wehub-resource-sync
1814 lines
95 KiB
Python
1814 lines
95 KiB
Python
"""
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Easy-to-use test-generating code:
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cases = '''
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exp 2.25
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log 2.25
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'''
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from mpmath import ae, fp, mp
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mp.dps = 20
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for test in cases.splitlines():
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if not test:
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continue
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words = test.split()
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fname = words[0]
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args = words[1:]
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argstr = ", ".join(args)
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testline = "%s(%s)" % (fname, argstr)
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ans = str(eval(testline))
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print " assert ae(fp.%s, %s)" % (testline, ans)
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"""
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import pytest
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from mpmath import fp
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def ae(x, y, tol=1e-12):
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if x == y:
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return True
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return abs(x-y) <= tol*abs(y)
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def test_conj():
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assert fp.conj(4) == 4
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assert fp.conj(3+4j) == 3-4j
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assert fp.fdot([1,2],[3,2+1j], conjugate=True) == 7-2j
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def test_fp_number_parts():
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assert ae(fp.arg(3), 0.0)
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assert ae(fp.arg(-3), 3.1415926535897932385)
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assert ae(fp.arg(3j), 1.5707963267948966192)
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assert ae(fp.arg(-3j), -1.5707963267948966192)
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assert ae(fp.arg(2+3j), 0.98279372324732906799)
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assert ae(fp.arg(-1-1j), -2.3561944901923449288)
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assert ae(fp.re(2.5), 2.5)
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assert ae(fp.re(2.5+3j), 2.5)
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assert ae(fp.im(2.5), 0.0)
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assert ae(fp.im(2.5+3j), 3.0)
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assert ae(fp.floor(2.5), 2.0)
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assert ae(fp.floor(2), 2.0)
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assert ae(fp.floor(2.0+0j), (2.0 + 0.0j))
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assert ae(fp.floor(-1.5-0.5j), (-2.0 - 1.0j))
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assert ae(fp.ceil(2.5), 3.0)
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assert ae(fp.ceil(2), 2.0)
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assert ae(fp.ceil(2.0+0j), (2.0 + 0.0j))
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assert ae(fp.ceil(-1.5-0.5j), (-1.0 + 0.0j))
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def test_fp_cospi_sinpi():
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assert ae(fp.sinpi(0), 0.0)
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assert ae(fp.sinpi(0.25), 0.7071067811865475244)
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assert ae(fp.sinpi(0.5), 1.0)
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assert ae(fp.sinpi(0.75), 0.7071067811865475244)
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assert ae(fp.sinpi(1), 0.0)
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assert ae(fp.sinpi(1.25), -0.7071067811865475244)
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assert ae(fp.sinpi(1.5), -1.0)
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assert ae(fp.sinpi(1.75), -0.7071067811865475244)
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assert ae(fp.sinpi(2), 0.0)
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assert ae(fp.sinpi(2.25), 0.7071067811865475244)
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assert ae(fp.sinpi(0+3j), (0.0 + 6195.8238636085899556j))
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assert ae(fp.sinpi(0.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
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assert ae(fp.sinpi(0.5+3j), (6195.8239443081075259 + 0.0j))
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assert ae(fp.sinpi(0.75+3j), (4381.1091260582448033 - 4381.1090689950686908j))
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assert ae(fp.sinpi(1+3j), (0.0 - 6195.8238636085899556j))
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assert ae(fp.sinpi(1.25+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
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assert ae(fp.sinpi(1.5+3j), (-6195.8239443081075259 + 0.0j))
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assert ae(fp.sinpi(1.75+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
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assert ae(fp.sinpi(2+3j), (0.0 + 6195.8238636085899556j))
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assert ae(fp.sinpi(2.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
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assert ae(fp.sinpi(-0.75), -0.7071067811865475244)
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assert ae(fp.sinpi(-1e-10), -3.1415926535897933529e-10)
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assert ae(fp.sinpi(1e-10), 3.1415926535897933529e-10)
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assert ae(fp.sinpi(1e-10+1e-10j), (3.141592653589793353e-10 + 3.1415926535897933528e-10j))
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assert ae(fp.sinpi(1e-10-1e-10j), (3.141592653589793353e-10 - 3.1415926535897933528e-10j))
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assert ae(fp.sinpi(-1e-10+1e-10j), (-3.141592653589793353e-10 + 3.1415926535897933528e-10j))
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assert ae(fp.sinpi(-1e-10-1e-10j), (-3.141592653589793353e-10 - 3.1415926535897933528e-10j))
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assert ae(fp.cospi(0), 1.0)
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assert ae(fp.cospi(0.25), 0.7071067811865475244)
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assert ae(fp.cospi(0.5), 0.0)
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assert ae(fp.cospi(0.75), -0.7071067811865475244)
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assert ae(fp.cospi(1), -1.0)
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assert ae(fp.cospi(1.25), -0.7071067811865475244)
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assert ae(fp.cospi(1.5), 0.0)
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assert ae(fp.cospi(1.75), 0.7071067811865475244)
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assert ae(fp.cospi(2), 1.0)
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assert ae(fp.cospi(2.25), 0.7071067811865475244)
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assert ae(fp.cospi(0+3j), (6195.8239443081075259 + 0.0j))
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assert ae(fp.cospi(0.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
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assert ae(fp.cospi(0.5+3j), (0.0 - 6195.8238636085899556j))
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assert ae(fp.cospi(0.75+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
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assert ae(fp.cospi(1+3j), (-6195.8239443081075259 + 0.0j))
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assert ae(fp.cospi(1.25+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
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assert ae(fp.cospi(1.5+3j), (0.0 + 6195.8238636085899556j))
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assert ae(fp.cospi(1.75+3j), (4381.1091260582448033 + 4381.1090689950686908j))
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assert ae(fp.cospi(2+3j), (6195.8239443081075259 + 0.0j))
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assert ae(fp.cospi(2.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
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assert ae(fp.cospi(-0.75), -0.7071067811865475244)
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assert ae(fp.sinpi(-0.7), -0.80901699437494750611)
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assert ae(fp.cospi(-0.7), -0.5877852522924730163)
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assert ae(fp.cospi(-3+2j), (-267.74676148374822225 + 0.0j))
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assert ae(fp.sinpi(-3+2j), (0.0 - 267.74489404101651426j))
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assert ae(fp.sinpi(-0.7+2j), (-216.6116802292079471 - 157.37650009392034693j))
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assert ae(fp.cospi(-0.7+2j), (-157.37759774921754565 + 216.61016943630197336j))
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def test_fp_asinh_acosh_atanh():
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assert ae(fp.asinh(0), 0.0)
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assert ae(fp.acosh(1), 0.0)
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assert ae(fp.atanh(0), 0.0)
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def test_fp_tanh():
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assert fp.tanh(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+1, 0)
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assert fp.tanh(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+1, 0)
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assert fp.tanh(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(-1, 0)
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assert fp.tanh(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(-1, 0)
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assert fp.tanh(fp.mpc(+fp.inf, 2)) == fp.mpc(+1, 0)
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assert fp.tanh(fp.mpc(-fp.inf, 2)) == fp.mpc(-1, 0)
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r = fp.tanh(fp.mpc(0, -fp.inf))
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assert r.real == 0 and fp.isnan(r.imag)
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r = fp.tanh(fp.mpc(2, -fp.inf))
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assert fp.isnan(r.real) and fp.isnan(r.imag)
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assert fp.tanh(fp.mpc(+fp.inf, fp.nan)) == fp.mpc(+1, 0)
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assert fp.tanh(fp.mpc(-fp.inf, fp.nan)) == fp.mpc(-1, 0)
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def test_fp_tan():
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assert fp.tan(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(0, +1)
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assert fp.tan(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(0, -1)
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assert fp.tan(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(0, +1)
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assert fp.tan(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(0, -1)
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assert fp.tan(fp.mpc(2, +fp.inf)) == fp.mpc(0, +1)
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assert fp.tan(fp.mpc(2, -fp.inf)) == fp.mpc(0, -1)
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r = fp.tan(fp.mpc(-fp.inf, 0))
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assert fp.isnan(r.real) and r.imag == 0
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r = fp.tan(fp.mpc(-fp.inf, 2))
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assert fp.isnan(r.real) and fp.isnan(r.imag)
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assert fp.tan(fp.mpc(fp.nan, +fp.inf)) == fp.mpc(0, +1)
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assert fp.tan(fp.mpc(fp.nan, -fp.inf)) == fp.mpc(0, -1)
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def test_fp_asin():
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pi4 = fp.pi/4
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assert fp.asin(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+pi4, +fp.inf)
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assert fp.asin(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+pi4, -fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(-pi4, +fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(-pi4, -fp.inf)
