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# This file is a part of Julia. License is MIT: https://julialang.org/license
# Small sanity tests to ensure changing the rounding of float functions work
using Base.MathConstants
using Test
@testset "Float64 checks" begin
# a + b returns a number exactly between prevfloat(1.) and 1., so its
# final result depends strongly on the utilized rounding direction.
a = prevfloat(0.5)
b = 0.5
c = 0x1p-54
d = prevfloat(1.)
@testset "Default rounding direction, RoundNearest" begin
@test a + b === 1.
@test - a - b === -1.
@test a - b === -c
@test b - a === c
end
end
@testset "Float32 checks" begin
a32 = prevfloat(0.5f0)
b32 = 0.5f0
c32 = (1.f0 - prevfloat(1.f0))/2
d32 = prevfloat(1.0f0)
@testset "Default rounding direction, RoundNearest" begin
@test a32 + b32 === 1.0f0
@test - a32 - b32 === -1.0f0
@test a32 - b32 === -c32
@test b32 - a32 === c32
end
end
@testset "convert with rounding" begin
for v = [sqrt(2),-1/3,nextfloat(1.0),prevfloat(1.0),nextfloat(-1.0),
prevfloat(-1.0),nextfloat(0.0),prevfloat(0.0)]
pn = Float32(v,RoundNearest)
@test pn == convert(Float32,v)
pz = Float32(v,RoundToZero)
@test abs(pz) <= abs(v) < nextfloat(abs(pz))
@test signbit(pz) == signbit(v)
pd = Float32(v,RoundDown)
@test pd <= v < nextfloat(pd)
pu = Float32(v,RoundUp)
@test prevfloat(pu) < v <= pu
@test pn == pd || pn == pu
@test v > 0 ? pz == pd : pz == pu
@test pu - pd == eps(pz)
end
for T in [Float32,Float64]
for v in [sqrt(big(2.0)),-big(1.0)/big(3.0),nextfloat(big(1.0)),
prevfloat(big(1.0)),nextfloat(big(0.0)),prevfloat(big(0.0)),
pi,ℯ,eulergamma,catalan,golden,
typemax(Int64),typemax(UInt64),typemax(Int128),typemax(UInt128),0xa2f30f6001bb2ec6]
pn = T(v,RoundNearest)
@test pn == convert(T,BigFloat(v))
pz = T(v,RoundToZero)
@test pz == setrounding(()->convert(T,BigFloat(v)), BigFloat, RoundToZero)
pd = T(v,RoundDown)
@test pd == setrounding(()->convert(T,BigFloat(v)), BigFloat, RoundDown)
pu = T(v,RoundUp)
@test pu == setrounding(()->convert(T,BigFloat(v)), BigFloat, RoundUp)
@test pn == pd || pn == pu
@test v > 0 ? pz == pd : pz == pu
@test isinf(pu) || pu - pd == eps(pz)
end
end
end
@testset "fenv" begin
@test Base.Rounding.from_fenv(Base.Rounding.to_fenv(RoundNearest)) == RoundNearest
@test Base.Rounding.from_fenv(Base.Rounding.to_fenv(RoundToZero)) == RoundToZero
@test Base.Rounding.from_fenv(Base.Rounding.to_fenv(RoundUp)) == RoundUp
@test Base.Rounding.from_fenv(Base.Rounding.to_fenv(RoundDown)) == RoundDown
@test_throws ArgumentError Base.Rounding.from_fenv(-99)
end
@testset "round error throwing" begin
badness = 1//0
@test_throws DivideError round(Int64,badness,RoundNearestTiesAway)
@test_throws DivideError round(Int64,badness,RoundNearestTiesUp)
end
@testset "rounding properties" for Tf in [Float16,Float32,Float64]
# these should hold for all u, but we just test the smallest and largest
# of each binade
for i in exponent(floatmin(Tf)):exponent(floatmax(Tf))
for u in [ldexp(Tf(1.0), i), -ldexp(Tf(1.0), i),
ldexp(prevfloat(Tf(2.0)), i), -ldexp(prevfloat(Tf(2.0)), i)]
r = round(u, RoundNearest)
if isfinite(u)
@test isfinite(r)
@test isinteger(r)
@test abs(r-u) < 0.5 || abs(r-u) == 0.5 && isinteger(r/2)
@test signbit(u) == signbit(r)
else
@test u === r
end
r = round(u, RoundNearestTiesAway)
if isfinite(u)
@test isfinite(r)
@test isinteger(r)
@test abs(r-u) < 0.5 || (r-u) == copysign(0.5,u)
@test signbit(u) == signbit(r)
else
@test u === r
end
r = round(u, RoundNearestTiesUp)
if isfinite(u)
@test isfinite(r)
@test isinteger(r)
@test -0.5 < r-u <= 0.5
@test signbit(u) == signbit(r)
else
@test u === r
end
end
end
end
@testset "rounding difficult values" begin
for x = 2^53-10:2^53+10
y = Float64(x)
i = trunc(Int64,y)
@test Int64(trunc(y)) == i
@test Int64(round(y)) == i
@test Int64(floor(y)) == i
@test Int64(ceil(y)) == i
