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checked.jl
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checked.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
# Checked integer arithmetic
import Base: checked_abs, checked_neg, checked_add, checked_sub, checked_mul,
checked_div, checked_rem, checked_fld, checked_mod, checked_cld,
add_with_overflow, sub_with_overflow, mul_with_overflow
# checked operations
for T in (Int8, Int16, Int32, Int64, Int128)
# regular cases
@test checked_abs(T(0)) === T(0)
@test checked_neg(T(0)) === T(0)
@test checked_add(T(0)) === T(0)
@test checked_mul(T(0)) === T(0)
for s in (-1, +1)
@test checked_abs(T(3s)) === T(abs(3s))
@test checked_neg(T(3s)) === T(-3s)
@test checked_add(T(3s)) === T(3s)
@test checked_mul(T(3s)) === T(3s)
@test checked_abs(T(s*typemax(T))) === typemax(T)
@test checked_neg(T(s*typemax(T))) === T(-s*typemax(T))
@test checked_add(T(s*typemax(T))) === T(s*typemax(T))
@test checked_mul(T(s*typemax(T))) === T(s*typemax(T))
end
# corner cases
@test_throws OverflowError checked_abs(typemin(T))
@test_throws OverflowError checked_neg(typemin(T))
# regular cases
for s1 in (-1, +1), s2 in (-1, +1)
@test checked_add(T(4s1), T(3s2)) === T(4s1 + 3s2)
@test checked_sub(T(4s1), T(3s2)) === T(4s1 - 3s2)
@test checked_mul(T(4s1), T(3s2)) === T(4s1 * 3s2)
@test checked_div(T(4s1), T(3s2)) === T(div(4s1, 3s2))
@test checked_rem(T(4s1), T(3s2)) === T(rem(4s1, 3s2))
@test checked_fld(T(4s1), T(3s2)) === T(fld(4s1, 3s2))
@test checked_mod(T(4s1), T(3s2)) === T(mod(4s1, 3s2))
@test checked_cld(T(4s1), T(3s2)) === T(cld(4s1, 3s2))
end
# corner cases
halfmax = T(typemax(T)÷2)
halfmax_plus1 = T(halfmax+1)
halfmin = T(typemin(T)÷2)
halfmin_minus1 = T(halfmin-1)
sqrtmax = T(1) << T(sizeof(T)*4)
half_sqrtmax = sqrtmax >> T(1)
half_sqrtmax_plus1 = half_sqrtmax + T(1)
@test checked_add(typemax(T), T(-1)) === T(typemax(T) - 1)
@test_throws OverflowError checked_add(typemin(T), T(-1))
@test checked_add(typemax(T), T(0)) === typemax(T)
@test checked_add(typemin(T), T(0)) === typemin(T)
@test_throws OverflowError checked_add(typemax(T), T(1))
@test checked_add(typemin(T), T(1)) === T(typemin(T) + 1)
@test checked_add(T(-1), typemax(T)) === T(typemax(T) - 1)
@test_throws OverflowError checked_add(T(-1), typemin(T))
@test checked_add(T(0), typemax(T)) === typemax(T)
@test checked_add(T(0), typemin(T)) === typemin(T)
@test_throws OverflowError checked_add(T(1), typemax(T))
@test checked_add(T(1), typemin(T)) === T(typemin(T) + 1)
@test checked_add(typemax(T), typemin(T)) === T(-1)
@test checked_add(typemin(T), typemax(T)) === T(-1)
@test_throws OverflowError checked_add(halfmax_plus1, halfmax_plus1)
@test_throws OverflowError checked_add(halfmin, halfmin_minus1)
@test add_with_overflow(typemax(T), T(-1)) === (T(typemax(T) - 1), false)
@test add_with_overflow(typemin(T), T(-1)) === (T(typemax(T)), true)
@test add_with_overflow(typemax(T), T(0)) === (typemax(T), false)
@test add_with_overflow(typemin(T), T(0)) === (typemin(T), false)
@test add_with_overflow(typemax(T), T(1)) === (typemin(T), true)
@test add_with_overflow(typemin(T), T(1)) === (T(typemin(T) + 1), false)
@test add_with_overflow(T(-1), typemax(T)) === (T(typemax(T) - 1), false)
@test add_with_overflow(T(-1), typemin(T)) === (typemax(T), true)
@test add_with_overflow(T(0), typemax(T)) === (typemax(T), false)
@test add_with_overflow(T(0), typemin(T)) === (typemin(T), false)
@test add_with_overflow(T(1), typemax(T)) === (typemin(T), true)
@test add_with_overflow(T(1), typemin(T)) === (T(typemin(T) + 1), false)
@test add_with_overflow(typemax(T), typemin(T)) === (T(-1), false)
