Tryag File Manager
Home
||
Turbo Force
||
B-F Config_Cpanel
Current Path :
/
usr
/
local
/
lib
/
python3.9
/
test
/
Or
Select Your Path :
Upload File :
New :
File
Dir
//usr/local/lib/python3.9/test/cmath_testcases.txt
-- 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. -- The majority of the values below were computed with the help of -- version 2.3 of the MPFR library for multiple-precision -- floating-point computations with correct rounding. All output -- values in this file are (modulo yet-to-be-discovered bugs) -- correctly rounded, provided that each input and output decimal -- floating-point value below is interpreted as a representation of -- the corresponding nearest IEEE 754 double-precision value. See the -- MPFR homepage at http://www.mpfr.org for more information about the -- MPFR project. -- A minority of the test cases were generated with the help of -- mpmath 0.19 at 100 bit accuracy (http://mpmath.org) to improve -- coverage of real functions with real-valued arguments. These are -- used in test.test_math.MathTests.test_testfile, as well as in -- test_cmath. -------------------------- -- acos: Inverse cosine -- -------------------------- -- 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 -- These are tested in testAtanSign in test_cmath.py -- 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 -- Additional real values (mpmath) atan0400 atan 1.7976931348623157e+308 0.0 -> 1.5707963267948966192 0.0 atan0401 atan -1.7976931348623157e+308 0.0 -> -1.5707963267948966192 0.0 atan0402 atan 1e-17 0.0 -> 1.0000000000000000715e-17 0.0 atan0403 atan -1e-17 0.0 -> -1.0000000000000000715e-17 0.0 atan0404 atan 0.0001 0.0 -> 0.000099999999666666673459 0.0 atan0405 atan -0.0001 0.0 -> -0.000099999999666666673459 0.0 atan0406 atan 0.999999999999999 0.0 -> 0.78539816339744781002 0.0 atan0407 atan 1.000000000000001 0.0 -> 0.78539816339744886473 0.0 atan0408 atan 14.101419947171719 0.0 -> 1.4999999999999999969 0.0 atan0409 atan 1255.7655915007897 0.0 -> 1.5700000000000000622 0.0 -- special values atan1000 atan -0.0 0.0 -> -0.0 0.0 atan1001 atan nan 0.0 -> nan 0.0 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 -- These are tested in testAtanhSign in test_cmath.py -- 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 -- Additional real values (mpmath) sqrt0150 sqrt 1.7976931348623157e+308 0.0 -> 1.3407807929942596355e+154 0.0 sqrt0151 sqrt 2.2250738585072014e-308 0.0 -> 1.4916681462400413487e-154 0.0 sqrt0152 sqrt 5e-324 0.0 -> 2.2227587494850774834e-162 0.0 -- special values sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0 sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0 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 -- Additional real values (mpmath) exp0070 exp 1e-08 0.0 -> 1.00000001000000005 0.0 exp0071 exp 0.0003 0.0 -> 1.0003000450045003375 0.0 exp0072 exp 0.2 0.0 -> 1.2214027581601698475 0.0 exp0073 exp 1.0 0.0 -> 2.7182818284590452354 0.0 exp0074 exp -1e-08 0.0 -> 0.99999999000000005 0.0 exp0075 exp -0.0003 0.0 -> 0.99970004499550033751 0.0 exp0076 exp -1.0 0.0 -> 0.3678794411714423216 0.0 exp0077 exp 2.220446049250313e-16 0.0 -> 1.000000000000000222 0.0 exp0078 exp -1.1102230246251565e-16 0.0 -> 0.99999999999999988898 0.0 exp0079 exp 2.302585092994046 0.0 -> 10.000000000000002171 0.0 exp0080 exp -2.302585092994046 0.0 -> 0.099999999999999978292 0.0 exp0081 exp 709.7827 