"""
Easy-to-use test-generating code:

cases = '''
exp 2.25
log 2.25
'''

from mpmath import ae, fp, mp
mp.dps = 20
for test in cases.splitlines():
    if not test:
        continue
    words = test.split()
    fname = words[0]
    args = words[1:]
    argstr = ", ".join(args)
    testline = "%s(%s)" % (fname, argstr)
    ans = str(eval(testline))
    print "    assert ae(fp.%s, %s)" % (testline, ans)

"""

import pytest

from mpmath import fp


def ae(x, y, tol=1e-12):
    if x == y:
        return True
    return abs(x-y) <= tol*abs(y)

def test_conj():
    assert fp.conj(4) == 4
    assert fp.conj(3+4j) == 3-4j
    assert fp.fdot([1,2],[3,2+1j], conjugate=True) == 7-2j

def test_fp_number_parts():
    assert ae(fp.arg(3), 0.0)
    assert ae(fp.arg(-3), 3.1415926535897932385)
    assert ae(fp.arg(3j), 1.5707963267948966192)
    assert ae(fp.arg(-3j), -1.5707963267948966192)
    assert ae(fp.arg(2+3j), 0.98279372324732906799)
    assert ae(fp.arg(-1-1j), -2.3561944901923449288)
    assert ae(fp.re(2.5), 2.5)
    assert ae(fp.re(2.5+3j), 2.5)
    assert ae(fp.im(2.5), 0.0)
    assert ae(fp.im(2.5+3j), 3.0)
    assert ae(fp.floor(2.5), 2.0)
    assert ae(fp.floor(2), 2.0)
    assert ae(fp.floor(2.0+0j), (2.0 + 0.0j))
    assert ae(fp.floor(-1.5-0.5j), (-2.0 - 1.0j))
    assert ae(fp.ceil(2.5), 3.0)
    assert ae(fp.ceil(2), 2.0)
    assert ae(fp.ceil(2.0+0j), (2.0 + 0.0j))
    assert ae(fp.ceil(-1.5-0.5j), (-1.0 + 0.0j))

def test_fp_cospi_sinpi():
    assert ae(fp.sinpi(0), 0.0)
    assert ae(fp.sinpi(0.25), 0.7071067811865475244)
    assert ae(fp.sinpi(0.5), 1.0)
    assert ae(fp.sinpi(0.75), 0.7071067811865475244)
    assert ae(fp.sinpi(1), 0.0)
    assert ae(fp.sinpi(1.25), -0.7071067811865475244)
    assert ae(fp.sinpi(1.5), -1.0)
    assert ae(fp.sinpi(1.75), -0.7071067811865475244)
    assert ae(fp.sinpi(2), 0.0)
    assert ae(fp.sinpi(2.25), 0.7071067811865475244)
    assert ae(fp.sinpi(0+3j), (0.0 + 6195.8238636085899556j))
    assert ae(fp.sinpi(0.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
    assert ae(fp.sinpi(0.5+3j), (6195.8239443081075259 + 0.0j))
    assert ae(fp.sinpi(0.75+3j), (4381.1091260582448033 - 4381.1090689950686908j))
    assert ae(fp.sinpi(1+3j), (0.0 - 6195.8238636085899556j))
    assert ae(fp.sinpi(1.25+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
    assert ae(fp.sinpi(1.5+3j), (-6195.8239443081075259 + 0.0j))
    assert ae(fp.sinpi(1.75+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
    assert ae(fp.sinpi(2+3j), (0.0 + 6195.8238636085899556j))
    assert ae(fp.sinpi(2.25+3j), (4381.1091260582448033 + 4381.1090689950686908j))
    assert ae(fp.sinpi(-0.75), -0.7071067811865475244)
    assert ae(fp.sinpi(-1e-10), -3.1415926535897933529e-10)
    assert ae(fp.sinpi(1e-10), 3.1415926535897933529e-10)
    assert ae(fp.sinpi(1e-10+1e-10j), (3.141592653589793353e-10 + 3.1415926535897933528e-10j))
    assert ae(fp.sinpi(1e-10-1e-10j), (3.141592653589793353e-10 - 3.1415926535897933528e-10j))
    assert ae(fp.sinpi(-1e-10+1e-10j), (-3.141592653589793353e-10 + 3.1415926535897933528e-10j))
    assert ae(fp.sinpi(-1e-10-1e-10j), (-3.141592653589793353e-10 - 3.1415926535897933528e-10j))
    assert ae(fp.cospi(0), 1.0)
    assert ae(fp.cospi(0.25), 0.7071067811865475244)
    assert ae(fp.cospi(0.5), 0.0)
    assert ae(fp.cospi(0.75), -0.7071067811865475244)
    assert ae(fp.cospi(1), -1.0)
    assert ae(fp.cospi(1.25), -0.7071067811865475244)
    assert ae(fp.cospi(1.5), 0.0)
    assert ae(fp.cospi(1.75), 0.7071067811865475244)
    assert ae(fp.cospi(2), 1.0)
    assert ae(fp.cospi(2.25), 0.7071067811865475244)
    assert ae(fp.cospi(0+3j), (6195.8239443081075259 + 0.0j))
    assert ae(fp.cospi(0.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
    assert ae(fp.cospi(0.5+3j), (0.0 - 6195.8238636085899556j))
    assert ae(fp.cospi(0.75+3j), (-4381.1091260582448033 - 4381.1090689950686908j))
    assert ae(fp.cospi(1+3j), (-6195.8239443081075259 + 0.0j))
    assert ae(fp.cospi(1.25+3j), (-4381.1091260582448033 + 4381.1090689950686908j))
    assert ae(fp.cospi(1.5+3j), (0.0 + 6195.8238636085899556j))
    assert ae(fp.cospi(1.75+3j), (4381.1091260582448033 + 4381.1090689950686908j))
    assert ae(fp.cospi(2+3j), (6195.8239443081075259 + 0.0j))
    assert ae(fp.cospi(2.25+3j), (4381.1091260582448033 - 4381.1090689950686908j))
    assert ae(fp.cospi(-0.75), -0.7071067811865475244)
    assert ae(fp.sinpi(-0.7), -0.80901699437494750611)
    assert ae(fp.cospi(-0.7), -0.5877852522924730163)
    assert ae(fp.cospi(-3+2j), (-267.74676148374822225 + 0.0j))
    assert ae(fp.sinpi(-3+2j), (0.0 - 267.74489404101651426j))
    assert ae(fp.sinpi(-0.7+2j), (-216.6116802292079471 - 157.37650009392034693j))
    assert ae(fp.cospi(-0.7+2j), (-157.37759774921754565 + 216.61016943630197336j))

