Skip to content

Add checked, wrapping and saturating arithmetic for div/cld/fld #226

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 1 commit into from
Sep 11, 2020
Merged

Add checked, wrapping and saturating arithmetic for div/cld/fld #226

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
56 changes: 49 additions & 7 deletions src/FixedPointNumbers.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -5,15 +5,15 @@ import Base: ==, <, <=, -, +, *, /, ~, isapprox,
isnan, isinf, isfinite, isinteger,
zero, oneunit, one, typemin, typemax, floatmin, floatmax, eps, reinterpret,
big, rationalize, float, trunc, round, floor, ceil, bswap, clamp,
div, fld, rem, mod, mod1, fld1, min, max, minmax,
div, fld, cld, rem, mod, mod1, fld1, min, max, minmax,
signed, unsigned, copysign, flipsign, signbit,
length

import Statistics # for _mean_promote
import Random: Random, AbstractRNG, SamplerType, rand!

import Base.Checked: checked_neg, checked_abs, checked_add, checked_sub, checked_mul,
checked_div
checked_div, checked_fld, checked_cld

using Base: @pure

Expand All @@ -38,9 +38,9 @@ export
# Functions
scaledual,
wrapping_neg, wrapping_abs, wrapping_add, wrapping_sub, wrapping_mul,
wrapping_fdiv,
wrapping_fdiv, wrapping_div, wrapping_fld, wrapping_cld,
saturating_neg, saturating_abs, saturating_add, saturating_sub, saturating_mul,
saturating_fdiv,
saturating_fdiv, saturating_div, saturating_fld, saturating_cld,
checked_fdiv

include("utilities.jl")
Expand Down Expand Up @@ -214,6 +214,17 @@ function wrapping_fdiv(x::X, y::X) where {X <: FixedPoint}
z = floattype(X)(x.i) / floattype(X)(y.i)
isfinite(z) ? z % X : zero(X)
end
function wrapping_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
isfinite(z) || return zero(T)
if T <: Unsigned
_unsafe_trunc(T, z)
else
z > typemax(T) ? typemin(T) : _unsafe_trunc(T, z)
end
end
wrapping_fld(x::X, y::X) where {X <: FixedPoint} = wrapping_div(x, y, RoundDown)
wrapping_cld(x::X, y::X) where {X <: FixedPoint} = wrapping_div(x, y, RoundUp)

# saturating arithmetic
saturating_neg(x::X) where {X <: FixedPoint} = X(~min(x.i - true, x.i), 0)
Expand All @@ -235,6 +246,18 @@ saturating_mul(x::X, y::X) where {X <: FixedPoint} = clamp(float(x) * float(y),
saturating_fdiv(x::X, y::X) where {X <: FixedPoint} =
clamp(floattype(X)(x.i) / floattype(X)(y.i), X)

function saturating_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
isnan(z) && return zero(T)
if T <: Unsigned
isfinite(z) ? _unsafe_trunc(T, z) : typemax(T)
else
_unsafe_trunc(T, clamp(z, typemin(T), typemax(T)))
end
end
saturating_fld(x::X, y::X) where {X <: FixedPoint} = saturating_div(x, y, RoundDown)
saturating_cld(x::X, y::X) where {X <: FixedPoint} = saturating_div(x, y, RoundUp)

# checked arithmetic
checked_neg(x::X) where {X <: FixedPoint} = checked_sub(zero(X), x)
function checked_abs(x::X) where {X <: FixedPoint}
Expand Down Expand Up @@ -268,6 +291,16 @@ function checked_fdiv(x::X, y::X) where {T, X <: FixedPoint{T}}
end
z % X
end
function checked_div(x::X, y::X, r::RoundingMode = RoundToZero) where {T, X <: FixedPoint{T}}
y === zero(X) && throw(DivideError())
z = round(floattype(X)(x.i) / floattype(X)(y.i), r)
if T <: Signed
z <= typemax(T) || throw_overflowerror_div(r, x, y)
end
_unsafe_trunc(T, z)
end
checked_fld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundDown)
checked_cld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundUp)

