340774793185929 -0.0 +logt0056 log10 2.0 0.0 -> 0.3010299956639812 0.0 +logt0057 log10 2.0 -0.0 -> 0.3010299956639812 -0.0 +logt0058 log10 23.0 0.0 -> 1.3617278360175928 0.0 +logt0059 log10 23.0 -0.0 -> 1.3617278360175928 -0.0 +logt0060 log10 10000000000000000.0 0.0 -> 16.0 0.0 +logt0061 log10 10000000000000000.0 -0.0 -> 16.0 -0.0 +logt0062 log10 9.9999999999999998e+149 0.0 -> 150.0 0.0 +logt0063 log10 9.9999999999999998e+149 -0.0 -> 150.0 -0.0 +logt0064 log10 1.0000000000000001e+299 0.0 -> 299.0 0.0 +logt0065 log10 1.0000000000000001e+299 -0.0 -> 299.0 -0.0 + +-- random inputs +logt0066 log10 -1.9830454945186191e-16 -2.0334448025673346 -> 0.30823238806798503 -0.68218817692092071 +logt0067 log10 -0.96745853024741857 -0.84995816228299692 -> 0.10984528422284802 -1.051321426174086 +logt0068 log10 -0.1603644313948418 -0.2929942111041835 -> -0.47624115633305419 -0.89967884023059597 +logt0069 log10 -0.15917913168438699 -0.25238799251132177 -> -0.52521304641665956 -0.92655790645688119 +logt0070 log10 -0.68907818535078802 -3.0693105853476346 -> 0.4977187885066448 -0.77809953119328823 +logt0071 log10 -17.268133447565589 6.8165120014604756 -> 1.2686912008098534 1.2010954629104202 +logt0072 log10 -1.7153894479690328 26.434055372802636 -> 1.423076309032751 0.71033145859005309 +logt0073 log10 -8.0456794648936578e-06 0.19722758057570208 -> -0.70503235244987561 0.68220589348055516 +logt0074 log10 -2.4306442691323173 0.6846919750700996 -> 0.40230257845332595 1.2451292533748923 +logt0075 log10 -3.5488049250888194 0.45324040643185254 -> 0.55359553977141063 1.3092085108866405 +logt0076 log10 0.18418516851510189 -0.26062518836212617 -> -0.49602019732913638 -0.41500503556604301 +logt0077 log10 2.7124837795638399 -13.148769067133387 -> 1.1279348613317008 -0.59383616643803216 +logt0078 log10 3.6521275476169149e-13 -3.7820543023170673e-05 -> -4.4222722398941112 -0.68218817272717114 +logt0079 log10 5.0877545813862239 -1.2834978326786852 -> 0.71992371806426847 -0.10732104352159283 +logt0080 log10 0.26477986808461512 -0.67659001194187429 -> -0.13873139935281681 -0.52018649631300229 +logt0081 log10 0.0014754261398071962 5.3514691608205442 -> 0.72847304354528819 0.6820684398178033 +logt0082 log10 0.29667334462157885 0.00020056045042584795 -> -0.52772137299296806 0.00029359659442937261 +logt0083 log10 0.82104233671099425 3.9005387130133102 -> 0.60053889028349361 0.59208690021184018 +logt0084 log10 0.27268135358180667 124.42088110945804 -> 2.094894315538069 0.68123637673656989 +logt0085 log10 0.0026286959168267485 0.47795808180573013 -> -0.32060362226100814 0.67979964816877081 + +-- values near infinity +logt0100 log10 1.0512025744003172e+308 7.2621669750664611e+307 -> 308.10641562682065 0.26255461408256975 +logt0101 log10 5.5344249034372126e+307 -1.2155859158431275e+308 -> 308.12569106009209 -0.496638782296212 +logt0102 log10 -1.3155575403469408e+308 1.1610793541663864e+308 -> 308.24419052091019 1.0503359777705266 +logt0103 log10 -1.632366720973235e+308 -1.54299446211448e+308 -> 308.3514500834093 -1.0355024924378222 +logt0104 log10 0.0 5.9449276692327712e+307 -> 307.77414657501117 0.68218817692092071 +logt0105 log10 -0.0 1.1201850459025692e+308 -> 308.04928977068465 0.68218817692092071 +logt0106 log10 0.0 -1.6214225933466528e+308 -> 308.20989622030174 -0.68218817692092071 +logt0107 log10 -0.0 -1.7453269791591058e+308 -> 308.24187680203539 -0.68218817692092071 +logt0108 log10 1.440860577601428e+308 0.0 -> 308.15862195908755 0.0 +logt0109 log10 1.391515176148282e+308 -0.0 -> 308.14348794720007 -0.0 +logt0110 log10 -1.201354401295296e+308 0.0 -> 308.07967114380773 1.3643763538418414 +logt0111 log10 -1.6704337825976804e+308 -0.0 -> 308.22282926451624 -1.3643763538418414 +logt0112 log10 7.2276974655190223e+307 7.94879711369164 -> 307.85899996571993 4.7762357800858463e-308 +logt0113 log10 1.1207859593716076e+308 -6.1956200868221147 -> 308.04952268169455 -2.4007470767963597e-308 +logt0114 log10 -4.6678933874471045e+307 9.947107893220382 -> 307.66912092839902 1.3643763538418414 +logt0115 log10 -1.5108012453950142e+308 -5.3117197179375619 -> 308.1792073341565 -1.3643763538418414 +logt0116 log10 7.4903750871504435 1.5320703776626352e+308 -> 308.18527871564157 0.68218817692092071 +logt0117 log10 5.9760325525654778 -8.0149473997349123e+307 -> 307.90390067652424 -0.68218817692092071 +logt0118 log10 -7.880194206386629 1.7861845814767441e+308 -> 308.25192633617331 0.68218817692092071 +logt0119 log10 -9.886438993852865 -6.19235781080747e+307 -> 307.79185604308338 -0.68218817692092071 + +-- values near 0 +logt0120 log10 2.2996867579227779e-308 6.7861840770939125e-312 -> -307.63833129662572 0.00012815668056362305 +logt0121 log10 6.9169190417774516e-323 -9.0414013188948118e-322 -> -321.04249706727148 -0.64902805353306059 +logt0122 log10 -1.5378064962914011e-316 1.8243628389354635e-310 -> -309.73888878263222 0.68218854299989429 +logt0123 log10 -2.3319898483706837e-321 -2.2358763941866371e-313 -> -312.65055220919641 -0.68218818145055538 +logt0124 log10 0.0 3.872770101081121e-315 -> -314.41197828323476 0.68218817692092071 +logt0125 log10 -0.0 9.6342800939043076e-322 -> -321.01618073175331 0.68218817692092071 +logt0126 log10 0.0 -2.266099393427834e-308 -> -307.64472104545649 -0.68218817692092071 +logt0127 log10 -0.0 -2.1184695673766626e-315 -> -314.67397777042407 -0.68218817692092071 +logt0128 log10 1.1363509854348671e-322 0.0 -> -321.94448750709819 0.0 +logt0129 log10 3.5572726500569751e-322 -0.0 -> -321.44888284668451 -0.0 +logt0130 log10 -2.3696071074040593e-310 0.0 -> -309.62532365619722 1.3643763538418414 +logt0131 log10 -2.813283897266934e-317 -0.0 -> -316.55078643961042 -1.3643763538418414 + +-- values near the unit circle +logt0200 log10 -0.59999999999999998 0.80000000000000004 -> 9.6432746655328709e-18 0.96165715756846815 +logt0201 log10 0.79999999999999993 0.60000000000000009 -> 2.6765463916147622e-33 0.2794689806475476 + +-- special values +logt1000 log10 -0.0 0.0 -> -inf 1.3643763538418414 divide-by-zero +logt1001 log10 0.0 0.0 -> -inf 0.0 divide-by-zero +logt1002 log10 0.0 inf -> inf 0.68218817692092071 +logt1003 log10 2.3 inf -> inf 0.68218817692092071 +logt1004 log10 -0.0 inf -> inf 0.68218817692092071 +logt1005 log10 -2.3 inf -> inf 0.68218817692092071 +logt1006 log10 0.0 nan -> nan nan +logt1007 log10 2.3 nan -> nan nan +logt1008 log10 -0.0 nan -> nan nan +logt1009 log10 -2.3 nan -> nan nan +logt1010 log10 -inf 0.0 -> inf 1.3643763538418414 +logt1011 log10 -inf 2.3 -> inf 1.3643763538418414 +logt1012 log10 inf 0.0 -> inf 0.0 +logt1013 log10 inf 2.3 -> inf 0.0 +logt1014 log10 -inf inf -> inf 1.0232822653813811 +logt1015 log10 inf inf -> inf 0.34109408846046035 +logt1016 log10 inf nan -> inf nan +logt1017 log10 -inf nan -> inf nan +logt1018 log10 nan 0.0 -> nan nan +logt1019 log10 nan 2.3 -> nan nan +logt1020 log10 nan inf -> inf nan +logt1021 log10 nan nan -> nan nan +logt1022 log10 -0.0 -0.0 -> -inf -1.3643763538418414 divide-by-zero +logt1023 log10 0.0 -0.0 -> -inf -0.0 divide-by-zero +logt1024 log10 0.0 -inf -> inf -0.68218817692092071 +logt1025 log10 2.3 -inf -> inf -0.68218817692092071 +logt1026 log10 -0.0 -inf -> inf -0.68218817692092071 +logt1027 log10 -2.3 -inf -> inf -0.68218817692092071 +logt1028 log10 -inf -0.0 -> inf -1.3643763538418414 +logt1029 log10 -inf -2.3 -> inf -1.3643763538418414 +logt1030 log10 inf -0.0 -> inf -0.0 +logt1031 log10 inf -2.3 -> inf -0.0 +logt1032 log10 -inf -inf -> inf -1.0232822653813811 +logt1033 log10 inf -inf -> inf -0.34109408846046035 +logt1034 log10 nan -0.0 -> nan nan +logt1035 log10 nan -2.3 -> nan nan +logt1036 log10 nan -inf -> inf nan + + +----------------------- +-- sqrt: Square root -- +----------------------- + +-- zeros +sqrt0000 sqrt 0.0 0.0 -> 0.0 0.0 +sqrt0001 sqrt 0.0 -0.0 -> 0.0 -0.0 +sqrt0002 sqrt -0.0 0.0 -> 0.0 0.0 +sqrt0003 sqrt -0.0 -0.0 -> 0.0 -0.0 + +-- values along both sides of real axis +sqrt0010 sqrt -9.8813129168249309e-324 0.0 -> 0.0 3.1434555694052576e-162 +sqrt0011 sqrt -9.8813129168249309e-324 -0.0 -> 0.0 -3.1434555694052576e-162 +sqrt0012 sqrt -1e-305 0.0 -> 0.0 3.1622776601683791e-153 +sqrt0013 sqrt -1e-305 -0.0 -> 0.0 -3.1622776601683791e-153 +sqrt0014 sqrt -1e-150 0.0 -> 0.0 9.9999999999999996e-76 +sqrt0015 sqrt -1e-150 -0.0 -> 0.0 -9.9999999999999996e-76 +sqrt0016 sqrt -9.9999999999999998e-17 0.0 -> 0.0 1e-08 +sqrt0017 sqrt -9.9999999999999998e-17 -0.0 -> 0.0 -1e-08 +sqrt0018 sqrt -0.001 0.0 -> 0.0 0.031622776601683791 +sqrt0019 sqrt -0.001 -0.0 -> 0.0 -0.031622776601683791 +sqrt0020 sqrt -0.57899999999999996 0.0 -> 0.0 0.76092049518987193 +sqrt0021 sqrt -0.57899999999999996 -0.0 -> 0.0 -0.76092049518987193 +sqrt0022 sqrt -0.99999999999999989 0.0 -> 0.0 0.99999999999999989 +sqrt0023 sqrt -0.99999999999999989 -0.0 -> 0.0 -0.99999999999999989 +sqrt0024 sqrt -1.0000000000000002 0.0 -> 0.0 1.0 +sqrt0025 sqrt -1.0000000000000002 -0.0 -> 0.0 -1.0 +sqrt0026 sqrt -1.0009999999999999 0.0 -> 0.0 1.000499875062461 +sqrt0027 sqrt -1.0009999999999999 -0.0 -> 0.0 -1.000499875062461 +sqrt0028 sqrt -2.0 0.0 -> 0.0 1.4142135623730951 +sqrt0029 sqrt -2.0 -0.0 -> 0.0 -1.4142135623730951 +sqrt0030 sqrt -23.0 0.0 -> 0.0 4.7958315233127191 +sqrt0031 sqrt -23.0 -0.0 -> 0.0 -4.7958315233127191 +sqrt0032 sqrt -10000000000000000.0 0.0 -> 0.0 100000000.0 +sqrt0033 sqrt -10000000000000000.0 -0.0 -> 0.0 -100000000.0 +sqrt0034 sqrt -9.9999999999999998e+149 0.0 -> 0.0 9.9999999999999993e+74 +sqrt0035 sqrt -9.9999999999999998e+149 -0.0 -> 0.0 -9.9999999999999993e+74 +sqrt0036 sqrt -1.0000000000000001e+299 0.0 -> 0.0 3.1622776601683796e+149 +sqrt0037 sqrt -1.0000000000000001e+299 -0.0 -> 0.0 -3.1622776601683796e+149 +sqrt0038 sqrt 9.8813129168249309e-324 0.0 -> 3.1434555694052576e-162 0.0 +sqrt0039 sqrt 9.8813129168249309e-324 -0.0 -> 3.1434555694052576e-162 -0.0 +sqrt0040 sqrt 1e-305 0.0 -> 3.1622776601683791e-153 0.0 +sqrt0041 sqrt 