def test_fp_asinh_acosh_atanh():
    assert ae(fp.asinh(0), 0.0)
    assert ae(fp.acosh(1), 0.0)
    assert ae(fp.atanh(0), 0.0)

def test_fp_tanh():
    assert fp.tanh(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+1, 0)
    assert fp.tanh(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+1, 0)
    assert fp.tanh(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(-1, 0)
    assert fp.tanh(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(-1, 0)
    assert fp.tanh(fp.mpc(+fp.inf, 2)) == fp.mpc(+1, 0)
    assert fp.tanh(fp.mpc(-fp.inf, 2)) == fp.mpc(-1, 0)
    r = fp.tanh(fp.mpc(0, -fp.inf))
    assert r.real == 0 and fp.isnan(r.imag)
    r = fp.tanh(fp.mpc(2, -fp.inf))
    assert fp.isnan(r.real) and fp.isnan(r.imag)
    assert fp.tanh(fp.mpc(+fp.inf, fp.nan)) == fp.mpc(+1, 0)
    assert fp.tanh(fp.mpc(-fp.inf, fp.nan)) == fp.mpc(-1, 0)

def test_fp_tan():
    assert fp.tan(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(0, +1)
    assert fp.tan(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(0, -1)
    assert fp.tan(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(0, +1)
    assert fp.tan(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(0, -1)
    assert fp.tan(fp.mpc(2, +fp.inf)) == fp.mpc(0, +1)
    assert fp.tan(fp.mpc(2, -fp.inf)) == fp.mpc(0, -1)
    r = fp.tan(fp.mpc(-fp.inf, 0))
    assert fp.isnan(r.real) and r.imag == 0
    r = fp.tan(fp.mpc(-fp.inf, 2))
    assert fp.isnan(r.real) and fp.isnan(r.imag)
    assert fp.tan(fp.mpc(fp.nan, +fp.inf)) == fp.mpc(0, +1)
    assert fp.tan(fp.mpc(fp.nan, -fp.inf)) == fp.mpc(0, -1)