# default arithmetic
const DEFAULT_ARITHMETIC = :wrapping
Expand All @@ -284,8 +317,11 @@ for (op, name) in ((:+, :add), (:-, :sub), (:*, :mul))
$op(x::X, y::X) where {X <: FixedPoint} = $f(x, y)
end
end
/(x::X, y::X) where {X <: FixedPoint} = checked_fdiv(x, y) # force checked arithmetic

# force checked arithmetic
/(x::X, y::X) where {X <: FixedPoint} = checked_fdiv(x, y)
div(x::X, y::X, r::RoundingMode = RoundToZero) where {X <: FixedPoint} = checked_div(x, y, r)
fld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundDown)
cld(x::X, y::X) where {X <: FixedPoint} = checked_div(x, y, RoundUp)

function minmax(x::X, y::X) where {X <: FixedPoint}
a, b = minmax(reinterpret(x), reinterpret(y))
Expand Down Expand Up @@ -331,7 +367,7 @@ for f in (:zero, :oneunit, :one, :eps, :rawone, :rawtype, :floattype)
$f(x::FixedPoint) = $f(typeof(x))
end
end
for f in (:(==), :<, :<=, :div, :fld, :fld1)
for f in (:(==), :<, :<=, :fld1)
@eval begin
$f(x::X, y::X) where {X <: FixedPoint} = $f(x.i, y.i)
end
Expand Down Expand Up @@ -502,6 +538,12 @@ end
showtype(io, typeof(x))
throw(OverflowError(String(take!(io))))
end
@noinline function throw_overflowerror_div(r::RoundingMode, @nospecialize(x), @nospecialize(y))
io = IOBuffer()
op = r === RoundUp ? "cld(" : r === RoundDown ? "fld(" : "div("
print(io, op, x, ", ", y, ") overflowed for type ", rawtype(x))
throw(OverflowError(String(take!(io))))
end

function Random.rand(r::AbstractRNG, ::SamplerType{X}) where X <: FixedPoint
X(rand(r, rawtype(X)), 0)
Expand Down
55 changes: 55 additions & 0 deletions test/common.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -234,6 +234,61 @@ function test_fdiv(TX::Type)
end
end

function test_div(TX::Type)
for X in target(TX, :i8; ex = :thin)
T = rawtype(X)
xys = xypairs(X)
fdiv(x, y) = oftype(float(x), big(x) / big(y))
@test all(xys) do (x, y)
rem_t(x) = x > typemax(T) ? typemin(T) : unsafe_trunc(T, x)
z = y === zero(y) ? float(y) : fdiv(x, y)
return (wrapping_div(x, y) === rem_t(trunc(z))) &
(wrapping_fld(x, y) === rem_t(floor(z))) &
(wrapping_cld(x, y) === rem_t( ceil(z)))
end
@test all(xys) do (x, y)
clamp_t(x) = isnan(x) ? zero(T) : trunc(T, clamp(x, typemin(T), typemax(T)))
z = fdiv(x, y)
return (saturating_div(x, y) === clamp_t(trunc(z))) &
(saturating_fld(x, y) === clamp_t(floor(z))) &
(saturating_cld(x, y) === clamp_t( ceil(z)))
end
@test all(xys) do (x, y)
z = fdiv(x, y)
t = !(typemin(T) <= trunc(z) <= typemax(T)) || wrapping_div(x, y) === checked_div(x, y)
f = !(typemin(T) <= floor(z) <= typemax(T)) || wrapping_fld(x, y) === checked_fld(x, y)
c = !(typemin(T) <= ceil(z) <= typemax(T)) || wrapping_cld(x, y) === checked_cld(x, y)
return t & f & c
end
end
end

function test_div_3arg(TX::Type)
for X in target(TX; ex = :thin)
@test div(eps(X), typemax(X), RoundToZero) === div(eps(X), typemax(X))
@test div(eps(X), typemax(X), RoundDown) === fld(eps(X), typemax(X))
@test div(eps(X), typemax(X), RoundUp) === cld(eps(X), typemax(X))
end
end

function test_fld1_mod1(TX::Type)
for X in target(TX, :i8, :i16; ex = :thin)
T = rawtype(X)
eps2 = eps(X) + eps(X)
xs = reinterpret.(X, T.((17, 16, 15, 14)))
@test all(fld1.(xs, eps2) .=== T.((9, 8, 8, 7)))
@test_throws DivideError fld1(eps(X), zero(X))