1e-305 -0.0 -> 3.1622776601683791e-153 -0.0 +sqrt0042 sqrt 1e-150 0.0 -> 9.9999999999999996e-76 0.0 +sqrt0043 sqrt 1e-150 -0.0 -> 9.9999999999999996e-76 -0.0 +sqrt0044 sqrt 9.9999999999999998e-17 0.0 -> 1e-08 0.0 +sqrt0045 sqrt 9.9999999999999998e-17 -0.0 -> 1e-08 -0.0 +sqrt0046 sqrt 0.001 0.0 -> 0.031622776601683791 0.0 +sqrt0047 sqrt 0.001 -0.0 -> 0.031622776601683791 -0.0 +sqrt0048 sqrt 0.57899999999999996 0.0 -> 0.76092049518987193 0.0 +sqrt0049 sqrt 0.57899999999999996 -0.0 -> 0.76092049518987193 -0.0 +sqrt0050 sqrt 0.99999999999999989 0.0 -> 0.99999999999999989 0.0 +sqrt0051 sqrt 0.99999999999999989 -0.0 -> 0.99999999999999989 -0.0 +sqrt0052 sqrt 1.0000000000000002 0.0 -> 1.0 0.0 +sqrt0053 sqrt 1.0000000000000002 -0.0 -> 1.0 -0.0 +sqrt0054 sqrt 1.0009999999999999 0.0 -> 1.000499875062461 0.0 +sqrt0055 sqrt 1.0009999999999999 -0.0 -> 1.000499875062461 -0.0 +sqrt0056 sqrt 2.0 0.0 -> 1.4142135623730951 0.0 +sqrt0057 sqrt 2.0 -0.0 -> 1.4142135623730951 -0.0 +sqrt0058 sqrt 23.0 0.0 -> 4.7958315233127191 0.0 +sqrt0059 sqrt 23.0 -0.0 -> 4.7958315233127191 -0.0 +sqrt0060 sqrt 10000000000000000.0 0.0 -> 100000000.0 0.0 +sqrt0061 sqrt 10000000000000000.0 -0.0 -> 100000000.0 -0.0 +sqrt0062 sqrt 9.9999999999999998e+149 0.0 -> 9.9999999999999993e+74 0.0 +sqrt0063 sqrt 9.9999999999999998e+149 -0.0 -> 9.9999999999999993e+74 -0.0 +sqrt0064 sqrt 1.0000000000000001e+299 0.0 -> 3.1622776601683796e+149 0.0 +sqrt0065 sqrt 1.0000000000000001e+299 -0.0 -> 3.1622776601683796e+149 -0.0 + +-- random inputs +sqrt0100 sqrt -0.34252542541549913 -223039880.15076211 -> 10560.300180587592 -10560.300196805192 +sqrt0101 sqrt -0.88790791393018909 -5.3307751730827402 -> 1.5027154613689004 -1.7737140896343291 +sqrt0102 sqrt -113916.89291310767 -0.018143374626153858 -> 2.6877817875351178e-05 -337.51576691038952 +sqrt0103 sqrt -0.63187172386197121 -0.26293913366617694 -> 0.16205707495266153 -0.81125471918761971 +sqrt0104 sqrt -0.058185169308906215 -2.3548312990430991 -> 1.0717660342420072 -1.0985752598086966 +sqrt0105 sqrt -1.0580584765935896 0.14400319259151736 -> 0.069837489270111242 1.030987755262468 +sqrt0106 sqrt -1.1667595947504932 0.11159711473953678 -> 0.051598531319315251 1.0813981705111229 +sqrt0107 sqrt -0.5123728411449906 0.026175433648339085 -> 0.018278026262418718 0.71603556293597614 +sqrt0108 sqrt -3.7453400060067228 1.0946500314809635 -> 0.27990088541692498 1.9554243814742367 +sqrt0109 sqrt -0.0027736121575097673 1.0367943000839817 -> 0.71903560338719175 0.72096172651250545 +sqrt0110 sqrt 1501.2559699453188 -1.1997325207283589 -> 38.746047664730959 -0.015481998720355024 +sqrt0111 sqrt 1.4830075326850578 -0.64100878436755349 -> 1.244712815741096 -0.25749264258434584 +sqrt0112 sqrt 0.095395618499734602 -0.48226565701639595 -> 0.54175904053472879 -0.44509239434231551 +sqrt0113 sqrt 0.50109185681863277 -0.54054037379892561 -> 0.7868179858332387 -0.34349772344520979 +sqrt0114 sqrt 0.98779807595367897 -0.00019848758437225191 -> 0.99388031770665153 -9.9854872279921968e-05 +sqrt0115 sqrt 11.845472380792259 0.0010051104581506761 -> 3.4417252072345397 0.00014601840612346451 +sqrt0116 sqrt 2.3558249686735975 0.25605157371744403 -> 1.5371278477386647 0.083288964575761404 +sqrt0117 sqrt 0.77584894123159098 1.0496420627016076 -> 1.0200744386390885 0.51449287568756552 +sqrt0118 sqrt 1.8961715669604893 0.34940793467158854 -> 1.3827991781411615 0.12634080935066902 +sqrt0119 sqrt 0.96025378316565801 0.69573224860140515 -> 1.0358710342209998 0.33581991658093457 + +-- values near 0 +sqrt0120 sqrt 7.3577938365086866e-313 8.1181408465112743e-319 -> 8.5777583531543516e-157 4.732087634251168e-163 +sqrt0121 sqrt 1.2406883874892108e-310 -5.1210133324269776e-312 -> 1.1140990057468052e-155 -2.2982756945349973e-157 +sqrt0122 sqrt -7.1145453001139502e-322 2.9561379244703735e-314 -> 1.2157585807480286e-157 1.2157586100077242e-157 +sqrt0123 sqrt -4.9963244206801218e-314 -8.4718424423690227e-319 -> 1.8950582312540437e-162 -2.2352459419578971e-157 +sqrt0124 sqrt 0.0 7.699553609385195e-318 -> 1.9620848107797476e-159 1.9620848107797476e-159 +sqrt0125 sqrt -0.0 3.3900826606499415e-309 -> 4.1170879639922327e-155 4.1170879639922327e-155 +sqrt0126 sqrt 0.0 -9.8907989772250828e-319 -> 7.032353438652342e-160 -7.032353438652342e-160 +sqrt0127 sqrt -0.0 -1.3722939367590908e-315 -> 2.6194407196566702e-158 -2.6194407196566702e-158 +sqrt0128 sqrt 7.9050503334599447e-323 0.0 -> 8.8910349979403099e-162 0.0 +sqrt0129 sqrt 1.8623241768349486e-309 -0.0 -> 4.3154654173506579e-155 -0.0 +sqrt0130 sqrt -2.665971134499887e-308 0.0 -> 0.0 1.6327801856036491e-154 +sqrt0131 sqrt -1.5477066694467245e-310 -0.0 -> 0.0 -1.2440685951533077e-155 + +-- inputs whose absolute value overflows +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 + +-- 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 ignore-imag-sign +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 +-- suffer correspondingly. +-- +-- Similarly, for cos, sin and tan we limit tests to arguments +-- with relatively small real part. + + +------------------------------- +-- exp: Exponential function -- +------------------------------- + +-- zeros +exp0000 exp 0.0 0.0 -> 1.0 0.0 +exp0001 exp 0.0 -0.0 -> 1.0 -0.0 +exp0002 exp -0.0 0.0 -> 1.0 0.0 +exp0003 exp -0.0 -0.0 -> 1.0 -0.0 + +-- random inputs +exp0004 exp -17.957359009564684 -1.108613895795274 -> 7.0869292576226611e-09 -1.4225929202377833e-08 +exp0005 exp -1.4456149663368642e-15 -0.75359817331772239 -> 0.72923148323917997 -0.68426708517419033 +exp0006 exp -0.76008654883512661 -0.46657235480105019 -> 0.41764393109928666 -0.21035108396792854 +exp0007 exp -5.7071614697735731 -2.3744161818115816e-11 -> 0.0033220890242068356 -7.8880219364953578e-14 +exp0008 exp -0.4653981327927097 -5.2236706667445587e-21 -> 0.62788507378216663 -3.2798648420026468e-21 +exp0009 exp -3.2444565242295518 1.1535625304243959 -> 0.015799936931457641 0.035644950380024749 +exp0010 exp -3.0651456337977727 0.87765086532391878 -> 0.029805595629855953 0.035882775180855669 +exp0011 exp -0.11080823753233926 0.96486386300873106 -> 0.50979112534376314 0.73575512419561562 +exp0012 exp -2.5629722598928648 0.019636235754708079 -> 0.077060452853917397 0.0015133717341137684 +exp0013 exp -3.3201709957983357e-10 1.2684017344487268 -> 0.29780699855434889 0.95462610007689186 +exp0014 exp 0.88767276057993272 -0.18953422986895557 -> 2.3859624049858095 -0.45771559132044426 +exp0015 exp 1.5738333486794742 -2.2576803075544328e-11 -> 4.8251091132458654 -1.0893553826776623e-10 +exp0016 exp 1.6408702341813795 -1.438879484380837 -> 0.6786733590689048 -5.1148284173168825 +exp0017 exp 1.820279424202033 -0.020812040370785722 -> 6.1722462896420902 -0.1284755888435051 +exp0018 exp 1.7273965735945873 -0.61140621328954947 -> 4.6067931898799976 -3.2294267694441308 +exp0019 exp 2.5606034306862995 0.098153136008435504 -> 12.881325889966629 1.2684184812864494 +exp0020 exp 10.280368619483029 3.4564622559748535 -> -27721.283321551502 -9028.9663215568835 +exp0021 exp 1.104007405129741e-155 0.21258803067317278 -> 0.97748813933531764 0.21099037290544478 +exp0022 exp 0.027364777809295172 0.00059226603500623363 -> 1.0277424518451876 0.0006086970181346579 +exp0023 exp 0.94356313429255245 3.418530463518592 -> -2.4712285695346194 -0.70242654900218349 + +-- cases where exp(z) representable, exp(z.real) not +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) 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 ignore-real-sign ignore-imag-sign +exp1023 exp inf inf -> inf nan invalid ignore-real-sign +exp1024 exp -inf nan -> 0.0 0.0 ignore-real-sign ignore-imag-sign +exp1025 exp inf nan -> inf nan ignore-real-sign +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 ignore-real-sign ignore-imag-sign +exp1049 exp inf -inf -> inf nan invalid ignore-real-sign +exp1050 exp nan -0.0 -> nan -0.0 +exp1051 exp nan -2.3 -> nan nan +exp1052 exp nan -inf -> nan nan + + +----------------------------- +-- cosh: Hyperbolic Cosine -- +----------------------------- + +-- zeros +cosh0000 cosh 0.0 0.0 -> 1.0 0.0 +cosh0001 cosh 0.0 -0.0 -> 1.0 -0.0 +cosh0002 cosh -0.0 0.0 -> 1.0 -0.0 +cosh0003 cosh -0.0 -0.0 -> 1.0 0.0 + +-- random inputs +cosh0004 cosh -0.85395264297414253 -8.8553756148671958 -> -1.1684340348021185 0.51842195359787435 +cosh0005 cosh -19.584904237211223 -0.066582627994906177 -> 159816812.23336992 10656776.050406246 +cosh0006 cosh -0.11072618401130772 -1.484820215073247 -> 0.086397164744949503 0.11054275637717284 +cosh0007 cosh -3.4764840250681752 -0.48440348288275276 -> 14.325931955190844 7.5242053548737955 +cosh0008 cosh -0.52047063604524602 -0.3603805382775585 -> 1.0653940354683802 0.19193293606252473 +cosh0009 cosh -1.39518962975995 0.0074738604700702906 -> 2.1417031027235969 -0.01415518712296308 +cosh0010 cosh -0.37107064757653541 0.14728085307856609 -> 1.0580601496776991 -0.055712531964568587 +cosh0011 cosh -5.8470200958739653 4.0021722388336292 -> -112.86220667618285 131.24734033545013 +cosh0012 cosh -0.1700261444851883 0.97167540135354513 -> 0.57208748253577946 -0.1410904820240203 +cosh0013 cosh -0.44042397902648783 1.0904791964139742 -> 0.50760322393058133 -0.40333966652010816 +cosh0014 cosh 0.052267552491867299 -3.8889011430644174 -> -0.73452303414639297 0.035540704833537134 +cosh0015 cosh 0.98000764177127453 -1.2548829247784097 -> 0.47220747341416142 -1.0879421432180316 +cosh0016 cosh 0.083594701222644008 -0.88847899930181284 -> 0.63279782419312613 -0.064954566816002285 +cosh0017 cosh 1.38173531783776 -0.43185040816732229 -> 1.9221663374671647 -0.78073830858849347 +cosh0018 cosh 0.57315681120148465 -0.22255760951027942 -> 1.1399733125173004 -0.1335512343605956 +cosh0019 cosh 1.8882512333062347 4.5024932182383797 -> -0.7041602065362691 -3.1573822131964615 +cosh0020 cosh 0.5618219206858317 0.92620452129575348 -> 0.69822380405378381 0.47309067471054522 +cosh0021 cosh 