@test round(Int64,y) == i
@test floor(Int64,y) == i
@test ceil(Int64,y) == i
end
for x = 2^24-10:2^24+10
y = Float32(x)
i = trunc(Int,y)
@test Int(trunc(y)) == i
@test Int(round(y)) == i
@test Int(floor(y)) == i
@test Int(ceil(y)) == i
@test round(Int,y) == i
@test floor(Int,y) == i
@test ceil(Int,y) == i
end
# rounding vectors
let ≈(x,y) = x==y && typeof(x)==typeof(y)
for t in [Float32,Float64]
# try different vector lengths
for n in [0,3,255,256]
r = (1:n) .- div(n,2)
y = t[x/4 for x in r]
@test trunc.(y) ≈ t[div(i,4) for i in r]
@test floor.(y) ≈ t[i>>2 for i in r]
@test ceil.(y) ≈ t[(i+3)>>2 for i in r]
@test round.(y) ≈ t[(i+1+isodd(i>>2))>>2 for i in r]
@test broadcast(x -> round(x, RoundNearestTiesAway), y) ≈ t[(i+1+(i>=0))>>2 for i in r]
@test broadcast(x -> round(x, RoundNearestTiesUp), y) ≈ t[(i+2)>>2 for i in r]
end
end
end
@test_throws InexactError round(Int,Inf)
@test_throws InexactError round(Int,NaN)
@test round(Int,2.5) == 2
@test round(Int,1.5) == 2
@test round(Int,-2.5) == -2
@test round(Int,-1.5) == -2
@test round(Int,2.5,RoundNearestTiesAway) == 3
@test round(Int,1.5,RoundNearestTiesAway) == 2
@test round(Int,2.5,RoundNearestTiesUp) == 3
@test round(Int,1.5,RoundNearestTiesUp) == 2
@test round(Int,-2.5,RoundNearestTiesAway) == -3
@test round(Int,-1.5,RoundNearestTiesAway) == -2
@test round(Int,-2.5,RoundNearestTiesUp) == -2
@test round(Int,-1.5,RoundNearestTiesUp) == -1
@test round(Int,-1.9) == -2
@test_throws InexactError round(Int64, 9.223372036854776e18)
@test round(Int64, 9.223372036854775e18) == 9223372036854774784
@test_throws InexactError round(Int64, -9.223372036854778e18)
@test round(Int64, -9.223372036854776e18) == typemin(Int64)
@test_throws InexactError round(UInt64, 1.8446744073709552e19)
@test round(UInt64, 1.844674407370955e19) == 0xfffffffffffff800
@test_throws InexactError round(Int32, 2.1474836f9)
@test round(Int32, 2.1474835f9) == 2147483520
@test_throws InexactError round(Int32, -2.147484f9)
@test round(Int32, -2.1474836f9) == typemin(Int32)
@test_throws InexactError round(UInt32, 4.2949673f9)
@test round(UInt32, 4.294967f9) == 0xffffff00
for Ti in [Int,UInt]
for Tf in [Float16,Float32,Float64]
@test round(Ti,Tf(-0.0)) == 0
@test round(Ti,Tf(-0.0),RoundNearestTiesAway) == 0
@test round(Ti,Tf(-0.0),RoundNearestTiesUp) == 0
@test round(Ti, Tf(0.5)) == 0
@test round(Ti, Tf(0.5), RoundNearestTiesAway) == 1
@test round(Ti, Tf(0.5), RoundNearestTiesUp) == 1
@test round(Ti, prevfloat(Tf(0.5))) == 0
@test round(Ti, prevfloat(Tf(0.5)), RoundNearestTiesAway) == 0
@test round(Ti, prevfloat(Tf(0.5)), RoundNearestTiesUp) == 0
@test round(Ti, nextfloat(Tf(0.5))) == 1
@test round(Ti, nextfloat(Tf(0.5)), RoundNearestTiesAway) == 1
@test round(Ti, nextfloat(Tf(0.5)), RoundNearestTiesUp) == 1
@test round(Ti, Tf(-0.5)) == 0
@test round(Ti, Tf(-0.5), RoundNearestTiesUp) == 0
@test round(Ti, nextfloat(Tf(-0.5))) == 0
@test round(Ti, nextfloat(Tf(-0.5)), RoundNearestTiesAway) == 0
@test round(Ti, nextfloat(Tf(-0.5)), RoundNearestTiesUp) == 0
if Ti <: Signed
@test round(Ti, Tf(-0.5), RoundNearestTiesAway) == -1
@test round(Ti, prevfloat(Tf(-0.5))) == -1
@test round(Ti, prevfloat(Tf(-0.5)), RoundNearestTiesAway) == -1
@test round(Ti, prevfloat(Tf(-0.5)), RoundNearestTiesUp) == -1
else
@test_throws InexactError round(Ti, Tf(-0.5), RoundNearestTiesAway)
@test_throws InexactError round(Ti, prevfloat(Tf(-0.5)))
@test_throws InexactError round(Ti, prevfloat(Tf(-0.5)), RoundNearestTiesAway)
@test_throws InexactError round(Ti, prevfloat(Tf(-0.5)), RoundNearestTiesUp)
end
end
end
# numbers that can't be rounded by trunc(x+0.5)
@test round(Int64, 2.0^52 + 1) == 4503599627370497
@test round(Int32, 2.0f0^23 + 1) == 8388609
end
# custom rounding and significant-digit ops
@testset "rounding to digits relative to the decimal point" begin
@test round(pi) ≈ 3.
