Lib/test/test_math.py

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

from test.test_support import run_unittest, verbose
import unittest
import math

seps='1e-05'
eps = eval(seps)

class MathTests(unittest.TestCase):

    def ftest(self, name, value, expected):
        if abs(value-expected) > eps:
            # Use %r instead of %f so the error message
            # displays full precision. Otherwise discrepancies
            # in the last few bits will lead to very confusing
            # error messages
            self.fail('%s returned %r, expected %r' %
                      (name, value, expected))

    def testConstants(self):
        self.ftest('pi', math.pi, 3.1415926)
        self.ftest('e', math.e, 2.7182818)

    def testAcos(self):
        self.assertRaises(TypeError, math.acos)
        self.ftest('acos(-1)', math.acos(-1), math.pi)
        self.ftest('acos(0)', math.acos(0), math.pi/2)
        self.ftest('acos(1)', math.acos(1), 0)

    def testAsin(self):
        self.assertRaises(TypeError, math.asin)
        self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
        self.ftest('asin(0)', math.asin(0), 0)
        self.ftest('asin(1)', math.asin(1), math.pi/2)

    def testAtan(self):
        self.assertRaises(TypeError, math.atan)
        self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
        self.ftest('atan(0)', math.atan(0), 0)
        self.ftest('atan(1)', math.atan(1), math.pi/4)

    def testAtan2(self):
        self.assertRaises(TypeError, math.atan2)
        self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
        self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
        self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
        self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
        self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)

    def testCeil(self):
        self.assertRaises(TypeError, math.ceil)
        # These types will be int in py3k.
        self.assertEquals(float, type(math.ceil(1)))
        self.assertEquals(float, type(math.ceil(1L)))
        self.assertEquals(float, type(math.ceil(1.0)))
        self.ftest('ceil(0.5)', math.ceil(0.5), 1)
        self.ftest('ceil(1.0)', math.ceil(1.0), 1)
        self.ftest('ceil(1.5)', math.ceil(1.5), 2)
        self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
        self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
        self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)

        class TestCeil(object):
            def __float__(self):
                return 41.3
        class TestNoCeil(object):
            pass
        self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
        self.assertRaises(TypeError, math.ceil, TestNoCeil())

        t = TestNoCeil()
        t.__ceil__ = lambda *args: args
        self.assertRaises(TypeError, math.ceil, t)
        self.assertRaises(TypeError, math.ceil, t, 0)

    def testCos(self):
        self.assertRaises(TypeError, math.cos)
        self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
        self.ftest('cos(0)', math.cos(0), 1)
        self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
        self.ftest('cos(pi)', math.cos(math.pi), -1)

    def testCosh(self):
        self.assertRaises(TypeError, math.cosh)
        self.ftest('cosh(0)', math.cosh(0), 1)
        self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert

    def testDegrees(self):
        self.assertRaises(TypeError, math.degrees)
        self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
        self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
        self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)

    def testExp(self):
        self.assertRaises(TypeError, math.exp)
        self.ftest('exp(-1)', math.exp(-1), 1/math.e)
        self.ftest('exp(0)', math.exp(0), 1)
        self.ftest('exp(1)', math.exp(1), math.e)

    def testFabs(self):
        self.assertRaises(TypeError, math.fabs)
        self.ftest('fabs(-1)', math.fabs(-1), 1)
        self.ftest('fabs(0)', math.fabs(0), 0)
        self.ftest('fabs(1)', math.fabs(1), 1)

    def testFloor(self):
        self.assertRaises(TypeError, math.floor)
        # These types will be int in py3k.
        self.assertEquals(float, type(math.floor(1)))
        self.assertEquals(float, type(math.floor(1L)))
        self.assertEquals(float, type(math.floor(1.0)))
        self.ftest('floor(0.5)', math.floor(0.5), 0)
        self.ftest('floor(1.0)', math.floor(1.0), 1)
        self.ftest('floor(1.5)', math.floor(1.5), 1)
        self.ftest('floor(-0.5)', math.floor(-0.5), -1)
        self.ftest('floor(-1.0)', math.floor(-1.0), -1)
        self.ftest('floor(-1.5)', math.floor(-1.5), -2)
        # pow() relies on floor() to check for integers
        # This fails on some platforms - so check it here
        self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
        self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)

        class TestFloor(object):
            def __float__(self):
                return 42.3
        class TestNoFloor(object):
            pass
        self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
        self.assertRaises(TypeError, math.floor, TestNoFloor())

        t = TestNoFloor()
        t.__floor__ = lambda *args: args
        self.assertRaises(TypeError, math.floor, t)
        self.assertRaises(TypeError, math.floor, t, 0)

