tests: use ≈ and ≉ instead of isapprox, !isapprox

test/error.jl

@@ -4,8 +4,7 @@
 @test collect(ExponentialBackOff(n=10, first_delay=0.01))[1] == 0.01
 @test maximum(ExponentialBackOff(n=10, max_delay=0.06)) == 0.06
 ratio(x) = x[2:end]./x[1:end-1]
-@test all(x->isapprox(x,10.0), ratio(collect(
- ExponentialBackOff(n=10, max_delay=Inf, factor=10, jitter=0.0))))
+@test all(x->x ≈ 10.0, ratio(collect(ExponentialBackOff(n=10, max_delay=Inf, factor=10, jitter=0.0))))
 srand(12345)
 @test (mean(ratio(collect(ExponentialBackOff(n=100, max_delay=Inf, factor=1, jitter=0.1)))) - 1.0) < 1e-4
 

test/fastmath.jl

@@ -39,12 +39,10 @@ fm_fast_64_upd(x) = @fastmath (r=x; r+=eps64_2; r+=eps64_2)
  fm_fast_64_upd(one64) == one64 + eps64 > one64)
 
 let epsf = 1.0f0/2^15, one_epsf = 1+epsf
- @test isapprox((@fastmath one_epsf * one_epsf - 1),
- Float32(65537/1073741824))
+ @test @fastmath(one_epsf * one_epsf - 1) ≈ Float32(65537/1073741824)
 end
 let eps = 1.0/2^30, one_eps = 1+eps
- @test isapprox((@fastmath one_eps * one_eps - 1),
- 2147483649/1152921504606846976)
+ @test @fastmath(one_eps * one_eps - 1) ≈ 2147483649/1152921504606846976
 end
 
 for T in (Float32, Float64, BigFloat)
@@ -53,52 +51,52 @@ for T in (Float32, Float64, BigFloat)
  two = convert(T, 2) + 1//10
  three = convert(T, 3) + 1//100
 
- @test isapprox((@fastmath +two), +two)
- @test isapprox((@fastmath -two), -two)
- @test isapprox((@fastmath zero+one+two), zero+one+two)
- @test isapprox((@fastmath zero-one-two), zero-one-two)
- @test isapprox((@fastmath one*two*three), one*two*three)
- @test isapprox((@fastmath one/two/three), one/two/three)
- @test isapprox((@fastmath rem(two, three)), rem(two, three))
- @test isapprox((@fastmath mod(two, three)), mod(two, three))
- @test (@fastmath cmp(two, two)) == cmp(two, two)
- @test (@fastmath cmp(two, three)) == cmp(two, three)
- @test (@fastmath cmp(three, two)) == cmp(three, two)
- @test (@fastmath one/zero) == convert(T, Inf)
- @test (@fastmath -one/zero) == -convert(T, Inf)
- @test isnan(@fastmath zero/zero) # must not throw
+ @test @fastmath(+two) ≈ +two
+ @test @fastmath(-two) ≈ -two
+ @test @fastmath(zero+one+two) ≈ zero+one+two
+ @test @fastmath(zero-one-two) ≈ zero-one-two
+ @test @fastmath(one*two*three) ≈ one*two*three
+ @test @fastmath(one/two/three) ≈ one/two/three
+ @test @fastmath(rem(two,three)) ≈ rem(two,three)
+ @test @fastmath(mod(two,three)) ≈ mod(two,three)
+ @test @fastmath(cmp(two,two)) == cmp(two,two)
+ @test @fastmath(cmp(two,three)) == cmp(two,three)
+ @test @fastmath(cmp(three,two)) == cmp(three,two)
+ @test @fastmath(one/zero) == convert(T,Inf)
+ @test @fastmath(-one/zero) == -convert(T,Inf)
+ @test isnan(@fastmath(zero/zero)) # must not throw
 
  for x in (zero, two, convert(T, Inf), convert(T, NaN))
- @test (@fastmath isfinite(x))
- @test !(@fastmath isinf(x))
- @test !(@fastmath isnan(x))
- @test !(@fastmath issubnormal(x))
+ @test @fastmath(isfinite(x))
+ @test !@fastmath(isinf(x))
+ @test !@fastmath(isnan(x))
+ @test !@fastmath(issubnormal(x))
  end
 end
 