def test_fp_asin():
    pi4 = fp.pi/4
    assert fp.asin(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+pi4, +fp.inf)
    assert fp.asin(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+pi4, -fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(-pi4, +fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(-pi4, -fp.inf)
    r = fp.asin(fp.mpc(+fp.inf, fp.nan))
    assert fp.isnan(r.real) and r.imag == -fp.inf
    r = fp.asin(fp.mpc(-fp.inf, fp.nan))
    assert fp.isnan(r.real) and r.imag == -fp.inf
    r = fp.asin(fp.mpc(fp.nan, +fp.inf))
    assert fp.isnan(r.real) and r.imag == +fp.inf
    r = fp.asin(fp.mpc(fp.nan, -fp.inf))
    assert fp.isnan(r.real) and r.imag == -fp.inf
    pi2 = fp.pi/2
    assert fp.asin(fp.mpc(+fp.inf, +1)) == fp.mpc(pi2, +fp.inf)
    assert fp.asin(fp.mpc(+fp.inf, -1)) == fp.mpc(pi2, -fp.inf)
    assert fp.asin(fp.mpc(+fp.inf, +0.0)) == fp.mpc(pi2, +fp.inf)
    assert fp.asin(fp.mpc(+fp.inf, -0.0)) == fp.mpc(pi2, -fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, +1)) == fp.mpc(-pi2, +fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, -1)) == fp.mpc(-pi2, -fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, +0.0)) == fp.mpc(-pi2, +fp.inf)
    assert fp.asin(fp.mpc(-fp.inf, -0.0)) == fp.mpc(-pi2, -fp.inf)
    assert fp.asin(fp.mpc(+1, +fp.inf)) == fp.mpc(+0.0, +fp.inf)
    assert fp.asin(fp.mpc(-1, +fp.inf)) == fp.mpc(-0.0, +fp.inf)
    assert fp.asin(fp.mpc(+0.0, +fp.inf)) == fp.mpc(+0.0, +fp.inf)
    assert fp.asin(fp.mpc(-0.0, +fp.inf)) == fp.mpc(-0.0, +fp.inf)
    assert fp.asin(fp.mpc(+1, -fp.inf)) == fp.mpc(+0.0, -fp.inf)
    assert fp.asin(fp.mpc(-1, -fp.inf)) == fp.mpc(-0.0, -fp.inf)
    assert fp.asin(fp.mpc(+0.0, -fp.inf)) == fp.mpc(+0.0, -fp.inf)
    assert fp.asin(fp.mpc(-0.0, -fp.inf)) == fp.mpc(-0.0, -fp.inf)
    assert ae(fp.asin(fp.mpc(-2, +0.0)), fp.mpc(-pi2, -fp.log(2 - fp.sqrt(3))))
    assert ae(fp.asin(fp.mpc(-2, -0.0)), fp.mpc(-pi2, +fp.log(2 - fp.sqrt(3))))
    assert ae(fp.asin(fp.mpc(+2, +0.0)), fp.mpc(+pi2, +fp.log(2 + fp.sqrt(3))))
    assert ae(fp.asin(fp.mpc(+2, -0.0)), fp.mpc(+pi2, -fp.log(2 + fp.sqrt(3))))
    assert ae(fp.asin(fp.mpc(0.5, +0.0)), fp.pi/6)
    assert ae(fp.asin(fp.mpc(0.5, -0.0)), fp.pi/6)

def test_fp_acos():
    pi4 = fp.pi/4
    assert fp.acos(fp.mpc(+fp.inf, +fp.inf)) == fp.mpc(+pi4, -fp.inf)
    assert fp.acos(fp.mpc(+fp.inf, -fp.inf)) == fp.mpc(+pi4, +fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, +fp.inf)) == fp.mpc(pi4*3, -fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, -fp.inf)) == fp.mpc(pi4*3, +fp.inf)
    r = fp.acos(fp.mpc(+fp.inf, fp.nan))
    assert fp.isnan(r.real) and r.imag == fp.inf
    r = fp.acos(fp.mpc(-fp.inf, fp.nan))
    assert fp.isnan(r.real) and r.imag == fp.inf
    r = fp.acos(fp.mpc(fp.nan, +fp.inf))
    assert fp.isnan(r.real) and r.imag == -fp.inf
    r = fp.acos(fp.mpc(fp.nan, -fp.inf))
    assert fp.isnan(r.real) and r.imag == +fp.inf
    pi2 = fp.pi/2
    assert fp.acos(fp.mpc(+fp.inf, +1)) == fp.mpc(0.0, -fp.inf)
    assert fp.acos(fp.mpc(+fp.inf, -1)) == fp.mpc(0.0, +fp.inf)
    assert fp.acos(fp.mpc(+fp.inf, +0.0)) == fp.mpc(0.0, -fp.inf)
    assert fp.acos(fp.mpc(+fp.inf, -0.0)) == fp.mpc(0.0, +fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, +1)) == fp.mpc(fp.pi, -fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, -1)) == fp.mpc(fp.pi, +fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, +0.0)) == fp.mpc(fp.pi, -fp.inf)
    assert fp.acos(fp.mpc(-fp.inf, -0.0)) == fp.mpc(fp.pi, +fp.inf)
    assert fp.acos(fp.mpc(+1, +fp.inf)) == fp.mpc(pi2, -fp.inf)
    assert fp.acos(fp.mpc(-1, +fp.inf)) == fp.mpc(pi2, -fp.inf)
    assert fp.acos(fp.mpc(+0.0, +fp.inf)) == fp.mpc(pi2, -fp.inf)
    assert fp.acos(fp.mpc(-0.0, +fp.inf)) == fp.mpc(pi2, -fp.inf)
    assert fp.acos(fp.mpc(+1, -fp.inf)) == fp.mpc(pi2, +fp.inf)
    assert fp.acos(fp.mpc(-1, -fp.inf)) == fp.mpc(pi2, +fp.inf)
    assert fp.acos(fp.mpc(+0.0, -fp.inf)) == fp.mpc(pi2, +fp.inf)
    assert fp.acos(fp.mpc(-0.0, -fp.inf)) == fp.mpc(pi2, +fp.inf)
    assert ae(fp.acos(fp.mpc(-2, +0.0)), fp.mpc(fp.pi, +fp.log(2 - fp.sqrt(3))))
    assert ae(fp.acos(fp.mpc(-2, -0.0)), fp.mpc(fp.pi, -fp.log(2 - fp.sqrt(3))))
    assert ae(fp.acos(fp.mpc(+2, +0.0)), fp.mpc(0, -fp.log(2 + fp.sqrt(3))))
    assert ae(fp.acos(fp.mpc(+2, -0.0)), fp.mpc(0, +fp.log(2 + fp.sqrt(3))))
    assert ae(fp.acos(fp.mpc(0.5, +0.0)), fp.pi/3)
    assert ae(fp.acos(fp.mpc(0.5, -0.0)), fp.pi/3)