0.54361442847062591 0.64176483583018462 -> 0.92234462074193491 0.34167906495845501 +cosh0022 cosh 0.0014777403107920331 1.3682028122677661 -> 0.2012106963899549 0.001447518137863219 +cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.1290269176083196 + +-- large real part +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 ignore-imag-sign +cosh1002 cosh 0.0 nan -> nan 0.0 ignore-imag-sign +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 ignore-real-sign +cosh1012 cosh inf nan -> inf nan +cosh1013 cosh nan 0.0 -> nan 0.0 ignore-imag-sign +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 ignore-imag-sign +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 ignore-real-sign +cosh1027 cosh nan -0.0 -> nan 0.0 ignore-imag-sign +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 ignore-imag-sign +cosh1032 cosh -0.0 nan -> nan 0.0 ignore-imag-sign +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 ignore-real-sign +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 ignore-imag-sign +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 ignore-real-sign + + +--------------------------- +-- sinh: Hyperbolic Sine -- +--------------------------- + +-- zeros +sinh0000 sinh 0.0 0.0 -> 0.0 0.0 +sinh0001 sinh 0.0 -0.0 -> 0.0 -0.0 +sinh0002 sinh -0.0 0.0 -> -0.0 0.0 +sinh0003 sinh -0.0 -0.0 -> -0.0 -0.0 + +-- random inputs +sinh0004 sinh -17.282588091462742 -0.38187948694103546 -> -14867386.857248396 -5970648.6553516639 +sinh0005 sinh -343.91971203143208 -5.0172868877771525e-22 -> -1.1518691776521735e+149 -5.7792581214689021e+127 +sinh0006 sinh -14.178122253300922 -1.9387157579351293 -> 258440.37909034826 -670452.58500946441 +sinh0007 sinh -1.0343810581686239 -1.0970235266369905 -> -0.56070858278092739 -1.4098883258046697 +sinh0008 sinh -0.066126561416368204 -0.070461584169961872 -> -0.066010558700938124 -0.070557276738637542 +sinh0009 sinh -0.37630149150308484 3.3621734692162173 -> 0.37591118119332617 -0.23447115926369383 +sinh0010 sinh -0.049941960978670055 0.40323767020414625 -> -0.045955482136329009 0.3928878494430646 +sinh0011 sinh -16.647852603903715 0.0026852219129082098 -> -8492566.5739382561 22804.480671133562 +sinh0012 sinh -1.476625314303694 0.89473773116683386 -> -1.2982943334382224 1.7966593367791204 +sinh0013 sinh -422.36429577556913 0.10366634502307912 -> -1.3400321008920044e+183 1.3941600948045599e+182 +sinh0014 sinh 0.09108340745641981 -0.40408227416070353 -> 0.083863724802237902 -0.39480716553935602 +sinh0015 sinh 2.036064132067386 -2.6831729961386239 -> -3.37621124363175 -1.723868330002817 +sinh0016 sinh 2.5616717223063317 -0.0078978498622717767 -> 6.4399415853815869 -0.051472264400722133 +sinh0017 sinh 0.336804011985188 -6.5654622971649337 -> 0.32962499307574578 -0.29449170159995197 +sinh0018 sinh 0.23774603755649693 -0.92467195799232049 -> 0.14449839490603389 -0.82109449053556793 +sinh0019 sinh 0.0011388273541465494 1.9676196882949855 -> -0.00044014605389634999 0.92229398407098806 +sinh0020 sinh 3.2443870105663759 0.8054287559616895 -> 8.8702890778527426 9.2610748597042196 +sinh0021 sinh 0.040628908857054738 0.098206391190944958 -> 0.04044426841671233 0.098129544739707392 +sinh0022 sinh 4.7252283918217696e-30 9.1198155642656697 -> -4.5071980561644404e-30 0.30025730701661713 +sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0.22344201231217961 + +-- large real part +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 +sinh1001 sinh 0.0 inf -> 0.0 nan invalid ignore-real-sign +sinh1002 sinh 0.0 nan -> 0.0 nan ignore-real-sign +sinh1003 sinh 2.3 inf -> nan nan invalid +sinh1004 sinh 2.3 nan -> nan nan +sinh1005 sinh inf 0.0 -> inf 0.0 +sinh1006 sinh inf 1.4 -> inf inf +sinh1007 sinh inf 2.8 -> -inf inf +sinh1008 sinh inf 4.2 -> -inf -inf +sinh1009 sinh inf 5.6 -> inf -inf +sinh1010 sinh inf 7.0 -> inf inf +sinh1011 sinh inf inf -> inf nan invalid ignore-real-sign +sinh1012 sinh inf nan -> inf nan ignore-real-sign +sinh1013 sinh nan 0.0 -> nan 0.0 +sinh1014 sinh nan 2.3 -> nan nan +sinh1015 sinh nan inf -> nan nan +sinh1016 sinh nan nan -> nan nan +sinh1017 sinh 0.0 -0.0 -> 0.0 -0.0 +sinh1018 sinh 0.0 -inf -> 0.0 nan invalid ignore-real-sign +sinh1019 sinh 2.3 -inf -> nan nan invalid +sinh1020 sinh inf -0.0 -> inf -0.0 +sinh1021 sinh inf -1.4 -> inf -inf +sinh1022 sinh inf -2.8 -> -inf -inf +sinh1023 sinh inf -4.2 -> -inf inf +sinh1024 sinh inf -5.6 -> inf inf +sinh1025 sinh inf -7.0 -> inf -inf +sinh1026 sinh inf -inf -> inf nan invalid ignore-real-sign +sinh1027 sinh nan -0.0 -> nan -0.0 +sinh1028 sinh nan -2.3 -> nan nan +sinh1029 sinh nan -inf -> nan nan +sinh1030 sinh -0.0 -0.0 -> -0.0 -0.0 +sinh1031 sinh -0.0 -inf -> 0.0 nan invalid ignore-real-sign +sinh1032 sinh -0.0 nan -> 0.0 nan ignore-real-sign +sinh1033 sinh -2.3 -inf -> nan nan invalid +sinh1034 sinh -2.3 nan -> nan nan +sinh1035 sinh -inf -0.0 -> -inf -0.0 +sinh1036 sinh -inf -1.4 -> -inf -inf +sinh1037 sinh -inf -2.8 -> inf -inf +sinh1038 sinh -inf -4.2 -> inf inf +sinh1039 sinh -inf -5.6 -> -inf inf +sinh1040 sinh -inf -7.0 -> -inf -inf +sinh1041 sinh -inf -inf -> inf nan invalid ignore-real-sign +sinh1042 sinh -inf nan -> inf nan ignore-real-sign +sinh1043 sinh -0.0 0.0 -> -0.0 0.0 +sinh1044 sinh -0.0 inf -> 0.0 nan invalid ignore-real-sign +sinh1045 sinh -2.3 inf -> nan nan invalid +sinh1046 sinh -inf 0.0 -> -inf 0.0 +sinh1047 sinh -inf 1.4 -> -inf inf +sinh1048 sinh -inf 2.8 -> inf inf +sinh1049 sinh -inf 4.2 -> inf -inf +sinh1050 sinh -inf 5.6 -> -inf -inf +sinh1051 sinh -inf 7.0 -> -inf inf +sinh1052 sinh -inf inf -> inf nan invalid ignore-real-sign + + +------------------------------ +-- tanh: Hyperbolic Tangent -- +------------------------------ + +-- zeros +tanh0000 tanh 0.0 0.0 -> 0.0 0.0 +tanh0001 tanh 0.0 -0.0 -> 0.0 -0.0 +tanh0002 tanh -0.0 0.0 -> -0.0 0.0 +tanh0003 tanh -0.0 -0.0 -> -0.0 -0.0 + +-- random inputs +tanh0004 tanh -21.200500450664993 -1.6970729480342996 -> -1.0 1.9241352344849399e-19 +tanh0005 tanh -0.34158771504251928 -8.0848504951747131 -> -2.123711225855613 1.2827526782026006 +tanh0006 tanh -15.454144725193689 -0.23619582288265617 -> -0.99999999999993283 -3.4336684248260036e-14 +tanh0007 tanh -7.6103163119661952 -0.7802748320307008 -> -0.99999999497219438 -4.9064845343755437e-07 +tanh0008 tanh -0.15374717235792129 -0.6351086327306138 -> -0.23246081703561869 -0.71083467433910219 +tanh0009 tanh -0.49101115474392465 0.09723001264886301 -> -0.45844445715492133 0.077191158541805888 +tanh0010 tanh -0.10690612157664491 2.861612800856395 -> -0.11519761626257358 -0.28400488355647507 +tanh0011 tanh -0.91505774192066702 1.5431174597727007 -> -1.381109893068114 0.025160819663709356 +tanh0012 tanh -0.057433367093792223 0.35491159541246459 -> -0.065220499046696953 0.36921788332369498 +tanh0013 tanh -1.3540418621233514 0.18969415642242535 -> -0.88235642861151387 0.043764069984411721 +tanh0014 tanh 0.94864783961003529 -0.11333689578867717 -> 0.74348401861861368 -0.051271042543855221 +tanh0015 tanh 1.9591698133845488 -0.0029654444904578339 -> 0.9610270776968135 -0.00022664240049212933 +tanh0016 tanh 1.0949715796669197 -0.24706642853984456 -> 0.81636574501369386 -0.087767436914149954 +tanh0017 tanh 5770428.2113731047 -3.7160580339833165 -> 1.0 -0.0 +tanh0018 tanh 1.5576782321399629 -1.0357943787966468 -> 1.0403002384895388 -0.081126347894671463 +tanh0019 tanh 0.62378536230552961 2.3471393579560216 -> 0.85582499238960363 -0.53569473646842869 +tanh0020 tanh 17.400628602508025 9.3987059533841979 -> 0.99999999999999845 -8.0175867720530832e-17 +tanh0021 tanh 0.15026177509871896 0.50630349159505472 -> 0.19367536571827768 0.53849847858853661 +tanh0022 tanh 0.57433977530711167 1.0071604546265627 -> 1.0857848159262844 0.69139213955872214 +tanh0023 tanh 0.16291181500449456 0.006972810241567544 -> 0.16149335907551157 0.0067910772903467817 + +-- large real part +tanh0030 tanh 710 0.13 -> 1.0 0.0 +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 + +--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 ignore-imag-sign +tanh1012 tanh inf nan -> 1.0 0.0 ignore-imag-sign +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 ignore-imag-sign +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 ignore-imag-sign +tanh1042 tanh -inf nan -> -1.0 0.0 ignore-imag-sign +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 ignore-imag-sign + + +----------------- +-- cos: Cosine -- +----------------- + +-- zeros +cos0000 cos 0.0 0.0 -> 1.0 -0.0 +cos0001 cos 0.0 -0.0 -> 1.0 0.0 +cos0002 cos -0.0 0.0 -> 1.0 0.0 +cos0003 cos -0.0 -0.0 -> 1.0 -0.0 + +-- random inputs +cos0004 cos -2.0689194692073034 -0.0016802181751734313 -> -0.47777827208561469 -0.0014760401501695971 +cos0005 cos -0.4209627318177977 -1.8238516774258027 -> 2.9010402201444108 -1.2329207042329617 +cos0006 cos -1.9402181630694557 -2.9751857392891217 -> -3.5465459297970985 -9.1119163586282248 +cos0007 cos -3.3118320290191616 -0.87871302909286142 -> -1.3911528636565498 0.16878141517391701 +cos0008 cos -4.9540404623376872 -0.57949232239026827 -> 0.28062445586552065 0.59467861308508008 +cos0009 cos -0.45374584316245026 1.3950283448373935 -> 1.9247665574290578 0.83004572204761107 +cos0010 cos -0.42578172040176843 1.2715881615413049 -> 1.7517161459489148 0.67863902697363332 +cos0011 cos -0.13862985354300136 0.43587635877670328 -> 1.0859880290361912 0.062157548146672272 +cos0012 cos -0.11073221308966584 9.9384082307326475e-15 -> 0.99387545040722947 1.0982543264065479e-15 +cos0013 cos -1.5027633662054623e-07 0.0069668060249955498 -> 1.0000242682912412 1.0469545565660995e-09 +cos0014 cos 4.9728645490503052 -0.00027479808860952822 -> 0.25754011731975501 -0.00026552849549083186 +cos0015 cos 7.81969303486719 -0.79621523445878783 -> 0.045734882501585063 0.88253139933082991 +cos0016 cos 0.13272421880766716 -0.74668445308718201 -> 1.2806012244432847 0.10825373267437005 +cos0017 cos 4.2396521985973274 -2.2178848380884881 -> -2.1165117057056855 -4.0416492444641401 +cos0018 cos 1.1622206624927296 -0.50400115461197081 -> 0.44884072613370379 0.4823469915034318 +cos0019 cos 1.628772864620884e-08 0.58205705428979282 -> 1.1742319995791435 -1.0024839481956604e-08 +cos0020 cos 2.6385212606111241 2.9886107100937296 -> -8.7209475927161417 -4.7748352107199796 +cos0021 cos 4.8048375263775256 0.0062248852898515658 -> 0.092318702015846243 0.0061983430422306142 +cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582 +cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477 + +-- special values +cos1000 cos -0.0 0.0 -> 1.0 0.0 +cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign +cos1002 cos nan 0.0 -> nan 0.0 ignore-imag-sign +cos1003 cos -inf 2.2999999999999998 -> nan nan invalid +cos1004 cos nan 2.2999999999999998 -> nan nan +cos1005 cos -0.0 inf -> inf 0.0 +cos1006 cos -1.3999999999999999 inf -> inf inf +cos1007 cos -2.7999999999999998 inf -> -inf inf +cos1008 cos -4.2000000000000002 inf -> -inf -inf +cos1009 cos -5.5999999999999996 inf -> inf -inf +cos1010 cos -7.0 inf -> inf inf +cos1011 cos -inf inf -> inf nan invalid ignore-real-sign +cos1012 cos nan inf -> inf nan +cos1013 cos -0.0 nan -> nan 0.0 ignore-imag-sign +cos1014 cos -2.2999999999999998 nan -> nan nan +cos1015 cos -inf nan -> nan nan +cos1016 cos nan nan -> nan nan +cos1017 cos 0.0 0.0 -> 1.0 -0.0 +cos1018 cos inf 0.0 -> nan 0.0 invalid ignore-imag-sign +cos1019 cos inf 2.2999999999999998 -> nan nan invalid +cos1020 cos 0.0 inf -> inf -0.0 +cos1021 cos 1.3999999999999999 inf -> inf -inf +cos1022 cos 2.7999999999999998 inf -> -inf -inf +cos1023 cos 4.2000000000000002 inf -> -inf inf +cos1024 cos 5.5999999999999996 inf -> inf inf +cos1025 cos 7.0 inf -> inf -inf +cos1026 cos inf inf -> inf nan invalid ignore-real-sign +cos1027 cos 0.0 nan -> nan 0.0 ignore-imag-sign +cos1028 cos 2.2999999999999998 nan -> nan nan +cos1029 cos inf nan -> nan nan +cos1030 cos 0.0 -0.0 -> 1.0 0.0 +cos1031 cos inf -0.0 -> nan 0.0 invalid ignore-imag-sign +cos1032 cos nan -0.0 -> nan 0.0 ignore-imag-sign +cos1033 cos inf -2.2999999999999998 -> nan nan invalid +cos1034 cos nan -2.2999999999999998 -> nan nan +cos1035 cos 0.0 -inf -> inf 0.0 +cos1036 cos 1.3999999999999999 -inf -> inf inf +cos1037 cos 2.7999999999999998 -inf -> -inf inf +cos1038 cos 4.2000000000000002 -inf -> -inf -inf +cos1039 cos 5.5999999999999996 -inf -> inf -inf +cos1040 cos 7.0 -inf -> inf inf +cos1041 cos inf -inf -> inf nan invalid ignore-real-sign +cos1042 cos nan -inf -> inf nan +cos1043 cos -0.0 -0.0 -> 1.0 -0.0 +cos1044 cos -inf -0.0 -> nan 0.0 invalid ignore-imag-sign +cos1045 cos -inf -2.2999999999999998 -> nan nan invalid +cos1046 cos -0.0 -inf -> inf -0.0 +cos1047 cos -1.3999999999999999 -inf -> inf -inf +cos1048 cos -2.7999999999999998 -inf -> -inf -inf +cos1049 cos -4.2000000000000002 -inf -> -inf inf +cos1050 cos -5.5999999999999996 -inf -> inf inf +cos1051 cos -7.0 -inf -> inf -inf +cos1052 cos -inf -inf -> inf nan invalid ignore-real-sign + + +--------------- +-- sin: Sine -- +--------------- + +-- zeros +sin0000 sin 0.0 0.0 -> 0.0 0.0 +sin0001 sin 0.0 -0.0 -> 0.0 -0.0 +sin0002 sin -0.0 0.0 -> -0.0 0.0 +sin0003 sin -0.0 -0.0 -> -0.0 -0.0 + +-- random inputs +sin0004 sin -0.18691829163163759 -0.74388741985507034 -> -0.2396636733773444 -0.80023231101856751 +sin0005 sin -0.45127453702459158 -461.81339920716164 -> -7.9722299331077877e+199 -1.6450205811004628e+200 +sin0006 sin -0.47669228345768921 -2.7369936564987514 -> -3.557238022267124 -6.8308030771226615 +sin0007 sin -0.31024285525950857 -1.4869219939188296 -> -0.70972676047175209 -1.9985029635426839 +sin0008 sin -4.4194573407025608 -1.405999210989288 -> 2.0702480800802685 0.55362250792180601 +sin0009 sin -1.7810832046434898e-05 0.0016439555384379083 -> -1.7810856113185261e-05 0.0016439562786668375 +sin0010 sin -0.8200017874897666 0.61724876887771929 -> -0.8749078195948865 0.44835295550987758 +sin0011 sin -1.4536502806107114 0.63998575534150415 -> -1.2035709929437679 0.080012187489163708 +sin0012 sin -2.2653412155506079 0.13172760685583729 -> -0.77502093809190431 -0.084554426868229532 +sin0013 sin -0.02613983069491858 0.18404766597776073 -> -0.026580778863127943 0.18502525396735642 +sin0014 sin 1.5743065001054617 -0.53125574272642029 -> 1.1444596332092725 0.0019537598099352077 +sin0015 sin 7.3833101791283289e-20 -0.16453221324236217 -> 7.4834720674379429e-20 -0.16527555646466915 +sin0016 sin 0.34763834641254038 -2.8377416421089565 -> 2.918883541504663 -8.0002718053250224 +sin0017 sin 0.077105785180421563 -0.090056027316200674 -> 0.077341973814471304 -0.089909869380524587 +sin0018 sin 3.9063227798142329e-17 -0.05954098654295524 -> 3.9132490348956512e-17 -0.059576172859837351 +sin0019 sin 0.57333917932544598 8.7785221430594696e-06 -> 0.54244029338302935 7.3747869125301368e-06 +sin0020 sin 0.024861722816513169 0.33044620756118515 -> 0.026228801369651 0.3363889671570689 +sin0021 sin 1.4342727387492671 0.81361889790284347 -> 1.3370960060947923 0.12336137961387163 +sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852 +sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62 + +-- special values +sin1000 sin -0.0 0.0 -> -0.0 0.0 +sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign +sin1002 sin nan 0.0 -> nan 0.0 ignore-imag-sign +sin1003 sin -inf 2.2999999999999998 -> nan nan invalid +sin1004 sin nan 2.2999999999999998 -> nan nan +sin1005 sin -0.0 inf -> -0.0 inf +sin1006 sin -1.3999999999999999 inf -> -inf inf +sin1007 sin -2.7999999999999998 inf -> -inf -inf +sin1008 sin -4.2000000000000002 inf -> inf -inf +sin1009 sin -5.5999999999999996 inf -> inf inf +sin1010 sin -7.0 inf -> -inf inf +sin1011 sin -inf inf -> nan inf invalid ignore-imag-sign +sin1012 sin nan inf -> nan inf ignore-imag-sign +sin1013 sin -0.0 nan -> -0.0 nan +sin1014 sin -2.2999999999999998 nan -> nan nan +sin1015 sin -inf nan -> nan nan +sin1016 sin nan nan -> nan nan +sin1017 sin 0.0 0.0 -> 0.0 0.0 +sin1018 sin inf 0.0 -> nan 0.0 invalid ignore-imag-sign +sin1019 sin inf 2.2999999999999998 -> nan nan invalid +sin1020 sin 0.0 inf -> 0.0 inf +sin1021 sin 1.3999999999999999 inf -> inf inf +sin1022 sin 2.7999999999999998 inf -> inf -inf +sin1023 sin 4.2000000000000002 inf -> -inf -inf +sin1024 sin 5.5999999999999996 inf -> -inf inf +sin1025 sin 7.0 inf -> inf inf +sin1026 sin inf inf -> nan inf invalid ignore-imag-sign +sin1027 sin 0.0 nan -> 0.0 nan +sin1028 sin 2.2999999999999998 nan -> nan nan +sin1029 sin inf nan -> nan nan +sin1030 sin 0.0 -0.0 -> 0.0 -0.0 +sin1031 sin inf -0.0 -> nan 0.0 invalid ignore-imag-sign +sin1032 sin nan -0.0 -> nan 0.0 ignore-imag-sign +sin1033 sin inf -2.2999999999999998 -> nan nan invalid +sin1034 sin nan -2.2999999999999998 -> nan nan +sin1035 sin 0.0 -inf -> 0.0 -inf +sin1036 sin 1.3999999999999999 -inf -> inf -inf +sin1037 sin 2.7999999999999998 -inf -> inf inf +sin1038 sin 4.2000000000000002 -inf -> -inf inf +sin1039 sin 5.5999999999999996 -inf -> -inf -inf +sin1040 sin 7.0 -inf -> inf -inf +sin1041 sin inf -inf -> nan inf invalid ignore-imag-sign +sin1042 sin nan -inf -> nan inf ignore-imag-sign +sin1043 sin -0.0 -0.0 -> -0.0 -0.0 +sin1044 sin -inf -0.0 -> nan 0.0 invalid ignore-imag-sign +sin1045 sin -inf -2.2999999999999998 -> nan nan invalid +sin1046 sin -0.0 -inf -> -0.0 -inf +sin1047 sin -1.3999999999999999 -inf -> -inf -inf +sin1048 sin -2.7999999999999998 -inf -> -inf inf +sin1049 sin -4.2000000000000002 -inf -> inf inf +sin1050 sin -5.5999999999999996 -inf -> inf -inf +sin1051 sin -7.0 -inf -> -inf -inf +sin1052 sin -inf -inf -> nan inf invalid ignore-imag-sign + + +------------------ +-- tan: Tangent -- +------------------ + +-- zeros +tan0000 tan 0.0 0.0 -> 0.0 0.0 +tan0001 tan 0.0 -0.0 -> 0.0 -0.0 +tan0002 tan -0.0 0.0 -> -0.0 0.0 +tan0003 tan -0.0 -0.0 -> -0.0 -0.0 + +-- random inputs +tan0004 tan -0.56378561833861074 -1.7110276237187664e+73 -> -0.0 -1.0 +tan0005 tan -3.5451633993471915e-12 -2.855471863564059 -> -4.6622441304889575e-14 -0.99340273843093951 +tan0006 tan -2.502442719638696 -0.26742234390504221 -> 0.66735215252994995 -0.39078997935420956 +tan0007 tan -0.87639597720371365 -55.586225523280206 -> -1.0285264565948176e-48 -1.0 +tan0008 tan -0.015783869596427243 -520.05944436039272 -> -0.0 -1.0 +tan0009 tan -0.84643549990725164 2.0749097935396343 -> -0.031412661676959573 1.0033548479526764 +tan0010 tan -0.43613792248559646 8.1082741629458059 -> -1.3879848444644593e-07 0.99999988344224011 +tan0011 tan -1.0820906367833114 0.28571868992480248 -> -1.3622485737936536 0.99089269377971245 +tan0012 tan -1.1477859580220084 1.9021637002708041 -> -0.034348450042071196 1.0293954097901687 +tan0013 tan -0.12465543176953409 3.0606851016344815e-05 -> -0.12530514290387343 3.1087420769945479e-05 +tan0014 tan 3.7582848717525343 -692787020.44038939 -> 0.0 -1.0 +tan0015 tan 2.2321967655142176e-06 -10.090069423008169 -> 1.5369846120622643e-14 -0.99999999655723759 +tan0016 tan 0.88371172390245012 -1.1635053630132823 -> 0.19705017118625889 -1.0196452280843129 +tan0017 tan 2.1347414231849267 -1.9311339960416831 -> -0.038663576915982524 -1.0174399993980778 +tan0018 tan 5.9027945255899974 -2.1574195684607135e-183 -> -0.39986591539281496 -2.5023753167976915e-183 +tan0019 tan 0.44811489490805362 683216075670.07556 -> 0.0 1.0 +tan0020 tan 4.1459766396068325 12.523017205605756 -> 2.4022514758988068e-11 1.0000000000112499 +tan0021 tan 1.7809617968443272 1.5052381702853379 -> -0.044066222118946903 1.0932684517702778 +tan0022 tan 1.1615313900880577 1.7956298728647107 -> 0.041793186826390362 1.0375339546034792 +tan0023 tan 0.067014779477908945 5.8517361577457097 -> 2.2088639754800034e-06 0.9999836182420061 + +-- special values +tan1000 tan -0.0 0.0 -> -0.0 0.0 +tan1001 tan -inf 0.0 -> nan nan invalid +tan1002 tan -inf 2.2999999999999998 -> nan nan invalid +tan1003 tan nan 