 for T in (Complex64, Complex128, Complex{BigFloat})
- zero = convert(T, 0)
- one = convert(T, 1) + im*eps(real(convert(T,1)))
- two = convert(T, 2) + im//10
- three = convert(T, 3) + im//100
-
- @test isapprox((@fastmath +two), +two)
- @test isapprox((@fastmath -two), -two)
- @test isapprox((@fastmath zero+one+two), zero+one+two)
- @test isapprox((@fastmath zero-one-two), zero-one-two)
- @test isapprox((@fastmath one*two*three), one*two*three)
- @test isapprox((@fastmath one/two/three), one/two/three)
- @test (@fastmath three == two) == (three == two)
- @test (@fastmath three != two) == (three != two)
- @test isnan(@fastmath one/zero) # must not throw
- @test isnan(@fastmath -one/zero) # must not throw
- @test isnan(@fastmath zero/zero) # must not throw
+ zero = convert(T,0)
+ one = convert(T,1) + im*eps(real(convert(T,1)))
+ two = convert(T,2) + im//10
+ three = convert(T,3) + im//100
+
+ @test @fastmath(+two) ≈ +two
+ @test @fastmath(-two) ≈ -two
+ @test @fastmath(zero+one+two) ≈ zero+one+two
+ @test @fastmath(zero-one-two) ≈ zero-one-two
+ @test @fastmath(one*two*three) ≈ one*two*three
+ @test @fastmath(one/two/three) ≈ one/two/three
+ @test @fastmath(three == two) == (three == two)
+ @test @fastmath(three != two) == (three != two)
+ @test isnan(@fastmath(one/zero)) # must not throw
+ @test isnan(@fastmath(-one/zero)) # must not throw
+ @test isnan(@fastmath(zero/zero)) # must not throw
 
  for x in (zero, two, convert(T, Inf), convert(T, NaN))
- @test (@fastmath isfinite(x))
- @test !(@fastmath isinf(x))
- @test !(@fastmath isnan(x))
- @test !(@fastmath issubnormal(x))
+ @test @fastmath(isfinite(x))
+ @test !@fastmath(isinf(x))
+ @test !@fastmath(isnan(x))
+ @test !@fastmath(issubnormal(x))
  end
 end
 
@@ -107,36 +105,38 @@ end
 
 # real arithmetic
 for T in (Float32, Float64, BigFloat)
- half = 1/convert(T, 2)
- third = 1/convert(T, 3)
+ half = 1/convert(T,2)
+ third = 1/convert(T,3)
 
  for f in (:+, :-, :abs, :abs2, :conj, :inv, :sign,
  :acos, :asin, :asinh, :atan, :atanh, :cbrt, :cos, :cosh,
  :exp10, :exp2, :exp, :expm1, :lgamma, :log10, :log1p,
  :log2, :log, :sin, :sinh, :sqrt, :tan, :tanh)
- @test isapprox((@eval @fastmath $f($half)), (@eval $f($half)))
- @test isapprox((@eval @fastmath $f($third)), (@eval $f($third)))
+ @eval begin
+ @test @fastmath($f($half)) ≈ $f($half)
+ @test @fastmath($f($third)) ≈ $f($third)
+ end
  end
  for f in (:acosh,)
- @test isapprox((@eval @fastmath $f(1+$half)), (@eval $f(1+$half)))
- @test isapprox((@eval @fastmath $f(1+$third)), (@eval $f(1+$third)))
+ @eval begin
+ @test @fastmath($f(1+$half)) ≈ $f(1+$half)
+ @test @fastmath($f(1+$third)) ≈ $f(1+$third)
+ end
  end
  for f in (:+, :-, :*, :/, :%, :(==), :!=, :<, :<=, :>, :>=, :^,
  :atan2, :hypot, :max, :min)
- @test isapprox((@eval @fastmath $f($half, $third)),
-  (@eval $f($half, $third)))
- @test isapprox((@eval @fastmath $f($third, $half)),
-  (@eval $f($third, $half)))
+ @eval begin
+ @test @fastmath($f($half, $third)) ≈ $f($half, $third)
+  @test @fastmath($f($third, $half)) ≈ $f($third, $half)
+ end
  end
  for f in (:minmax,)
- @test isapprox((@eval @fastmath $f($half, $third))[1],
- (@eval $f($half, $third))[1])
- @test isapprox((@eval @fastmath $f($half, $third))[2],
- (@eval $f($half, $third))[2])
- @test isapprox((@eval @fastmath $f($third, $half))[1],
- (@eval $f($third, $half))[1])
- @test isapprox((@eval @fastmath $f($third, $half))[2],
- (@eval $f($third, $half))[2])
+ @eval begin
+ @test @fastmath($f($half, $third)[1]) ≈ $f($half, $third)[1]
+ @test @fastmath($f($half, $third)[2]) ≈ $f($half, $third)[2]
+ @test @fastmath($f($third, $half)[1]) ≈ $f($third, $half)[1]
+ @test @fastmath($f($third, $half)[2]) ≈ $f($third, $half)[2]
+ end
  end
 end
 