@test add_with_overflow(typemin(T), typemax(T)) === (T(-1), false)
@test add_with_overflow(halfmax_plus1, halfmax_plus1) === (typemin(T), true)
@test add_with_overflow(halfmin, halfmin_minus1) === (typemax(T), true)
@test_throws OverflowError checked_sub(typemax(T), T(-1))
@test checked_sub(typemax(T), T(0)) === typemax(T)
@test checked_sub(typemax(T), T(1)) === T(typemax(T) - 1)
@test checked_sub(typemin(T), T(-1)) === T(typemin(T) + 1)
@test checked_sub(typemin(T), T(0)) === typemin(T)
@test_throws OverflowError checked_sub(typemin(T), T(1))
@test checked_sub(T(0), typemax(T)) === T(typemin(T) + 1)
@test checked_sub(T(1), typemax(T)) === T(typemin(T) + 2)
@test checked_sub(T(-1), typemin(T)) === typemax(T)
@test_throws OverflowError checked_sub(T(0), typemin(T))
@test checked_sub(typemax(T), typemax(T)) === T(0)
@test checked_sub(typemin(T), typemin(T)) === T(0)
@test checked_sub(halfmax, T(-halfmin)) === T(-1)
@test_throws OverflowError checked_sub(halfmin, T(-halfmin_minus1))
@test sub_with_overflow(typemax(T), T(-1)) === (typemin(T), true)
@test sub_with_overflow(typemax(T), T(0)) === (typemax(T), false)
@test sub_with_overflow(typemax(T), T(1)) === (T(typemax(T) - 1), false)
@test sub_with_overflow(typemin(T), T(-1)) === (T(typemin(T) + 1), false)
@test sub_with_overflow(typemin(T), T(0)) === (typemin(T), false)
@test sub_with_overflow(typemin(T), T(1)) === (typemax(T), true)
@test sub_with_overflow(T(0), typemax(T)) === (T(typemin(T) + 1), false)
@test sub_with_overflow(T(1), typemax(T)) === (T(typemin(T) + 2), false)
@test sub_with_overflow(T(-1), typemin(T)) === (typemax(T), false)
@test sub_with_overflow(T(0), typemin(T)) === (typemin(T), true)
@test sub_with_overflow(typemax(T), typemax(T)) === (T(0), false)
@test sub_with_overflow(typemin(T), typemin(T)) === (T(0), false)
@test sub_with_overflow(halfmax, T(-halfmin)) === (T(-1), false)
@test sub_with_overflow(halfmin, T(-halfmin_minus1)) === (typemax(T), true)
@test checked_mul(typemax(T), T(0)) === T(0)
@test checked_mul(typemin(T), T(0)) === T(0)
@test checked_mul(typemax(T), T(1)) === typemax(T)
@test checked_mul(typemin(T), T(1)) === typemin(T)
@test_throws OverflowError checked_mul(sqrtmax, half_sqrtmax)
@test checked_mul(sqrtmax, -half_sqrtmax) === T(sqrtmax * -half_sqrtmax)
@test_throws OverflowError checked_mul(sqrtmax, -half_sqrtmax_plus1)
@test checked_mul(-sqrtmax, half_sqrtmax) === T(-sqrtmax * half_sqrtmax)
@test_throws OverflowError checked_mul(-sqrtmax, half_sqrtmax_plus1)
@test_throws OverflowError checked_mul(-sqrtmax, -half_sqrtmax)
@test mul_with_overflow(typemax(T), T(0)) === (T(0), false)
@test mul_with_overflow(typemin(T), T(0)) === (T(0), false)
@test mul_with_overflow(typemax(T), T(1)) === (typemax(T), false)
@test mul_with_overflow(typemin(T), T(1)) === (typemin(T), false)
@test mul_with_overflow(sqrtmax, half_sqrtmax) === (typemin(T), true)
@test mul_with_overflow(sqrtmax, -half_sqrtmax) === (T(sqrtmax * -half_sqrtmax), false)
@test mul_with_overflow(sqrtmax, -half_sqrtmax_plus1) === (T(sqrtmax * -half_sqrtmax_plus1), true)
@test mul_with_overflow(-sqrtmax, half_sqrtmax) === (T(-sqrtmax * half_sqrtmax), false)
@test mul_with_overflow(-sqrtmax, half_sqrtmax_plus1) === (T(-sqrtmax * half_sqrtmax_plus1), true)
@test mul_with_overflow(-sqrtmax, -half_sqrtmax) === (T(-sqrtmax * -half_sqrtmax), true)
@test checked_div(typemax(T), T(1)) === typemax(T)
@test_throws DivideError checked_div(typemax(T), T(0))
@test checked_div(typemax(T), T(-1)) === T(-typemax(T))
@test checked_div(typemin(T), T(1)) === typemin(T)
@test_throws DivideError checked_div(typemin(T), T(0))