0.0 -> nan nan +tan1004 tan nan 2.2999999999999998 -> nan nan +tan1005 tan -0.0 inf -> -0.0 1.0 +tan1006 tan -0.69999999999999996 inf -> -0.0 1.0 +tan1007 tan -1.3999999999999999 inf -> -0.0 1.0 +tan1008 tan -2.1000000000000001 inf -> 0.0 1.0 +tan1009 tan -2.7999999999999998 inf -> 0.0 1.0 +tan1010 tan -3.5 inf -> -0.0 1.0 +tan1011 tan -inf inf -> -0.0 1.0 ignore-real-sign +tan1012 tan nan inf -> -0.0 1.0 ignore-real-sign +tan1013 tan -0.0 nan -> -0.0 nan +tan1014 tan -2.2999999999999998 nan -> nan nan +tan1015 tan -inf nan -> nan nan +tan1016 tan nan nan -> nan nan +tan1017 tan 0.0 0.0 -> 0.0 0.0 +tan1018 tan inf 0.0 -> nan nan invalid +tan1019 tan inf 2.2999999999999998 -> nan nan invalid +tan1020 tan 0.0 inf -> 0.0 1.0 +tan1021 tan 0.69999999999999996 inf -> 0.0 1.0 +tan1022 tan 1.3999999999999999 inf -> 0.0 1.0 +tan1023 tan 2.1000000000000001 inf -> -0.0 1.0 +tan1024 tan 2.7999999999999998 inf -> -0.0 1.0 +tan1025 tan 3.5 inf -> 0.0 1.0 +tan1026 tan inf inf -> -0.0 1.0 ignore-real-sign +tan1027 tan 0.0 nan -> 0.0 nan +tan1028 tan 2.2999999999999998 nan -> nan nan +tan1029 tan inf nan -> nan nan +tan1030 tan 0.0 -0.0 -> 0.0 -0.0 +tan1031 tan inf -0.0 -> nan nan invalid +tan1032 tan inf -2.2999999999999998 -> nan nan invalid +tan1033 tan nan -0.0 -> nan nan +tan1034 tan nan -2.2999999999999998 -> nan nan +tan1035 tan 0.0 -inf -> 0.0 -1.0 +tan1036 tan 0.69999999999999996 -inf -> 0.0 -1.0 +tan1037 tan 1.3999999999999999 -inf -> 0.0 -1.0 +tan1038 tan 2.1000000000000001 -inf -> -0.0 -1.0 +tan1039 tan 2.7999999999999998 -inf -> -0.0 -1.0 +tan1040 tan 3.5 -inf -> 0.0 -1.0 +tan1041 tan inf -inf -> -0.0 -1.0 ignore-real-sign +tan1042 tan nan -inf -> -0.0 -1.0 ignore-real-sign +tan1043 tan -0.0 -0.0 -> -0.0 -0.0 +tan1044 tan -inf -0.0 -> nan nan invalid +tan1045 tan -inf -2.2999999999999998 -> nan nan invalid +tan1046 tan -0.0 -inf -> -0.0 -1.0 +tan1047 tan -0.69999999999999996 -inf -> -0.0 -1.0 +tan1048 tan -1.3999999999999999 -inf -> -0.0 -1.0 +tan1049 tan -2.1000000000000001 -inf -> 0.0 -1.0 +tan1050 tan -2.7999999999999998 -inf -> 0.0 -1.0 +tan1051 tan -3.5 -inf -> -0.0 -1.0 +tan1052 tan -inf -inf -> -0.0 -1.0 ignore-real-sign + + +------------------------------------------------------------------------ +-- rect: Conversion from polar coordinates to rectangular coordinates -- +------------------------------------------------------------------------ +-- +-- For cmath.rect, we can use the same testcase syntax as for the +-- complex -> complex functions above, but here the input arguments +-- should be interpreted as a pair of floating-point numbers rather +-- than the real and imaginary parts of a complex number. +-- +-- Here are the 'spirit of C99' rules for rect. First, the short +-- version: +-- +-- rect(x, t) = exp(log(x)+it) for positive-signed x +-- rect(x, t) = -exp(log(-x)+it) for negative-signed x +-- rect(nan, t) = exp(nan + it), except that in rect(nan, +-0) the +-- sign of the imaginary part is unspecified. +-- +-- and now the long version: +-- +-- rect(x, -t) = conj(rect(x, t)) for all x and t +-- rect(-x, t) = -rect(x, t) for all x and t +-- rect(+0, +0) returns +0 + i0 +-- rect(+0, inf) returns +- 0 +- i0, where the signs of the real and +-- imaginary parts are unspecified. +-- rect(x, inf) returns NaN + i NaN and raises the "invalid" +-- floating-point exception, for finite nonzero x. +-- rect(inf, inf) returns +-inf + i NaN and raises the "invalid" +-- floating-point exception (where the sign of the real part of the +-- result is unspecified). +-- rect(inf, +0) returns inf+i0 +-- rect(inf, x) returns inf*cis(x), for finite nonzero x +-- rect(inf, NaN) returns +-inf+i NaN, where the sign of the real part +-- of the result is unspecified. +-- rect(NaN, x) returns NaN + i NaN for all nonzero numbers (including +-- infinities) x +-- rect(NaN, 0) returns NaN +- i0, where the sign of the imaginary +-- part is unspecified +-- rect(NaN, NaN) returns NaN + i NaN +-- rect(x, NaN) returns NaN + i NaN for finite nonzero x +-- rect(+0, NaN) return +-0 +- i0, where the signs of the real and +-- imaginary parts are unspecified. + +-- special values +rect1000 rect 0.0 0.0 -> 0.0 0.0 +rect1001 rect 0.0 inf -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1002 rect 2.3 inf -> nan nan invalid +rect1003 rect inf inf -> inf nan invalid ignore-real-sign +rect1004 rect inf 0.0 -> inf 0.0 +rect1005 rect inf 1.4 -> inf inf +rect1006 rect inf 2.8 -> -inf inf +rect1007 rect inf 4.2 -> -inf -inf +rect1008 rect inf 5.6 -> inf -inf +rect1009 rect inf 7.0 -> inf inf +rect1010 rect nan 0.0 -> nan 0.0 ignore-imag-sign +rect1011 rect nan 2.3 -> nan nan +rect1012 rect nan inf -> nan nan +rect1013 rect nan nan -> nan nan +rect1014 rect inf nan -> inf nan ignore-real-sign +rect1015 rect 2.3 nan -> nan nan +rect1016 rect 0.0 nan -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1017 rect 0.0 -0.0 -> 0.0 -0.0 +rect1018 rect 0.0 -inf -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1019 rect 2.3 -inf -> nan nan invalid +rect1020 rect inf -inf -> inf nan invalid ignore-real-sign +rect1021 rect inf -0.0 -> inf -0.0 +rect1022 rect inf -1.4 -> inf -inf +rect1023 rect inf -2.8 -> -inf -inf +rect1024 rect inf -4.2 -> -inf inf +rect1025 rect inf -5.6 -> inf inf +rect1026 rect inf -7.0 -> inf -inf +rect1027 rect nan -0.0 -> nan 0.0 ignore-imag-sign +rect1028 rect nan -2.3 -> nan nan +rect1029 rect nan -inf -> nan nan +rect1030 rect -0.0 0.0 -> -0.0 -0.0 +rect1031 rect -0.0 inf -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1032 rect -2.3 inf -> nan nan invalid +rect1033 rect -inf inf -> -inf nan invalid ignore-real-sign +rect1034 rect -inf 0.0 -> -inf -0.0 +rect1035 rect -inf 1.4 -> -inf -inf +rect1036 rect -inf 2.8 -> inf -inf +rect1037 rect -inf 4.2 -> inf inf +rect1038 rect -inf 5.6 -> -inf inf +rect1039 rect -inf 7.0 -> -inf -inf +rect1040 rect -inf nan -> inf nan ignore-real-sign +rect1041 rect -2.3 nan -> nan nan +rect1042 rect -0.0 nan -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1043 rect -0.0 -0.0 -> -0.0 0.0 +rect1044 rect -0.0 -inf -> 0.0 0.0 ignore-real-sign ignore-imag-sign +rect1045 rect -2.3 -inf -> nan nan invalid +rect1046 rect -inf -inf -> -inf nan invalid ignore-real-sign +rect1047 rect -inf -0.0 -> -inf 0.0 +rect1048 rect -inf -1.4 -> -inf inf +rect1049 rect -inf -2.8 -> inf inf +rect1050 rect -inf -4.2 -> inf -inf +rect1051 rect -inf -5.6 -> -inf -inf +rect1052 rect -inf -7.0 -> -inf inf + +------------------------------------------------------------------------- +-- polar: Conversion from rectangular coordinates to polar coordinates -- +------------------------------------------------------------------------- +-- +-- For cmath.polar, we can use the same testcase syntax as for the +-- complex -> complex functions above, but here the output arguments +-- should be interpreted as a pair of floating-point numbers rather +-- than the real and imaginary parts of a complex number. +-- +-- Annex G of the C99 standard describes fully both the real and +-- imaginary parts of polar (as cabs and carg, respectively, which in turn +-- are defined in terms of the functions hypot and atan2). + +-- overflow +polar0100 polar 1.4e308 1.4e308 -> inf 0.78539816339744828 overflow + +-- special values +polar1000 polar 0.0 0.0 -> 0.0 0.0 +polar1001 polar 0.0 -0.0 -> 0.0 -0.0 +polar1002 polar -0.0 0.0 -> 0.0 3.1415926535897931 +polar1003 polar -0.0 -0.0 -> 0.0 -3.1415926535897931 +polar1004 polar inf 0.0 -> inf 0.0 +polar1005 polar inf 2.3 -> inf 0.0 +polar1006 polar inf inf -> inf 0.78539816339744828 +polar1007 polar 2.3 inf -> inf 1.5707963267948966 +polar1008 polar 0.0 inf -> inf 1.5707963267948966 +polar1009 polar -0.0 inf -> inf 1.5707963267948966 +polar1010 polar -2.3 inf -> inf 1.5707963267948966 +polar1011 polar -inf inf -> inf 2.3561944901923448 +polar1012 polar -inf 2.3 -> inf 3.1415926535897931 +polar1013 polar -inf 0.0 -> inf 3.1415926535897931 +polar1014 polar -inf -0.0 -> inf -3.1415926535897931 +polar1015 polar -inf -2.3 -> inf -3.1415926535897931 +polar1016 polar -inf -inf -> inf -2.3561944901923448 +polar1017 polar -2.3 -inf -> inf -1.5707963267948966 +polar1018 polar -0.0 -inf -> inf -1.5707963267948966 +polar1019 polar 0.0 -inf -> inf -1.5707963267948966 +polar1020 polar 2.3 -inf -> inf -1.5707963267948966 +polar1021 polar inf -inf -> inf -0.78539816339744828 +polar1022 polar inf -2.3 -> inf -0.0 +polar1023 polar inf -0.0 -> inf -0.0 +polar1024 polar nan -inf -> inf nan +polar1025 polar nan -2.3 -> nan nan +polar1026 polar nan -0.0 -> nan nan +polar1027 polar nan 0.0 -> nan nan +polar1028 polar nan 2.3 -> nan nan +polar1029 polar nan inf -> inf nan +polar1030 polar nan nan -> nan nan +polar1031 polar inf nan -> inf nan +polar1032 polar 2.3 nan -> nan nan +polar1033 polar 0.0 nan -> nan nan +polar1034 polar -0.0 nan -> nan nan +polar1035 polar -2.3 nan -> nan nan +polar1036 polar -inf nan -> inf nan diff --git a/Lib/test/ieee754.txt b/Lib/test/ieee754.txt new file mode 100644 index 0000000..5a41c8f --- /dev/null +++ b/Lib/test/ieee754.txt @@ -0,0 +1,183 @@ +====================================== +Python IEEE 754 floating point support +====================================== + +>>> from sys import float_info as FI +>>> from math import * +>>> PI = pi +>>> E = e + +You must never compare two floats with == because you are not going to get +what you expect. We treat two floats as equal if the difference between them +is small than epsilon. +>>> EPS = 1E-15 +>>> def equal(x, y): +... """Almost equal helper for floats""" +... return abs(x - y) < EPS + + +NaNs and INFs +============= + +In Python 2.6 and newer NaNs (not a number) and infinity can be constructed +from the strings 'inf' and 'nan'. + +>>> INF = float('inf') +>>> NINF = float('-inf') +>>> NAN = float('nan') + +>>> INF +inf +>>> NINF +-inf +>>> NAN +nan + +The math module's ``isnan`` and ``isinf`` functions can be used to detect INF +and NAN: +>>> isinf(INF), isinf(NINF), isnan(NAN) +(True, True, True) +>>> INF == -NINF +True + +Infinity +-------- + +Ambiguous operations like ``0 * inf`` or ``inf - inf`` result in NaN. +>>> INF * 0 +nan +>>> INF - INF +nan +>>> INF / INF +nan + +However unambigous operations with inf return inf: +>>> INF * INF +inf +>>> 1.5 * INF +inf +>>> 0.5 * INF +inf +>>> INF / 1000 +inf + +Not a Number +------------ + +NaNs are never equal to another number, even itself +>>> NAN == NAN +False +>>> NAN < 0 +False +>>> NAN >= 0 +False + +All operations involving a NaN return a NaN except for the power of *0* and *1*. +>>> 1 + NAN +nan +>>> 1 * NAN +nan +>>> 0 * NAN +nan +>>> 1 ** NAN +1.0 +>>> 0 ** NAN +0.0 +>>> (1.0 + FI.epsilon) * NAN +nan + +Misc Functions +============== + +The power of 1 raised to x is always 1.0, even for special values like 0, +infinity and NaN. + +>>> pow(1, 0) +1.0 +>>> pow(1, INF) +1.0 +>>> pow(1, -INF) +1.0 +>>> pow(1, NAN) +1.0 + +The power of 0 raised to x is defined as 0, if x is positive. Negative +values are a domain error or zero division error and NaN result in a +silent NaN. + +>>> pow(0, 0) +1.0 +>>> pow(0, INF) +0.0 +>>> pow(0, -INF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> 0 ** -1 +Traceback (most recent call last): +... +ZeroDivisionError: 0.0 cannot be raised to a negative power +>>> pow(0, NAN) +nan + + +Trigonometric Functions +======================= + +>>> sin(INF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> sin(NINF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> sin(NAN) +nan +>>> cos(INF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> cos(NINF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> cos(NAN) +nan +>>> tan(INF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> tan(NINF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> tan(NAN) +nan + +Neither pi nor tan are exact, but you can assume that tan(pi/2) is a large value +and tan(pi) is a very small value: +>>> tan(PI/2) > 1E10 +True +>>> -tan(-PI/2) > 1E10 +True +>>> tan(PI) < 1E-15 +True + +>>> asin(NAN), acos(NAN), atan(NAN) +(nan, nan, nan) +>>> asin(INF), asin(NINF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> acos(INF), acos(NINF) +Traceback (most recent call last): +... +ValueError: math domain error +>>> equal(atan(INF), PI/2), equal(atan(NINF), -PI/2) +(True, True) + + +Hyberbolic Functions +==================== + diff --git a/Lib/test/test_cmath.py b/Lib/test/test_cmath.py index 7c5f4a5..ca4945d 100755 --- a/Lib/test/test_cmath.py +++ b/Lib/test/test_cmath.py @@ -1,6 +1,81 @@ from test.test_support import run_unittest +from test.test_math import parse_testfile, test_file import unittest +import os, sys import cmath, math +from cmath import phase, polar, rect, pi + +INF = float('inf') +NAN = float('nan') + +complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]] +complex_infinities = [complex(x, y) for x, y in [ + (INF, 0.0), # 1st quadrant + (INF, 2.3), + (INF, INF), + (2.3, INF), + (0.0, INF), + (-0.0, INF), # 2nd quadrant + (-2.3, INF), + (-INF, INF), + (-INF, 2.3), + (-INF, 0.0), + (-INF, -0.0), # 3rd quadrant + (-INF, -2.3), + (-INF, -INF), + (-2.3, -INF), + (-0.0, -INF), + (0.0, -INF), # 4th quadrant + (2.3, -INF), + (INF, -INF), + (INF, -2.3), + (INF, -0.0) + ]] +complex_nans = [complex(x, y) for x, y in [ + (NAN, -INF), + (NAN, -2.3), + (NAN, -0.0), + (NAN, 0.0), + (NAN, 2.3), + (NAN, INF), + (-INF, NAN), + (-2.3, NAN), + (-0.0, NAN), + (0.0, NAN), + (2.3, NAN), + (INF, NAN) + ]] + +def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323): + """Determine whether floating-point values a and b are equal to within + a (small) rounding error. The default values for rel_err and + abs_err are chosen to be suitable for platforms where a float is + represented by an IEEE 754 double. They allow an error of between + 9 and 19 ulps.""" + + # special values testing + if math.isnan(a): + return math.isnan(b) + if math.isinf(a): + return a == b + + # if both a and b are zero, check whether they have the same sign + # (in theory there are examples where it would be legitimate for a + # and b to have opposite signs; in practice these hardly ever + # occur). + if not a and not b: + return math.copysign(1., a) == math.copysign(1., b) + + # if a-b overflows, or b is infinite, return False. Again, in + # theory there are examples where a is within a few ulps of the + # max representable float, and then b could legitimately be + # infinite. In practice these examples are rare. + try: + absolute_error = abs(b-a) + except OverflowError: + return False + else: + return absolute_error <= max(abs_err, rel_err * abs(a)) class CMathTests(unittest.TestCase): # list of all functions in cmath @@ -12,25 +87,51 @@ class CMathTests(unittest.TestCase): test_functions.append(lambda x : cmath.log(x, 1729. + 0j)) test_functions.append(lambda x : cmath.log(14.-27j, x)) - def cAssertAlmostEqual(self, a, b, rel_eps = 1e-10, abs_eps = 1e-100): - """Check that two complex numbers are almost equal.""" - # the two complex numbers are considered almost equal if - # either the relative error is <= rel_eps or the absolute error - # is tiny, <= abs_eps. - if a == b == 0: - return - absolute_error = abs(a-b) - relative_error = absolute_error/max(abs(a), abs(b)) - if relative_error > rel_eps and absolute_error > abs_eps: - self.fail("%s and %s are not almost equal" % (a, b)) + def setUp(self): + self.test_values = open(test_file) + + def tearDown(self): + self.test_values.close() + + def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 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 + # machine. + + try: + absolute_error = abs(b-a) + except OverflowError: + pass + else: + if absolute_error <= max(abs_err, rel_err * abs(a)): + return + self.fail("%s and %s are not sufficiently close" % (repr(a), repr(b))) def test_constants(self): e_expected = 2.71828182845904523536 pi_expected = 3.14159265358979323846 - self.assertAlmostEqual(cmath.pi, pi_expected, places=9, - msg="cmath.pi is %s; should be %s" % (cmath.pi, pi_expected)) - self.assertAlmostEqual(cmath.e, e_expected, places=9, - msg="cmath.e is %s; should be %s" % (cmath.e, e_expected)) + self.assertAlmostEqual(cmath.pi, pi_expected) + self.assertAlmostEqual(cmath.e, e_expected) def test_user_object(self): # Test automatic calling of __complex__ and __float__ by cmath @@ -109,13 +210,13 @@ class CMathTests(unittest.TestCase): for f in self.test_functions: # usual usage - self.cAssertAlmostEqual(f(MyComplex(cx_arg)), f(cx_arg)) - self.cAssertAlmostEqual(f(MyComplexOS(cx_arg)), f(cx_arg)) + self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg)) + self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg)) # other combinations of __float__ and __complex__ - self.cAssertAlmostEqual(f(FloatAndComplex()), f(cx_arg)) - self.cAssertAlmostEqual(f(FloatAndComplexOS()), f(cx_arg)) - self.cAssertAlmostEqual(f(JustFloat()), f(flt_arg)) - self.cAssertAlmostEqual(f(JustFloatOS()), f(flt_arg)) + self.assertEqual(f(FloatAndComplex()), f(cx_arg)) + self.assertEqual(f(FloatAndComplexOS()), f(cx_arg)) + self.assertEqual(f(JustFloat()), f(flt_arg)) + self.assertEqual(f(JustFloatOS()), f(flt_arg)) # TypeError should be raised for classes not providing # either __complex__ or __float__, even if they provide # __int__, __long__ or __index__. An old-style class @@ -138,7 +239,7 @@ class CMathTests(unittest.TestCase): # functions, by virtue of providing a __float__ method for f in self.test_functions: for arg in [2, 2.]: - self.cAssertAlmostEqual(f(arg), f(arg.__float__())) + self.assertEqual(f(arg), f(arg.__float__())) # but strings should give a TypeError for f in self.test_functions: @@ -182,12 +283,201 @@ class CMathTests(unittest.TestCase): float_fn = getattr(math, fn) complex_fn = getattr(cmath, fn) for v in values: - self.cAssertAlmostEqual(float_fn(v), complex_fn(v)) + z = complex_fn(v) + self.rAssertAlmostEqual(float_fn(v), z.real) + self.assertEqual(0., z.imag) # test two-argument version of log with various bases for base in [0.5, 2., 10.]: for v in positive: - self.cAssertAlmostEqual(cmath.log(v, base), math.log(v, base)) + z = cmath.log(v, base) + self.rAssertAlmostEqual(math.log(v, base), z.real) + self.assertEqual(0., z.imag) + + def test_specific_values(self): + if not float.__getformat__("double").startswith("IEEE"): + return + + def rect_complex(z): + """Wrapped version of rect that accepts a complex number instead of + two float arguments.""" + return cmath.rect(z.real, z.imag) + + def polar_complex(z): + """Wrapped version of polar that returns a complex number instead of + two floats.""" + return complex(*polar(z)) + + for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): + arg = complex(ar, ai) + expected = complex(er, ei) + if fn == 'rect': + function = rect_complex + elif fn == 'polar': + function = polar_complex + else: + function = getattr(cmath, fn) + if 'divide-by-zero' in flags or 'invalid' in flags: + try: + actual = function(arg) + except ValueError: + continue + else: + test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai) + self.fail('ValueError not raised in test %s' % test_str) + + if 'overflow' in flags: + try: + actual = function(arg) + except OverflowError: + continue + else: + test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai) + self.fail('OverflowError not raised in test %s' % test_str) + + actual = function(arg) + + if 'ignore-real-sign' in flags: + actual = complex(abs(actual.real), actual.imag) + expected = complex(abs(expected.real), expected.imag) + if 'ignore-imag-sign' in flags: + actual = complex(actual.real, abs(actual.imag)) + expected = complex(expected.real, abs(expected.imag)) + + # for the real part of the log function, we allow an + # absolute error of up to 2e-15. + if fn in ('log', 'log10'): + real_abs_err = 2e-15 + else: + real_abs_err = 5e-323 + + if not (almostEqualF(expected.real, actual.real, + abs_err = real_abs_err) and + almostEqualF(expected.imag, actual.imag)): + error_message = ( + "%s: %s(complex(%r, %r))\n" % (id, fn, ar, ai) + + "Expected: complex(%r, %r)\n" % + (expected.real, expected.imag) + + "Received: complex(%r, %r)\n" % + (actual.real, actual.imag) + + "Received value insufficiently close to expected value.") + self.fail(error_message) + + def assertCISEqual(self, a, b): + eps = 1E-7 + if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps: + self.fail((a ,b)) + + def test_polar(self): + self.assertCISEqual(polar(0), (0., 0.)) + self.assertCISEqual(polar(1.), (1., 0.)) + self.assertCISEqual(polar(-1.), (1., pi)) + self.assertCISEqual(polar(1j), (1., pi/2)) + self.assertCISEqual(polar(-1j), (1., -pi/2)) + + def test_phase(self): + self.assertAlmostEqual(phase(0), 0.) + self.assertAlmostEqual(phase(1.), 0.) + self.assertAlmostEqual(phase(-1.), pi) + self.assertAlmostEqual(phase(-1.