@@ -153,14 +153,16 @@ for T in (Complex64, Complex128, Complex{BigFloat})
  :acos, :acosh, :asin, :asinh, :atan, :atanh, :cis, :cos,
  :cosh, :exp10, :exp2, :exp, :expm1, :log10, :log1p,
  :log2, :log, :sin, :sinh, :sqrt, :tan, :tanh)
- @test isapprox((@eval @fastmath $f($half)), (@eval $f($half)), rtol=rtol)
- @test isapprox((@eval @fastmath $f($third)), (@eval $f($third)), rtol=rtol)
+ @eval begin
+ @test @fastmath($f($half)) ≈ $f($half) rtol=$rtol
+ @test @fastmath($f($third)) ≈ $f($third) rtol=$rtol
+ end
  end
  for f in (:+, :-, :*, :/, :(==), :!=, :^)
- @test isapprox((@eval @fastmath $f($half, $third)),
-  (@eval $f($half, $third)), rtol=rtol)
- @test isapprox((@eval @fastmath $f($third, $half)),
-  (@eval $f($third, $half)), rtol=rtol)
+ @eval begin
+ @test @fastmath($f($half, $third)) ≈ $f($half, $third) rtol=$rtol
+  @test @fastmath($f($third, $half)) ≈ $f($third, $half) rtol=$rtol
+ end
  end
 end
 
@@ -173,32 +175,29 @@ for T in (Float32, Float64, BigFloat)
  cthird = (1-1im)/CT(3)
 
  for f in (:+, :-, :*, :/, :(==), :!=, :^)
- @test isapprox((@eval @fastmath $f($chalf, $third)),
- (@eval $f($chalf, $third)))
- @test isapprox((@eval @fastmath $f($half, $cthird)),
- (@eval $f($half, $cthird)))
- @test isapprox((@eval @fastmath $f($cthird, $half)),
- (@eval $f($cthird, $half)))
- @test isapprox((@eval @fastmath $f($third, $chalf)),
- (@eval $f($third, $chalf)))
+ @eval begin
+ @test @fastmath($f($chalf, $third)) ≈ $f($chalf, $third)
+ @test @fastmath($f($half, $cthird)) ≈ $f($half, $cthird)
+ @test @fastmath($f($cthird, $half)) ≈ $f($cthird, $half)
+ @test @fastmath($f($third, $chalf)) ≈ $f($third, $chalf)
+ end
  end
 
- @test isapprox((@fastmath third^3), third^3)
-
- @test isapprox((@fastmath chalf/third), chalf/third)
- @test isapprox((@fastmath chalf^3), chalf^3)
- @test isapprox((@fastmath cis(third)), cis(third))
+ @test @fastmath(third^3) ≈ third^3
+ @test @fastmath(chalf/third) ≈ chalf/third
+ @test @fastmath(chalf^3) ≈ chalf^3
+ @test @fastmath(cis(third)) ≈ cis(third)
 end
 
 # issue #10544
 let a = ones(2,2), b = ones(2,2)
- @test isapprox((@fastmath a[1] += 2.0), b[1] += 2.0)
- @test isapprox((@fastmath a[2] -= 2.0), b[2] -= 2.0)
- @test isapprox((@fastmath a[1,1] *= 2.0), b[1,1] *= 2.0)
- @test isapprox((@fastmath a[2,2] /= 2.0), b[2,2] /= 2.0)
- @test isapprox((@fastmath a[1,2] ^= 2.0), b[1,2] ^= 2.0)
+ @test @fastmath(a[1] += 2.0) ≈ (b[1] += 2.0)
+ @test @fastmath(a[2] -= 2.0) ≈ (b[2] -= 2.0)
+ @test @fastmath(a[1,1] *= 2.0) ≈ (b[1,1] *= 2.0)
+ @test @fastmath(a[2,2] /= 2.0) ≈ (b[2,2] /= 2.0)
+ @test @fastmath(a[1,2] ^= 2.0) ≈ (b[1,2] ^= 2.0)
 
