bacovia/t/trigonometry.sf

#!/usr/bin/ruby

include('../lib/bacovia.sf')

var x = Symbol('x', +43)
var y = Symbol('y', -43)
var z = Symbol('z', 1.5)
var k = Symbol('k', -0.5)

assert_eq(asin(sin(+z)) -> numeric.round(-20), +1.5)
assert_eq(asin(sin(-z)) -> numeric.round(-20), -1.5)

assert_eq(acos(cos(+z)) -> numeric.round(-20), +1.5)
assert_eq(acos(cos(-z)) -> numeric.round(-20), +1.5)

assert_eq(atanh(tanh(+x)) -> numeric.round(-20), +43)
assert_eq(atanh(tanh(-x)) -> numeric.round(-20), -43)
assert_eq(atanh(tanh(+y)) -> numeric.round(-20), -43)

assert_eq(acosh(cosh(+x)) -> numeric, +43)
assert_eq(acosh(cosh(-x)) -> numeric, +43)
assert_eq(acosh(cosh(+y)) -> numeric, +43)

assert_eq(asinh(sinh(+x)) -> numeric, +43)
assert_eq(asinh(sinh(-x)) -> numeric.round(-20), -43)
assert_eq(asinh(sinh(+y)) -> numeric.round(-20), -43)

assert_eq(asinh(sinh(k)) -> numeric.round(-20), -0.5)
assert_eq(atanh(tanh(k)) -> numeric.round(-20), -0.5)
assert_eq(acsch(csch(k)) -> numeric.round(-20), -0.5)
assert_eq(acoth(coth(k)) -> numeric.round(-20), -0.5)
assert_eq(acosh(cosh(k)) -> numeric.round(-20), 0.5)
assert_eq(asech(sech(k)) -> numeric.round(-20), 0.5)

var n = Symbol('n', 42)

assert_eq(cos(Log(n)) -> simple.pretty, '((n^-i + n^i)/2)')
assert_eq(sin(Log(n)) -> simple.pretty, '((n^i - n^-i)/(2i))')

assert_eq(cosh(Log(n)) -> simple.pretty, '((1 + n^2)/(2 * n))')
assert_eq(sinh(Log(n)) -> simple.pretty, '((n^2 - 1)/(2 * n))')

assert_eq(asinh(sinh(n)) -> numeric, 42)
assert_eq(acosh(cosh(n)) -> numeric, 42)

#
## asinh(x)
#
do {
    var z = (x**2 - 1)/(2*x)
    assert_eq(Exp(asinh(z)) -> numeric.round(-50), +43)
}

#
## acosh(x)
#
do {
    var z = (x**2 + 1)/(2*x)
    assert_eq(Exp(acosh(z)) -> numeric.round(-50), +43)
}

do {
    var z = (y**2 + 1)/(2*y)
    assert_eq(Exp(acosh(z)) -> numeric, exp(acosh(((-43)**2 + 1)/(2*-43))))
}

#
## atanh(x)
#
do {
    var z = (x**2 - 1)/(x**2 + 1)
    assert_eq(Exp(atanh(z)) -> numeric.round(-50), +43)
}

do {
    var z = (y**2 - 1)/(y**2 + 1)
    assert_eq(Exp(atanh(z)) -> numeric.round(-50), 43)
}

say "** Test passed!"