+1E-300j), pi) + self.assertAlmostEqual(phase(-1.-1E-300j), -pi) + self.assertAlmostEqual(phase(1j), pi/2) + self.assertAlmostEqual(phase(-1j), -pi/2) + + # zeros + self.assertEqual(phase(complex(0.0, 0.0)), 0.0) + self.assertEqual(phase(complex(0.0, -0.0)), -0.0) + self.assertEqual(phase(complex(-0.0, 0.0)), pi) + self.assertEqual(phase(complex(-0.0, -0.0)), -pi) + + # infinities + self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi) + self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi) + self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi) + self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4) + self.assertEqual(phase(complex(INF, -2.3)), -0.0) + self.assertEqual(phase(complex(INF, -0.0)), -0.0) + self.assertEqual(phase(complex(INF, 0.0)), 0.0) + self.assertEqual(phase(complex(INF, 2.3)), 0.0) + self.assertAlmostEqual(phase(complex(INF, INF)), pi/4) + self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2) + self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi) + self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi) + self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi) + + # real or imaginary part NaN + for z in complex_nans: + self.assert_(math.isnan(phase(z))) + + def test_abs(self): + # zeros + for z in complex_zeros: + self.assertEqual(abs(z), 0.0) + + # infinities + for z in complex_infinities: + self.assertEqual(abs(z), INF) + + # real or imaginary part NaN + self.assertEqual(abs(complex(NAN, -INF)), INF) + self.assert_(math.isnan(abs(complex(NAN, -2.3)))) + self.assert_(math.isnan(abs(complex(NAN, -0.0)))) + self.assert_(math.isnan(abs(complex(NAN, 0.0)))) + self.assert_(math.isnan(abs(complex(NAN, 2.3)))) + self.assertEqual(abs(complex(NAN, INF)), INF) + self.assertEqual(abs(complex(-INF, NAN)), INF) + self.assert_(math.isnan(abs(complex(-2.3, NAN)))) + self.assert_(math.isnan(abs(complex(-0.0, NAN)))) + self.assert_(math.isnan(abs(complex(0.0, NAN)))) + self.assert_(math.isnan(abs(complex(2.3, NAN)))) + self.assertEqual(abs(complex(INF, NAN)), INF) + self.assert_(math.isnan(abs(complex(NAN, NAN)))) + + # result overflows + if float.__getformat__("double").startswith("IEEE"): + self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308)) + + def assertCEqual(self, a, b): + eps = 1E-7 + if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps: + self.fail((a ,b)) + + def test_rect(self): + self.assertCEqual(rect(0, 0), (0, 0)) + self.assertCEqual(rect(1, 0), (1., 0)) + self.assertCEqual(rect(1, -pi), (-1., 0)) + self.assertCEqual(rect(1, pi/2), (0, 1.)) + self.assertCEqual(rect(1, -pi/2), (0, -1.)) + + def test_isnan(self): + self.failIf(cmath.isnan(1)) + self.failIf(cmath.isnan(1j)) + self.failIf(cmath.isnan(INF)) + self.assert_(cmath.isnan(NAN)) + self.assert_(cmath.isnan(complex(NAN, 0))) + self.assert_(cmath.isnan(complex(0, NAN))) + self.assert_(cmath.isnan(complex(NAN, NAN))) + self.assert_(cmath.isnan(complex(NAN, INF))) + self.assert_(cmath.isnan(complex(INF, NAN))) + + def test_isinf(self): + self.failIf(cmath.isinf(1)) + self.failIf(cmath.isinf(1j)) + self.failIf(cmath.isinf(NAN)) + self.assert_(cmath.isinf(INF)) + self.assert_(cmath.isinf(complex(INF, 0))) + self.assert_(cmath.isinf(complex(0, INF))) + self.assert_(cmath.isinf(complex(INF, INF))) + self.assert_(cmath.isinf(complex(NAN, INF))) + self.assert_(cmath.isinf(complex(INF, NAN))) + def test_main(): run_unittest(CMathTests) diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py index b9ad8c5..e89d723 100644 --- a/Lib/test/test_float.py +++ b/Lib/test/test_float.py @@ -2,12 +2,12 @@ import unittest, struct import os from test import test_support +import math +from math import isinf, isnan +import operator -def isinf(x): - return x * 0.5 == x - -def isnan(x): - return x != x +INF = float("inf") +NAN = float("nan") class FormatFunctionsTestCase(unittest.TestCase): @@ -239,6 +239,17 @@ class InfNanTest(unittest.TestCase): self.assertEqual(str(1e300 * 1e300 * 0), "nan") self.assertEqual(str(-1e300 * 1e300 * 0), "nan") + def notest_float_nan(self): + self.assert_(NAN.is_nan()) + self.failIf(INF.is_nan()) + self.failIf((0.).is_nan()) + + def notest_float_inf(self): + self.assert_(INF.is_inf()) + self.failIf(NAN.is_inf()) + self.failIf((0.).is_inf()) + + def test_main(): test_support.run_unittest( FormatFunctionsTestCase, diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py index aa44253..b8c23db 100644 --- a/Lib/test/test_math.py +++ b/Lib/test/test_math.py @@ -4,9 +4,45 @@ from test.test_support import run_unittest, verbose import unittest import math +import os +import sys -seps='1e-05' -eps = eval(seps) +eps = 1E-05 +NAN = float('nan') +INF = float('inf') +NINF = float('-inf') + +# locate file with test values +if __name__ == '__main__': + file = sys.argv[0] +else: + file = __file__ +test_dir = os.path.dirname(file) or os.curdir +test_file = os.path.join(test_dir, 'cmath_testcases.txt') + +def parse_testfile(fname): + """Parse a file with test values + + Empty lines or lines starting with -- are ignored + yields id, fn, arg_real, arg_imag, exp_real, exp_imag + """ + with open(fname) as fp: + for line in fp: + # skip comment lines and blank lines + if line.startswith('--') or not line.strip(): + continue + + lhs, rhs = line.split('->') + id, fn, arg_real, arg_imag = lhs.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), + flags + ) class MathTests(unittest.TestCase): @@ -28,18 +64,57 @@ class MathTests(unittest.TestCase): self.ftest('acos(-1)', math.acos(-1), math.pi) self.ftest('acos(0)', math.acos(0), math.pi/2) self.ftest('acos(1)', math.acos(1), 0) + self.assertRaises(ValueError, math.acos, INF) + self.assertRaises(ValueError, math.acos, NINF) + self.assert_(math.isnan(math.acos(NAN))) + + def testAcosh(self): + self.assertRaises(TypeError, math.acosh) + self.ftest('acosh(1)', math.acosh(1), 0) + self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168) + self.assertRaises(ValueError, math.acosh, 0) + self.assertRaises(ValueError, math.acosh, -1) + self.assertEquals(math.acosh(INF), INF) + self.assertRaises(ValueError, math.acosh, NINF) + self.assert_(math.isnan(math.acosh(NAN))) def testAsin(self): self.assertRaises(TypeError, math.asin) self.ftest('asin(-1)', math.asin(-1), -math.pi/2) self.ftest('asin(0)', math.asin(0), 0) self.ftest('asin(1)', math.asin(1), math.pi/2) + self.assertRaises(ValueError, math.asin, INF) + self.assertRaises(ValueError, math.asin, NINF) + self.assert_(math.isnan(math.asin(NAN))) + + def testAsinh(self): + self.assertRaises(TypeError, math.asinh) + self.ftest('asinh(0)', math.asinh(0), 0) + self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305) + self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305) + self.assertEquals(math.asinh(INF), INF) + self.assertEquals(math.asinh(NINF), NINF) + self.assert_(math.isnan(math.asinh(NAN))) def testAtan(self): self.assertRaises(TypeError, math.atan) self.ftest('atan(-1)', math.atan(-1), -math.pi/4) self.ftest('atan(0)', math.atan(0), 0) self.ftest('atan(1)', math.atan(1), math.pi/4) + self.ftest('atan(inf)', math.atan(INF), math.pi/2) + self.ftest('atan(-inf)', math.atan(-INF), -math.pi/2) + self.assert_(math.isnan(math.atan(NAN))) + + def testAtanh(self): + self.assertRaises(TypeError, math.atan) + self.ftest('atanh(0)', math.atanh(0), 0) + self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489) + self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489) + self.assertRaises(ValueError, math.atanh, 1) + self.assertRaises(ValueError, math.atanh, -1) + self.assertRaises(ValueError, math.atanh, INF) + self.assertRaises(ValueError, math.atanh, NINF) + self.assert_(math.isnan(math.atanh(NAN))) def testAtan2(self): self.assertRaises(TypeError, math.atan2) @@ -58,6 +133,9 @@ class MathTests(unittest.TestCase): self.ftest('ceil(-0.5)', math.ceil(-0.5), 0) self.ftest('ceil(-1.0)', math.ceil(-1.0), -1) self.ftest('ceil(-1.5)', math.ceil(-1.5), -1) + #self.assertEquals(math.ceil(INF), INF) + #self.assertEquals(math.ceil(NINF), NINF) + #self.assert_(math.isnan(math.ceil(NAN))) class TestCeil: def __ceil__(self): @@ -72,17 +150,55 @@ class MathTests(unittest.TestCase): self.assertRaises(TypeError, math.ceil, t) self.assertRaises(TypeError, math.ceil, t, 0) + if float.