### This file is grabbed from Python's Lib/test/test_math.py
###---------------------------------------------------------
# Python test set -- math module
# XXXX Should not do tests around zero only

eps = 0.00001
#print('math module, testing with eps ', eps)
import math

def testit(name, value, expected):
    if abs(value-expected) > eps:
        msg = name + " returned " + str(value) + " expected " + str(expected)
        raise msg

#print 'constants'
testit('pi', math.pi, 3.1415926)
testit('e', math.e, 2.7182818)

#print 'acos'
testit('acos(-1)', math.acos(-1), math.pi)
testit('acos(0)', math.acos(0), math.pi/2)
testit('acos(1)', math.acos(1), 0)

#print 'asin'
testit('asin(-1)', math.asin(-1), -math.pi/2)
testit('asin(0)', math.asin(0), 0)
testit('asin(1)', math.asin(1), math.pi/2)

#print 'atan'
testit('atan(-1)', math.atan(-1), -math.pi/4)
testit('atan(0)', math.atan(0), 0)
testit('atan(1)', math.atan(1), math.pi/4)

#print 'atan2'
testit('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
testit('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
testit('atan2(0, 1)', math.atan2(0, 1), 0)
testit('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
testit('atan2(1, 0)', math.atan2(1, 0), math.pi/2)

#print 'ceil'
testit('ceil(0.5)', math.ceil(0.5), 1)
testit('ceil(1.0)', math.ceil(1.0), 1)
testit('ceil(1.5)', math.ceil(1.5), 2)
testit('ceil(-0.5)', math.ceil(-0.5), 0)
testit('ceil(-1.0)', math.ceil(-1.0), -1)
testit('ceil(-1.5)', math.ceil(-1.5), -1)

#print 'cos'
testit('cos(-pi/2)', math.cos(-math.pi/2), 0)
testit('cos(0)', math.cos(0), 1)
testit('cos(pi/2)', math.cos(math.pi/2), 0)
testit('cos(pi)', math.cos(math.pi), -1)

#print 'cosh'
testit('cosh(0)', math.cosh(0), 1)
testit('cosh(2)-2*(cosh(1)**2)', math.cosh(2)-2*(math.cosh(1)**2), -1) # Thanks to Lambert

#print 'degrees'
testit('degrees(pi)', math.degrees(math.pi), 180.0)
testit('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
testit('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)

#print 'exp'
testit('exp(-1)', math.exp(-1), 1/math.e)
testit('exp(0)', math.exp(0), 1)
testit('exp(1)', math.exp(1), math.e)

#print 'fabs'
testit('fabs(-1)', math.fabs(-1), 1)
testit('fabs(0)', math.fabs(0), 0)
testit('fabs(1)', math.fabs(1), 1)

#print 'floor'
testit('floor(0.5)', math.floor(0.5), 0)
testit('floor(1.0)', math.floor(1.0), 1)
testit('floor(1.5)', math.floor(1.5), 1)
testit('floor(-0.5)', math.floor(-0.5), -1)
testit('floor(-1.0)', math.floor(-1.0), -1)
testit('floor(-1.5)', math.floor(-1.5), -2)

#print 'fmod'
testit('fmod(10,1)', math.fmod(10,1), 0)
testit('fmod(10,0.5)', math.fmod(10,0.5), 0)
testit('fmod(10,1.5)', math.fmod(10,1.5), 1)
testit('fmod(-10,1)', math.fmod(-10,1), 0)
testit('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
testit('fmod(-10,1.5)', math.fmod(-10,1.5), -1)

#print 'frexp'
def testfrexp(name, value, expected):
    mant = value[0]
    exp  = value[1]
    emant = expected[0]
    eexp  = expected[1]
    if abs(mant-emant) > eps or exp != eexp:
        raise '%s returned (%f, %f), expected (%f, %f)'%\
              (name, mant, exp, emant,eexp)

testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
testfrexp('frexp(0)', math.frexp(0), (0, 0))
testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
testfrexp('frexp(2)', math.frexp(2), (0.5, 2))

#print 'hypot'
testit('hypot(0,0)', math.hypot(0,0), 0)
testit('hypot(3,4)', math.hypot(3,4), 5)

#print 'ldexp'
testit('ldexp(0,1)', math.ldexp(0,1), 0)
testit('ldexp(1,1)', math.ldexp(1,1), 2)
testit('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
testit('ldexp(-1,1)', math.ldexp(-1,1), -2)

#print 'log'
testit('log(1/e)', math.log(1/math.e), -1)
testit('log(1)', math.log(1), 0)
testit('log(e)', math.log(math.e), 1)
testit('log(32,2)', math.log(32,2), 5)
testit('log(10**40, 10)', math.log(10**40, 10), 40)
testit('log(10**40, 10**20)', math.log(10**40, 10**20), 2)

#print 'log10'
testit('log10(0.1)', math.log10(0.1), -1)
testit('log10(1)', math.log10(1), 0)
testit('log10(10)', math.log10(10), 1)

#print 'modf'
def testmodf(name, value, expected):
    v1 = value[0]
    v2 = value[1]
    e1 = expected[0]
    e2 = expected[1]
    if abs(v1-e1) > eps or abs(v2-e2):
        raise '%s returned (%f, %f), expected (%f, %f)'%\
              (name, v1,v2, e1,e2)

testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))

#print 'pow'
testit('pow(0,1)', math.pow(0,1), 0)
testit('pow(1,0)', math.pow(1,0), 1)
testit('pow(2,1)', math.pow(2,1), 2)
testit('pow(2,-1)', math.pow(2,-1), 0.5)

#print 'radians'
testit('radians(180)', math.radians(180), math.pi)
testit('radians(90)', math.radians(90), math.pi/2)
testit('radians(-45)', math.radians(-45), -math.pi/4)

#print 'sin'
testit('sin(0)', math.sin(0), 0)
testit('sin(pi/2)', math.sin(math.pi/2), 1)
testit('sin(-pi/2)', math.sin(-math.pi/2), -1)

#print 'sinh'
testit('sinh(0)', math.sinh(0), 0)
testit('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
testit('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)

#print 'sqrt'
testit('sqrt(0)', math.sqrt(0), 0)
testit('sqrt(1)', math.sqrt(1), 1)
testit('sqrt(4)', math.sqrt(4), 2)

#print 'tan'
testit('tan(0)', math.tan(0), 0)
testit('tan(pi/4)', math.tan(math.pi/4), 1)
testit('tan(-pi/4)', math.tan(-math.pi/4), -1)

#print 'tanh'
testit('tanh(0)', math.tanh(0), 0)
testit('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)

#print("OK: math module test pass")