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r = fp.asin(fp.mpc(+fp.inf, fp.nan))
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assert fp.isnan(r.real) and r.imag == -fp.inf
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r = fp.asin(fp.mpc(-fp.inf, fp.nan))
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assert fp.isnan(r.real) and r.imag == -fp.inf
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r = fp.asin(fp.mpc(fp.nan, +fp.inf))
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assert fp.isnan(r.real) and r.imag == +fp.inf
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r = fp.asin(fp.mpc(fp.nan, -fp.inf))
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assert fp.isnan(r.real) and r.imag == -fp.inf
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pi2 = fp.pi/2
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assert fp.asin(fp.mpc(+fp.inf, +1)) == fp.mpc(pi2, +fp.inf)
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assert fp.asin(fp.mpc(+fp.inf, -1)) == fp.mpc(pi2, -fp.inf)
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assert fp.asin(fp.mpc(+fp.inf, +0.0)) == fp.mpc(pi2, +fp.inf)
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assert fp.asin(fp.mpc(+fp.inf, -0.0)) == fp.mpc(pi2, -fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, +1)) == fp.mpc(-pi2, +fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, -1)) == fp.mpc(-pi2, -fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, +0.0)) == fp.mpc(-pi2, +fp.inf)
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assert fp.asin(fp.mpc(-fp.inf, -0.0)) == fp.mpc(-pi2, -fp.inf)
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assert fp.asin(fp.mpc(+1, +fp.inf)) == fp.mpc(+0.0, +fp.inf)
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assert fp.asin(fp.mpc(-1, +fp.inf)) == fp.mpc(-0.0, +fp.inf)
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assert fp.asin(fp.mpc(+0.0, +fp.inf)) == fp.mpc(+0.0, +fp.inf)
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assert fp.asin(fp.mpc(-0.0, +fp.inf)) == fp.mpc(-0.0, +fp.inf)
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assert fp.asin(fp.mpc(+1, -fp.inf)) == fp.mpc(+0.0, -fp.inf)
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assert fp.asin(fp.mpc(-1, -fp.inf)) == fp.mpc(-0.0, -fp.inf)
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assert fp.asin(fp.mpc(+0.0, -fp.inf)) == fp.mpc(+0.0, -fp.inf)
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assert fp.asin(fp.mpc(-0.0, -fp.inf)) == fp.mpc(-0.0, -fp.inf)
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assert ae(fp.asin(fp.mpc(-2, +0.0)), fp.mpc(-pi2, -fp.log(2 - fp.sqrt(3))))
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assert ae(fp.asin(fp.mpc(-2, -0.0)), fp.mpc(-pi2, +fp.log(2 - fp.sqrt(3))))
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assert ae(fp.asin(fp.mpc(+2, +0.0)), fp.mpc(+pi2, +fp.log(2 + fp.sqrt(3))))
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assert ae(fp.asin(fp.mpc(+2, -0.0)), fp.mpc(+pi2, -fp.log(2 + fp.sqrt(3))))
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assert ae(fp.asin(fp.mpc(0.5, +0.0)), fp.pi/6)
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assert ae(fp.asin(fp.mpc(0.5, -0.0)), fp.pi/6)
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def test_fp_acos():
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pi4 = fp.pi/4
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assert fp.acos(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+pi4, -fp.inf)
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assert fp.acos(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+pi4, +fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(pi4*3, -fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(pi4*3, +fp.inf)
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r = fp.acos(fp.mpc(+fp.inf, fp.nan))
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assert fp.isnan(r.real) and r.imag == fp.inf
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r = fp.acos(fp.mpc(-fp.inf, fp.nan))
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assert fp.isnan(r.real) and r.imag == fp.inf
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r = fp.acos(fp.mpc(fp.nan, +fp.inf))
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assert fp.isnan(r.real) and r.imag == -fp.inf
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r = fp.acos(fp.mpc(fp.nan, -fp.inf))
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assert fp.isnan(r.real) and r.imag == +fp.inf
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pi2 = fp.pi/2
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assert fp.acos(fp.mpc(+fp.inf, +1)) == fp.mpc(0.0, -fp.inf)
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assert fp.acos(fp.mpc(+fp.inf, -1)) == fp.mpc(0.0, +fp.inf)
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assert fp.acos(fp.mpc(+fp.inf, +0.0)) == fp.mpc(0.0, -fp.inf)
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assert fp.acos(fp.mpc(+fp.inf, -0.0)) == fp.mpc(0.0, +fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, +1)) == fp.mpc(fp.pi, -fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, -1)) == fp.mpc(fp.pi, +fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, +0.0)) == fp.mpc(fp.pi, -fp.inf)
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assert fp.acos(fp.mpc(-fp.inf, -0.0)) == fp.mpc(fp.pi, +fp.inf)
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assert fp.acos(fp.mpc(+1, +fp.inf)) == fp.mpc(pi2, -fp.inf)
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assert fp.acos(fp.mpc(-1, +fp.inf)) == fp.mpc(pi2, -fp.inf)
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assert fp.acos(fp.mpc(+0.0, +fp.inf)) == fp.mpc(pi2, -fp.inf)
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assert fp.acos(fp.mpc(-0.0, +fp.inf)) == fp.mpc(pi2, -fp.inf)
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assert fp.acos(fp.mpc(+1, -fp.inf)) == fp.mpc(pi2, +fp.inf)
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assert fp.acos(fp.mpc(-1, -fp.inf)) == fp.mpc(pi2, +fp.inf)
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assert fp.acos(fp.mpc(+0.0, -fp.inf)) == fp.mpc(pi2, +fp.inf)
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assert fp.acos(fp.mpc(-0.0, -fp.inf)) == fp.mpc(pi2, +fp.inf)
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assert ae(fp.acos(fp.mpc(-2, +0.0)), fp.mpc(fp.pi, +fp.log(2 - fp.sqrt(3))))
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assert ae(fp.acos(fp.mpc(-2, -0.0)), fp.mpc(fp.pi, -fp.log(2 - fp.sqrt(3))))
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assert ae(fp.acos(fp.mpc(+2, +0.0)), fp.mpc(0, -fp.log(2 + fp.sqrt(3))))
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assert ae(fp.acos(fp.mpc(+2, -0.0)), fp.mpc(0, +fp.log(2 + fp.sqrt(3))))
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assert ae(fp.acos(fp.mpc(0.5, +0.0)), fp.pi/3)
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assert ae(fp.acos(fp.mpc(0.5, -0.0)), fp.pi/3)
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def test_fp_expj():
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assert ae(fp.expj(0), (1.0 + 0.0j))
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assert ae(fp.expj(1), (0.5403023058681397174 + 0.84147098480789650665j))
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assert ae(fp.expj(2), (-0.416146836547142387 + 0.9092974268256816954j))
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assert ae(fp.expj(0.75), (0.73168886887382088631 + 0.68163876002333416673j))
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assert ae(fp.expj(2+3j), (-0.020718731002242879378 + 0.045271253156092975488j))
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assert ae(fp.expjpi(0), (1.0 + 0.0j))
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assert ae(fp.expjpi(1), (-1.0 + 0.0j))
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assert ae(fp.expjpi(2), (1.0 + 0.0j))
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assert ae(fp.expjpi(0.75), (-0.7071067811865475244 + 0.7071067811865475244j))
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assert ae(fp.expjpi(2+3j), (0.000080699517570304599239 + 0.0j))
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@pytest.mark.parametrize('plus', [True, False])
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def test_fp_bernoulli(plus):
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assert ae(fp.bernoulli(0, plus), 1.0)
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assert ae(fp.bernoulli(1, plus), 0.5 if plus else -0.5)
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assert ae(fp.bernoulli(2, plus), 0.16666666666666666667)
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assert ae(fp.bernoulli(10, plus), 0.075757575757575757576)
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assert ae(fp.bernoulli(11, plus), 0.0)
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def test_fp_gamma():
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assert ae(fp.gamma(1), 1.0)
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assert ae(fp.gamma(1.5), 0.88622692545275801365)
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assert ae(fp.gamma(10), 362880.0)
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assert ae(fp.gamma(-0.5), -3.5449077018110320546)
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assert ae(fp.gamma(-7.1), 0.0016478244570263333622)
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assert ae(fp.gamma(12.3), 83385367.899970000963)
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assert ae(fp.gamma(2+0j), (1.0 + 0.0j))
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assert fp.isnan(fp.gamma(-fp.inf))
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assert ae(fp.gamma(-2.5+0j), (-0.94530872048294188123 + 0.0j))
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assert ae(fp.gamma(3+4j), (0.0052255384713692141947 - 0.17254707929430018772j))
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assert ae(fp.gamma(-3-4j), (0.00001460997305874775607 - 0.000020760733311509070396j))
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assert ae(fp.fac(0), 1.0)
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assert ae(fp.fac(1), 1.0)
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assert ae(fp.fac(20), 2432902008176640000.0)
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assert ae(fp.fac(-3.5), -0.94530872048294188123)
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assert ae(fp.fac(2+3j), (-0.44011340763700171113 - 0.06363724312631702183j))
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assert ae(fp.loggamma(1.0), 0.0)
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assert ae(fp.loggamma(2.0), 0.0)
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assert ae(fp.loggamma(3.0), 0.69314718055994530942)
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assert ae(fp.loggamma(7.25), 7.0521854507385394449)
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assert ae(fp.loggamma(1000.0), 5905.2204232091812118)
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assert ae(fp.loggamma(1e50), 1.1412925464970229298e+52)
|
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assert ae(fp.loggamma(1e25+1e25j), (5.6125802751733671621e+26 + 5.7696599078528568383e+26j))
|
|
assert ae(fp.loggamma(3+4j), (-1.7566267846037841105 + 4.7426644380346579282j))
|
|
assert ae(fp.loggamma(-0.5), (1.2655121234846453965 - 3.1415926535897932385j))
|
|
assert ae(fp.loggamma(-1.25), (1.3664317612369762346 - 6.2831853071795864769j))
|
|
assert ae(fp.loggamma(-2.75), (0.0044878975359557733115 - 9.4247779607693797154j))
|
|
assert ae(fp.loggamma(-3.5), (-1.3090066849930420464 - 12.566370614359172954j))
|
|
assert ae(fp.loggamma(-4.5), (-2.8130840817693161197 - 15.707963267948966192j))
|
|
assert ae(fp.loggamma(-2+3j), (-6.776523813485657093 - 4.568791367260286402j))
|
|
assert ae(fp.loggamma(-1000.3), (-5912.8440347785205041 - 3144.7342462433830317j))
|
|
assert ae(fp.loggamma(-100-100j), (-632.35117666833135562 - 158.37641469650352462j))
|
|
assert ae(fp.loggamma(1e-10), 23.025850929882735237)
|
|
assert ae(fp.loggamma(-1e-10), (23.02585092999817837 - 3.1415926535897932385j))
|
|
assert ae(fp.loggamma(1e-10j), (23.025850929940456804 - 1.5707963268526181857j))
|
|
assert ae(fp.loggamma(1e-10j-1e-10), (22.679277339718205716 - 2.3561944902500664954j))
|
|
|
|
def test_fp_psi():
|
|
assert ae(fp.psi(0, 3.7), 1.1671535393615114409)
|
|
assert ae(fp.psi(0, 0.5), -1.9635100260214234794)
|
|
assert ae(fp.psi(0, 1), -0.57721566490153286061)
|
|
assert ae(fp.psi(0, -2.5), 1.1031566406452431872)
|
|
assert ae(fp.psi(0, 12.9), 2.5179671503279156347)
|
|
assert ae(fp.psi(0, 100), 4.6001618527380874002)
|
|
assert ae(fp.psi(0, 2500.3), 7.8239660143238547877)
|
|
assert ae(fp.psi(0, 1e40), 92.103403719761827391)
|
|
assert ae(fp.psi(0, 1e200), 460.51701859880913677)
|
|
assert ae(fp.psi(0, 3.7+0j), (1.1671535393615114409 + 0.0j))
|
|
assert ae(fp.psi(1, 3), 0.39493406684822643647)
|
|
assert ae(fp.psi(3, 2+3j), (-0.05383196209159972116 + 0.0076890935247364805218j))
|
|
assert ae(fp.psi(4, -0.5+1j), (1.2719531355492328195 - 18.211833410936276774j))
|
|
assert ae(fp.harmonic(0), 0.0)
|
|
assert ae(fp.harmonic(1), 1.0)
|
|
assert ae(fp.harmonic(2), 1.5)
|
|
assert ae(fp.harmonic(100), 5.1873775176396202608)
|
|
assert ae(fp.harmonic(-2.5), 1.2803723055467760478)
|
|