    def testFmod(self):
        self.assertRaises(TypeError, math.fmod)
        self.ftest('fmod(10,1)', math.fmod(10,1), 0)
        self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
        self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
        self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
        self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
        self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)

    def testFrexp(self):
        self.assertRaises(TypeError, math.frexp)

        def testfrexp(name, (mant, exp), (emant, eexp)):
            if abs(mant-emant) > eps or exp != eexp:
                self.fail('%s returned %r, expected %r'%\
                          (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))

    def testHypot(self):
        self.assertRaises(TypeError, math.hypot)
        self.ftest('hypot(0,0)', math.hypot(0,0), 0)
        self.ftest('hypot(3,4)', math.hypot(3,4), 5)

    def testLdexp(self):
        self.assertRaises(TypeError, math.ldexp)
        self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
        self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
        self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
        self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)

    def testLog(self):
        self.assertRaises(TypeError, math.log)
        self.ftest('log(1/e)', math.log(1/math.e), -1)
        self.ftest('log(1)', math.log(1), 0)
        self.ftest('log(e)', math.log(math.e), 1)
        self.ftest('log(32,2)', math.log(32,2), 5)
        self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
        self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)

    def testLog10(self):
        self.assertRaises(TypeError, math.log10)
        self.ftest('log10(0.1)', math.log10(0.1), -1)
        self.ftest('log10(1)', math.log10(1), 0)
        self.ftest('log10(10)', math.log10(10), 1)

    def testModf(self):
        self.assertRaises(TypeError, math.modf)

        def testmodf(name, (v1, v2), (e1, e2)):
            if abs(v1-e1) > eps or abs(v2-e2):
                self.fail('%s returned %r, expected %r'%\
                          (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))

    def testPow(self):
        self.assertRaises(TypeError, math.pow)
        self.ftest('pow(0,1)', math.pow(0,1), 0)
        self.ftest('pow(1,0)', math.pow(1,0), 1)
        self.ftest('pow(2,1)', math.pow(2,1), 2)
        self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)

    def testRadians(self):
        self.assertRaises(TypeError, math.radians)
        self.ftest('radians(180)', math.radians(180), math.pi)
        self.ftest('radians(90)', math.radians(90), math.pi/2)
        self.ftest('radians(-45)', math.radians(-45), -math.pi/4)

    def testSin(self):
        self.assertRaises(TypeError, math.sin)
        self.ftest('sin(0)', math.sin(0), 0)
        self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
        self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)

    def testSinh(self):
        self.assertRaises(TypeError, math.sinh)
        self.ftest('sinh(0)', math.sinh(0), 0)
        self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
        self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)

    def testSqrt(self):
        self.assertRaises(TypeError, math.sqrt)
        self.ftest('sqrt(0)', math.sqrt(0), 0)
        self.ftest('sqrt(1)', math.sqrt(1), 1)
        self.ftest('sqrt(4)', math.sqrt(4), 2)

    def testTan(self):
        self.assertRaises(TypeError, math.tan)
        self.ftest('tan(0)', math.tan(0), 0)
        self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
        self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)

    def testTanh(self):
        self.assertRaises(TypeError, math.tanh)
        self.ftest('tanh(0)', math.tanh(0), 0)
        self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)

    def testCopysign(self):
        self.assertEqual(math.copysign(1, 42), 1.0)
        self.assertEqual(math.copysign(0., 42), 0.0)
        self.assertEqual(math.copysign(1., -42), -1.0)
        self.assertEqual(math.copysign(3, 0.), 3.0)
        self.assertEqual(math.copysign(4., -0.), -4.0)

    def testIsnan(self):
        self.assert_(math.isnan(float("nan")))
        self.assert_(math.isnan(float("inf")* 0.))
        self.failIf(math.isnan(float("inf")))
        self.failIf(math.isnan(0.))
        self.failIf(math.isnan(1.))

    def testIsinf(self):
        self.assert_(math.isinf(float("inf")))
        self.assert_(math.isinf(float("-inf")))
        self.assert_(math.isinf(1E400))
        self.assert_(math.isinf(-1E400))
        self.failIf(math.isinf(float("nan")))
        self.failIf(math.isinf(0.))
        self.failIf(math.isinf(1.))

    # 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.

    if verbose:
        def test_exceptions(self):
            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
                self.fail("underflowing exp() should not have raised "
                          "an exception")
            if x != 0:
                self.fail("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:
                self.fail("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:
                self.fail("sqrt(-1) didn't raise ValueError")


def test_main():
    run_unittest(MathTests)

if __name__ == '__main__':
    test_main()