@test round(pi, base=10) ≈ 3.
@test round(pi, digits=0) ≈ 3.
@test round(pi, digits=1) ≈ 3.1
@test round(pi, digits=3, base=2) ≈ 3.125
@test round(pi, sigdigits=1) ≈ 3.
@test round(pi, sigdigits=3) ≈ 3.14
@test round(pi, sigdigits=4, base=2) ≈ 3.25
@test round(big(pi)) ≈ big"3."
@test round(big(pi), digits=0) ≈ big"3."
@test round(big(pi), digits=1) ≈ big"3.1"
@test round(big(pi), digits=3, base=2) ≈ big"3.125"
@test round(big(pi), sigdigits=1) ≈ big"3."
@test round(big(pi), sigdigits=3) ≈ big"3.14"
@test round(big(pi), sigdigits=4, base=2) ≈ big"3.25"
@test round(10*pi, digits=-1) ≈ 30.
@test round(.1, digits=0) == 0.
@test round(-.1, digits=0) == -0.
@test isnan(round(NaN, digits=2))
@test isinf(round(Inf, digits=2))
@test isinf(round(-Inf, digits=2))
end
@testset "round vs trunc vs floor vs ceil" begin
@test round(123.456, digits=1) ≈ 123.5
@test round(-123.456, digits=1) ≈ -123.5
@test trunc(123.456, digits=1) ≈ 123.4
@test trunc(-123.456, digits=1) ≈ -123.4
@test ceil(123.456, digits=1) ≈ 123.5
@test ceil(-123.456, digits=1) ≈ -123.4
@test floor(123.456, digits=1) ≈ 123.4
@test floor(-123.456, digits=1) ≈ -123.5
end
@testset "rounding with too much (or too few) precision" begin
for x in (12345.6789, 0, -12345.6789)
y = float(x)
@test y == trunc(x, digits=1000)
@test y == round(x, digits=1000)
@test y == floor(x, digits=1000)
@test y == ceil(x, digits=1000)
end
let x = 12345.6789
@test 0.0 == trunc(x, digits=-1000)
@test 0.0 == round(x, digits=-1000)
@test 0.0 == floor(x, digits=-1000)
@test Inf == ceil(x, digits=-1000)
end
let x = -12345.6789
@test -0.0 == trunc(x, digits=-1000)
@test -0.0 == round(x, digits=-1000)
@test -Inf == floor(x, digits=-1000)
@test -0.0 == ceil(x, digits=-1000)
end
let x = 0.0
@test 0.0 == trunc(x, digits=-1000)
@test 0.0 == round(x, digits=-1000)
@test 0.0 == floor(x, digits=-1000)
@test 0.0 == ceil(x, digits=-1000)
end
end
@testset "rounding in other bases" begin
@test round(pi, digits = 2, base = 2) ≈ 3.25
@test round(pi, digits = 3, base = 2) ≈ 3.125
@test round(pi, digits = 3, base = 5) ≈ 3.144
end
@testset "vectorized trunc/round/floor/ceil with digits/base argument" begin
a = rand(2, 2, 2)
for f in (round, trunc, floor, ceil)
@test f.(a[:, 1, 1], digits=2) == map(x->f(x, digits=2), a[:, 1, 1])
@test f.(a[:, :, 1], digits=2) == map(x->f(x, digits=2), a[:, :, 1])
@test f.(a, digits=9, base = 2) == map(x->f(x, digits=9, base = 2), a)
@test f.(a[:, 1, 1], digits=9, base = 2) == map(x->f(x, digits=9, base = 2), a[:, 1, 1])
@test f.(a[:, :, 1], digits=9, base = 2) == map(x->f(x, digits=9, base = 2), a[:, :, 1])
@test f.(a, digits=9, base = 2) == map(x->f(x, digits=9, base = 2), a)
end
end
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