assert ae(fp.harmonic(2+3j), (1.9390425294578375875 + 0.87336044981834544043j))
|
|
assert ae(fp.harmonic(-5-4j), (2.3725754822349437733 - 2.4160904444801621j))
|
|
|
|
def test_fp_zeta():
|
|
assert ae(fp.zeta(1e100), 1.0)
|
|
assert ae(fp.zeta(3), 1.2020569031595942854)
|
|
assert ae(fp.zeta(2+0j), (1.6449340668482264365 + 0.0j))
|
|
assert ae(fp.zeta(0.93), -13.713619351638164784)
|
|
assert ae(fp.zeta(1.74), 1.9796863545771774095)
|
|
assert ae(fp.zeta(0.0), -0.5)
|
|
assert ae(fp.zeta(-1.0), -0.083333333333333333333)
|
|
assert ae(fp.zeta(-2.0), 0.0)
|
|
assert ae(fp.zeta(-3.0), 0.0083333333333333333333)
|
|
assert ae(fp.zeta(-500.0), 0.0)
|
|
assert ae(fp.zeta(-7.4), 0.0036537321227995882447)
|
|
assert ae(fp.zeta(2.1), 1.5602165335033620158)
|
|
assert ae(fp.zeta(26.9), 1.0000000079854809935)
|
|
assert ae(fp.zeta(26), 1.0000000149015548284)
|
|
assert ae(fp.zeta(27), 1.0000000074507117898)
|
|
assert ae(fp.zeta(28), 1.0000000037253340248)
|
|
assert ae(fp.zeta(27.1), 1.000000006951755045)
|
|
assert ae(fp.zeta(32.7), 1.0000000001433243232)
|
|
assert ae(fp.zeta(100), 1.0)
|
|
assert ae(fp.altzeta(3.5), 0.92755357777394803511)
|
|
assert ae(fp.altzeta(1), 0.69314718055994530942)
|
|
assert ae(fp.altzeta(2), 0.82246703342411321824)
|
|
assert ae(fp.altzeta(0), 0.5)
|
|
assert ae(fp.zeta(-2+3j, 1), (0.13297115587929864827 + 0.12305330040458776494j))
|
|
assert ae(fp.zeta(-2+3j, 5), (18.384866151867576927 - 11.377015110597711009j))
|
|
assert ae(fp.zeta(1.0000000001), 9999999173.1735741337)
|
|
assert ae(fp.zeta(0.9999999999), -9999999172.0191428039)
|
|
assert ae(fp.zeta(1+0.000000001j), (0.57721566490153286061 - 999999999.99999993765j))
|
|
assert ae(fp.primezeta(2.5+4j), (-0.16922458243438033385 - 0.010847965298387727811j))
|
|
assert ae(fp.primezeta(4), 0.076993139764246844943)
|
|
assert ae(fp.riemannr(3.7), 2.3034079839110855717)
|
|
assert ae(fp.riemannr(8), 3.9011860449341499474)
|
|
assert ae(fp.riemannr(3+4j), (2.2369653314259991796 + 1.6339943856990281694j))
|
|
|
|
def test_fp_hyp2f1():
|
|
assert ae(fp.hyp2f1(1, (3,2), 3.25, 5.0), (-0.46600275923108143059 - 0.74393667908854842325j))
|
|
assert ae(fp.hyp2f1(1+1j, (3,2), 3.25, 5.0), (-5.9208875603806515987 - 2.3813557707889590686j))
|
|
assert ae(fp.hyp2f1(1+1j, (3,2), 3.25, 2+3j), (0.17174552030925080445 + 0.19589781970539389999j))
|
|
|
|
def test_fp_erf():
|
|
assert fp.erf(2) == fp.erf(2.0) == fp.erf(2.0+0.0j)
|
|
assert fp.erf(fp.inf) == 1.0
|
|
assert fp.erf(fp.ninf) == -1.0
|
|
assert ae(fp.erf(0), 0.0)
|
|
assert ae(fp.erf(-0), -0.0)
|
|
assert ae(fp.erf(0.3), 0.32862675945912741619)
|
|
assert ae(fp.erf(-0.3), -0.32862675945912741619)
|
|
assert ae(fp.erf(0.9), 0.79690821242283213966)
|
|
assert ae(fp.erf(-0.9), -0.79690821242283213966)
|
|
assert ae(fp.erf(1.0), 0.84270079294971486934)
|
|
assert ae(fp.erf(-1.0), -0.84270079294971486934)
|
|
assert ae(fp.erf(1.1), 0.88020506957408172966)
|
|
assert ae(fp.erf(-1.1), -0.88020506957408172966)
|
|
assert ae(fp.erf(8.5), 1.0)
|
|
assert ae(fp.erf(-8.5), -1.0)
|
|
assert ae(fp.erf(9.1), 1.0)
|
|
assert ae(fp.erf(-9.1), -1.0)
|
|
assert ae(fp.erf(20.0), 1.0)
|
|
assert ae(fp.erf(-20.0), -1.0)
|
|
assert ae(fp.erf(10000.0), 1.0)
|
|
assert ae(fp.erf(-10000.0), -1.0)
|
|
assert ae(fp.erf(1e+50), 1.0)
|
|
assert ae(fp.erf(-1e+50), -1.0)
|
|
assert ae(fp.erf(1j), 1.650425758797542876j)
|
|
assert ae(fp.erf(-1j), -1.650425758797542876j)
|
|
assert ae(fp.erf((2+3j)), (-20.829461427614568389 + 8.6873182714701631444j))
|
|
assert ae(fp.erf(-(2+3j)), -(-20.829461427614568389 + 8.6873182714701631444j))
|
|
assert ae(fp.erf((8+9j)), (-1072004.2525062051158 + 364149.91954310255423j))
|
|
assert ae(fp.erf(-(8+9j)), -(-1072004.2525062051158 + 364149.91954310255423j))
|
|
assert fp.erfc(fp.inf) == 0.0
|
|
assert fp.erfc(fp.ninf) == 2.0
|
|
assert fp.erfc(0) == 1
|
|
assert fp.erfc(-0.0) == 1
|
|
assert fp.erfc(0+0j) == 1
|
|
assert ae(fp.erfc(0.3), 0.67137324054087258381)
|
|
assert ae(fp.erfc(-0.3), 1.3286267594591274162)
|
|
assert ae(fp.erfc(0.9), 0.20309178757716786034)
|
|
assert ae(fp.erfc(-0.9), 1.7969082124228321397)
|
|
assert ae(fp.erfc(1.0), 0.15729920705028513066)
|
|
assert ae(fp.erfc(-1.0), 1.8427007929497148693)
|
|
assert ae(fp.erfc(1.1), 0.11979493042591827034)
|
|
assert ae(fp.erfc(-1.1), 1.8802050695740817297)
|
|
assert ae(fp.erfc(8.5), 2.7623240713337714461e-33)
|
|
assert ae(fp.erfc(-8.5), 2.0)
|
|
assert ae(fp.erfc(9.1), 6.6969004279886077452e-38)
|
|
assert ae(fp.erfc(-9.1), 2.0)
|
|
assert ae(fp.erfc(20.0), 5.3958656116079009289e-176)
|
|
assert ae(fp.erfc(-20.0), 2.0)
|
|
assert ae(fp.erfc(10000.0), 0.0)
|
|
assert ae(fp.erfc(-10000.0), 2.0)
|
|
assert ae(fp.erfc(1e+50), 0.0)
|
|
assert ae(fp.erfc(-1e+50), 2.0)
|
|
assert ae(fp.erfc(1j), (1.0 - 1.650425758797542876j))
|
|
assert ae(fp.erfc(-1j), (1.0 + 1.650425758797542876j))
|
|
assert ae(fp.erfc((2+3j)), (21.829461427614568389 - 8.6873182714701631444j), 1e-13)
|
|
assert ae(fp.erfc(-(2+3j)), (-19.829461427614568389 + 8.6873182714701631444j), 1e-13)
|
|
assert ae(fp.erfc((8+9j)), (1072005.2525062051158 - 364149.91954310255423j))
|
|
assert ae(fp.erfc(-(8+9j)), (-1072003.2525062051158 + 364149.91954310255423j))
|
|
assert ae(fp.erfc(20+0j), (5.3958656116079009289e-176 + 0.0j))
|
|
|
|
def test_fp_lambertw():
|
|
assert ae(fp.lambertw(0.0), 0.0)
|
|
assert ae(fp.lambertw(1.0), 0.567143290409783873)
|
|
assert ae(fp.lambertw(7.5), 1.5662309537823875394)
|
|
assert ae(fp.lambertw(-0.25), -0.35740295618138890307)
|
|
assert ae(fp.lambertw(-10.0), (1.3699809685212708156 + 2.140194527074713196j))
|
|
assert ae(fp.lambertw(0+0j), (0.0 + 0.0j))
|
|
assert ae(fp.lambertw(4+0j), (1.2021678731970429392 + 0.0j))
|
|
assert ae(fp.lambertw(1000.5), 5.2500227450408980127)
|
|
assert ae(fp.lambertw(1e100), 224.84310644511850156)
|
|
assert ae(fp.lambertw(-1000.0), (5.1501630246362515223 + 2.6641981432905204596j))
|
|
assert ae(fp.lambertw(1e-10), 9.9999999990000003645e-11)
|
|
assert ae(fp.lambertw(1e-10j), (1.0000000000000000728e-20 + 1.0000000000000000364e-10j))
|
|
assert ae(fp.lambertw(3+4j), (1.2815618061237758782 + 0.53309522202097107131j))
|
|
assert ae(fp.lambertw(-3-4j), (1.0750730665692549276 - 1.3251023817343588823j))
|
|
assert ae(fp.lambertw(10000+1000j), (7.2361526563371602186 + 0.087567810943839352034j))
|
|
assert ae(fp.lambertw(0.0, -1), -fp.inf)
|
|
assert ae(fp.lambertw(1.0, -1), (-1.5339133197935745079 - 4.3751851530618983855j))
|
|
assert ae(fp.lambertw(7.5, -1), (0.44125668415098614999 - 4.8039842008452390179j))
|
|
assert ae(fp.lambertw(-0.25, -1), -2.1532923641103496492)
|
|
assert ae(fp.lambertw(-10.0, -1), (1.3699809685212708156 - 2.140194527074713196j))
|
|
assert ae(fp.lambertw(0+0j, -1), -fp.inf)
|
|
assert ae(fp.lambertw(4+0j, -1), (-0.15730793189620765317 - 4.6787800704666656212j))
|
|
assert ae(fp.lambertw(1000.5, -1), (4.9153765415404024736 - 5.4465682700815159569j))
|
|
assert ae(fp.lambertw(1e100, -1), (224.84272130101601052 - 6.2553713838167244141j))
|
|
assert ae(fp.lambertw(-1000.0, -1), (5.1501630246362515223 - 2.6641981432905204596j))
|
|
assert ae(fp.lambertw(1e-10, -1), (-26.303186778379041521 - 3.2650939117038283975j))
|
|
assert ae(fp.lambertw(1e-10j, -1), (-26.297238779529035028 - 1.6328071613455765135j))
|
|
assert ae(fp.lambertw(3+4j, -1), (0.25856740686699741676 - 3.8521166861614355895j))
|
|
assert ae(fp.lambertw(-3-4j, -1), (-0.32028750204310768396 - 6.8801677192091972343j))
|
|
assert ae(fp.lambertw(10000+1000j, -1), (7.0255308742285435567 - 5.5177506835734067601j))
|
|
assert ae(fp.lambertw(0.0, 2), -fp.inf)
|
|
assert ae(fp.lambertw(1.0, 2), (-2.4015851048680028842 + 10.776299516115070898j))
|
|
assert ae(fp.lambertw(7.5, 2), (-0.38003357962843791529 + 10.960916473368746184j))
|
|
assert ae(fp.lambertw(-0.25, 2), (-4.0558735269061511898 + 13.852334658567271386j))
|
|
assert ae(fp.lambertw(-10.0, 2), (-0.34479123764318858696 + 14.112740596763592363j))
|
|
assert ae(fp.lambertw(0+0j, 2), -fp.inf)
|
|
assert ae(fp.lambertw(4+0j, 2), (-1.0070343323804262788 + 10.903476551861683082j))
|
|
assert ae(fp.lambertw(1000.5, 2), (4.4076185165459395295 + 11.365524591091402177j))
|
|
assert ae(fp.lambertw(1e100, 2), (224.84156762724875878 + 12.510785262632255672j))
|
|
assert ae(fp.lambertw(-1000.0, 2), (4.1984245610246530756 + 14.420478573754313845j))
|
|
assert ae(fp.lambertw(1e-10, 2), (-26.362258095445866488 + 9.7800247407031482519j))
|
|
assert ae(fp.lambertw(1e-10j, 2), (-26.384250801683084252 + 11.403535950607739763j))
|
|
assert ae(fp.lambertw(3+4j, 2), (-0.86554679943333993562 + 11.849956798331992027j))
|
|
assert ae(fp.lambertw(-3-4j, 2), (-0.55792273874679112639 + 8.7173627024159324811j))
|
|
assert ae(fp.lambertw(10000+1000j, 2), (6.6223802254585662734 + 11.61348646825020766j))
|
|
|
|
def test_fp_stress_ei_e1():
|
|
# Can be tightened on recent Pythons with more accurate math/cmath
|
|
ATOL = 1e-13
|
|
PTOL = 1e-12
|
|
v = fp.e1(1.1641532182693481445e-10)
|
|
assert ae(v, 22.296641293693077672, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(0.25)
|
|
assert ae(v, 1.0442826344437381945, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(1.0)
|
|
assert ae(v, 0.21938393439552027368, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(2.0)
|
|
assert ae(v, 0.048900510708061119567, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(5.0)
|
|
assert ae(v, 0.0011482955912753257973, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(20.0)
|
|
assert ae(v, 9.8355252906498816904e-11, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(30.0)
|
|
assert ae(v, 3.0215520106888125448e-15, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(40.0)
|
|
assert ae(v, 1.0367732614516569722e-19, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(50.0)
|
|
assert ae(v, 3.7832640295504590187e-24, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1(80.0)
|
|
assert ae(v, 2.2285432586884729112e-37, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.e1((1.1641532182693481445e-10 + 0.0j))
|
|
assert ae(v, (22.296641293693077672 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 22.296641293693077672, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((0.25 + 0.0j))
|
|
assert ae(v, (1.0442826344437381945 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 1.0442826344437381945, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((1.0 + 0.0j))
|
|
assert ae(v, (0.21938393439552027368 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 0.21938393439552027368, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((2.0 + 0.0j))
|
|
assert ae(v, (0.048900510708061119567 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 0.048900510708061119567, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((5.0 + 0.0j))
|
|
assert ae(v, (0.0011482955912753257973 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 0.0011482955912753257973, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((20.0 + 0.0j))
|
|
assert ae(v, (9.8355252906498816904e-11 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 9.8355252906498816904e-11, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((30.0 + 0.0j))
|
|
assert ae(v, (3.0215520106888125448e-15 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 3.0215520106888125448e-15, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((40.0 + 0.0j))
|
|
assert ae(v, (1.0367732614516569722e-19 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 1.0367732614516569722e-19, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((50.0 + 0.0j))
|
|
assert ae(v, (3.7832640295504590187e-24 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 3.7832640295504590187e-24, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((80.0 + 0.0j))
|
|
assert ae(v, (2.2285432586884729112e-37 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 2.2285432586884729112e-37, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.e1((4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (20.880034622014215597 - 0.24497866301044883237j), tol=ATOL)
|
|
assert ae(v.real, 20.880034622014215597, tol=PTOL)
|
|
assert ae(v.imag, -0.24497866301044883237, tol=PTOL)
|
|
v = fp.e1((1.0 + 0.25j))
|
|
assert ae(v, (0.19731063945004229095 - 0.087366045774299963672j), tol=ATOL)
|
|
assert ae(v.real, 0.19731063945004229095, tol=PTOL)
|
|
assert ae(v.imag, -0.087366045774299963672, tol=PTOL)
|
|
v = fp.e1((4.0 + 1.0j))
|
|
assert ae(v, (0.0013106173980145506944 - 0.0034542480199350626699j), tol=ATOL)
|
|
assert ae(v.real, 0.0013106173980145506944, tol=PTOL)
|
|
assert ae(v.imag, -0.0034542480199350626699, tol=PTOL)
|
|
v = fp.e1((8.0 + 2.0j))
|
|
assert ae(v, (-0.000022278049065270225945 - 0.000029191940456521555288j), tol=ATOL)
|
|
assert ae(v.real, -0.000022278049065270225945, tol=PTOL)
|
|
assert ae(v.imag, -0.000029191940456521555288, tol=PTOL)
|
|
v = fp.e1((20.0 + 5.0j))
|
|
assert ae(v, (4.7711374515765346894e-11 + 8.2902652405126947359e-11j), tol=ATOL)
|
|
assert ae(v.real, 4.7711374515765346894e-11, tol=PTOL)
|
|
assert ae(v.imag, 8.2902652405126947359e-11, tol=PTOL)
|
|
v = fp.e1((80.0 + 20.0j))
|
|
assert ae(v, (3.8353473865788235787e-38 - 2.129247592349605139e-37j), tol=ATOL)
|
|
assert ae(v.real, 3.8353473865788235787e-38, tol=PTOL)
|
|
assert ae(v.imag, -2.129247592349605139e-37, tol=PTOL)
|
|
v = fp.e1((120.0 + 30.0j))
|
|
assert ae(v, (2.3836002337480334716e-55 + 5.6704043587126198306e-55j), tol=ATOL)
|
|
assert ae(v.real, 2.3836002337480334716e-55, tol=PTOL)
|
|
assert ae(v.imag, 5.6704043587126198306e-55, tol=PTOL)
|
|
v = fp.e1((160.0 + 40.0j))