@test all(mod1.(xs, eps2) .=== reinterpret.(X, T.((1, 2, 1, 2))))
@test_throws DivideError mod1(eps(X), zero(X))

d, r = fldmod1(typemin(X), eps2)
@test d isa T && r isa X && ((d - 1) * eps2 + r) % X === typemin(X)
d, r = fldmod1(typemax(X), eps2)
@test d isa T && r isa X && ((d - 1) * eps2 + r) % X === typemax(X)
end
end

function test_isapprox(TX::Type)
@testset "approx $X" for X in target(TX, :i8, :i16; ex = :light)
xs = typemin(X):eps(X):typemax(X)-eps(X)
Expand Down
50 changes: 50 additions & 0 deletions test/fixed.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -402,6 +402,56 @@ end
test_fdiv(Fixed)
end

@testset "div/cld/fld" begin
for F in target(Fixed; ex = :thin)
fm, fn, fz, fe = typemax(F), typemin(F), zero(F), eps(F)
T = rawtype(F)
@test wrapping_div(fm, fm) === wrapping_fld(fm, fm) === wrapping_cld(fm, fm) === one(T)
@test saturating_div(fm, fm) === saturating_fld(fm, fm) === saturating_cld(fm, fm) === one(T)
@test checked_div(fm, fm) === checked_fld(fm, fm) === checked_cld(fm, fm) === one(T)

@test wrapping_div(fz, fe) === wrapping_fld(fz, fe) === wrapping_cld(fz, fe) === zero(T)
@test saturating_div(fz, fe) === saturating_fld(fz, fe) === saturating_cld(fz, fe) === zero(T)
@test checked_div(fz, fe) === checked_fld(fz, fe) === checked_cld(fz, fe) === zero(T)

@test wrapping_div(fm, fe) === wrapping_fld(fm, fe) === wrapping_cld(fm, fe) === typemax(T)
@test saturating_div(fm, fe) === saturating_fld(fm, fe) === saturating_cld(fm, fe) === typemax(T)
@test checked_div(fm, fe) === checked_fld(fm, fe) === checked_cld(fm, fe) === typemax(T)

@test wrapping_div(fz, fz) === wrapping_fld(fz, fz) === wrapping_cld(fz, fz) === zero(T)
@test saturating_div(fz, fz) === saturating_fld(fz, fz) === saturating_cld(fz, fz) === zero(T)
@test_throws DivideError checked_div(fz, fz)
@test_throws DivideError checked_fld(fz, fz)
@test_throws DivideError checked_cld(fz, fz)

@test wrapping_div(fe, fz) === wrapping_fld(fe, fz) === wrapping_cld(fe, fz) === zero(T)
@test saturating_div(fe, fz) === saturating_fld(fe, fz) === saturating_cld(fe, fz) === typemax(T)
@test_throws DivideError checked_div(fe, fz)
@test_throws DivideError checked_fld(fe, fz)
@test_throws DivideError checked_cld(fe, fz)

@test wrapping_div(fn, -fe) === wrapping_fld(fn, -fe) === wrapping_cld(fn, -fe) === typemin(T)
@test saturating_div(fn, -fe) === saturating_fld(fn, -fe) === saturating_cld(fn, -fe) === typemax(T)
@test_throws OverflowError checked_div(fn, -fe)
@test_throws OverflowError checked_fld(fn, -fe)
@test_throws OverflowError checked_cld(fn, -fe)

@test wrapping_div(fe, fm) === saturating_div(fe, fm) === checked_div(fe, fm) === zero(T)
@test wrapping_fld(fe, fm) === saturating_fld(fe, fm) === checked_fld(fe, fm) === zero(T)
@test wrapping_cld(fe, fm) === saturating_cld(fe, fm) === checked_cld(fe, fm) === one(T)

