364 lines
13 KiB
Ruby
364 lines
13 KiB
Ruby
# frozen_string_literal: false
|
|
require 'test/unit'
|
|
|
|
class TestMath < Test::Unit::TestCase
|
|
def assert_infinity(a, *rest)
|
|
rest = ["not infinity: #{a.inspect}"] if rest.empty?
|
|
assert_predicate(a, :infinite?, *rest)
|
|
end
|
|
|
|
def assert_nan(a, *rest)
|
|
rest = ["not nan: #{a.inspect}"] if rest.empty?
|
|
assert_predicate(a, :nan?, *rest)
|
|
end
|
|
|
|
def assert_float(a, b)
|
|
err = [Float::EPSILON * 4, [a.abs, b.abs].max * Float::EPSILON * 256].max
|
|
assert_in_delta(a, b, err)
|
|
end
|
|
alias check assert_float
|
|
|
|
def assert_float_and_int(exp_ary, act_ary)
|
|
flo_exp, int_exp, flo_act, int_act = *exp_ary, *act_ary
|
|
assert_float(flo_exp, flo_act)
|
|
assert_equal(int_exp, int_act)
|
|
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))
|
|
|
|
inf = Float::INFINITY
|
|
expected = 3.0 * Math::PI / 4.0
|
|
assert_nothing_raised { check(+expected, Math.atan2(+inf, -inf)) }
|
|
assert_nothing_raised { check(-expected, Math.atan2(-inf, -inf)) }
|
|
expected = Math::PI / 4.0
|
|
assert_nothing_raised { check(+expected, Math.atan2(+inf, +inf)) }
|
|
assert_nothing_raised { check(-expected, Math.atan2(-inf, +inf)) }
|
|
|
|
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))
|
|
check(0.5403023058681398, Math.cos(1))
|
|
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_operator(Math.tan(2 * Math::PI / 4).abs, :>, 1024)
|
|
check(0.0, Math.tan(4 * Math::PI / 4))
|
|
assert_operator(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_with_message(Math::DomainError, /\bacos\b/) { Math.acos(+1.0 + Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\bacos\b/) { Math.acos(-1.0 - Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\bacos\b/) { 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_with_message(Math::DomainError, /\basin\b/) { Math.asin(+1.0 + Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\basin\b/) { Math.asin(-1.0 - Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\basin\b/) { 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))
|
|
check(+1.0, Math.tanh(+1000.0))
|
|
check(-1.0, Math.tanh(-1000.0))
|
|
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_with_message(Math::DomainError, /\bacosh\b/) { Math.acosh(1.0 - Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\bacosh\b/) { 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_with_message(Math::DomainError, /\batanh\b/) { Math.atanh(+1.0 + Float::EPSILON) }
|
|
assert_raise_with_message(Math::DomainError, /\batanh\b/) { 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))
|
|
check(Math.log(2.0 ** 64), Math.log(1 << 64))
|
|
check(Math.log(2) * 1024.0, Math.log(2 ** 1024))
|
|
assert_nothing_raised { assert_infinity(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_with_message(Math::DomainError, /\blog\b/) { Math.log(-1.0) }
|
|
assert_raise_with_message(Math::DomainError, /\blog\b/) { Math.log(-Float::EPSILON) }
|
|