__getformat__("double").startswith("IEEE"): + def testCopysign(self): + self.assertRaises(TypeError, math.copysign) + # copysign should let us distinguish signs of zeros + self.assertEquals(copysign(1., 0.), 1.) + self.assertEquals(copysign(1., -0.), -1.) + self.assertEquals(copysign(INF, 0.), INF) + self.assertEquals(copysign(INF, -0.), NINF) + self.assertEquals(copysign(NINF, 0.), INF) + self.assertEquals(copysign(NINF, -0.), NINF) + # and of infinities + self.assertEquals(copysign(1., INF), 1.) + self.assertEquals(copysign(1., NINF), -1.) + self.assertEquals(copysign(INF, INF), INF) + self.assertEquals(copysign(INF, NINF), NINF) + self.assertEquals(copysign(NINF, INF), INF) + self.assertEquals(copysign(NINF, NINF), NINF) + self.assert_(math.isnan(copysign(NAN, 1.))) + self.assert_(math.isnan(copysign(NAN, INF))) + self.assert_(math.isnan(copysign(NAN, NINF))) + self.assert_(math.isnan(copysign(NAN, NAN))) + # copysign(INF, NAN) may be INF or it may be NINF, since + # we don't know whether the sign bit of NAN is set on any + # given platform. + self.assert_(math.isinf(copysign(INF, NAN))) + # similarly, copysign(2., NAN) could be 2. or -2. + self.assertEquals(abs(copysign(2., NAN)), 2.) + def testCos(self): self.assertRaises(TypeError, math.cos) self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0) self.ftest('cos(0)', math.cos(0), 1) self.ftest('cos(pi/2)', math.cos(math.pi/2), 0) self.ftest('cos(pi)', math.cos(math.pi), -1) + try: + self.assert_(math.isnan(math.cos(INF))) + self.assert_(math.isnan(math.cos(NINF))) + except ValueError: + self.assertRaises(ValueError, math.cos, INF) + self.assertRaises(ValueError, math.cos, NINF) + self.assert_(math.isnan(math.cos(NAN))) def testCosh(self): self.assertRaises(TypeError, math.cosh) self.ftest('cosh(0)', math.cosh(0), 1) self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert + self.assertEquals(math.cosh(INF), INF) + self.assertEquals(math.cosh(NINF), INF) + self.assert_(math.isnan(math.cosh(NAN))) def testDegrees(self): self.assertRaises(TypeError, math.degrees) @@ -95,6 +211,9 @@ class MathTests(unittest.TestCase): self.ftest('exp(-1)', math.exp(-1), 1/math.e) self.ftest('exp(0)', math.exp(0), 1) self.ftest('exp(1)', math.exp(1), math.e) + self.assertEquals(math.exp(INF), INF) + self.assertEquals(math.exp(NINF), 0.) + self.assert_(math.isnan(math.exp(NAN))) def testFabs(self): self.assertRaises(TypeError, math.fabs) @@ -115,6 +234,9 @@ class MathTests(unittest.TestCase): # This fails on some platforms - so check it here self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167) self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167) + #self.assertEquals(math.ceil(INF), INF) + #self.assertEquals(math.ceil(NINF), NINF) + #self.assert_(math.isnan(math.floor(NAN))) class TestFloor: def __floor__(self): @@ -137,6 +259,19 @@ class MathTests(unittest.TestCase): self.ftest('fmod(-10,1)', math.fmod(-10,1), 0) self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0) self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1) + self.assert_(math.isnan(math.fmod(NAN, 1.))) + self.assert_(math.isnan(math.fmod(1., NAN))) + self.assert_(math.isnan(math.fmod(NAN, NAN))) + self.assertRaises(ValueError, math.fmod, 1., 0.) + self.assertRaises(ValueError, math.fmod, INF, 1.) + self.assertRaises(ValueError, math.fmod, NINF, 1.) + self.assertRaises(ValueError, math.fmod, INF, 0.) + self.assertEquals(math.fmod(3.0, INF), 3.0) + self.assertEquals(math.fmod(-3.0, INF), -3.0) + self.assertEquals(math.fmod(3.0, NINF), 3.0) + self.assertEquals(math.fmod(-3.0, NINF), -3.0) + self.assertEquals(math.fmod(0.0, 3.0), 0.0) + self.assertEquals(math.fmod(0.0, NINF), 0.0) def testFrexp(self): self.assertRaises(TypeError, math.frexp) @@ -152,10 +287,20 @@ class MathTests(unittest.TestCase): testfrexp('frexp(1)', math.frexp(1), (0.5, 1)) testfrexp('frexp(2)', math.frexp(2), (0.5, 2)) + self.assertEquals(math.frexp(INF)[0], INF) + self.assertEquals(math.frexp(NINF)[0], NINF) + self.assert_(math.isnan(math.frexp(NAN)[0])) + def testHypot(self): self.assertRaises(TypeError, math.hypot) self.ftest('hypot(0,0)', math.hypot(0,0), 0) self.ftest('hypot(3,4)', math.hypot(3,4), 5) + self.assertEqual(math.hypot(NAN, INF), INF) + self.assertEqual(math.hypot(INF, NAN), INF) + self.assertEqual(math.hypot(NAN, NINF), INF) + self.assertEqual(math.hypot(NINF, NAN), INF) + self.assert_(math.isnan(math.hypot(1.0, NAN))) + self.assert_(math.isnan(math.hypot(NAN, -2.0))) def testLdexp(self): self.assertRaises(TypeError, math.ldexp) @@ -163,6 +308,13 @@ class MathTests(unittest.TestCase): self.ftest('ldexp(1,1)', math.ldexp(1,1), 2) self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5) self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2) + self.assertRaises(OverflowError, math.ldexp, 1., 1000000) + self.assertRaises(OverflowError, math.ldexp, -1., 1000000) + self.assertEquals(math.ldexp(1., -1000000), 0.) + self.assertEquals(math.ldexp(-1., -1000000), -0.) + self.assertEquals(math.ldexp(INF, 30), INF) + self.assertEquals(math.ldexp(NINF, -213), NINF) + self.assert_(math.isnan(math.ldexp(NAN, 0))) def testLog(self): self.assertRaises(TypeError, math.log) @@ -172,12 +324,31 @@ class MathTests(unittest.TestCase): self.ftest('log(32,2)', math.log(32,2), 5) self.ftest('log(10**40, 10)', math.log(10**40, 10), 40) self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2) + self.assertEquals(math.log(INF), INF) + self.assertRaises(ValueError, math.log, NINF) + self.assert_(math.isnan(math.log(NAN))) + + def testLog1p(self): + self.assertRaises(TypeError, math.log1p) + self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1) + self.ftest('log1p(0)', math.log1p(0), 0) + self.ftest('log1p(e-1)', math.log1p(math.e-1), 1) + self.ftest('log1p(1)', math.log1p(1), math.log(2)) + self.assertEquals(math.log1p(INF), INF) + self.assertRaises(ValueError, math.log1p, NINF) + self.assert_(math.isnan(math.log1p(NAN))) + n= 2**90 + self.assertAlmostEquals(math.log1p(n), 62.383246250395075) + self.assertAlmostEquals(math.log1p(n), math.log1p(float(n))) def testLog10(self): self.assertRaises(TypeError, math.log10) self.ftest('log10(0.1)', math.log10(0.1), -1) self.ftest('log10(1)', math.log10(1), 0) self.ftest('log10(10)', math.log10(10), 1) + self.assertEquals(math.log(INF), INF) + self.assertRaises(ValueError, math.log10, NINF) + self.assert_(math.isnan(math.log10(NAN))) def testModf(self): self.assertRaises(TypeError, math.modf) @@ -191,12 +362,35 @@ class MathTests(unittest.TestCase): testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0)) testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0)) + self.assertEquals(math.modf(INF), (0.0, INF)) + self.assertEquals(math.modf(NINF), (-0.0, NINF)) + + modf_nan = math.modf(NAN) + self.assert_(math.isnan(modf_nan[0])) + self.assert_(math.isnan(modf_nan[1])) + def testPow(self): self.assertRaises(TypeError, math.pow) self.ftest('pow(0,1)', math.pow(0,1), 0) self.ftest('pow(1,0)', math.pow(1,0), 1) self.ftest('pow(2,1)', math.pow(2,1), 2) self.ftest('pow(2,-1)', math.pow(2,-1), 0.5) + self.assertEqual(math.pow(INF, 1), INF) + self.assertEqual(math.pow(NINF, 1), NINF) + self.assertEqual((math.pow(1, INF)), 1.) + self.assertEqual((math.pow(1, NINF)), 1.) + self.assert_(math.isnan(math.pow(NAN, 1))) + self.assert_(math.isnan(math.pow(2, NAN))) + self.assert_(math.isnan(math.pow(0, NAN))) + self.assertEqual(math.pow(1, NAN), 1) + self.assertEqual(1**NAN, 1) + self.assertEqual(1**INF, 1) + self.assertEqual(1**NINF, 1) + self.assertEqual(1**0, 1) + self.assertEqual(1.**NAN, 1) + self.assertEqual(1.**INF, 1) + self.assertEqual(1.**NINF, 1) + self.assertEqual(1.**0, 1) def testRadians(self): self.assertRaises(TypeError, math.radians) @@ -209,29 +403,52 @@ class MathTests(unittest.TestCase): self.ftest('sin(0)', math.sin(0), 0) self.ftest('sin(pi/2)', math.sin(math.pi/2), 1) self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1) + try: + self.assert_(math.isnan(math.sin(INF))) + self.assert_(math.isnan(math.sin(NINF))) + except ValueError: + self.assertRaises(ValueError, math.sin, INF) + self.assertRaises(ValueError, math.sin, NINF) + self.assert_(math.isnan(math.sin(NAN))) def testSinh(self): self.assertRaises(TypeError, math.sinh) self.ftest('sinh(0)', math.sinh(0), 0) self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1) self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0) + self.assertEquals(math.sinh(INF), INF) + self.assertEquals(math.sinh(-INF), -INF) + self.assert_(math.isnan(math.sinh(NAN))) def testSqrt(self): self.assertRaises(TypeError, math.sqrt) self.ftest('sqrt(0)', math.sqrt(0), 0) self.ftest('sqrt(1)', math.sqrt(1), 1) self.ftest('sqrt(4)', math.sqrt(4), 2) + self.assertEquals(math.sqrt(INF), INF) + self.assertRaises(ValueError, math.sqrt, NINF) + self.assert_(math.isnan(math.sqrt(NAN))) def testTan(self): self.assertRaises(TypeError, math.tan) self.ftest('tan(0)', math.tan(0), 0) self.ftest('tan(pi/4)', math.tan(math.pi/4), 1) self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1) + try: + self.assert_(math.isnan(math.tan(INF))) + self.assert_(math.isnan(math.tan(NINF))) + except: + self.assertRaises(ValueError, math.tan, INF) + self.assertRaises(ValueError, math.tan, NINF) + self.assert_(math.isnan(math.tan(NAN))) def testTanh(self): self.assertRaises(TypeError, math.tanh) self.ftest('tanh(0)', math.tanh(0), 0) self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0) + self.ftest('tanh(inf)', math.tanh(INF), 1) + self.ftest('tanh(-inf)', math.tanh(NINF), -1) + self.assert_(math.isnan(math.tanh(NAN))) def test_trunc(self): self.assertEqual(math.trunc(1), 1) @@ -326,9 +543,27 @@ class MathTests(unittest.TestCase): else: self.fail("sqrt(-1) didn't raise ValueError") + def test_testfile(self): + if not float.__getformat__("double").startswith("IEEE"): + return + 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 + if fn in ['rect', 'polar']: + # no real versions of rect, polar + continue + func = getattr(math, fn) + result = func(ar) + self.ftest("%s:%s(%r)" % (id, fn, ar), result, er) def test_main(): - run_unittest(MathTests) + from doctest import DocFileSuite + suite = unittest.TestSuite() + suite.addTest(unittest.makeSuite(MathTests)) + suite.addTest(DocFileSuite("ieee754.txt")) + run_unittest(suite) if __name__ == '__main__': test_main() |