require 'test/unit'
class TestMath < Test::Unit::TestCase
def assert_infinity(a, *rest)
rest = ["not infinity: #{a.inspect}"] if rest.empty?
assert(!a.finite?, *rest)
end
def assert_nan(a, *rest)
rest = ["not nan: #{a.inspect}"] if rest.empty?
assert(a.nan?, *rest)
end
def check(a, b)
err = [Float::EPSILON * 4, [a.abs, b.abs].max * Float::EPSILON * 256].max
assert_in_delta(a, b, err)
end
def test_atan2
check(+0.0, Math.atan2(+0.0, +0.0))
check(-0.0, Math.atan2(-0.0, +0.0))
check(+Math::PI, Math.atan2(+0.0, -0.0))
check(-Math::PI, Math.atan2(-0.0, -0.0))
assert_raise(Math::DomainError) { Math.atan2(Float::INFINITY, Float::INFINITY) }
assert_raise(Math::DomainError) { Math.atan2(Float::INFINITY, -Float::INFINITY) }
assert_raise(Math::DomainError) { Math.atan2(-Float::INFINITY, Float::INFINITY) }
assert_raise(Math::DomainError) { Math.atan2(-Float::INFINITY, -Float::INFINITY) }
check(0, Math.atan2(0, 1))
check(Math::PI / 4, Math.atan2(1, 1))
check(Math::PI / 2, Math.atan2(1, 0))
end
def test_cos
check(1.0, Math.cos(0 * Math::PI / 4))
check(1.0 / Math.sqrt(2), Math.cos(1 * Math::PI / 4))
check(0.0, Math.cos(2 * Math::PI / 4))
check(-1.0, Math.cos(4 * Math::PI / 4))
check(0.0, Math.cos(6 * Math::PI / 4))
end
def test_sin
check(0.0, Math.sin(0 * Math::PI / 4))
check(1.0 / Math.sqrt(2), Math.sin(1 * Math::PI / 4))
check(1.0, Math.sin(2 * Math::PI / 4))
check(0.0, Math.sin(4 * Math::PI / 4))
check(-1.0, Math.sin(6 * Math::PI / 4))
end
def test_tan
check(0.0, Math.tan(0 * Math::PI / 4))
check(1.0, Math.tan(1 * Math::PI / 4))
assert(Math.tan(2 * Math::PI / 4).abs > 1024)
check(0.0, Math.tan(4 * Math::PI / 4))
assert(Math.tan(6 * Math::PI / 4).abs > 1024)
end
def test_acos
check(0 * Math::PI / 4, Math.acos( 1.0))
check(1 * Math::PI / 4, Math.acos( 1.0 / Math.sqrt(2)))
check(2 * Math::PI / 4, Math.acos( 0.0))
check(4 * Math::PI / 4, Math.acos(-1.0))
assert_raise(Math::DomainError) { Math.acos(+1.0 + Float::EPSILON) }
assert_raise(Math::DomainError) { Math.acos(-1.0 - Float::EPSILON) }
assert_raise(Math::DomainError) { Math.acos(2.0) }
end
def test_asin
check( 0 * Math::PI / 4, Math.asin( 0.0))
check( 1 * Math::PI / 4, Math.asin( 1.0 / Math.sqrt(2)))
check( 2 * Math::PI / 4, Math.asin( 1.0))
check(-2 * Math::PI / 4, Math.asin(-1.0))
assert_raise(Math::DomainError) { Math.asin(+1.0 + Float::EPSILON) }
assert_raise(Math::DomainError) { Math.asin(-1.0 - Float::EPSILON) }
assert_raise(Math::DomainError) { Math.asin(2.0) }
end
def test_atan
check( 0 * Math::PI / 4, Math.atan( 0.0))
check( 1 * Math::PI / 4, Math.atan( 1.0))
check( 2 * Math::PI / 4, Math.atan(1.0 / 0.0))
check(-1 * Math::PI / 4, Math.atan(-1.0))
end
def test_cosh
check(1, Math.cosh(0))
check((Math::E ** 1 + Math::E ** -1) / 2, Math.cosh(1))
check((Math::E ** 2 + Math::E ** -2) / 2, Math.cosh(2))
end
def test_sinh
check(0, Math.sinh(0))
check((Math::E ** 1 - Math::E ** -1) / 2, Math.sinh(1))
check((Math::E ** 2 - Math::E ** -2) / 2, Math.sinh(2))
end
def test_tanh
check(Math.sinh(0) / Math.cosh(0), Math.tanh(0))
check(Math.sinh(1) / Math.cosh(1), Math.tanh(1))
check(Math.sinh(2) / Math.cosh(2), Math.tanh(2))
end
def test_acosh
check(0, Math.acosh(1))
check(1, Math.acosh((Math::E ** 1 + Math::E ** -1) / 2))
check(2, Math.acosh((Math::E ** 2 + Math::E ** -2) / 2))
assert_raise(Math::DomainError) { Math.acosh(1.0 - Float::EPSILON) }
assert_raise(Math::DomainError) { Math.acosh(0) }
end
def test_asinh
check(0, Math.asinh(0))
check(1, Math.asinh((Math::E ** 1 - Math::E ** -1) / 2))
check(2, Math.asinh((Math::E ** 2 - Math::E ** -2) / 2))
end
def test_atanh
check(0, Math.atanh(Math.sinh(0) / Math.cosh(0)))
check(1, Math.atanh(Math.sinh(1) / Math.cosh(1)))
check(2, Math.atanh(Math.sinh(2) / Math.cosh(2)))
assert_nothing_raised { assert_infinity(Math.atanh(1)) }