@test wrapping_div(fe, fn) === saturating_div(fe, fn) === checked_div(fe, fn) === zero(T)
@test wrapping_fld(fe, fn) === saturating_fld(fe, fn) === checked_fld(fe, fn) === -one(T)
@test wrapping_cld(fe, fn) === saturating_cld(fe, fn) === checked_cld(fe, fn) === zero(T)
end
test_div(Fixed)
test_div_3arg(Fixed)
end

@testset "fld1/mod1" begin
test_fld1_mod1(Fixed)
end

@testset "rounding" begin
for sym in (:i8, :i16, :i32, :i64)
T = symbol_to_inttype(Fixed, sym)
Expand Down
45 changes: 38 additions & 7 deletions test/normed.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -405,18 +405,49 @@ end
test_fdiv(Normed)
end

@testset "div/fld1" begin
@test div(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == fld(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == 8
@test div(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == fld(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == 7
@test fld1(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == 8
@test fld1(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == 8
@testset "div/cld/fld" begin
for N in target(Normed; ex = :thin)
nm, nz, ne = typemax(N), zero(N), eps(N)
T = rawtype(N)
@test wrapping_div(nm, nm) === wrapping_fld(nm, nm) === wrapping_cld(nm, nm) === one(T)
@test saturating_div(nm, nm) === saturating_fld(nm, nm) === saturating_cld(nm, nm) === one(T)
@test checked_div(nm, nm) === checked_fld(nm, nm) === checked_cld(nm, nm) === one(T)

@test wrapping_div(nz, ne) === wrapping_fld(nz, ne) === wrapping_cld(nz, ne) === zero(T)
@test saturating_div(nz, ne) === saturating_fld(nz, ne) === saturating_cld(nz, ne) === zero(T)
@test checked_div(nz, ne) === checked_fld(nz, ne) === checked_cld(nz, ne) === zero(T)

@test wrapping_div(nm, ne) === wrapping_fld(nm, ne) === wrapping_cld(nm, ne) === typemax(T)
@test saturating_div(nm, ne) === saturating_fld(nm, ne) === saturating_cld(nm, ne) === typemax(T)
@test checked_div(nm, ne) === checked_fld(nm, ne) === checked_cld(nm, ne) === typemax(T)

@test wrapping_div(nz, nz) === wrapping_fld(nz, nz) === wrapping_cld(nz, nz) === zero(T)
@test saturating_div(nz, nz) === saturating_fld(nz, nz) === saturating_cld(nz, nz) === zero(T)
@test_throws DivideError checked_div(nz, nz)
@test_throws DivideError checked_fld(nz, nz)
@test_throws DivideError checked_cld(nz, nz)

@test wrapping_div(ne, nz) === wrapping_fld(ne, nz) === wrapping_cld(ne, nz) === zero(T)
@test saturating_div(ne, nz) === saturating_fld(ne, nz) === saturating_cld(ne, nz) === typemax(T)
@test_throws DivideError checked_div(ne, nz)
@test_throws DivideError checked_fld(ne, nz)
@test_throws DivideError checked_cld(ne, nz)

@test wrapping_div(ne, nm) === saturating_div(ne, nm) === checked_div(ne, nm) === zero(T)
@test wrapping_fld(ne, nm) === saturating_fld(ne, nm) === checked_fld(ne, nm) === zero(T)
@test wrapping_cld(ne, nm) === saturating_cld(ne, nm) === checked_cld(ne, nm) === one(T)
end
test_div(Normed)
test_div_3arg(Normed)
end

@testset "rem/mod" begin
@test mod(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == rem(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == 0
@test mod(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == rem(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == reinterpret(N0f8, 0x01)
@test mod1(reinterpret(N0f8, 0x10), reinterpret(N0f8, 0x02)) == reinterpret(N0f8, 0x02)
@test mod1(reinterpret(N0f8, 0x0f), reinterpret(N0f8, 0x02)) == reinterpret(N0f8, 0x01)
end

@testset "fld1/mod1" begin
test_fld1_mod1(Normed)
end

@testset "rounding" begin
Expand Down