assert_raise(TypeError) { Math.log(1,nil) }
|
|
assert_raise_with_message(Math::DomainError, /\blog\b/, '[ruby-core:62309] [ruby-Bug #9797]') { Math.log(1.0, -1.0) }
|
|
assert_raise_with_message(Math::DomainError, /\blog\b/) { Math.log(1.0, -Float::EPSILON) }
|
|
assert_nothing_raised { assert_nan(Math.log(0.0, 0.0)) }
|
|
assert_nothing_raised { assert_nan(Math.log(Float::NAN)) }
|
|
assert_nothing_raised { assert_nan(Math.log(1.0, Float::NAN)) }
|
|
end
|
|
|
|
def test_log2
|
|
check(0, Math.log2(1))
|
|
check(1, Math.log2(2))
|
|
check(2, Math.log2(4))
|
|
check(Math.log2(2.0 ** 64), Math.log2(1 << 64))
|
|
check(1024.0, Math.log2(2 ** 1024))
|
|
assert_nothing_raised { assert_infinity(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_with_message(Math::DomainError, /\blog2\b/) { Math.log2(-1.0) }
|
|
assert_raise_with_message(Math::DomainError, /\blog2\b/) { Math.log2(-Float::EPSILON) }
|
|
assert_nothing_raised { assert_nan(Math.log2(Float::NAN)) }
|
|
end
|
|
|
|
def test_log10
|
|
check(0, Math.log10(1))
|
|
check(1, Math.log10(10))
|
|
check(2, Math.log10(100))
|
|
check(Math.log10(2.0 ** 64), Math.log10(1 << 64))
|
|
check(Math.log10(2) * 1024, Math.log10(2 ** 1024))
|
|
assert_nothing_raised { assert_infinity(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_with_message(Math::DomainError, /\blog10\b/) { Math.log10(-1.0) }
|
|
assert_raise_with_message(Math::DomainError, /\blog10\b/) { Math.log10(-Float::EPSILON) }
|
|
assert_nothing_raised { assert_nan(Math.log10(Float::NAN)) }
|
|
end
|
|
|
|
def test_sqrt
|
|
check(0, Math.sqrt(0))
|
|
check(1, Math.sqrt(1))
|
|
check(2, Math.sqrt(4))
|
|
assert_nothing_raised { assert_infinity(Math.sqrt(1.0/0)) }
|
|
assert_equal("0.0", Math.sqrt(-0.0).to_s) # insure it is +0.0, not -0.0
|
|
assert_raise_with_message(Math::DomainError, /\bsqrt\b/) { Math.sqrt(-1.0) }
|
|
assert_raise_with_message(Math::DomainError, /\bsqrt\b/) { Math.sqrt(-Float::EPSILON) }
|
|
assert_nothing_raised { assert_nan(Math.sqrt(Float::NAN)) }
|
|
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))
|
|
check(0.0, Math.cbrt(0.0))
|
|
assert_nothing_raised { assert_infinity(Math.cbrt(1.0/0)) }
|
|
assert_operator(Math.cbrt(1.0 - Float::EPSILON), :<=, 1.0)
|
|
assert_nothing_raised { assert_nan(Math.sqrt(Float::NAN)) }
|
|
assert_nothing_raised { assert_nan(Math.cbrt(Float::NAN)) }
|
|
end
|
|
|
|
def test_frexp
|
|
assert_float_and_int([0.0, 0], Math.frexp(0.0))
|
|
assert_float_and_int([0.5, 0], Math.frexp(0.5))
|
|
assert_float_and_int([0.5, 1], Math.frexp(1.0))
|
|
assert_float_and_int([0.5, 2], Math.frexp(2.0))
|
|
assert_float_and_int([0.75, 2], Math.frexp(3.0))
|
|
assert_nan(Math.frexp(Float::NAN)[0])
|
|
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))
|
|
assert_nan(Math.erf(Float::NAN))
|
|
end
|
|
|
|
def test_erfc
|
|
check(1, Math.erfc(0))
|
|
check(0, Math.erfc(1.0 / 0.0))
|
|
assert_nan(Math.erfc(Float::NAN))
|
|
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))
|
|
