# Python test set -- math module
# XXXX Should not do tests around zero only

from test.test_support import TestFailed, verbose

seps='1e-05'
eps = eval(seps)
print 'math module, testing with eps', seps
import math

def testit(name, value, expected):
    if abs(value-expected) > eps:
        raise TestFailed, '%s returned %f, expected %f'%\
              (name, value, expected)

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, (mant, exp), (emant, eexp)):
    if abs(mant-emant) > eps or exp != eexp:
        raise TestFailed, '%s returned %s, expected %s'%\
              (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, (v1, v2), (e1, e2)):
    if abs(v1-e1) > eps or abs(v2-e2):
        raise TestFailed, '%s returned %s, expected %s'%\
              (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)

# RED_FLAG 16-Oct-2000 Tim
# While 2.0 is more consistent about exceptions than previous releases, it
# still fails this part of the test on some platforms.  For now, we only
# *run* test_exceptions() in verbose mode, so that this isn't normally
# tested.

def test_exceptions():
    print 'exceptions'
    try:
        x = math.exp(-1000000000)
    except:
        # mathmodule.c is failing to weed out underflows from libm, or
        # we've got an fp format with huge dynamic range
        raise TestFailed("underflowing exp() should not have raised "
                         "an exception")
    if x != 0:
        raise TestFailed("underflowing exp() should have returned 0")

    # If this fails, probably using a strict IEEE-754 conforming libm, and x
    # is +Inf afterwards.  But Python wants overflows detected by default.
    try:
        x = math.exp(1000000000)
    except OverflowError:
        pass
    else:
        raise TestFailed("overflowing exp() didn't trigger OverflowError")

    # If this fails, it could be a puzzle.  One odd possibility is that
    # mathmodule.c's macros are getting confused while comparing
    # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
    # as a result (and so raising OverflowError instead).
    try:
        x = math.sqrt(-1.0)
    except ValueError:
        pass
    else:
        raise TestFailed("sqrt(-1) didn't raise ValueError")

if verbose:
    test_exceptions()
