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##
# Math Test
MATH_TOLERANCE = 1E-12
def check(a,b)
a = a.to_f
b = b.to_f
if a.finite? and b.finite?
(a-b).abs < MATH_TOLERANCE
else
true
end
end
assert('Math.sin 0') do
check(Math.sin(0), 0)
end
assert('Math.sin PI/2') do
check(Math.sin(Math::PI / 2), 1)
end
assert('Fundamental trig identities') do
result = true
N = 15
N.times do |i|
a = Math::PI / N * i
s = Math.sin(a)
c = Math.cos(a)
t = Math.tan(a)
result &= check(s, Math.cos(Math::PI / 2 - a))
result &= check(t, 1 / Math.tan(Math::PI / 2 - a))
result &= check(s ** 2 + c ** 2, 1)
result &= check(t ** 2 + 1, (1/c) ** 2)
result &= check((1/t) ** 2 + 1, (1/s) ** 2)
end
result
end
assert('Math.erf 0') do
check(Math.erf(0), 0)
end
assert('Math.exp 0') do
check(Math.exp(0), 1.0)
end
assert('Math.exp 1') do
check(Math.exp(1), 2.718281828459045)
end
assert('Math.exp 1.5') do
check(Math.exp(1.5), 4.4816890703380645)
end
assert('Math.log 1') do
check(Math.log(1), 0)
end
assert('Math.log E') do
check(Math.log(Math::E), 1.0)
end
assert('Math.log E**3') do
check(Math.log(Math::E**3), 3.0)
end
assert('Math.log2 1') do
check(Math.log2(1), 0.0)
end
assert('Math.log2 2') do
check(Math.log2(2), 1.0)
end
assert('Math.log10 1') do
check(Math.log10(1), 0.0)
end
assert('Math.log10 10') do
check(Math.log10(10), 1.0)
end
assert('Math.log10 10**100') do
check(Math.log10(10**100), 100.0)
end
assert('Math.cbrt') do
num = [-2.0, -1.0, 0.0, 1.0, 2.0]
cub = [-8, -1, 0, 1, 8]
result = true
cub.each_with_index do |v,i|
result &= check(Math.cbrt(v), num[i])
end
result
end
assert('Math.hypot') do
check(Math.hypot(3, 4), 5.0)
end
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