@test_throws DivideError checked_div(typemin(T), T(-1))
@test checked_rem(typemax(T), T(1)) === T(0)
@test_throws DivideError checked_rem(typemax(T), T(0))
@test checked_rem(typemax(T), T(-1)) === T(0)
@test checked_rem(typemin(T), T(1)) === T(0)
@test_throws DivideError checked_rem(typemin(T), T(0))
@test checked_rem(typemin(T), T(-1)) === T(0)
@test checked_fld(typemax(T), T(1)) === typemax(T)
@test_throws DivideError checked_fld(typemax(T), T(0))
@test checked_fld(typemax(T), T(-1)) === T(-typemax(T))
@test checked_fld(typemin(T), T(1)) === typemin(T)
@test_throws DivideError checked_fld(typemin(T), T(0))
@test_throws DivideError checked_fld(typemin(T), T(-1))
@test checked_mod(typemax(T), T(1)) === T(0)
@test_throws DivideError checked_mod(typemax(T), T(0))
@test checked_mod(typemax(T), T(-1)) === T(0)
@test checked_mod(typemin(T), T(1)) === T(0)
@test_throws DivideError checked_mod(typemin(T), T(0))
@test checked_mod(typemin(T), T(-1)) === T(0)
@test_throws DivideError checked_cld(typemax(T), T(0))
@test checked_cld(typemax(T), T(-1)) === T(-typemax(T))
@test checked_cld(typemin(T), T(1)) === typemin(T)
@test_throws DivideError checked_cld(typemin(T), T(0))
@test_throws DivideError checked_cld(typemin(T), T(-1))
end
for T in (UInt8, UInt16, UInt32, UInt64, UInt128)
# regular cases
@test checked_abs(T(0)) === T(0)
@test checked_neg(T(0)) === T(0)
@test checked_add(T(0)) === T(0)
@test checked_mul(T(0)) === T(0)
@test checked_abs(T(3)) === T(3)
@test_throws OverflowError checked_neg(T(3))
@test checked_add(T(3)) === T(3)
@test checked_mul(T(3)) === T(3)
# regular cases
@test checked_add(T(4), T(3)) === T(7)
@test checked_sub(T(4), T(3)) === T(1)
@test checked_mul(T(4), T(3)) === T(12)
# corner cases
halfmax = T(typemax(T)÷2)
halfmax_plus1 = T(halfmax+1)
sqrtmax = T(1) << T(sizeof(T)*4)
@test checked_add(typemax(T), T(0)) === typemax(T)
@test checked_add(T(0), T(0)) === T(0)
@test_throws OverflowError checked_add(typemax(T), T(1))
@test checked_add(T(0), T(1)) === T(T(0) + 1)
@test checked_add(T(0), typemax(T)) === typemax(T)
@test checked_add(T(0), T(0)) === T(0)
@test_throws OverflowError checked_add(T(1), typemax(T))
@test checked_add(T(1), T(0)) === T(T(0) + 1)
@test checked_add(typemax(T), T(0)) === typemax(T)
@test checked_add(T(0), typemax(T)) === typemax(T)
@test_throws OverflowError checked_add(halfmax_plus1, halfmax_plus1)
@test add_with_overflow(typemax(T), T(0)) === (typemax(T), false)
@test add_with_overflow(T(0), T(0)) === (T(0), false)
@test add_with_overflow(typemax(T), T(1)) === (T(0), true)
@test add_with_overflow(T(0), T(1)) === (T(T(0) + 1), false)
@test add_with_overflow(T(0), typemax(T)) === (typemax(T), false)
@test add_with_overflow(T(0), T(0)) === (T(0), false)
@test add_with_overflow(T(1), typemax(T)) === (T(0), true)
@test add_with_overflow(T(1), T(0)) === (T(T(0) + 1), false)
@test add_with_overflow(typemax(T), T(0)) === (typemax(T), false)
@test add_with_overflow(T(0), typemax(T)) === (typemax(T), false)
@test add_with_overflow(halfmax_plus1, halfmax_plus1) === (T(0), true)
@test checked_sub(typemax(T), T(0)) === typemax(T)
@test checked_sub(typemax(T), T(1)) === T(typemax(T) - 1)
@test checked_sub(T(0), T(0)) === T(0)
@test_throws OverflowError checked_sub(T(0), T(1))
@test_throws OverflowError checked_sub(T(0), typemax(T))
@test_throws OverflowError checked_sub(T(1), typemax(T))
@test checked_sub(T(0), T(0)) === T(0)
@test checked_sub(typemax(T), typemax(T)) === T(0)
@test sub_with_overflow(typemax(T), T(0)) === (typemax(T), false)
@test sub_with_overflow(typemax(T), T(1)) === (T(typemax(T) - 1), false)
@test sub_with_overflow(T(0), T(0)) === (T(0), false)