0.0 -> 1.7976699566638014654e+308 0.0 -- special values exp1000 exp 0.0 0.0 -> 1.0 0.0 exp1001 exp -0.0 0.0 -> 1.0 0.0 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 -- Additional real values (mpmath) cosh0050 cosh 1e-150 0.0 -> 1.0 0.0 cosh0051 cosh 1e-18 0.0 -> 1.0 0.0 cosh0052 cosh 1e-09 0.0 -> 1.0000000000000000005 0.0 cosh0053 cosh 0.0003 0.0 -> 1.0000000450000003375 0.0 cosh0054 cosh 0.2 0.0 -> 1.0200667556190758485 0.0 cosh0055 cosh 1.0 0.0 -> 1.5430806348152437785 0.0 cosh0056 cosh -1e-18 0.0 -> 1.0 -0.0 cosh0057 cosh -0.0003 0.0 -> 1.0000000450000003375 -0.0 cosh0058 cosh -1.0 0.0 -> 1.5430806348152437785 -0.0 cosh0059 cosh 1.3169578969248168 0.0 -> 2.0000000000000001504 0.0 cosh0060 cosh -1.3169578969248168 0.0 -> 2.0000000000000001504 -0.0 cosh0061 cosh 17.328679513998633 0.0 -> 16777216.000000021938 0.0 cosh0062 cosh 18.714973875118524 0.0 -> 67108864.000000043662 0.0 cosh0063 cosh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0 cosh0064 cosh -709.7827 0.0 -> 8.9883497833190073272e+307 -0.0 -- special values cosh1000 cosh 0.0 0.0 -> 1.0 0.0 cosh1001 cosh 0.0 inf -> nan 0.0 invalid ignore-imag-sign 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 -- Additional real values (mpmath) sinh0050 sinh 1e-100 0.0 -> 1.00000000000000002e-100 0.0 sinh0051 sinh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0 sinh0052 sinh 1e-16 0.0 -> 9.999999999999999791e-17 0.0 sinh0053 sinh 3.7e-08 0.0 -> 3.7000000000000008885e-8 0.0 sinh0054 sinh 0.001 0.0 -> 0.0010000001666666750208 0.0 sinh0055 sinh 0.2 0.0 -> 0.20133600254109399895 0.0 sinh0056 sinh 1.0 0.0 -> 1.1752011936438014569 0.0 sinh0057 sinh -3.7e-08 0.0 -> -3.7000000000000008885e-8 0.0 sinh0058 sinh -0.001 0.0 -> -0.0010000001666666750208 0.0 sinh0059 sinh -1.0 0.0 -> -1.1752011936438014569 0.0 sinh0060 sinh 1.4436354751788103 0.0 -> 1.9999999999999999078 0.0 sinh0061 sinh -1.4436354751788103 0.0 -> -1.9999999999999999078 0.0 sinh0062 sinh 17.328679513998633 0.0 -> 16777215.999999992136 0.0 sinh0063 sinh 18.714973875118524 0.0 -> 67108864.000000036211 0.0 sinh0064 sinh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0 sinh0065 sinh -709.7827 0.0 -> -8.9883497833190073272e+307 0.0 -- special values sinh1000 sinh 0.0 0.0 -> 0.0 0.0 sinh1001 sinh 0.0 inf -> 0.0 nan invalid ignore-real-sign 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 -- ------------------------------ -- Disabled test: replaced by test_math.testTanhSign() -- and test_cmath.testTanhSign() -- -- 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 -- Additional real values (mpmath) tanh0050 tanh 1e-100 0.0 -> 1.00000000000000002e-100 0.0 tanh0051 tanh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0 tanh0052 tanh 1e-16 0.0 -> 9.999999999999999791e-17 0.0 tanh0053 tanh 3.7e-08 0.0 -> 3.6999999999999983559e-8 0.0 tanh0054 tanh 0.001 0.0 -> 0.00099999966666680002076 0.0 tanh0055 tanh 0.2 0.0 -> 0.19737532022490401141 0.0 tanh0056 tanh 1.0 0.0 -> 0.76159415595576488812 0.0 tanh0057 tanh -3.7e-08 0.0 -> -3.6999999999999983559e-8 0.0 tanh0058 tanh -0.001 0.0 -> -0.00099999966666680002076 0.0 tanh0059 tanh -1.0 0.0 -> -0.76159415595576488812 0.0 tanh0060 tanh 0.5493061443340549 0.0 -> 0.50000000000000003402 0.0 tanh0061 tanh -0.5493061443340549 0.0 -> -0.50000000000000003402 0.0 tanh0062 tanh 17.328679513998633 0.0 -> 0.99999999999999822364 0.0 tanh0063 tanh 18.714973875118524 