|
|
assert ae(v, (-1.6238022898654510661e-72 - 1.104172355572287367e-72j), tol=ATOL)
|
|
assert ae(v.real, -1.6238022898654510661e-72, tol=PTOL)
|
|
assert ae(v.imag, -1.104172355572287367e-72, tol=PTOL)
|
|
v = fp.e1((200.0 + 50.0j))
|
|
assert ae(v, (6.6800061461666228487e-90 + 1.4473816083541016115e-91j), tol=ATOL)
|
|
assert ae(v.real, 6.6800061461666228487e-90, tol=PTOL)
|
|
assert ae(v.imag, 1.4473816083541016115e-91, tol=PTOL)
|
|
v = fp.e1((320.0 + 80.0j))
|
|
assert ae(v, (4.2737871527778786157e-143 + 3.1789935525785660314e-142j), tol=ATOL)
|
|
assert ae(v.real, 4.2737871527778786157e-143, tol=PTOL)
|
|
assert ae(v.imag, 3.1789935525785660314e-142, tol=PTOL)
|
|
v = fp.e1((1.1641532182693481445e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (21.950067703413105017 - 0.7853981632810329878j), tol=ATOL)
|
|
assert ae(v.real, 21.950067703413105017, tol=PTOL)
|
|
assert ae(v.imag, -0.7853981632810329878, tol=PTOL)
|
|
v = fp.e1((0.25 + 0.25j))
|
|
assert ae(v, (0.71092525792923287894 - 0.56491812441304194711j), tol=ATOL)
|
|
assert ae(v.real, 0.71092525792923287894, tol=PTOL)
|
|
assert ae(v.imag, -0.56491812441304194711, tol=PTOL)
|
|
v = fp.e1((1.0 + 1.0j))
|
|
assert ae(v, (0.00028162445198141832551 - 0.17932453503935894015j), tol=ATOL)
|
|
assert ae(v.real, 0.00028162445198141832551, tol=PTOL)
|
|
assert ae(v.imag, -0.17932453503935894015, tol=PTOL)
|
|
v = fp.e1((2.0 + 2.0j))
|
|
assert ae(v, (-0.033767089606562004246 - 0.018599414169750541925j), tol=ATOL)
|
|
assert ae(v.real, -0.033767089606562004246, tol=PTOL)
|
|
assert ae(v.imag, -0.018599414169750541925, tol=PTOL)
|
|
v = fp.e1((5.0 + 5.0j))
|
|
assert ae(v, (0.0007266506660356393891 + 0.00047102780163522245054j), tol=ATOL)
|
|
assert ae(v.real, 0.0007266506660356393891, tol=PTOL)
|
|
assert ae(v.imag, 0.00047102780163522245054, tol=PTOL)
|
|
v = fp.e1((20.0 + 20.0j))
|
|
assert ae(v, (-2.3824537449367396579e-11 - 6.6969873156525615158e-11j), tol=ATOL)
|
|
assert ae(v.real, -2.3824537449367396579e-11, tol=PTOL)
|
|
assert ae(v.imag, -6.6969873156525615158e-11, tol=PTOL)
|
|
v = fp.e1((30.0 + 30.0j))
|
|
assert ae(v, (1.7316045841744061617e-15 + 1.3065678019487308689e-15j), tol=ATOL)
|
|
assert ae(v.real, 1.7316045841744061617e-15, tol=PTOL)
|
|
assert ae(v.imag, 1.3065678019487308689e-15, tol=PTOL)
|
|
v = fp.e1((40.0 + 40.0j))
|
|
assert ae(v, (-7.4001043002899232182e-20 - 4.991847855336816304e-21j), tol=ATOL)
|
|
assert ae(v.real, -7.4001043002899232182e-20, tol=PTOL)
|
|
assert ae(v.imag, -4.991847855336816304e-21, tol=PTOL)
|
|
v = fp.e1((50.0 + 50.0j))
|
|
assert ae(v, (2.3566128324644641219e-24 - 1.3188326726201614778e-24j), tol=ATOL)
|
|
assert ae(v.real, 2.3566128324644641219e-24, tol=PTOL)
|
|
assert ae(v.imag, -1.3188326726201614778e-24, tol=PTOL)
|
|
v = fp.e1((80.0 + 80.0j))
|
|
assert ae(v, (9.8279750572186526673e-38 + 1.243952841288868831e-37j), tol=ATOL)
|
|
assert ae(v.real, 9.8279750572186526673e-38, tol=PTOL)
|
|
assert ae(v.imag, 1.243952841288868831e-37, tol=PTOL)
|
|
v = fp.e1((1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
|
|
assert ae(v, (20.880034621664969632 - 1.3258176632023711778j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621664969632, tol=PTOL)
|
|
assert ae(v.imag, -1.3258176632023711778, tol=PTOL)
|
|
v = fp.e1((0.25 + 1.0j))
|
|
assert ae(v, (-0.16868306393667788761 - 0.4858011885947426971j), tol=ATOL)
|
|
assert ae(v.real, -0.16868306393667788761, tol=PTOL)
|
|
assert ae(v.imag, -0.4858011885947426971, tol=PTOL)
|
|
v = fp.e1((1.0 + 4.0j))
|
|
assert ae(v, (0.03373591813926547318 + 0.073523452241083821877j), tol=ATOL)
|
|
assert ae(v.real, 0.03373591813926547318, tol=PTOL)
|
|
assert ae(v.imag, 0.073523452241083821877, tol=PTOL)
|
|
v = fp.e1((2.0 + 8.0j))
|
|
assert ae(v, (-0.015392833434733785143 - 0.0031747121557605415914j), tol=ATOL)
|
|
assert ae(v.real, -0.015392833434733785143, tol=PTOL)
|
|
assert ae(v.imag, -0.0031747121557605415914, tol=PTOL)
|
|
v = fp.e1((5.0 + 20.0j))
|
|
assert ae(v, (-0.00024419662286542966525 - 0.00021008322966152755674j), tol=ATOL)
|
|
assert ae(v.real, -0.00024419662286542966525, tol=PTOL)
|
|
assert ae(v.imag, -0.00021008322966152755674, tol=PTOL)
|
|
v = fp.e1((20.0 + 80.0j))
|
|
assert ae(v, (2.3255552781051330088e-11 + 8.9463918891349438007e-12j), tol=ATOL)
|
|
assert ae(v.real, 2.3255552781051330088e-11, tol=PTOL)
|
|
assert ae(v.imag, 8.9463918891349438007e-12, tol=PTOL)
|
|
v = fp.e1((30.0 + 120.0j))
|
|
assert ae(v, (-2.7068919097124652332e-16 - 7.0477762411705130239e-16j), tol=ATOL)
|
|
assert ae(v.real, -2.7068919097124652332e-16, tol=PTOL)
|
|
assert ae(v.imag, -7.0477762411705130239e-16, tol=PTOL)
|
|
v = fp.e1((40.0 + 160.0j))
|
|
assert ae(v, (-1.1695597827678024687e-20 + 2.2907401455645736661e-20j), tol=ATOL)
|
|
assert ae(v.real, -1.1695597827678024687e-20, tol=PTOL)
|
|
assert ae(v.imag, 2.2907401455645736661e-20, tol=PTOL)
|
|
v = fp.e1((50.0 + 200.0j))
|
|
assert ae(v, (9.0323746914410162531e-25 - 2.3950601790033530935e-25j), tol=ATOL)
|
|
assert ae(v.real, 9.0323746914410162531e-25, tol=PTOL)
|
|
assert ae(v.imag, -2.3950601790033530935e-25, tol=PTOL)
|
|
v = fp.e1((80.0 + 320.0j))
|
|
assert ae(v, (3.4819106748728063576e-38 - 4.215653005615772724e-38j), tol=ATOL)
|
|
assert ae(v.real, 3.4819106748728063576e-38, tol=PTOL)
|
|
assert ae(v.imag, -4.215653005615772724e-38, tol=PTOL)
|
|
v = fp.e1((0.0 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (22.29664129357666235 - 1.5707963266784812974j), tol=ATOL)
|
|
assert ae(v.real, 22.29664129357666235, tol=PTOL)
|
|
assert ae(v.imag, -1.5707963266784812974, tol=PTOL)
|
|
v = fp.e1((0.0 + 0.25j))
|
|
assert ae(v, (0.82466306258094565309 - 1.3216627564751394551j), tol=ATOL)
|
|
assert ae(v.real, 0.82466306258094565309, tol=PTOL)
|
|
assert ae(v.imag, -1.3216627564751394551, tol=PTOL)
|
|
v = fp.e1((0.0 + 1.0j))
|
|
assert ae(v, (-0.33740392290096813466 - 0.62471325642771360429j), tol=ATOL)
|
|
assert ae(v.real, -0.33740392290096813466, tol=PTOL)
|
|
assert ae(v.imag, -0.62471325642771360429, tol=PTOL)
|
|
v = fp.e1((0.0 + 2.0j))
|
|
assert ae(v, (-0.4229808287748649957 + 0.034616650007798229345j), tol=ATOL)
|
|
assert ae(v.real, -0.4229808287748649957, tol=PTOL)
|
|
assert ae(v.imag, 0.034616650007798229345, tol=PTOL)
|
|
v = fp.e1((0.0 + 5.0j))
|
|
assert ae(v, (0.19002974965664387862 - 0.020865081850222481957j), tol=ATOL)
|
|
assert ae(v.real, 0.19002974965664387862, tol=PTOL)
|
|
assert ae(v.imag, -0.020865081850222481957, tol=PTOL)
|
|
v = fp.e1((0.0 + 20.0j))
|
|
assert ae(v, (-0.04441982084535331654 - 0.022554625751456779068j), tol=ATOL)
|
|
assert ae(v.real, -0.04441982084535331654, tol=PTOL)
|
|
assert ae(v.imag, -0.022554625751456779068, tol=PTOL)
|
|
v = fp.e1((0.0 + 30.0j))
|
|
assert ae(v, (0.033032417282071143779 - 0.0040397867645455082476j), tol=ATOL)
|
|
assert ae(v.real, 0.033032417282071143779, tol=PTOL)
|
|
assert ae(v.imag, -0.0040397867645455082476, tol=PTOL)
|
|
v = fp.e1((0.0 + 40.0j))
|
|
assert ae(v, (-0.019020007896208766962 + 0.016188792559887887544j), tol=ATOL)
|
|
assert ae(v.real, -0.019020007896208766962, tol=PTOL)
|
|
assert ae(v.imag, 0.016188792559887887544, tol=PTOL)
|
|
v = fp.e1((0.0 + 50.0j))
|
|
assert ae(v, (0.0056283863241163054402 - 0.019179254308960724503j), tol=ATOL)
|
|
assert ae(v.real, 0.0056283863241163054402, tol=PTOL)
|
|
assert ae(v.imag, -0.019179254308960724503, tol=PTOL)
|
|
v = fp.e1((0.0 + 80.0j))
|
|
assert ae(v, (0.012402501155070958192 + 0.0015345601175906961199j), tol=ATOL)
|
|
assert ae(v.real, 0.012402501155070958192, tol=PTOL)
|
|
assert ae(v.imag, 0.0015345601175906961199, tol=PTOL)
|
|
v = fp.e1((-1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
|
|
assert ae(v, (20.880034621432138988 - 1.8157749894560994861j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621432138988, tol=PTOL)
|
|
assert ae(v.imag, -1.8157749894560994861, tol=PTOL)
|
|
v = fp.e1((-0.25 + 1.0j))
|
|
assert ae(v, (-0.59066621214766308594 - 0.74474454765205036972j), tol=ATOL)
|
|
assert ae(v.real, -0.59066621214766308594, tol=PTOL)
|
|
assert ae(v.imag, -0.74474454765205036972, tol=PTOL)
|
|
v = fp.e1((-1.0 + 4.0j))
|
|
assert ae(v, (0.49739047283060471093 + 0.41543605404038863174j), tol=ATOL)
|
|
assert ae(v.real, 0.49739047283060471093, tol=PTOL)
|
|
assert ae(v.imag, 0.41543605404038863174, tol=PTOL)
|
|
v = fp.e1((-2.0 + 8.0j))
|
|
assert ae(v, (-0.8705211147733730969 + 0.24099328498605539667j), tol=ATOL)
|
|
assert ae(v.real, -0.8705211147733730969, tol=PTOL)
|
|
assert ae(v.imag, 0.24099328498605539667, tol=PTOL)
|
|
v = fp.e1((-5.0 + 20.0j))
|
|
assert ae(v, (-7.0789514293925893007 - 1.6102177171960790536j), tol=ATOL)
|
|
assert ae(v.real, -7.0789514293925893007, tol=PTOL)
|
|
assert ae(v.imag, -1.6102177171960790536, tol=PTOL)
|
|
v = fp.e1((-20.0 + 80.0j))
|
|
assert ae(v, (5855431.4907298084434 - 720920.93315409165707j), tol=ATOL)
|
|
assert ae(v.real, 5855431.4907298084434, tol=PTOL)
|
|
assert ae(v.imag, -720920.93315409165707, tol=PTOL)
|
|
v = fp.e1((-30.0 + 120.0j))
|
|
assert ae(v, (-65402491644.703470747 - 56697658399.657460294j), tol=ATOL)
|
|
assert ae(v.real, -65402491644.703470747, tol=PTOL)
|
|
assert ae(v.imag, -56697658399.657460294, tol=PTOL)
|
|
v = fp.e1((-40.0 + 160.0j))
|
|
assert ae(v, (25504929379604.776769 + 1429035198630573.2463j), tol=ATOL)
|
|
assert ae(v.real, 25504929379604.776769, tol=PTOL)
|
|
assert ae(v.imag, 1429035198630573.2463, tol=PTOL)
|
|
v = fp.e1((-50.0 + 200.0j))
|
|
assert ae(v, (18437746526988116954.0 - 17146362239046152345.0j), tol=ATOL)
|
|
assert ae(v.real, 18437746526988116954.0, tol=PTOL)
|
|
assert ae(v.imag, -17146362239046152345.0, tol=PTOL)
|
|
v = fp.e1((-80.0 + 320.0j))
|
|
assert ae(v, (3.3464697299634526706e+31 - 1.6473152633843023919e+32j), tol=ATOL)
|
|
assert ae(v.real, 3.3464697299634526706e+31, tol=PTOL)
|
|
assert ae(v.imag, -1.6473152633843023919e+32, tol=PTOL)
|
|
v = fp.e1((-4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (20.880034621082893023 - 2.8966139903465137624j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621082893023, tol=PTOL)
|
|
assert ae(v.imag, -2.8966139903465137624, tol=PTOL)
|
|
v = fp.e1((-1.0 + 0.25j))
|
|
assert ae(v, (-1.8942716983721074932 - 2.4689102827070540799j), tol=ATOL)
|
|
assert ae(v.real, -1.8942716983721074932, tol=PTOL)
|
|
assert ae(v.imag, -2.4689102827070540799, tol=PTOL)
|
|
v = fp.e1((-4.0 + 1.0j))
|
|
assert ae(v, (-14.806699492675420438 + 9.1384225230837893776j), tol=ATOL)
|
|
assert ae(v.real, -14.806699492675420438, tol=PTOL)
|
|
assert ae(v.imag, 9.1384225230837893776, tol=PTOL)
|
|
v = fp.e1((-8.0 + 2.0j))
|
|
assert ae(v, (54.633252667426386294 + 413.20318163814670688j), tol=ATOL)
|
|
assert ae(v.real, 54.633252667426386294, tol=PTOL)
|
|
assert ae(v.imag, 413.20318163814670688, tol=PTOL)
|
|
v = fp.e1((-20.0 + 5.0j))
|
|
assert ae(v, (-711836.97165402624643 - 24745250.939695900956j), tol=ATOL)
|
|
assert ae(v.real, -711836.97165402624643, tol=PTOL)
|
|
assert ae(v.imag, -24745250.939695900956, tol=PTOL)
|
|
v = fp.e1((-80.0 + 20.0j))
|
|
assert ae(v, (-4.2139911108612653091e+32 + 5.3367124741918251637e+32j), tol=ATOL)
|
|
assert ae(v.real, -4.2139911108612653091e+32, tol=PTOL)
|
|
assert ae(v.imag, 5.3367124741918251637e+32, tol=PTOL)
|
|
v = fp.e1((-120.0 + 30.0j))
|
|
assert ae(v, (9.7760616203707508892e+48 - 1.058257682317195792e+50j), tol=ATOL)
|
|
assert ae(v.real, 9.7760616203707508892e+48, tol=PTOL)
|
|
assert ae(v.imag, -1.058257682317195792e+50, tol=PTOL)
|
|
v = fp.e1((-160.0 + 40.0j))
|
|
assert ae(v, (8.7065541466623638861e+66 + 1.6577106725141739889e+67j), tol=ATOL)
|
|
assert ae(v.real, 8.7065541466623638861e+66, tol=PTOL)
|
|
assert ae(v.imag, 1.6577106725141739889e+67, tol=PTOL)
|
|
v = fp.e1((-200.0 + 50.0j))
|
|
assert ae(v, (-3.070744996327018106e+84 - 1.7243244846769415903e+84j), tol=ATOL)
|
|
assert ae(v.real, -3.070744996327018106e+84, tol=PTOL)
|
|
assert ae(v.imag, -1.7243244846769415903e+84, tol=PTOL)
|
|
v = fp.e1((-320.0 + 80.0j))
|
|
assert ae(v, (9.9960598637998647276e+135 - 2.6855081527595608863e+136j), tol=ATOL)
|
|
assert ae(v.real, 9.9960598637998647276e+135, tol=PTOL)
|
|
assert ae(v.imag, -2.6855081527595608863e+136, tol=PTOL)
|
|
v = fp.e1(-1.1641532182693481445e-10)
|
|
assert ae(v, (22.296641293460247028 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 22.296641293460247028, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-0.25)
|
|
assert ae(v, (0.54254326466191372953 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 0.54254326466191372953, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-1.0)
|
|
assert ae(v, (-1.8951178163559367555 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -1.8951178163559367555, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-2.0)
|
|
assert ae(v, (-4.9542343560018901634 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -4.9542343560018901634, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-5.0)
|
|
assert ae(v, (-40.185275355803177455 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -40.185275355803177455, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-20.0)
|
|
assert ae(v, (-25615652.66405658882 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -25615652.66405658882, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-30.0)
|
|
assert ae(v, (-368973209407.27419706 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -368973209407.27419706, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-40.0)
|
|