@test sub_with_overflow(T(0), T(1)) === (typemax(T), true)
@test sub_with_overflow(T(0), typemax(T)) === (T(1), true)
@test sub_with_overflow(T(1), typemax(T)) === (T(2), true)
@test sub_with_overflow(T(0), T(0)) === (T(0), false)
@test sub_with_overflow(typemax(T), typemax(T)) === (T(0), false)
@test checked_mul(typemax(T), T(0)) === T(0)
@test checked_mul(T(0), T(0)) === T(0)
@test checked_mul(typemax(T), T(1)) === typemax(T)
@test checked_mul(T(0), T(1)) === T(0)
@test_throws OverflowError checked_mul(sqrtmax, sqrtmax)
@test mul_with_overflow(typemax(T), T(0)) === (T(0), false)
@test mul_with_overflow(T(0), T(0)) === (T(0), false)
@test mul_with_overflow(typemax(T), T(1)) === (typemax(T), false)
@test mul_with_overflow(T(0), T(1)) === (T(0), false)
@test mul_with_overflow(sqrtmax, sqrtmax) === (T(0), true)
@test checked_div(typemax(T), T(1)) === typemax(T)
@test_throws DivideError checked_div(typemax(T), T(0))
@test checked_rem(typemax(T), T(1)) === T(0)
@test_throws DivideError checked_rem(typemax(T), T(0))
@test checked_fld(typemax(T), T(1)) === typemax(T)
@test_throws DivideError checked_fld(typemax(T), T(0))
@test checked_mod(typemax(T), T(1)) === T(0)
@test_throws DivideError checked_mod(typemax(T), T(0))
@test checked_cld(typemax(T), T(1)) === typemax(T)
@test_throws DivideError checked_cld(typemax(T), T(0))
end
# Boolean
@test checked_add(false) === 0
@test checked_add(true) === 1
@test checked_neg(false) === 0
@test checked_neg(true) === -1
@test checked_abs(true) === true
@test checked_abs(false) === false
@test checked_mul(false) === false
@test checked_mul(true) === true
@test checked_add(true, true) === 2
@test checked_add(true, false) === 1
@test checked_add(false, false) === 0
@test checked_add(false, true) === 1
@test checked_sub(true, true) === 0
@test checked_sub(true, false) === 1
@test checked_sub(false, false) === 0
@test checked_sub(false, true) === -1
@test checked_mul(true, false) === false
@test checked_mul(false, false) === false
@test checked_mul(true, true) === true
@test checked_mul(false, true) === false
@test checked_div(true, true) === true
@test checked_div(false, true) === false
@test_throws DivideError checked_div(true, false)
@test checked_rem(true, true) === false
@test checked_rem(false, true) === false
@test_throws DivideError checked_rem(true, false)
@test checked_fld(true, true) === true
@test checked_fld(false, true) === false
@test_throws DivideError checked_fld(true, false)
@test checked_mod(true, true) === false
@test checked_mod(false, true) === false
@test_throws DivideError checked_mod(true, false)
@test checked_cld(true, true) === true
@test checked_cld(false, true) === false
@test_throws DivideError checked_cld(true, false)
# BigInt
@test checked_abs(BigInt(-1)) == BigInt(1)
@test checked_abs(BigInt(1)) == BigInt(1)
@test checked_neg(BigInt(-1)) == BigInt(1)
@test checked_neg(BigInt(1)) == BigInt(-1)
# Additional tests
@test checked_sub(UInt(4), UInt(3)) === UInt(1)
@test_throws OverflowError checked_sub(UInt(5), UInt(6))
@test checked_mul(UInt(4), UInt(3)) === UInt(12)
@test checked_sub(Int128(-1),Int128(-2)) === Int128(1)
@test_throws OverflowError checked_mul(UInt32(2)^30, UInt32(2)^2)
@test_throws OverflowError checked_mul(UInt64(2)^62, UInt64(2)^2)
@test checked_add(UInt128(1), UInt128(2)) === UInt128(3)
@test_throws OverflowError checked_add(UInt128(2)^127, UInt128(2)^127)
@test checked_sub(UInt128(2), UInt128(1)) === UInt128(1)
@test_throws OverflowError checked_sub(UInt128(3), UInt128(4))
@test checked_mul(UInt128(3), UInt128(4)) === UInt128(12)
@test_throws OverflowError checked_mul(UInt128(2)^127, UInt128(2))