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#ISAPPROX Check for nearly equal values.
# ISAPPROX(x::T1, y::T2) checks if x and y are nearly equal. The default tolerance is
# determined by the types. If tol = max(eps(T1), eps(T2)), then the values need to be
# within sqrt(tol)+tol^(1/3)*max(abs(x), abs(y)).
# ISAPPROX(x, y, rtol, atol) provides specific values in place of tol^(1/3) and sqrt(tol),
# respectively.
# ISAPPROX(x::T1, y::T2) where T1<:Integer and T2<:Integer is the same as ISEQUAL.
function isapprox(x, y, rtol, atol)
if isinf(x) || isinf(y)
return x == y
abs(x-y) <= atol+rtol.*max(abs(x), abs(y))
#ISAPPROXN Check for nearly equal values, treating NaNs as mutually equal.
# ISAPPROXN(x, y, ...) checks if x and y are nearly equal in the same way as ISAPPROX, but
# allowing NaNs to evaluate as equal. This is useful if two methods of computing the same
# values are being verified against one another, and that computation can produce NaNs.
# ISAPPROXN(x, y, ...) gives the same results as ISAPPROX(x, y, ...) if neither x nor
# y contain NaN values.
isapproxn(x, y, rtol, atol) = isapprox(x, y, rtol, atol) || (isnan(x) && isnan(y))
for fun in (:isapprox, :isapproxn)
@eval begin
function ($fun){T1<:Float, T2<:Float}(x::T1, y::T2)
tol = max(eps(T1), eps(T2))
($fun)(x, y, tol^(1/3), sqrt(tol))
($fun){T1<:Integer, T2<:Float}(x::T1, y::T2) = ($fun)(float(x), y)
($fun){T1<:Float, T2<:Integer}(x::T1, y::T2) = ($fun)(x, float(y))
($fun)(X::AbstractArray, y::Number) = map(x -> ($fun)(x, y), X)
($fun)(x::Number, Y::AbstractArray) = map(y -> ($fun)(y, x), Y)
function ($fun)(X::AbstractArray, Y::AbstractArray)
if size(X) != size(Y)
error("Arrays must have the same sizes (first is $(size(X)), second is $(size(Y))).")
Z = similar(X, Bool)
for i in 1:numel(X)
Z[i] = ($fun)(X[i], Y[i])
# For integers, isapprox() is just isequal() unless you specify nondefault tolerances.
isapprox{T1<:Integer, T2<:Integer}(x::T1, y::T2) = isequal(x, y)
#isapproxn() doesn't apply to two Integer types, since typeof(NaN)<:Float
#ISEQUALN Check for equality, treating NaNs as mutually equal.
# ISEQUALN(x, y) gives the same results as ISEQUAL(x, y), unless both x and y are NaN
# values. In this case, ISEQUALN(x, y) returns true instead of false.
isequaln(x, y) = isequal(x, y) || (isnan(x) && isnan(y))
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