assert ae(v, (-6039718263611241.5784 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -6039718263611241.5784, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-50.0)
|
|
assert ae(v, (-1.0585636897131690963e+20 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -1.0585636897131690963e+20, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1(-80.0)
|
|
assert ae(v, (-7.0146000049047999696e+32 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -7.0146000049047999696e+32, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-1.1641532182693481445e-10 + 0.0j))
|
|
assert ae(v, (22.296641293460247028 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 22.296641293460247028, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-0.25 + 0.0j))
|
|
assert ae(v, (0.54254326466191372953 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 0.54254326466191372953, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-1.0 + 0.0j))
|
|
assert ae(v, (-1.8951178163559367555 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -1.8951178163559367555, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-2.0 + 0.0j))
|
|
assert ae(v, (-4.9542343560018901634 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -4.9542343560018901634, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-5.0 + 0.0j))
|
|
assert ae(v, (-40.185275355803177455 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -40.185275355803177455, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-20.0 + 0.0j))
|
|
assert ae(v, (-25615652.66405658882 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -25615652.66405658882, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-30.0 + 0.0j))
|
|
assert ae(v, (-368973209407.27419706 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -368973209407.27419706, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-40.0 + 0.0j))
|
|
assert ae(v, (-6039718263611241.5784 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -6039718263611241.5784, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-50.0 + 0.0j))
|
|
assert ae(v, (-1.0585636897131690963e+20 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -1.0585636897131690963e+20, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-80.0 + 0.0j))
|
|
assert ae(v, (-7.0146000049047999696e+32 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -7.0146000049047999696e+32, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.e1((-4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (20.880034621082893023 + 2.8966139903465137624j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621082893023, tol=PTOL)
|
|
assert ae(v.imag, 2.8966139903465137624, tol=PTOL)
|
|
v = fp.e1((-1.0 - 0.25j))
|
|
assert ae(v, (-1.8942716983721074932 + 2.4689102827070540799j), tol=ATOL)
|
|
assert ae(v.real, -1.8942716983721074932, tol=PTOL)
|
|
assert ae(v.imag, 2.4689102827070540799, tol=PTOL)
|
|
v = fp.e1((-4.0 - 1.0j))
|
|
assert ae(v, (-14.806699492675420438 - 9.1384225230837893776j), tol=ATOL)
|
|
assert ae(v.real, -14.806699492675420438, tol=PTOL)
|
|
assert ae(v.imag, -9.1384225230837893776, tol=PTOL)
|
|
v = fp.e1((-8.0 - 2.0j))
|
|
assert ae(v, (54.633252667426386294 - 413.20318163814670688j), tol=ATOL)
|
|
assert ae(v.real, 54.633252667426386294, tol=PTOL)
|
|
assert ae(v.imag, -413.20318163814670688, tol=PTOL)
|
|
v = fp.e1((-20.0 - 5.0j))
|
|
assert ae(v, (-711836.97165402624643 + 24745250.939695900956j), tol=ATOL)
|
|
assert ae(v.real, -711836.97165402624643, tol=PTOL)
|
|
assert ae(v.imag, 24745250.939695900956, tol=PTOL)
|
|
v = fp.e1((-80.0 - 20.0j))
|
|
assert ae(v, (-4.2139911108612653091e+32 - 5.3367124741918251637e+32j), tol=ATOL)
|
|
assert ae(v.real, -4.2139911108612653091e+32, tol=PTOL)
|
|
assert ae(v.imag, -5.3367124741918251637e+32, tol=PTOL)
|
|
v = fp.e1((-120.0 - 30.0j))
|
|
assert ae(v, (9.7760616203707508892e+48 + 1.058257682317195792e+50j), tol=ATOL)
|
|
assert ae(v.real, 9.7760616203707508892e+48, tol=PTOL)
|
|
assert ae(v.imag, 1.058257682317195792e+50, tol=PTOL)
|
|
v = fp.e1((-160.0 - 40.0j))
|
|
assert ae(v, (8.7065541466623638861e+66 - 1.6577106725141739889e+67j), tol=ATOL)
|
|
assert ae(v.real, 8.7065541466623638861e+66, tol=PTOL)
|
|
assert ae(v.imag, -1.6577106725141739889e+67, tol=PTOL)
|
|
v = fp.e1((-200.0 - 50.0j))
|
|
assert ae(v, (-3.070744996327018106e+84 + 1.7243244846769415903e+84j), tol=ATOL)
|
|
assert ae(v.real, -3.070744996327018106e+84, tol=PTOL)
|
|
assert ae(v.imag, 1.7243244846769415903e+84, tol=PTOL)
|
|
v = fp.e1((-320.0 - 80.0j))
|
|
assert ae(v, (9.9960598637998647276e+135 + 2.6855081527595608863e+136j), tol=ATOL)
|
|
assert ae(v.real, 9.9960598637998647276e+135, tol=PTOL)
|
|
assert ae(v.imag, 2.6855081527595608863e+136, tol=PTOL)
|
|
v = fp.e1((-1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (21.950067703180274374 + 2.356194490075929607j), tol=ATOL)
|
|
assert ae(v.real, 21.950067703180274374, tol=PTOL)
|
|
assert ae(v.imag, 2.356194490075929607, tol=PTOL)
|
|
v = fp.e1((-0.25 - 0.25j))
|
|
assert ae(v, (0.21441047326710323254 + 2.0732153554307936389j), tol=ATOL)
|
|
assert ae(v.real, 0.21441047326710323254, tol=PTOL)
|
|
assert ae(v.imag, 2.0732153554307936389, tol=PTOL)
|
|
v = fp.e1((-1.0 - 1.0j))
|
|
assert ae(v, (-1.7646259855638540684 + 0.7538228020792708192j), tol=ATOL)
|
|
assert ae(v.real, -1.7646259855638540684, tol=PTOL)
|
|
assert ae(v.imag, 0.7538228020792708192, tol=PTOL)
|
|
v = fp.e1((-2.0 - 2.0j))
|
|
assert ae(v, (-1.8920781621855474089 - 2.1753697842428647236j), tol=ATOL)
|
|
assert ae(v.real, -1.8920781621855474089, tol=PTOL)
|
|
assert ae(v.imag, -2.1753697842428647236, tol=PTOL)
|
|
v = fp.e1((-5.0 - 5.0j))
|
|
assert ae(v, (13.470936071475245856 + 18.464085049321024206j), tol=ATOL)
|
|
assert ae(v.real, 13.470936071475245856, tol=PTOL)
|
|
assert ae(v.imag, 18.464085049321024206, tol=PTOL)
|
|
v = fp.e1((-20.0 - 20.0j))
|
|
assert ae(v, (-16589317.398788971896 - 5831702.3296441771206j), tol=ATOL)
|
|
assert ae(v.real, -16589317.398788971896, tol=PTOL)
|
|
assert ae(v.imag, -5831702.3296441771206, tol=PTOL)
|
|
v = fp.e1((-30.0 - 30.0j))
|
|
assert ae(v, (154596484273.69322527 + 204179357837.41389696j), tol=ATOL)
|
|
assert ae(v.real, 154596484273.69322527, tol=PTOL)
|
|
assert ae(v.imag, 204179357837.41389696, tol=PTOL)
|
|
v = fp.e1((-40.0 - 40.0j))
|
|
assert ae(v, (-287512180321448.45408 - 4203502407932314.974j), tol=ATOL)
|
|
assert ae(v.real, -287512180321448.45408, tol=PTOL)
|
|
assert ae(v.imag, -4203502407932314.974, tol=PTOL)
|
|
v = fp.e1((-50.0 - 50.0j))
|
|
assert ae(v, (-36128528616649268826.0 + 64648801861338741963.0j), tol=ATOL)
|
|
assert ae(v.real, -36128528616649268826.0, tol=PTOL)
|
|
assert ae(v.imag, 64648801861338741963.0, tol=PTOL)
|
|
v = fp.e1((-80.0 - 80.0j))
|
|
assert ae(v, (3.8674816337930010217e+32 + 3.0540709639658071041e+32j), tol=ATOL)
|
|
assert ae(v.real, 3.8674816337930010217e+32, tol=PTOL)
|
|
assert ae(v.imag, 3.0540709639658071041e+32, tol=PTOL)
|
|
v = fp.e1((-1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
|
|
assert ae(v, (20.880034621432138988 + 1.8157749894560994861j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621432138988, tol=PTOL)
|
|
assert ae(v.imag, 1.8157749894560994861, tol=PTOL)
|
|
v = fp.e1((-0.25 - 1.0j))
|
|
assert ae(v, (-0.59066621214766308594 + 0.74474454765205036972j), tol=ATOL)
|
|
assert ae(v.real, -0.59066621214766308594, tol=PTOL)
|
|
assert ae(v.imag, 0.74474454765205036972, tol=PTOL)
|
|
v = fp.e1((-1.0 - 4.0j))
|
|
assert ae(v, (0.49739047283060471093 - 0.41543605404038863174j), tol=ATOL)
|
|
assert ae(v.real, 0.49739047283060471093, tol=PTOL)
|
|
assert ae(v.imag, -0.41543605404038863174, tol=PTOL)
|
|
v = fp.e1((-2.0 - 8.0j))
|
|
assert ae(v, (-0.8705211147733730969 - 0.24099328498605539667j), tol=ATOL)
|
|
assert ae(v.real, -0.8705211147733730969, tol=PTOL)
|
|
assert ae(v.imag, -0.24099328498605539667, tol=PTOL)
|
|
v = fp.e1((-5.0 - 20.0j))
|
|
assert ae(v, (-7.0789514293925893007 + 1.6102177171960790536j), tol=ATOL)
|
|
assert ae(v.real, -7.0789514293925893007, tol=PTOL)
|
|
assert ae(v.imag, 1.6102177171960790536, tol=PTOL)
|
|
v = fp.e1((-20.0 - 80.0j))
|
|
assert ae(v, (5855431.4907298084434 + 720920.93315409165707j), tol=ATOL)
|
|
assert ae(v.real, 5855431.4907298084434, tol=PTOL)
|
|
assert ae(v.imag, 720920.93315409165707, tol=PTOL)
|
|
v = fp.e1((-30.0 - 120.0j))
|
|
assert ae(v, (-65402491644.703470747 + 56697658399.657460294j), tol=ATOL)
|
|
assert ae(v.real, -65402491644.703470747, tol=PTOL)
|
|
assert ae(v.imag, 56697658399.657460294, tol=PTOL)
|
|
v = fp.e1((-40.0 - 160.0j))
|
|
assert ae(v, (25504929379604.776769 - 1429035198630573.2463j), tol=ATOL)
|
|
assert ae(v.real, 25504929379604.776769, tol=PTOL)
|
|
assert ae(v.imag, -1429035198630573.2463, tol=PTOL)
|
|
v = fp.e1((-50.0 - 200.0j))
|
|
assert ae(v, (18437746526988116954.0 + 17146362239046152345.0j), tol=ATOL)
|
|
assert ae(v.real, 18437746526988116954.0, tol=PTOL)
|
|
assert ae(v.imag, 17146362239046152345.0, tol=PTOL)
|
|
v = fp.e1((-80.0 - 320.0j))
|
|
assert ae(v, (3.3464697299634526706e+31 + 1.6473152633843023919e+32j), tol=ATOL)
|
|
assert ae(v.real, 3.3464697299634526706e+31, tol=PTOL)
|
|
assert ae(v.imag, 1.6473152633843023919e+32, tol=PTOL)
|
|
v = fp.e1((0.0 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (22.29664129357666235 + 1.5707963266784812974j), tol=ATOL)
|
|
assert ae(v.real, 22.29664129357666235, tol=PTOL)
|
|
assert ae(v.imag, 1.5707963266784812974, tol=PTOL)
|
|
v = fp.e1((0.0 - 0.25j))
|
|
assert ae(v, (0.82466306258094565309 + 1.3216627564751394551j), tol=ATOL)
|
|
assert ae(v.real, 0.82466306258094565309, tol=PTOL)
|
|
assert ae(v.imag, 1.3216627564751394551, tol=PTOL)
|
|
v = fp.e1((0.0 - 1.0j))
|
|
assert ae(v, (-0.33740392290096813466 + 0.62471325642771360429j), tol=ATOL)
|
|
assert ae(v.real, -0.33740392290096813466, tol=PTOL)
|
|
assert ae(v.imag, 0.62471325642771360429, tol=PTOL)
|
|
v = fp.e1((0.0 - 2.0j))
|
|
assert ae(v, (-0.4229808287748649957 - 0.034616650007798229345j), tol=ATOL)
|
|
assert ae(v.real, -0.4229808287748649957, tol=PTOL)
|
|
assert ae(v.imag, -0.034616650007798229345, tol=PTOL)
|
|
v = fp.e1((0.0 - 5.0j))
|
|
assert ae(v, (0.19002974965664387862 + 0.020865081850222481957j), tol=ATOL)
|
|
assert ae(v.real, 0.19002974965664387862, tol=PTOL)
|
|
assert ae(v.imag, 0.020865081850222481957, tol=PTOL)
|
|
v = fp.e1((0.0 - 20.0j))
|
|
assert ae(v, (-0.04441982084535331654 + 0.022554625751456779068j), tol=ATOL)
|
|
assert ae(v.real, -0.04441982084535331654, tol=PTOL)
|
|
assert ae(v.imag, 0.022554625751456779068, tol=PTOL)
|
|
v = fp.e1((0.0 - 30.0j))
|
|
assert ae(v, (0.033032417282071143779 + 0.0040397867645455082476j), tol=ATOL)
|
|
assert ae(v.real, 0.033032417282071143779, tol=PTOL)
|
|
assert ae(v.imag, 0.0040397867645455082476, tol=PTOL)
|
|
v = fp.e1((0.0 - 40.0j))
|
|
assert ae(v, (-0.019020007896208766962 - 0.016188792559887887544j), tol=ATOL)
|
|
assert ae(v.real, -0.019020007896208766962, tol=PTOL)
|
|
assert ae(v.imag, -0.016188792559887887544, tol=PTOL)
|
|
v = fp.e1((0.0 - 50.0j))
|
|
assert ae(v, (0.0056283863241163054402 + 0.019179254308960724503j), tol=ATOL)
|
|
assert ae(v.real, 0.0056283863241163054402, tol=PTOL)
|
|
assert ae(v.imag, 0.019179254308960724503, tol=PTOL)
|
|
v = fp.e1((0.0 - 80.0j))
|
|
assert ae(v, (0.012402501155070958192 - 0.0015345601175906961199j), tol=ATOL)
|
|
assert ae(v.real, 0.012402501155070958192, tol=PTOL)
|
|
assert ae(v.imag, -0.0015345601175906961199, tol=PTOL)
|
|
v = fp.e1((1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
|
|
assert ae(v, (20.880034621664969632 + 1.3258176632023711778j), tol=ATOL)
|
|
assert ae(v.real, 20.880034621664969632, tol=PTOL)
|
|
assert ae(v.imag, 1.3258176632023711778, tol=PTOL)
|
|
v = fp.e1((0.25 - 1.0j))
|
|
assert ae(v, (-0.16868306393667788761 + 0.4858011885947426971j), tol=ATOL)
|
|
assert ae(v.real, -0.16868306393667788761, tol=PTOL)
|
|
assert ae(v.imag, 0.4858011885947426971, tol=PTOL)
|
|
v = fp.e1((1.0 - 4.0j))
|
|
assert ae(v, (0.03373591813926547318 - 0.073523452241083821877j), tol=ATOL)
|
|
assert ae(v.real, 0.03373591813926547318, tol=PTOL)
|
|
assert ae(v.imag, -0.073523452241083821877, tol=PTOL)
|
|
v = fp.e1((2.0 - 8.0j))
|
|
assert ae(v, (-0.015392833434733785143 + 0.0031747121557605415914j), tol=ATOL)
|
|
assert ae(v.real, -0.015392833434733785143, tol=PTOL)
|
|
assert ae(v.imag, 0.0031747121557605415914, tol=PTOL)
|
|
v = fp.e1((5.0 - 20.0j))
|
|
assert ae(v, (-0.00024419662286542966525 + 0.00021008322966152755674j), tol=ATOL)
|
|
assert ae(v.real, -0.00024419662286542966525, tol=PTOL)
|
|
assert ae(v.imag, 0.00021008322966152755674, tol=PTOL)
|
|
v = fp.e1((20.0 - 80.0j))
|
|
assert ae(v, (2.3255552781051330088e-11 - 8.9463918891349438007e-12j), tol=ATOL)
|
|
assert ae(v.real, 2.3255552781051330088e-11, tol=PTOL)
|
|
assert ae(v.imag, -8.9463918891349438007e-12, tol=PTOL)
|
|
v = fp.e1((30.0 - 120.0j))
|
|
assert ae(v, (-2.7068919097124652332e-16 + 7.0477762411705130239e-16j), tol=ATOL)
|
|
assert ae(v.real, -2.7068919097124652332e-16, tol=PTOL)
|
|
assert ae(v.imag, 7.0477762411705130239e-16, tol=PTOL)
|
|
v = fp.e1((40.0 - 160.0j))
|
|
assert ae(v, (-1.1695597827678024687e-20 - 2.2907401455645736661e-20j), tol=ATOL)
|
|
assert ae(v.real, -1.1695597827678024687e-20, tol=PTOL)
|
|
assert ae(v.imag, -2.2907401455645736661e-20, tol=PTOL)
|
|
v = fp.e1((50.0 - 200.0j))
|
|
assert ae(v, (9.0323746914410162531e-25 + 2.3950601790033530935e-25j), tol=ATOL)
|
|
assert ae(v.real, 9.0323746914410162531e-25, tol=PTOL)
|
|
assert ae(v.imag, 2.3950601790033530935e-25, tol=PTOL)