0.0 -> 0.99999999999999988898 0.0 tanh0064 tanh 711 0.0 -> 1.0 0.0 tanh0065 tanh 1.797e+308 0.0 -> 1.0 0.0 --special values tanh1000 tanh 0.0 0.0 -> 0.0 0.0 tanh1001 tanh 0.0 inf -> nan nan invalid 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 -- Additional real values (mpmath) cos0050 cos 1e-150 0.0 -> 1.0 -0.0 cos0051 cos 1e-18 0.0 -> 1.0 -0.0 cos0052 cos 1e-09 0.0 -> 0.9999999999999999995 -0.0 cos0053 cos 0.0003 0.0 -> 0.9999999550000003375 -0.0 cos0054 cos 0.2 0.0 -> 0.98006657784124162892 -0.0 cos0055 cos 1.0 0.0 -> 0.5403023058681397174 -0.0 cos0056 cos -1e-18 0.0 -> 1.0 0.0 cos0057 cos -0.0003 0.0 -> 0.9999999550000003375 0.0 cos0058 cos -1.0 0.0 -> 0.5403023058681397174 0.0 cos0059 cos 1.0471975511965976 0.0 -> 0.50000000000000009945 -0.0 cos0060 cos 2.5707963267948966 0.0 -> -0.84147098480789647357 -0.0 cos0061 cos -2.5707963267948966 0.0 -> -0.84147098480789647357 0.0 cos0062 cos 7.225663103256523 0.0 -> 0.58778525229247407559 -0.0 cos0063 cos -8.79645943005142 0.0 -> -0.80901699437494722255 0.0 -- special values cos1000 cos -0.0 0.0 -> 1.0 0.0 cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign 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 -- Additional real values (mpmath) sin0050 sin 1e-100 0.0 -> 1.00000000000000002e-100 0.0 sin0051 sin 3.7e-08 0.0 -> 3.6999999999999992001e-8 0.0 sin0052 sin 0.001 0.0 -> 0.00099999983333334168748 0.0 sin0053 sin 0.2 0.0 -> 0.19866933079506122634 0.0 sin0054 sin 1.0 0.0 -> 0.84147098480789650665 0.0 sin0055 sin -3.7e-08 0.0 -> -3.6999999999999992001e-8 0.0 sin0056 sin -0.001 0.0 -> -0.00099999983333334168748 0.0 sin0057 sin -1.0 0.0 -> -0.84147098480789650665 0.0 sin0058 sin 0.5235987755982989 0.0 -> 0.50000000000000004642 0.0 sin0059 sin -0.5235987755982989 0.0 -> -0.50000000000000004642 0.0 sin0060 sin 2.6179938779914944 0.0 -> 0.49999999999999996018 -0.0 sin0061 sin -2.6179938779914944 0.0 -> -0.49999999999999996018 -0.0 sin0062 sin 7.225663103256523 0.0 -> 0.80901699437494673648 0.0 sin0063 sin -8.79645943005142 0.0 -> -0.58778525229247340658 -0.0 -- special values sin1000 sin -0.0 0.0 -> -0.0 0.0 sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign 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 -- Additional real values (mpmath) tan0050 tan 1e-100 0.0 -> 1.00000000000000002e-100 0.0 tan0051 tan 3.7e-08 0.0 -> 3.7000000000000017328e-8 0.0 tan0052 tan 0.001 0.0 -> 0.0010000003333334666875 0.0 tan0053 tan 0.2 0.0 -> 0.20271003550867249488 0.0 tan0054 tan 1.0 0.0 -> 1.5574077246549022305 0.0 tan0055 tan -3.7e-08 0.0 -> -3.7000000000000017328e-8 0.0 tan0056 tan -0.001 0.0 -> -0.0010000003333334666875 0.0 tan0057 tan -1.0 0.0 -> -1.5574077246549022305 0.0 tan0058 tan 0.4636476090008061 0.0 -> 0.49999999999999997163 0.0 tan0059 tan -0.4636476090008061 0.0 -> -0.49999999999999997163 0.0 tan0060 tan 1.1071487177940904 0.0 -> 1.9999999999999995298 0.0 tan0061 tan -1.1071487177940904 0.0 -> -1.9999999999999995298 0.0 tan0062 tan 1.5 0.0 -> 14.101419947171719388 0.0 tan0063 tan 1.57 0.0 -> 1255.7655915007896475 0.0 tan0064 tan 1.5707963267948961 0.0 -> 1978937966095219.0538 0.0 tan0065 tan 7.225663103256523 0.0 -> 1.3763819204711701522 0.0 tan0066 tan -8.79645943005142 0.0 -> 0.7265425280053614098 0.0 -- special values tan1000 tan -0.0 0.0 -> -0.0 0.0 tan1001 tan -inf 0.0 -> nan nan invalid 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