assert_nothing_raised { assert_infinity(-Math.atanh(-1)) }
assert_raise(Math::DomainError) { Math.atanh(+1.0 + Float::EPSILON) }
assert_raise(Math::DomainError) { Math.atanh(-1.0 - Float::EPSILON) }
end
def test_exp
check(1, Math.exp(0))
check(Math.sqrt(Math::E), Math.exp(0.5))
check(Math::E, Math.exp(1))
check(Math::E ** 2, Math.exp(2))
end
def test_log
check(0, Math.log(1))
check(1, Math.log(Math::E))
check(0, Math.log(1, 10))
check(1, Math.log(10, 10))
check(2, Math.log(100, 10))
assert_equal(1.0/0, Math.log(1.0/0))
assert_nothing_raised { assert_infinity(-Math.log(+0.0)) }
assert_nothing_raised { assert_infinity(-Math.log(-0.0)) }
assert_raise(Math::DomainError) { Math.log(-1.0) }
assert_raise(TypeError) { Math.log(1,nil) }
end
def test_log2
check(0, Math.log2(1))
check(1, Math.log2(2))
check(2, Math.log2(4))
assert_equal(1.0/0, Math.log2(1.0/0))
assert_nothing_raised { assert_infinity(-Math.log2(+0.0)) }
assert_nothing_raised { assert_infinity(-Math.log2(-0.0)) }
assert_raise(Math::DomainError) { Math.log2(-1.0) }
end
def test_log10
check(0, Math.log10(1))
check(1, Math.log10(10))
check(2, Math.log10(100))
assert_equal(1.0/0, Math.log10(1.0/0))
assert_nothing_raised { assert_infinity(-Math.log10(+0.0)) }
assert_nothing_raised { assert_infinity(-Math.log10(-0.0)) }
assert_raise(Math::DomainError) { Math.log10(-1.0) }
end
def test_sqrt
check(0, Math.sqrt(0))
check(1, Math.sqrt(1))
check(2, Math.sqrt(4))
assert_equal(1.0/0, Math.sqrt(1.0/0))
assert_equal("0.0", Math.sqrt(-0.0).to_s) assert_raise(Math::DomainError) { Math.sqrt(-1.0) }
end
def test_frexp
check(0.0, Math.frexp(0.0).first)
assert_equal(0, Math.frexp(0).last)
check(0.5, Math.frexp(0.5).first)
assert_equal(0, Math.frexp(0.5).last)
check(0.5, Math.frexp(1.0).first)
assert_equal(1, Math.frexp(1.0).last)
check(0.5, Math.frexp(2.0).first)
assert_equal(2, Math.frexp(2.0).last)
check(0.75, Math.frexp(3.0).first)
assert_equal(2, Math.frexp(3.0).last)
end
def test_ldexp
check(0.0, Math.ldexp(0.0, 0.0))
check(0.5, Math.ldexp(0.5, 0.0))
check(1.0, Math.ldexp(0.5, 1.0))
check(2.0, Math.ldexp(0.5, 2.0))
check(3.0, Math.ldexp(0.75, 2.0))
end
def test_hypot
check(5, Math.hypot(3, 4))
end
def test_erf
check(0, Math.erf(0))
check(1, Math.erf(1.0 / 0.0))
end
def test_erfc
check(1, Math.erfc(0))
check(0, Math.erfc(1.0 / 0.0))
end
def test_gamma
sqrt_pi = Math.sqrt(Math::PI)
check(4 * sqrt_pi / 3, Math.gamma(-1.5))
check(-2 * sqrt_pi, Math.gamma(-0.5))
check(sqrt_pi, Math.gamma(0.5))
check(1, Math.gamma(1))
check(sqrt_pi / 2, Math.gamma(1.5))
check(1, Math.gamma(2))
check(3 * sqrt_pi / 4, Math.gamma(2.5))
check(2, Math.gamma(3))
check(15 * sqrt_pi / 8, Math.gamma(3.5))
check(6, Math.gamma(4))
31.upto(65) do |i|
i = 1 << i
assert_infinity(Math.gamma(i), "Math.gamma(#{i}) should be INF")
assert_infinity(Math.gamma(i-1), "Math.gamma(#{i-1}) should be INF")
end
assert_raise(Math::DomainError) { Math.gamma(-Float::INFINITY) }
end
def test_lgamma
sqrt_pi = Math.sqrt(Math::PI)
g, s = Math.lgamma(-1.5)
check(Math.log(4 * sqrt_pi / 3), g)
assert_equal(s, 1)
g, s = Math.lgamma(-0.5)
check(Math.log(2 * sqrt_pi), g)
assert_equal(s, -1)
g, s = Math.lgamma(0.5)
check(Math.log(sqrt_pi), g)
assert_equal(s, 1)
assert_equal([0, 1], Math.lgamma(1))
g, s = Math.lgamma(1.5)
check(Math.log(sqrt_pi / 2), g)
assert_equal(s, 1)
assert_equal([0, 1], Math.lgamma(2))
g, s = Math.lgamma(2.5)
check(Math.log(3 * sqrt_pi / 4), g)
assert_equal(s, 1)
g, s = Math.lgamma(3)
check(Math.log(2), g)
assert_equal(s, 1)
g, s = Math.lgamma(3.5)
check(Math.log(15 * sqrt_pi / 8), g)
assert_equal(s, 1)
g, s = Math.lgamma(4)
check(Math.log(6), g)
assert_equal(s, 1)
assert_raise(Math::DomainError) { Math.lgamma(-Float::INFINITY) }
end
def test_cbrt
check(1, Math.cbrt(1))
check(-2, Math.cbrt(-8))
check(3, Math.cbrt(27))
check(-0.1, Math.cbrt(-0.001))
end
end