|
|
v = fp.e1((80.0 - 320.0j))
|
|
assert ae(v, (3.4819106748728063576e-38 + 4.215653005615772724e-38j), tol=ATOL)
|
|
assert ae(v.real, 3.4819106748728063576e-38, tol=PTOL)
|
|
assert ae(v.imag, 4.215653005615772724e-38, tol=PTOL)
|
|
v = fp.e1((1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (21.950067703413105017 + 0.7853981632810329878j), tol=ATOL)
|
|
assert ae(v.real, 21.950067703413105017, tol=PTOL)
|
|
assert ae(v.imag, 0.7853981632810329878, tol=PTOL)
|
|
v = fp.e1((0.25 - 0.25j))
|
|
assert ae(v, (0.71092525792923287894 + 0.56491812441304194711j), tol=ATOL)
|
|
assert ae(v.real, 0.71092525792923287894, tol=PTOL)
|
|
assert ae(v.imag, 0.56491812441304194711, tol=PTOL)
|
|
v = fp.e1((1.0 - 1.0j))
|
|
assert ae(v, (0.00028162445198141832551 + 0.17932453503935894015j), tol=ATOL)
|
|
assert ae(v.real, 0.00028162445198141832551, tol=PTOL)
|
|
assert ae(v.imag, 0.17932453503935894015, tol=PTOL)
|
|
v = fp.e1((2.0 - 2.0j))
|
|
assert ae(v, (-0.033767089606562004246 + 0.018599414169750541925j), tol=ATOL)
|
|
assert ae(v.real, -0.033767089606562004246, tol=PTOL)
|
|
assert ae(v.imag, 0.018599414169750541925, tol=PTOL)
|
|
v = fp.e1((5.0 - 5.0j))
|
|
assert ae(v, (0.0007266506660356393891 - 0.00047102780163522245054j), tol=ATOL)
|
|
assert ae(v.real, 0.0007266506660356393891, tol=PTOL)
|
|
assert ae(v.imag, -0.00047102780163522245054, tol=PTOL)
|
|
v = fp.e1((20.0 - 20.0j))
|
|
assert ae(v, (-2.3824537449367396579e-11 + 6.6969873156525615158e-11j), tol=ATOL)
|
|
assert ae(v.real, -2.3824537449367396579e-11, tol=PTOL)
|
|
assert ae(v.imag, 6.6969873156525615158e-11, tol=PTOL)
|
|
v = fp.e1((30.0 - 30.0j))
|
|
assert ae(v, (1.7316045841744061617e-15 - 1.3065678019487308689e-15j), tol=ATOL)
|
|
assert ae(v.real, 1.7316045841744061617e-15, tol=PTOL)
|
|
assert ae(v.imag, -1.3065678019487308689e-15, tol=PTOL)
|
|
v = fp.e1((40.0 - 40.0j))
|
|
assert ae(v, (-7.4001043002899232182e-20 + 4.991847855336816304e-21j), tol=ATOL)
|
|
assert ae(v.real, -7.4001043002899232182e-20, tol=PTOL)
|
|
assert ae(v.imag, 4.991847855336816304e-21, tol=PTOL)
|
|
v = fp.e1((50.0 - 50.0j))
|
|
assert ae(v, (2.3566128324644641219e-24 + 1.3188326726201614778e-24j), tol=ATOL)
|
|
assert ae(v.real, 2.3566128324644641219e-24, tol=PTOL)
|
|
assert ae(v.imag, 1.3188326726201614778e-24, tol=PTOL)
|
|
v = fp.e1((80.0 - 80.0j))
|
|
assert ae(v, (9.8279750572186526673e-38 - 1.243952841288868831e-37j), tol=ATOL)
|
|
assert ae(v.real, 9.8279750572186526673e-38, tol=PTOL)
|
|
assert ae(v.imag, -1.243952841288868831e-37, tol=PTOL)
|
|
v = fp.e1((4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (20.880034622014215597 + 0.24497866301044883237j), tol=ATOL)
|
|
assert ae(v.real, 20.880034622014215597, tol=PTOL)
|
|
assert ae(v.imag, 0.24497866301044883237, tol=PTOL)
|
|
v = fp.e1((1.0 - 0.25j))
|
|
assert ae(v, (0.19731063945004229095 + 0.087366045774299963672j), tol=ATOL)
|
|
assert ae(v.real, 0.19731063945004229095, tol=PTOL)
|
|
assert ae(v.imag, 0.087366045774299963672, tol=PTOL)
|
|
v = fp.e1((4.0 - 1.0j))
|
|
assert ae(v, (0.0013106173980145506944 + 0.0034542480199350626699j), tol=ATOL)
|
|
assert ae(v.real, 0.0013106173980145506944, tol=PTOL)
|
|
assert ae(v.imag, 0.0034542480199350626699, tol=PTOL)
|
|
v = fp.e1((8.0 - 2.0j))
|
|
assert ae(v, (-0.000022278049065270225945 + 0.000029191940456521555288j), tol=ATOL)
|
|
assert ae(v.real, -0.000022278049065270225945, tol=PTOL)
|
|
assert ae(v.imag, 0.000029191940456521555288, tol=PTOL)
|
|
v = fp.e1((20.0 - 5.0j))
|
|
assert ae(v, (4.7711374515765346894e-11 - 8.2902652405126947359e-11j), tol=ATOL)
|
|
assert ae(v.real, 4.7711374515765346894e-11, tol=PTOL)
|
|
assert ae(v.imag, -8.2902652405126947359e-11, tol=PTOL)
|
|
v = fp.e1((80.0 - 20.0j))
|
|
assert ae(v, (3.8353473865788235787e-38 + 2.129247592349605139e-37j), tol=ATOL)
|
|
assert ae(v.real, 3.8353473865788235787e-38, tol=PTOL)
|
|
assert ae(v.imag, 2.129247592349605139e-37, tol=PTOL)
|
|
v = fp.e1((120.0 - 30.0j))
|
|
assert ae(v, (2.3836002337480334716e-55 - 5.6704043587126198306e-55j), tol=ATOL)
|
|
assert ae(v.real, 2.3836002337480334716e-55, tol=PTOL)
|
|
assert ae(v.imag, -5.6704043587126198306e-55, tol=PTOL)
|
|
v = fp.e1((160.0 - 40.0j))
|
|
assert ae(v, (-1.6238022898654510661e-72 + 1.104172355572287367e-72j), tol=ATOL)
|
|
assert ae(v.real, -1.6238022898654510661e-72, tol=PTOL)
|
|
assert ae(v.imag, 1.104172355572287367e-72, tol=PTOL)
|
|
v = fp.e1((200.0 - 50.0j))
|
|
assert ae(v, (6.6800061461666228487e-90 - 1.4473816083541016115e-91j), tol=ATOL)
|
|
assert ae(v.real, 6.6800061461666228487e-90, tol=PTOL)
|
|
assert ae(v.imag, -1.4473816083541016115e-91, tol=PTOL)
|
|
v = fp.e1((320.0 - 80.0j))
|
|
assert ae(v, (4.2737871527778786157e-143 - 3.1789935525785660314e-142j), tol=ATOL)
|
|
assert ae(v.real, 4.2737871527778786157e-143, tol=PTOL)
|
|
assert ae(v.imag, -3.1789935525785660314e-142, tol=PTOL)
|
|
v = fp.ei(1.1641532182693481445e-10)
|
|
assert ae(v, -22.296641293460247028, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(0.25)
|
|
assert ae(v, -0.54254326466191372953, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(1.0)
|
|
assert ae(v, 1.8951178163559367555, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(2.0)
|
|
assert ae(v, 4.9542343560018901634, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(5.0)
|
|
assert ae(v, 40.185275355803177455, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(20.0)
|
|
assert ae(v, 25615652.66405658882, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(30.0)
|
|
assert ae(v, 368973209407.27419706, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(40.0)
|
|
assert ae(v, 6039718263611241.5784, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(50.0)
|
|
assert ae(v, 1.0585636897131690963e+20, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(80.0)
|
|
assert ae(v, 7.0146000049047999696e+32, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei((1.1641532182693481445e-10 + 0.0j))
|
|
assert ae(v, (-22.296641293460247028 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -22.296641293460247028, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((0.25 + 0.0j))
|
|
assert ae(v, (-0.54254326466191372953 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -0.54254326466191372953, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((1.0 + 0.0j))
|
|
assert ae(v, (1.8951178163559367555 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 1.8951178163559367555, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((2.0 + 0.0j))
|
|
assert ae(v, (4.9542343560018901634 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 4.9542343560018901634, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((5.0 + 0.0j))
|
|
assert ae(v, (40.185275355803177455 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 40.185275355803177455, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((20.0 + 0.0j))
|
|
assert ae(v, (25615652.66405658882 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 25615652.66405658882, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((30.0 + 0.0j))
|
|
assert ae(v, (368973209407.27419706 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 368973209407.27419706, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((40.0 + 0.0j))
|
|
assert ae(v, (6039718263611241.5784 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 6039718263611241.5784, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((50.0 + 0.0j))
|
|
assert ae(v, (1.0585636897131690963e+20 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 1.0585636897131690963e+20, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((80.0 + 0.0j))
|
|
assert ae(v, (7.0146000049047999696e+32 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, 7.0146000049047999696e+32, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (-20.880034621082893023 + 0.24497866324327947603j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621082893023, tol=PTOL)
|
|
assert ae(v.imag, 0.24497866324327947603, tol=PTOL)
|
|
v = fp.ei((1.0 + 0.25j))
|
|
assert ae(v, (1.8942716983721074932 + 0.67268237088273915854j), tol=ATOL)
|
|
assert ae(v.real, 1.8942716983721074932, tol=PTOL)
|
|
assert ae(v.imag, 0.67268237088273915854, tol=PTOL)
|
|
v = fp.ei((4.0 + 1.0j))
|
|
assert ae(v, (14.806699492675420438 + 12.280015176673582616j), tol=ATOL)
|
|
assert ae(v.real, 14.806699492675420438, tol=PTOL)
|
|
assert ae(v.imag, 12.280015176673582616, tol=PTOL)
|
|
v = fp.ei((8.0 + 2.0j))
|
|
assert ae(v, (-54.633252667426386294 + 416.34477429173650012j), tol=ATOL)
|
|
assert ae(v.real, -54.633252667426386294, tol=PTOL)
|
|
assert ae(v.imag, 416.34477429173650012, tol=PTOL)
|
|
v = fp.ei((20.0 + 5.0j))
|
|
assert ae(v, (711836.97165402624643 - 24745247.798103247366j), tol=ATOL)
|
|
assert ae(v.real, 711836.97165402624643, tol=PTOL)
|
|
assert ae(v.imag, -24745247.798103247366, tol=PTOL)
|
|
v = fp.ei((80.0 + 20.0j))
|
|
assert ae(v, (4.2139911108612653091e+32 + 5.3367124741918251637e+32j), tol=ATOL)
|
|
assert ae(v.real, 4.2139911108612653091e+32, tol=PTOL)
|
|
assert ae(v.imag, 5.3367124741918251637e+32, tol=PTOL)
|
|
v = fp.ei((120.0 + 30.0j))
|
|
assert ae(v, (-9.7760616203707508892e+48 - 1.058257682317195792e+50j), tol=ATOL)
|
|
assert ae(v.real, -9.7760616203707508892e+48, tol=PTOL)
|
|
assert ae(v.imag, -1.058257682317195792e+50, tol=PTOL)
|
|
v = fp.ei((160.0 + 40.0j))
|
|
assert ae(v, (-8.7065541466623638861e+66 + 1.6577106725141739889e+67j), tol=ATOL)
|
|
assert ae(v.real, -8.7065541466623638861e+66, tol=PTOL)
|
|
assert ae(v.imag, 1.6577106725141739889e+67, tol=PTOL)
|
|
v = fp.ei((200.0 + 50.0j))
|
|
assert ae(v, (3.070744996327018106e+84 - 1.7243244846769415903e+84j), tol=ATOL)
|
|
assert ae(v.real, 3.070744996327018106e+84, tol=PTOL)
|
|
assert ae(v.imag, -1.7243244846769415903e+84, tol=PTOL)
|
|
v = fp.ei((320.0 + 80.0j))
|
|
assert ae(v, (-9.9960598637998647276e+135 - 2.6855081527595608863e+136j), tol=ATOL)
|
|
assert ae(v.real, -9.9960598637998647276e+135, tol=PTOL)
|
|
assert ae(v.imag, -2.6855081527595608863e+136, tol=PTOL)
|
|
v = fp.ei((1.1641532182693481445e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (-21.950067703180274374 + 0.78539816351386363145j), tol=ATOL)
|
|
assert ae(v.real, -21.950067703180274374, tol=PTOL)
|
|
assert ae(v.imag, 0.78539816351386363145, tol=PTOL)
|
|
v = fp.ei((0.25 + 0.25j))
|
|
assert ae(v, (-0.21441047326710323254 + 1.0683772981589995996j), tol=ATOL)
|
|
assert ae(v.real, -0.21441047326710323254, tol=PTOL)
|
|
assert ae(v.imag, 1.0683772981589995996, tol=PTOL)
|
|
v = fp.ei((1.0 + 1.0j))
|
|
assert ae(v, (1.7646259855638540684 + 2.3877698515105224193j), tol=ATOL)
|
|
assert ae(v.real, 1.7646259855638540684, tol=PTOL)
|
|
assert ae(v.imag, 2.3877698515105224193, tol=PTOL)
|
|
v = fp.ei((2.0 + 2.0j))
|
|
assert ae(v, (1.8920781621855474089 + 5.3169624378326579621j), tol=ATOL)
|
|
assert ae(v.real, 1.8920781621855474089, tol=PTOL)
|
|
assert ae(v.imag, 5.3169624378326579621, tol=PTOL)
|
|
v = fp.ei((5.0 + 5.0j))
|
|
assert ae(v, (-13.470936071475245856 - 15.322492395731230968j), tol=ATOL)
|
|
assert ae(v.real, -13.470936071475245856, tol=PTOL)
|
|
assert ae(v.imag, -15.322492395731230968, tol=PTOL)
|
|
v = fp.ei((20.0 + 20.0j))
|
|
assert ae(v, (16589317.398788971896 + 5831705.4712368307104j), tol=ATOL)
|
|
assert ae(v.real, 16589317.398788971896, tol=PTOL)
|
|
assert ae(v.imag, 5831705.4712368307104, tol=PTOL)
|
|
v = fp.ei((30.0 + 30.0j))
|
|
assert ae(v, (-154596484273.69322527 - 204179357834.2723043j), tol=ATOL)
|
|
assert ae(v.real, -154596484273.69322527, tol=PTOL)
|
|
assert ae(v.imag, -204179357834.2723043, tol=PTOL)
|
|
v = fp.ei((40.0 + 40.0j))
|
|
assert ae(v, (287512180321448.45408 + 4203502407932318.1156j), tol=ATOL)
|
|
assert ae(v.real, 287512180321448.45408, tol=PTOL)
|
|
assert ae(v.imag, 4203502407932318.1156, tol=PTOL)
|
|
v = fp.ei((50.0 + 50.0j))
|
|
assert ae(v, (36128528616649268826.0 - 64648801861338741960.0j), tol=ATOL)
|
|
assert ae(v.real, 36128528616649268826.0, tol=PTOL)
|
|
assert ae(v.imag, -64648801861338741960.0, tol=PTOL)
|
|
v = fp.ei((80.0 + 80.0j))
|
|
assert ae(v, (-3.8674816337930010217e+32 - 3.0540709639658071041e+32j), tol=ATOL)
|
|
assert ae(v.real, -3.8674816337930010217e+32, tol=PTOL)
|
|
assert ae(v.imag, -3.0540709639658071041e+32, tol=PTOL)
|
|
v = fp.ei((1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
|
|
assert ae(v, (-20.880034621432138988 + 1.3258176641336937524j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621432138988, tol=PTOL)
|
|
assert ae(v.imag, 1.3258176641336937524, tol=PTOL)
|
|
v = fp.ei((0.25 + 1.0j))
|
|
assert ae(v, (0.59066621214766308594 + 2.3968481059377428687j), tol=ATOL)
|
|
assert ae(v.real, 0.59066621214766308594, tol=PTOL)
|
|
assert ae(v.imag, 2.3968481059377428687, tol=PTOL)
|
|
v = fp.ei((1.0 + 4.0j))
|
|
assert ae(v, (-0.49739047283060471093 + 3.5570287076301818702j), tol=ATOL)
|
|
assert ae(v.real, -0.49739047283060471093, tol=PTOL)
|
|
assert ae(v.imag, 3.5570287076301818702, tol=PTOL)
|
|
v = fp.ei((2.0 + 8.0j))
|
|
assert ae(v, (0.8705211147733730969 + 3.3825859385758486351j), tol=ATOL)
|
|
assert ae(v.real, 0.8705211147733730969, tol=PTOL)
|
|
assert ae(v.imag, 3.3825859385758486351, tol=PTOL)
|
|
v = fp.ei((5.0 + 20.0j))
|
|
assert ae(v, (7.0789514293925893007 + 1.5313749363937141849j), tol=ATOL)
|
|
assert ae(v.real, 7.0789514293925893007, tol=PTOL)
|
|
assert ae(v.imag, 1.5313749363937141849, tol=PTOL)
|
|
v = fp.ei((20.0 + 80.0j))
|
|
assert ae(v, (-5855431.4907298084434 - 720917.79156143806727j), tol=ATOL)