check(1.1240007277776077e+21, Math.gamma(23))
|
|
check(2.5852016738885062e+22, Math.gamma(24))
|
|
|
|
# no SEGV [ruby-core:25257]
|
|
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_with_message(Math::DomainError, /\bgamma\b/) { Math.gamma(-Float::INFINITY) }
|
|
assert_raise_with_message(Math::DomainError, /\bgamma\b/) { Math.gamma(-1.0) }
|
|
x = Math.gamma(-0.0)
|
|
mesg = "Math.gamma(-0.0) should be -INF"
|
|
assert_infinity(x, mesg)
|
|
assert_predicate(x, :negative?, mesg)
|
|
assert_nan(Math.gamma(Float::NAN))
|
|
end
|
|
|
|
def test_lgamma
|
|
sqrt_pi = Math.sqrt(Math::PI)
|
|
assert_float_and_int([Math.log(4 * sqrt_pi / 3), 1], Math.lgamma(-1.5))
|
|
assert_float_and_int([Math.log(2 * sqrt_pi), -1], Math.lgamma(-0.5))
|
|
assert_float_and_int([Math.log(sqrt_pi), 1], Math.lgamma(0.5))
|
|
assert_float_and_int([0, 1], Math.lgamma(1))
|
|
assert_float_and_int([Math.log(sqrt_pi / 2), 1], Math.lgamma(1.5))
|
|
assert_float_and_int([0, 1], Math.lgamma(2))
|
|
assert_float_and_int([Math.log(3 * sqrt_pi / 4), 1], Math.lgamma(2.5))
|
|
assert_float_and_int([Math.log(2), 1], Math.lgamma(3))
|
|
assert_float_and_int([Math.log(15 * sqrt_pi / 8), 1], Math.lgamma(3.5))
|
|
assert_float_and_int([Math.log(6), 1], Math.lgamma(4))
|
|
|
|
assert_raise_with_message(Math::DomainError, /\blgamma\b/) { Math.lgamma(-Float::INFINITY) }
|
|
x, sign = Math.lgamma(-0.0)
|
|
mesg = "Math.lgamma(-0.0) should be [INF, -1]"
|
|
assert_infinity(x, mesg)
|
|
assert_predicate(x, :positive?, mesg)
|
|
assert_equal(-1, sign, mesg)
|
|
x, sign = Math.lgamma(Float::NAN)
|
|
assert_nan(x)
|
|
end
|
|
|
|
def test_fixnum_to_f
|
|
check(12.0, Math.sqrt(144))
|
|
end
|
|
|
|
def test_override_integer_to_f
|
|
Integer.class_eval do
|
|
alias _to_f to_f
|
|
def to_f
|
|
(self + 1)._to_f
|
|
end
|
|
end
|
|
|
|
check(Math.cos((0 + 1)._to_f), Math.cos(0))
|
|
check(Math.exp((0 + 1)._to_f), Math.exp(0))
|
|
check(Math.log((0 + 1)._to_f), Math.log(0))
|
|
ensure
|
|
Integer.class_eval { undef to_f; alias to_f _to_f; undef _to_f }
|
|
end
|
|
|
|
def test_bignum_to_f
|
|
check((1 << 65).to_f, Math.sqrt(1 << 130))
|
|
end
|
|
|
|
def test_override_bignum_to_f
|
|
Integer.class_eval do
|
|
alias _to_f to_f
|
|
def to_f
|
|
(self << 1)._to_f
|
|
end
|
|
end
|
|
|
|
check(Math.cos((1 << 64 << 1)._to_f), Math.cos(1 << 64))
|
|
check(Math.log((1 << 64 << 1)._to_f), Math.log(1 << 64))
|
|
ensure
|
|
Integer.class_eval { undef to_f; alias to_f _to_f; undef _to_f }
|
|
end
|
|
|
|
def test_rational_to_f
|
|
check((2 ** 31).fdiv(3 ** 20), Math.sqrt((2 ** 62)/(3 ** 40).to_r))
|
|
end
|
|
|
|
def test_override_rational_to_f
|
|
Rational.class_eval do
|
|
alias _to_f to_f
|
|
def to_f
|
|
(self + 1)._to_f
|
|
end
|
|
end
|
|
|
|
check(Math.cos((0r + 1)._to_f), Math.cos(0r))
|
|
check(Math.exp((0r + 1)._to_f), Math.exp(0r))
|
|
check(Math.log((0r + 1)._to_f), Math.log(0r))
|
|
ensure
|
|
Rational.class_eval { undef to_f; alias to_f _to_f; undef _to_f }
|
|
end
|
|
end
|