def test_fp_expj():
    assert ae(fp.expj(0), (1.0 + 0.0j))
    assert ae(fp.expj(1), (0.5403023058681397174 + 0.84147098480789650665j))
    assert ae(fp.expj(2), (-0.416146836547142387 + 0.9092974268256816954j))
    assert ae(fp.expj(0.75), (0.73168886887382088631 + 0.68163876002333416673j))
    assert ae(fp.expj(2+3j), (-0.020718731002242879378 + 0.045271253156092975488j))
    assert ae(fp.expjpi(0), (1.0 + 0.0j))
    assert ae(fp.expjpi(1), (-1.0 + 0.0j))
    assert ae(fp.expjpi(2), (1.0 + 0.0j))
    assert ae(fp.expjpi(0.75), (-0.7071067811865475244 + 0.7071067811865475244j))
    assert ae(fp.expjpi(2+3j), (0.000080699517570304599239 + 0.0j))

@pytest.mark.parametrize('plus', [True, False])
def test_fp_bernoulli(plus):
    assert ae(fp.bernoulli(0, plus), 1.0)
    assert ae(fp.bernoulli(1, plus), 0.5 if plus else -0.5)
    assert ae(fp.bernoulli(2, plus), 0.16666666666666666667)
    assert ae(fp.bernoulli(10, plus), 0.075757575757575757576)
    assert ae(fp.bernoulli(11, plus), 0.0)

def test_fp_gamma():
    assert ae(fp.gamma(1), 1.0)
    assert ae(fp.gamma(1.5), 0.88622692545275801365)
    assert ae(fp.gamma(10), 362880.0)
    assert ae(fp.gamma(-0.5), -3.5449077018110320546)
    assert ae(fp.gamma(-7.1), 0.0016478244570263333622)
    assert ae(fp.gamma(12.3), 83385367.899970000963)
    assert ae(fp.gamma(2+0j), (1.0 + 0.0j))
    assert fp.isnan(fp.gamma(-fp.inf))
    assert ae(fp.gamma(-2.5+0j), (-0.94530872048294188123 + 0.0j))
    assert ae(fp.gamma(3+4j), (0.0052255384713692141947 - 0.17254707929430018772j))
    assert ae(fp.gamma(-3-4j), (0.00001460997305874775607 - 0.000020760733311509070396j))
    assert ae(fp.fac(0), 1.0)
    assert ae(fp.fac(1), 1.0)
    assert ae(fp.fac(20), 2432902008176640000.0)
    assert ae(fp.fac(-3.5), -0.94530872048294188123)
    assert ae(fp.fac(2+3j), (-0.44011340763700171113 - 0.06363724312631702183j))
    assert ae(fp.loggamma(1.0), 0.0)
    assert ae(fp.loggamma(2.0), 0.0)
    assert ae(fp.loggamma(3.0), 0.69314718055994530942)
    assert ae(fp.loggamma(7.25), 7.0521854507385394449)
    assert ae(fp.loggamma(1000.0), 5905.2204232091812118)
    assert ae(fp.loggamma(1e50), 1.1412925464970229298e+52)
    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))