|
|
assert ae(v.real, -5855431.4907298084434, tol=PTOL)
|
|
assert ae(v.imag, -720917.79156143806727, tol=PTOL)
|
|
v = fp.ei((30.0 + 120.0j))
|
|
assert ae(v, (65402491644.703470747 - 56697658396.51586764j), tol=ATOL)
|
|
assert ae(v.real, 65402491644.703470747, tol=PTOL)
|
|
assert ae(v.imag, -56697658396.51586764, tol=PTOL)
|
|
v = fp.ei((40.0 + 160.0j))
|
|
assert ae(v, (-25504929379604.776769 + 1429035198630576.3879j), tol=ATOL)
|
|
assert ae(v.real, -25504929379604.776769, tol=PTOL)
|
|
assert ae(v.imag, 1429035198630576.3879, tol=PTOL)
|
|
v = fp.ei((50.0 + 200.0j))
|
|
assert ae(v, (-18437746526988116954.0 - 17146362239046152342.0j), tol=ATOL)
|
|
assert ae(v.real, -18437746526988116954.0, tol=PTOL)
|
|
assert ae(v.imag, -17146362239046152342.0, tol=PTOL)
|
|
v = fp.ei((80.0 + 320.0j))
|
|
assert ae(v, (-3.3464697299634526706e+31 - 1.6473152633843023919e+32j), tol=ATOL)
|
|
assert ae(v.real, -3.3464697299634526706e+31, tol=PTOL)
|
|
assert ae(v.imag, -1.6473152633843023919e+32, tol=PTOL)
|
|
v = fp.ei((0.0 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (-22.29664129357666235 + 1.5707963269113119411j), tol=ATOL)
|
|
assert ae(v.real, -22.29664129357666235, tol=PTOL)
|
|
assert ae(v.imag, 1.5707963269113119411, tol=PTOL)
|
|
v = fp.ei((0.0 + 0.25j))
|
|
assert ae(v, (-0.82466306258094565309 + 1.8199298971146537833j), tol=ATOL)
|
|
assert ae(v.real, -0.82466306258094565309, tol=PTOL)
|
|
assert ae(v.imag, 1.8199298971146537833, tol=PTOL)
|
|
v = fp.ei((0.0 + 1.0j))
|
|
assert ae(v, (0.33740392290096813466 + 2.5168793971620796342j), tol=ATOL)
|
|
assert ae(v.real, 0.33740392290096813466, tol=PTOL)
|
|
assert ae(v.imag, 2.5168793971620796342, tol=PTOL)
|
|
v = fp.ei((0.0 + 2.0j))
|
|
assert ae(v, (0.4229808287748649957 + 3.1762093035975914678j), tol=ATOL)
|
|
assert ae(v.real, 0.4229808287748649957, tol=PTOL)
|
|
assert ae(v.imag, 3.1762093035975914678, tol=PTOL)
|
|
v = fp.ei((0.0 + 5.0j))
|
|
assert ae(v, (-0.19002974965664387862 + 3.1207275717395707565j), tol=ATOL)
|
|
assert ae(v.real, -0.19002974965664387862, tol=PTOL)
|
|
assert ae(v.imag, 3.1207275717395707565, tol=PTOL)
|
|
v = fp.ei((0.0 + 20.0j))
|
|
assert ae(v, (0.04441982084535331654 + 3.1190380278383364594j), tol=ATOL)
|
|
assert ae(v.real, 0.04441982084535331654, tol=PTOL)
|
|
assert ae(v.imag, 3.1190380278383364594, tol=PTOL)
|
|
v = fp.ei((0.0 + 30.0j))
|
|
assert ae(v, (-0.033032417282071143779 + 3.1375528668252477302j), tol=ATOL)
|
|
assert ae(v.real, -0.033032417282071143779, tol=PTOL)
|
|
assert ae(v.imag, 3.1375528668252477302, tol=PTOL)
|
|
v = fp.ei((0.0 + 40.0j))
|
|
assert ae(v, (0.019020007896208766962 + 3.157781446149681126j), tol=ATOL)
|
|
assert ae(v.real, 0.019020007896208766962, tol=PTOL)
|
|
assert ae(v.imag, 3.157781446149681126, tol=PTOL)
|
|
v = fp.ei((0.0 + 50.0j))
|
|
assert ae(v, (-0.0056283863241163054402 + 3.122413399280832514j), tol=ATOL)
|
|
assert ae(v.real, -0.0056283863241163054402, tol=PTOL)
|
|
assert ae(v.imag, 3.122413399280832514, tol=PTOL)
|
|
v = fp.ei((0.0 + 80.0j))
|
|
assert ae(v, (-0.012402501155070958192 + 3.1431272137073839346j), tol=ATOL)
|
|
assert ae(v.real, -0.012402501155070958192, tol=PTOL)
|
|
assert ae(v.imag, 3.1431272137073839346, tol=PTOL)
|
|
v = fp.ei((-1.1641532182693481445e-10 + 4.6566128730773925781e-10j))
|
|
assert ae(v, (-20.880034621664969632 + 1.8157749903874220607j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621664969632, tol=PTOL)
|
|
assert ae(v.imag, 1.8157749903874220607, tol=PTOL)
|
|
v = fp.ei((-0.25 + 1.0j))
|
|
assert ae(v, (0.16868306393667788761 + 2.6557914649950505414j), tol=ATOL)
|
|
assert ae(v.real, 0.16868306393667788761, tol=PTOL)
|
|
assert ae(v.imag, 2.6557914649950505414, tol=PTOL)
|
|
v = fp.ei((-1.0 + 4.0j))
|
|
assert ae(v, (-0.03373591813926547318 + 3.2151161058308770603j), tol=ATOL)
|
|
assert ae(v.real, -0.03373591813926547318, tol=PTOL)
|
|
assert ae(v.imag, 3.2151161058308770603, tol=PTOL)
|
|
v = fp.ei((-2.0 + 8.0j))
|
|
assert ae(v, (0.015392833434733785143 + 3.1384179414340326969j), tol=ATOL)
|
|
assert ae(v.real, 0.015392833434733785143, tol=PTOL)
|
|
assert ae(v.imag, 3.1384179414340326969, tol=PTOL)
|
|
v = fp.ei((-5.0 + 20.0j))
|
|
assert ae(v, (0.00024419662286542966525 + 3.1413825703601317109j), tol=ATOL)
|
|
assert ae(v.real, 0.00024419662286542966525, tol=PTOL)
|
|
assert ae(v.imag, 3.1413825703601317109, tol=PTOL)
|
|
v = fp.ei((-20.0 + 80.0j))
|
|
assert ae(v, (-2.3255552781051330088e-11 + 3.1415926535987396304j), tol=ATOL)
|
|
assert ae(v.real, -2.3255552781051330088e-11, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535987396304, tol=PTOL)
|
|
v = fp.ei((-30.0 + 120.0j))
|
|
assert ae(v, (2.7068919097124652332e-16 + 3.1415926535897925337j), tol=ATOL)
|
|
assert ae(v.real, 2.7068919097124652332e-16, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897925337, tol=PTOL)
|
|
v = fp.ei((-40.0 + 160.0j))
|
|
assert ae(v, (1.1695597827678024687e-20 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 1.1695597827678024687e-20, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-50.0 + 200.0j))
|
|
assert ae(v, (-9.0323746914410162531e-25 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -9.0323746914410162531e-25, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-80.0 + 320.0j))
|
|
assert ae(v, (-3.4819106748728063576e-38 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -3.4819106748728063576e-38, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-4.6566128730773925781e-10 + 1.1641532182693481445e-10j))
|
|
assert ae(v, (-20.880034622014215597 + 2.8966139905793444061j), tol=ATOL)
|
|
assert ae(v.real, -20.880034622014215597, tol=PTOL)
|
|
assert ae(v.imag, 2.8966139905793444061, tol=PTOL)
|
|
v = fp.ei((-1.0 + 0.25j))
|
|
assert ae(v, (-0.19731063945004229095 + 3.0542266078154932748j), tol=ATOL)
|
|
assert ae(v.real, -0.19731063945004229095, tol=PTOL)
|
|
assert ae(v.imag, 3.0542266078154932748, tol=PTOL)
|
|
v = fp.ei((-4.0 + 1.0j))
|
|
assert ae(v, (-0.0013106173980145506944 + 3.1381384055698581758j), tol=ATOL)
|
|
assert ae(v.real, -0.0013106173980145506944, tol=PTOL)
|
|
assert ae(v.imag, 3.1381384055698581758, tol=PTOL)
|
|
v = fp.ei((-8.0 + 2.0j))
|
|
assert ae(v, (0.000022278049065270225945 + 3.1415634616493367169j), tol=ATOL)
|
|
assert ae(v.real, 0.000022278049065270225945, tol=PTOL)
|
|
assert ae(v.imag, 3.1415634616493367169, tol=PTOL)
|
|
v = fp.ei((-20.0 + 5.0j))
|
|
assert ae(v, (-4.7711374515765346894e-11 + 3.1415926536726958909j), tol=ATOL)
|
|
assert ae(v.real, -4.7711374515765346894e-11, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926536726958909, tol=PTOL)
|
|
v = fp.ei((-80.0 + 20.0j))
|
|
assert ae(v, (-3.8353473865788235787e-38 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -3.8353473865788235787e-38, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-120.0 + 30.0j))
|
|
assert ae(v, (-2.3836002337480334716e-55 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -2.3836002337480334716e-55, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-160.0 + 40.0j))
|
|
assert ae(v, (1.6238022898654510661e-72 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 1.6238022898654510661e-72, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-200.0 + 50.0j))
|
|
assert ae(v, (-6.6800061461666228487e-90 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -6.6800061461666228487e-90, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-320.0 + 80.0j))
|
|
assert ae(v, (-4.2737871527778786157e-143 + 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -4.2737871527778786157e-143, tol=PTOL)
|
|
assert ae(v.imag, 3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei(-1.1641532182693481445e-10)
|
|
assert ae(v, -22.296641293693077672, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-0.25)
|
|
assert ae(v, -1.0442826344437381945, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-1.0)
|
|
assert ae(v, -0.21938393439552027368, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-2.0)
|
|
assert ae(v, -0.048900510708061119567, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-5.0)
|
|
assert ae(v, -0.0011482955912753257973, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-20.0)
|
|
assert ae(v, -9.8355252906498816904e-11, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-30.0)
|
|
assert ae(v, -3.0215520106888125448e-15, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-40.0)
|
|
assert ae(v, -1.0367732614516569722e-19, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-50.0)
|
|
assert ae(v, -3.7832640295504590187e-24, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei(-80.0)
|
|
assert ae(v, -2.2285432586884729112e-37, tol=ATOL)
|
|
assert type(v) is float
|
|
v = fp.ei((-1.1641532182693481445e-10 + 0.0j))
|
|
assert ae(v, (-22.296641293693077672 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -22.296641293693077672, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-0.25 + 0.0j))
|
|
assert ae(v, (-1.0442826344437381945 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -1.0442826344437381945, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-1.0 + 0.0j))
|
|
assert ae(v, (-0.21938393439552027368 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -0.21938393439552027368, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-2.0 + 0.0j))
|
|
assert ae(v, (-0.048900510708061119567 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -0.048900510708061119567, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-5.0 + 0.0j))
|
|
assert ae(v, (-0.0011482955912753257973 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -0.0011482955912753257973, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-20.0 + 0.0j))
|
|
assert ae(v, (-9.8355252906498816904e-11 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -9.8355252906498816904e-11, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-30.0 + 0.0j))
|
|
assert ae(v, (-3.0215520106888125448e-15 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -3.0215520106888125448e-15, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-40.0 + 0.0j))
|
|
assert ae(v, (-1.0367732614516569722e-19 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -1.0367732614516569722e-19, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-50.0 + 0.0j))
|
|
assert ae(v, (-3.7832640295504590187e-24 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -3.7832640295504590187e-24, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-80.0 + 0.0j))
|
|
assert ae(v, (-2.2285432586884729112e-37 + 0.0j), tol=ATOL)
|
|
assert ae(v.real, -2.2285432586884729112e-37, tol=PTOL)
|
|
assert v.imag == 0
|
|
v = fp.ei((-4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (-20.880034622014215597 - 2.8966139905793444061j), tol=ATOL)
|
|
assert ae(v.real, -20.880034622014215597, tol=PTOL)
|
|
assert ae(v.imag, -2.8966139905793444061, tol=PTOL)
|
|
v = fp.ei((-1.0 - 0.25j))
|
|
assert ae(v, (-0.19731063945004229095 - 3.0542266078154932748j), tol=ATOL)
|
|
assert ae(v.real, -0.19731063945004229095, tol=PTOL)
|
|
assert ae(v.imag, -3.0542266078154932748, tol=PTOL)
|
|
v = fp.ei((-4.0 - 1.0j))
|
|
assert ae(v, (-0.0013106173980145506944 - 3.1381384055698581758j), tol=ATOL)
|
|
assert ae(v.real, -0.0013106173980145506944, tol=PTOL)
|
|
assert ae(v.imag, -3.1381384055698581758, tol=PTOL)
|
|
v = fp.ei((-8.0 - 2.0j))
|
|
assert ae(v, (0.000022278049065270225945 - 3.1415634616493367169j), tol=ATOL)
|
|
assert ae(v.real, 0.000022278049065270225945, tol=PTOL)
|
|
assert ae(v.imag, -3.1415634616493367169, tol=PTOL)
|
|
v = fp.ei((-20.0 - 5.0j))
|
|
assert ae(v, (-4.7711374515765346894e-11 - 3.1415926536726958909j), tol=ATOL)
|
|
assert ae(v.real, -4.7711374515765346894e-11, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926536726958909, tol=PTOL)
|
|
v = fp.ei((-80.0 - 20.0j))
|
|
assert ae(v, (-3.8353473865788235787e-38 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -3.8353473865788235787e-38, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-120.0 - 30.0j))
|
|
assert ae(v, (-2.3836002337480334716e-55 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -2.3836002337480334716e-55, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-160.0 - 40.0j))
|
|
assert ae(v, (1.6238022898654510661e-72 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 1.6238022898654510661e-72, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-200.0 - 50.0j))
|
|
assert ae(v, (-6.6800061461666228487e-90 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -6.6800061461666228487e-90, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-320.0 - 80.0j))
|
|
assert ae(v, (-4.2737871527778786157e-143 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -4.2737871527778786157e-143, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (-21.950067703413105017 - 2.3561944903087602507j), tol=ATOL)
|
|
assert ae(v.real, -21.950067703413105017, tol=PTOL)
|
|
assert ae(v.imag, -2.3561944903087602507, tol=PTOL)
|
|
v = fp.ei((-0.25 - 0.25j))
|
|
assert ae(v, (-0.71092525792923287894 - 2.5766745291767512913j), tol=ATOL)
|
|
assert ae(v.real, -0.71092525792923287894, tol=PTOL)
|
|
assert ae(v.imag, -2.5766745291767512913, tol=PTOL)
|
|
v = fp.ei((-1.0 - 1.0j))
|
|
assert ae(v, (-0.00028162445198141832551 - 2.9622681185504342983j), tol=ATOL)
|
|
assert ae(v.real, -0.00028162445198141832551, tol=PTOL)
|
|
assert ae(v.imag, -2.9622681185504342983, tol=PTOL)
|
|
v = fp.ei((-2.0 - 2.0j))
|
|
assert ae(v, (0.033767089606562004246 - 3.1229932394200426965j), tol=ATOL)
|
|
assert ae(v.real, 0.033767089606562004246, tol=PTOL)