  # test fallthrough for unsupported ops
  local c = 0
- @test Bool((@fastmath c |= 1))
+ @test @fastmath(c |= 1) == 1
 end

test/floatapprox.jl

@@ -6,19 +6,19 @@
 @test 4.000000002 ≉ 4.00300002
 
 # Other tolerance levels
-@test isapprox(4.32, 4.3; rtol=0.1, atol=0.01)
-@test isapprox(1.001, 1.002; rtol=0.001, atol=0.0001)
-@test !isapprox(4.5, 4.9; rtol=0.001, atol=0.001)
+@test 4.32 ≈ 4.3 rtol=0.1 atol=0.01
+@test 1.001 ≈ 1.002 rtol=0.001 atol=0.0001
+@test 4.5 ≉ 4.9 rtol=0.001 atol=0.001
 
 # Complex numbers
 @test 1.0 + 1.0im ≈ 1.0 + 1.00000000000001im
 @test 0.9999999999999 + 1.0im ≈ 1.0 + 1.000000000000001im
-@test isapprox(0.9999 + 1.0im, 1.0 + 1.1im; rtol = 0.0001, atol=1.1)
+@test 0.9999 + 1.0im ≈ 1.0 + 1.1im rtol=0.0001 atol=1.1
 
 # Complex <-> reals
 @test 1.0 + 0im ≈ 1.0000000000001
-@test isapprox(0.9999999999999, 1.0 + 0im)
-@test !isapprox(1.0+1im, 1.000000000000001)
+@test 0.9999999999999 ≈ 1.0 + 0im
+@test 1.0+1im ≉ 1.000000000000001
 
 # Comparing NaNs
 @test 4.0 ≉ NaN
@@ -37,22 +37,22 @@
 @test complex(0.0,Inf) ≉ complex(0.0,-Inf)
 
 # Tests for integers and rationals
-@test isapprox(4,4)
-@test isapprox(4,5; atol=1)
-@test !isapprox(4,6; atol=1)
-@test !isapprox(4,5)
+@test 4 ≈ 4
+@test 4 ≈ 5 atol=1
+@test 4 ≉ 6 atol=1
+@test 4 ≉ 5
 
-@test isapprox(1//2+3im, 1//2+3im)
-@test isapprox(1//3, 0.33333333333333333)
-@test isapprox(1//3, 0.3333; rtol=0.0001, atol=0.0001)
-@test isapprox(1+1im, 1im+1)
+@test 1//2+3im ≈ 1//2+3im
+@test 1//3 ≈ 0.33333333333333333
+@test 1//3 ≈ 0.3333 rtol=0.0001 atol=0.0001
+@test 1+1im ≈ 1im+1
 
 # Notably missing from this test suite at the moment
 # * Tests for other magnitudes of numbers - very small, very big, and combinations of small and big
-# * Tests for various odd combinations of types, e.g. isapprox(x::Integer, y::Rational)
+# * Tests for various odd combinations of types, e.g. x::Integer ≈ y::Rational
 
 # issue #12375:
-@test !isapprox(1e17, 1)
+@test 1e17 ≉ 1
 
 # Tests for arrays:
 @test [1,2,3] ≈ [1,2,3+1e-9]
@@ -64,8 +64,8 @@
 for elty in (Float16,Float32,Float64)
  nan = elty(NaN)
  half = elty(0.5)
- @test !isapprox(nan, nan)
- @test isapprox(nan, nan, nans=true)
- @test !isapprox([half, nan, half], [half, nan, half])
- @test isapprox([half, nan, half], [half, nan, half], nans=true)
+ @test nan ≉ nan
+ @test nan ≈ nan nans=true
+ @test [half, nan, half] ≉ [half, nan, half]
+ @test [half, nan, half] ≈ [half, nan, half] nans=true
 end