|
|
assert ae(v.imag, -3.1229932394200426965, tol=PTOL)
|
|
v = fp.ei((-5.0 - 5.0j))
|
|
assert ae(v, (-0.0007266506660356393891 - 3.1420636813914284609j), tol=ATOL)
|
|
assert ae(v.real, -0.0007266506660356393891, tol=PTOL)
|
|
assert ae(v.imag, -3.1420636813914284609, tol=PTOL)
|
|
v = fp.ei((-20.0 - 20.0j))
|
|
assert ae(v, (2.3824537449367396579e-11 - 3.1415926535228233653j), tol=ATOL)
|
|
assert ae(v.real, 2.3824537449367396579e-11, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535228233653, tol=PTOL)
|
|
v = fp.ei((-30.0 - 30.0j))
|
|
assert ae(v, (-1.7316045841744061617e-15 - 3.141592653589794545j), tol=ATOL)
|
|
assert ae(v.real, -1.7316045841744061617e-15, tol=PTOL)
|
|
assert ae(v.imag, -3.141592653589794545, tol=PTOL)
|
|
v = fp.ei((-40.0 - 40.0j))
|
|
assert ae(v, (7.4001043002899232182e-20 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 7.4001043002899232182e-20, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-50.0 - 50.0j))
|
|
assert ae(v, (-2.3566128324644641219e-24 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -2.3566128324644641219e-24, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-80.0 - 80.0j))
|
|
assert ae(v, (-9.8279750572186526673e-38 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -9.8279750572186526673e-38, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
|
|
assert ae(v, (-20.880034621664969632 - 1.8157749903874220607j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621664969632, tol=PTOL)
|
|
assert ae(v.imag, -1.8157749903874220607, tol=PTOL)
|
|
v = fp.ei((-0.25 - 1.0j))
|
|
assert ae(v, (0.16868306393667788761 - 2.6557914649950505414j), tol=ATOL)
|
|
assert ae(v.real, 0.16868306393667788761, tol=PTOL)
|
|
assert ae(v.imag, -2.6557914649950505414, tol=PTOL)
|
|
v = fp.ei((-1.0 - 4.0j))
|
|
assert ae(v, (-0.03373591813926547318 - 3.2151161058308770603j), tol=ATOL)
|
|
assert ae(v.real, -0.03373591813926547318, tol=PTOL)
|
|
assert ae(v.imag, -3.2151161058308770603, tol=PTOL)
|
|
v = fp.ei((-2.0 - 8.0j))
|
|
assert ae(v, (0.015392833434733785143 - 3.1384179414340326969j), tol=ATOL)
|
|
assert ae(v.real, 0.015392833434733785143, tol=PTOL)
|
|
assert ae(v.imag, -3.1384179414340326969, tol=PTOL)
|
|
v = fp.ei((-5.0 - 20.0j))
|
|
assert ae(v, (0.00024419662286542966525 - 3.1413825703601317109j), tol=ATOL)
|
|
assert ae(v.real, 0.00024419662286542966525, tol=PTOL)
|
|
assert ae(v.imag, -3.1413825703601317109, tol=PTOL)
|
|
v = fp.ei((-20.0 - 80.0j))
|
|
assert ae(v, (-2.3255552781051330088e-11 - 3.1415926535987396304j), tol=ATOL)
|
|
assert ae(v.real, -2.3255552781051330088e-11, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535987396304, tol=PTOL)
|
|
v = fp.ei((-30.0 - 120.0j))
|
|
assert ae(v, (2.7068919097124652332e-16 - 3.1415926535897925337j), tol=ATOL)
|
|
assert ae(v.real, 2.7068919097124652332e-16, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897925337, tol=PTOL)
|
|
v = fp.ei((-40.0 - 160.0j))
|
|
assert ae(v, (1.1695597827678024687e-20 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, 1.1695597827678024687e-20, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-50.0 - 200.0j))
|
|
assert ae(v, (-9.0323746914410162531e-25 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -9.0323746914410162531e-25, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((-80.0 - 320.0j))
|
|
assert ae(v, (-3.4819106748728063576e-38 - 3.1415926535897932385j), tol=ATOL)
|
|
assert ae(v.real, -3.4819106748728063576e-38, tol=PTOL)
|
|
assert ae(v.imag, -3.1415926535897932385, tol=PTOL)
|
|
v = fp.ei((0.0 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (-22.29664129357666235 - 1.5707963269113119411j), tol=ATOL)
|
|
assert ae(v.real, -22.29664129357666235, tol=PTOL)
|
|
assert ae(v.imag, -1.5707963269113119411, tol=PTOL)
|
|
v = fp.ei((0.0 - 0.25j))
|
|
assert ae(v, (-0.82466306258094565309 - 1.8199298971146537833j), tol=ATOL)
|
|
assert ae(v.real, -0.82466306258094565309, tol=PTOL)
|
|
assert ae(v.imag, -1.8199298971146537833, tol=PTOL)
|
|
v = fp.ei((0.0 - 1.0j))
|
|
assert ae(v, (0.33740392290096813466 - 2.5168793971620796342j), tol=ATOL)
|
|
assert ae(v.real, 0.33740392290096813466, tol=PTOL)
|
|
assert ae(v.imag, -2.5168793971620796342, tol=PTOL)
|
|
v = fp.ei((0.0 - 2.0j))
|
|
assert ae(v, (0.4229808287748649957 - 3.1762093035975914678j), tol=ATOL)
|
|
assert ae(v.real, 0.4229808287748649957, tol=PTOL)
|
|
assert ae(v.imag, -3.1762093035975914678, tol=PTOL)
|
|
v = fp.ei((0.0 - 5.0j))
|
|
assert ae(v, (-0.19002974965664387862 - 3.1207275717395707565j), tol=ATOL)
|
|
assert ae(v.real, -0.19002974965664387862, tol=PTOL)
|
|
assert ae(v.imag, -3.1207275717395707565, tol=PTOL)
|
|
v = fp.ei((0.0 - 20.0j))
|
|
assert ae(v, (0.04441982084535331654 - 3.1190380278383364594j), tol=ATOL)
|
|
assert ae(v.real, 0.04441982084535331654, tol=PTOL)
|
|
assert ae(v.imag, -3.1190380278383364594, tol=PTOL)
|
|
v = fp.ei((0.0 - 30.0j))
|
|
assert ae(v, (-0.033032417282071143779 - 3.1375528668252477302j), tol=ATOL)
|
|
assert ae(v.real, -0.033032417282071143779, tol=PTOL)
|
|
assert ae(v.imag, -3.1375528668252477302, tol=PTOL)
|
|
v = fp.ei((0.0 - 40.0j))
|
|
assert ae(v, (0.019020007896208766962 - 3.157781446149681126j), tol=ATOL)
|
|
assert ae(v.real, 0.019020007896208766962, tol=PTOL)
|
|
assert ae(v.imag, -3.157781446149681126, tol=PTOL)
|
|
v = fp.ei((0.0 - 50.0j))
|
|
assert ae(v, (-0.0056283863241163054402 - 3.122413399280832514j), tol=ATOL)
|
|
assert ae(v.real, -0.0056283863241163054402, tol=PTOL)
|
|
assert ae(v.imag, -3.122413399280832514, tol=PTOL)
|
|
v = fp.ei((0.0 - 80.0j))
|
|
assert ae(v, (-0.012402501155070958192 - 3.1431272137073839346j), tol=ATOL)
|
|
assert ae(v.real, -0.012402501155070958192, tol=PTOL)
|
|
assert ae(v.imag, -3.1431272137073839346, tol=PTOL)
|
|
v = fp.ei((1.1641532182693481445e-10 - 4.6566128730773925781e-10j))
|
|
assert ae(v, (-20.880034621432138988 - 1.3258176641336937524j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621432138988, tol=PTOL)
|
|
assert ae(v.imag, -1.3258176641336937524, tol=PTOL)
|
|
v = fp.ei((0.25 - 1.0j))
|
|
assert ae(v, (0.59066621214766308594 - 2.3968481059377428687j), tol=ATOL)
|
|
assert ae(v.real, 0.59066621214766308594, tol=PTOL)
|
|
assert ae(v.imag, -2.3968481059377428687, tol=PTOL)
|
|
v = fp.ei((1.0 - 4.0j))
|
|
assert ae(v, (-0.49739047283060471093 - 3.5570287076301818702j), tol=ATOL)
|
|
assert ae(v.real, -0.49739047283060471093, tol=PTOL)
|
|
assert ae(v.imag, -3.5570287076301818702, tol=PTOL)
|
|
v = fp.ei((2.0 - 8.0j))
|
|
assert ae(v, (0.8705211147733730969 - 3.3825859385758486351j), tol=ATOL)
|
|
assert ae(v.real, 0.8705211147733730969, tol=PTOL)
|
|
assert ae(v.imag, -3.3825859385758486351, tol=PTOL)
|
|
v = fp.ei((5.0 - 20.0j))
|
|
assert ae(v, (7.0789514293925893007 - 1.5313749363937141849j), tol=ATOL)
|
|
assert ae(v.real, 7.0789514293925893007, tol=PTOL)
|
|
assert ae(v.imag, -1.5313749363937141849, tol=PTOL)
|
|
v = fp.ei((20.0 - 80.0j))
|
|
assert ae(v, (-5855431.4907298084434 + 720917.79156143806727j), tol=ATOL)
|
|
assert ae(v.real, -5855431.4907298084434, tol=PTOL)
|
|
assert ae(v.imag, 720917.79156143806727, tol=PTOL)
|
|
v = fp.ei((30.0 - 120.0j))
|
|
assert ae(v, (65402491644.703470747 + 56697658396.51586764j), tol=ATOL)
|
|
assert ae(v.real, 65402491644.703470747, tol=PTOL)
|
|
assert ae(v.imag, 56697658396.51586764, tol=PTOL)
|
|
v = fp.ei((40.0 - 160.0j))
|
|
assert ae(v, (-25504929379604.776769 - 1429035198630576.3879j), tol=ATOL)
|
|
assert ae(v.real, -25504929379604.776769, tol=PTOL)
|
|
assert ae(v.imag, -1429035198630576.3879, tol=PTOL)
|
|
v = fp.ei((50.0 - 200.0j))
|
|
assert ae(v, (-18437746526988116954.0 + 17146362239046152342.0j), tol=ATOL)
|
|
assert ae(v.real, -18437746526988116954.0, tol=PTOL)
|
|
assert ae(v.imag, 17146362239046152342.0, tol=PTOL)
|
|
v = fp.ei((80.0 - 320.0j))
|
|
assert ae(v, (-3.3464697299634526706e+31 + 1.6473152633843023919e+32j), tol=ATOL)
|
|
assert ae(v.real, -3.3464697299634526706e+31, tol=PTOL)
|
|
assert ae(v.imag, 1.6473152633843023919e+32, tol=PTOL)
|
|
v = fp.ei((1.1641532182693481445e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (-21.950067703180274374 - 0.78539816351386363145j), tol=ATOL)
|
|
assert ae(v.real, -21.950067703180274374, tol=PTOL)
|
|
assert ae(v.imag, -0.78539816351386363145, tol=PTOL)
|
|
v = fp.ei((0.25 - 0.25j))
|
|
assert ae(v, (-0.21441047326710323254 - 1.0683772981589995996j), tol=ATOL)
|
|
assert ae(v.real, -0.21441047326710323254, tol=PTOL)
|
|
assert ae(v.imag, -1.0683772981589995996, tol=PTOL)
|
|
v = fp.ei((1.0 - 1.0j))
|
|
assert ae(v, (1.7646259855638540684 - 2.3877698515105224193j), tol=ATOL)
|
|
assert ae(v.real, 1.7646259855638540684, tol=PTOL)
|
|
assert ae(v.imag, -2.3877698515105224193, tol=PTOL)
|
|
v = fp.ei((2.0 - 2.0j))
|
|
assert ae(v, (1.8920781621855474089 - 5.3169624378326579621j), tol=ATOL)
|
|
assert ae(v.real, 1.8920781621855474089, tol=PTOL)
|
|
assert ae(v.imag, -5.3169624378326579621, tol=PTOL)
|
|
v = fp.ei((5.0 - 5.0j))
|
|
assert ae(v, (-13.470936071475245856 + 15.322492395731230968j), tol=ATOL)
|
|
assert ae(v.real, -13.470936071475245856, tol=PTOL)
|
|
assert ae(v.imag, 15.322492395731230968, tol=PTOL)
|
|
v = fp.ei((20.0 - 20.0j))
|
|
assert ae(v, (16589317.398788971896 - 5831705.4712368307104j), tol=ATOL)
|
|
assert ae(v.real, 16589317.398788971896, tol=PTOL)
|
|
assert ae(v.imag, -5831705.4712368307104, tol=PTOL)
|
|
v = fp.ei((30.0 - 30.0j))
|
|
assert ae(v, (-154596484273.69322527 + 204179357834.2723043j), tol=ATOL)
|
|
assert ae(v.real, -154596484273.69322527, tol=PTOL)
|
|
assert ae(v.imag, 204179357834.2723043, tol=PTOL)
|
|
v = fp.ei((40.0 - 40.0j))
|
|
assert ae(v, (287512180321448.45408 - 4203502407932318.1156j), tol=ATOL)
|
|
assert ae(v.real, 287512180321448.45408, tol=PTOL)
|
|
assert ae(v.imag, -4203502407932318.1156, tol=PTOL)
|
|
v = fp.ei((50.0 - 50.0j))
|
|
assert ae(v, (36128528616649268826.0 + 64648801861338741960.0j), tol=ATOL)
|
|
assert ae(v.real, 36128528616649268826.0, tol=PTOL)
|
|
assert ae(v.imag, 64648801861338741960.0, tol=PTOL)
|
|
v = fp.ei((80.0 - 80.0j))
|
|
assert ae(v, (-3.8674816337930010217e+32 + 3.0540709639658071041e+32j), tol=ATOL)
|
|
assert ae(v.real, -3.8674816337930010217e+32, tol=PTOL)
|
|
assert ae(v.imag, 3.0540709639658071041e+32, tol=PTOL)
|
|
v = fp.ei((4.6566128730773925781e-10 - 1.1641532182693481445e-10j))
|
|
assert ae(v, (-20.880034621082893023 - 0.24497866324327947603j), tol=ATOL)
|
|
assert ae(v.real, -20.880034621082893023, tol=PTOL)
|
|
assert ae(v.imag, -0.24497866324327947603, tol=PTOL)
|
|
v = fp.ei((1.0 - 0.25j))
|
|
assert ae(v, (1.8942716983721074932 - 0.67268237088273915854j), tol=ATOL)
|
|
assert ae(v.real, 1.8942716983721074932, tol=PTOL)
|
|
assert ae(v.imag, -0.67268237088273915854, tol=PTOL)
|
|
v = fp.ei((4.0 - 1.0j))
|
|
assert ae(v, (14.806699492675420438 - 12.280015176673582616j), tol=ATOL)
|
|
assert ae(v.real, 14.806699492675420438, tol=PTOL)
|
|
assert ae(v.imag, -12.280015176673582616, tol=PTOL)
|
|
v = fp.ei((8.0 - 2.0j))
|
|
assert ae(v, (-54.633252667426386294 - 416.34477429173650012j), tol=ATOL)
|
|
assert ae(v.real, -54.633252667426386294, tol=PTOL)
|
|
assert ae(v.imag, -416.34477429173650012, tol=PTOL)
|
|
v = fp.ei((20.0 - 5.0j))
|
|
assert ae(v, (711836.97165402624643 + 24745247.798103247366j), tol=ATOL)
|
|
assert ae(v.real, 711836.97165402624643, tol=PTOL)
|
|
assert ae(v.imag, 24745247.798103247366, tol=PTOL)
|
|
v = fp.ei((80.0 - 20.0j))
|
|
assert ae(v, (4.2139911108612653091e+32 - 5.3367124741918251637e+32j), tol=ATOL)
|
|
assert ae(v.real, 4.2139911108612653091e+32, tol=PTOL)
|
|
assert ae(v.imag, -5.3367124741918251637e+32, tol=PTOL)
|
|
v = fp.ei((120.0 - 30.0j))
|
|
assert ae(v, (-9.7760616203707508892e+48 + 1.058257682317195792e+50j), tol=ATOL)
|
|
assert ae(v.real, -9.7760616203707508892e+48, tol=PTOL)
|
|
assert ae(v.imag, 1.058257682317195792e+50, tol=PTOL)
|
|
v = fp.ei((160.0 - 40.0j))
|
|
assert ae(v, (-8.7065541466623638861e+66 - 1.6577106725141739889e+67j), tol=ATOL)
|
|
assert ae(v.real, -8.7065541466623638861e+66, tol=PTOL)
|
|
assert ae(v.imag, -1.6577106725141739889e+67, tol=PTOL)
|
|
v = fp.ei((200.0 - 50.0j))
|
|
assert ae(v, (3.070744996327018106e+84 + 1.7243244846769415903e+84j), tol=ATOL)
|
|
assert ae(v.real, 3.070744996327018106e+84, tol=PTOL)
|
|
assert ae(v.imag, 1.7243244846769415903e+84, tol=PTOL)
|
|
v = fp.ei((320.0 - 80.0j))
|
|
assert ae(v, (-9.9960598637998647276e+135 + 2.6855081527595608863e+136j), tol=ATOL)
|
|
assert ae(v.real, -9.9960598637998647276e+135, tol=PTOL)
|
|
assert ae(v.imag, 2.6855081527595608863e+136, tol=PTOL)
|
|
|
|
def test_fp_isfinite():
|
|
assert fp.isfinite(1.2)
|
|
assert fp.isfinite(1+2j)
|
|
assert not fp.isfinite(fp.inf)
|
|
assert not fp.isfinite(fp.nan)
|
|
|
|
def test_fp_nan_in_args():
|
|
assert fp.isnan(fp.ei(fp.nan)) # issue 483
|
|
assert fp.isnan(fp.li(fp.nan)) # issue 484
|
|
assert fp.isnan(fp.ci(fp.nan)) # issue 480
|
|
assert fp.isnan(fp.si(fp.nan)) # issue 481
|
|
assert fp.isnan(fp.chi(fp.nan)) # issue 482
|
|
assert fp.isnan(fp.shi(fp.nan))
|
|
assert fp.isnan(fp.e1(fp.nan)) # issue 487
|
|
assert fp.isnan(fp.chebyt(1.3, fp.nan)) # issue 478
|
|
assert fp.isnan(fp.chebyt(13, fp.nan))
|
|
assert fp.isnan(fp.hyp2f2(0.4, 2.5, 2.2, 0.7, fp.nan)) # issue 509
|
|
|
|
def test_issue_510():
|
|
assert fp.rgamma(fp.inf) == fp.zero
|
|
|
|
def test_issue_491():
|
|
assert fp.appellf1(0, 0.4, 2.5, 2.2, fp.inf, 1.4) == fp.one
|
|
|
|
def test_issue_521():
|
|
assert fp.ff(1, -fp.inf) == 0.0
|
|
assert fp.isnan(fp.ff(1, fp.inf))
|