test/linalg/arnoldi.jl

@@ -135,9 +135,9 @@ let
  @test d[1] ≈ 1. # largest eigenvalue should be 1.
  v=reshape(v,(50,50)) # reshape to matrix
  v/=trace(v) # factor out arbitrary phase
- @test isapprox(vecnorm(imag(v)),0.) # it should be real
+ @test vecnorm(imag(v)) ≈ 0. # it should be real
  v=real(v)
- # @test isapprox(vecnorm(v-v')/2,0.) # it should be Hermitian
+ # @test vecnorm(v-v')/2 ≈ 0. # it should be Hermitian
  # Since this fails sometimes (numerical precision error),this test is commented out
  v=(v+v')/2
  @test isposdef(v)

test/linalg/uniformscaling.jl

@@ -27,8 +27,8 @@ end
  @test issymmetric(UniformScaling(complex(1.0,1.0)))
  @test ishermitian(I)
  @test !ishermitian(UniformScaling(complex(1.0,1.0)))
- @test isapprox(UniformScaling(4.00000000000001), UniformScaling(4.0))
- @test isapprox(UniformScaling(4.32), UniformScaling(4.3); rtol=0.1, atol=0.01)
+ @test UniformScaling(4.00000000000001) ≈ UniformScaling(4.0)
+ @test UniformScaling(4.32) ≈ UniformScaling(4.3) rtol=0.1 atol=0.01
 end
 
 @testset "* and / with number" begin

test/math.jl

@@ -650,7 +650,7 @@ end
  0.00169495384841964531409376316336552555952269360134349446910im)
 end
 
-# useful test functions for relative error, which differ from isapprox
+# useful test functions for relative error, which differ from isapprox (≈)
 # in that relerrc separately looks at the real and imaginary parts
 relerr(z, x) = z == x ? 0.0 : abs(z - x) / abs(x)
 relerrc(z, x) = max(relerr(real(z),real(x)), relerr(imag(z),imag(x)))

test/numbers.jl

@@ -155,26 +155,23 @@ let eps = 1//BigInt(2)^30, one_eps = 1+eps,
  @test eps64 == Float64(eps)
  @test one_eps64 == Float64(one_eps)
  @test one_eps64 * one_eps64 - 1 != Float64(one_eps * one_eps - 1)
- @test isapprox(muladd(one_eps64, one_eps64, -1),
- Float64(one_eps * one_eps - 1))
+ @test muladd(one_eps64, one_eps64, -1) ≈ Float64(one_eps * one_eps - 1)
 end
 
 let eps = 1//BigInt(2)^15, one_eps = 1+eps,
  eps32 = Float32(eps), one_eps32 = Float32(one_eps)
  @test eps32 == Float32(eps)
  @test one_eps32 == Float32(one_eps)
  @test one_eps32 * one_eps32 - 1 != Float32(one_eps * one_eps - 1)
- @test isapprox(muladd(one_eps32, one_eps32, -1),
- Float32(one_eps * one_eps - 1))
+ @test muladd(one_eps32, one_eps32, -1) ≈ Float32(one_eps * one_eps - 1)
 end
 
 let eps = 1//BigInt(2)^7, one_eps = 1+eps,
  eps16 = Float16(Float32(eps)), one_eps16 = Float16(Float32(one_eps))
  @test eps16 == Float16(Float32(eps))
  @test one_eps16 == Float16(Float32(one_eps))
  @test one_eps16 * one_eps16 - 1 != Float16(Float32(one_eps * one_eps - 1))
- @test isapprox(muladd(one_eps16, one_eps16, -1),
- Float16(Float32(one_eps * one_eps - 1)))
+ @test muladd(one_eps16, one_eps16, -1) ≈ Float16(Float32(one_eps * one_eps - 1))
 end
 
 @test muladd(1,2,3) == 1*2+3
@@ -1678,10 +1675,10 @@ end
 @test isnan(eps(-Inf))
 
 @test .1+.1+.1 != .3
-@test isapprox(.1+.1+.1, .3)
-@test !isapprox(.1+.1+.1-.3, 0)
-@test isapprox(.1+.1+.1-.3, 0, atol=eps(.3))
-@test isapprox(1.1,1.1f0)
+@test .1+.1+.1 ≈ .3
+@test .1+.1+.1-.3 ≉ 0
+@test .1+.1+.1-.3 ≈ 0 atol=eps(.3)
+@test 1.1 ≈ 1.1f0
 
 @test div(1e50,1) == 1e50
 @test fld(1e50,1) == 1e50