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nim-stint/tests/test_int_muldiv.nim

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# Stint
# Copyright 2018 Status Research & Development GmbH
# Licensed under either of
#
# * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
# * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
#
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import ../stint, unittest, test_helpers
template chkMul(chk: untyped, a, b, c: string, bits: int) =
chk (fromHex(StInt[bits], a) * fromHex(StInt[bits], b)) == fromHex(StInt[bits], c)
template chkDiv(chk: untyped, a, b, c: string, bits: int) =
chk (fromHex(StInt[bits], a) div fromHex(StInt[bits], b)) == fromHex(StInt[bits], c)
template chkMod(chk: untyped, a, b, c: string, bits: int) =
chk (fromHex(StInt[bits], a) mod fromHex(StInt[bits], b)) == fromHex(StInt[bits], c)
template chkMod(chk: untyped, a, b, c: int, bits: int) =
chk (stint(a, bits) mod stint(b, bits)) == stint(c, bits)
template chkDivMod(chk: untyped, a, b, c, d: string, bits: int) =
chk divmod(fromHex(StInt[bits], a), fromHex(StInt[bits], b)) == (fromHex(StInt[bits], c), fromHex(StInt[bits], d))
template testMuldiv(chk, tst: untyped) =
tst "operator `mul`":
chkMul(chk, "0", "3", "0", 8)
chkMul(chk, "1", "3", "3", 8)
chkMul(chk, "F0", "3", "D0", 8)
chkMul(chk, "FF", "FF", "1", 8)
chkMul(chk, "0", "3", "0", 16)
chkMul(chk, "1", "3", "3", 16)
chkMul(chk, "F0", "3", "2D0", 16)
chkMul(chk, "F000", "3", "D000", 16)
chkMul(chk, "FFFF", "FFFF", "1", 16)
chkMul(chk, "0", "3", "0", 32)
chkMul(chk, "1", "3", "3", 32)
chkMul(chk, "F0", "3", "2D0", 32)
chkMul(chk, "F000", "3", "2D000", 32)
chkMul(chk, "F0000000", "3", "D0000000", 32)
chkMul(chk, "FFFFFFFF", "FFFFFFFF", "1", 32)
chkMul(chk, "0", "3", "0", 64)
chkMul(chk, "1", "3", "3", 64)
chkMul(chk, "F0", "3", "2D0", 64)
chkMul(chk, "F000", "3", "2D000", 64)
chkMul(chk, "F0000000", "3", "2D0000000", 64)
chkMul(chk, "F000000000000000", "3", "D000000000000000", 64)
chkMul(chk, "FFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFF", "1", 64)
chkMul(chk, "0", "3", "0", 128)
chkMul(chk, "1", "3", "3", 128)
chkMul(chk, "F0", "3", "2D0", 128)
chkMul(chk, "F000", "3", "2D000", 128)
chkMul(chk, "F0000000", "3", "2D0000000", 128)
chkMul(chk, "F000000000000000", "3", "2D000000000000000", 128)
chkMul(chk, "F0000000000000000000000000000000", "3", "D0000000000000000000000000000000", 128)
chkMul(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "1", 128)
tst "operator `div`":
chkDiv(chk, "0", "3", "0", 8)
chkDiv(chk, "1", "3", "0", 8)
chkDiv(chk, "3", "3", "1", 8)
chkDiv(chk, "3", "1", "3", 8)
chkDiv(chk, "FF", "3", "0", 8)
chkDiv(chk, "0F", "FF", "F1", 8)
chkDiv(chk, "FF", "FF", "1", 8)
chkDiv(chk, "0", "3", "0", 16)
chkDiv(chk, "1", "3", "0", 16)
chkDiv(chk, "3", "3", "1", 16)
chkDiv(chk, "3", "1", "3", 16)
chkDiv(chk, "FF", "3", "55", 16)
chkDiv(chk, "0F", "FF", "0", 16)
chkDiv(chk, "FF", "FF", "1", 16)
chkDiv(chk, "FFFF", "3", "0", 16)
chkDiv(chk, "0F", "FFFF", "FFF1", 16)
chkDiv(chk, "FFFF", "FFFF", "1", 16)
chkDiv(chk, "0", "3", "0", 32)
chkDiv(chk, "1", "3", "0", 32)
chkDiv(chk, "3", "3", "1", 32)
chkDiv(chk, "3", "1", "3", 32)
chkDiv(chk, "FF", "3", "55", 32)
chkDiv(chk, "0F", "FF", "0", 32)
chkDiv(chk, "FF", "FF", "1", 32)
chkDiv(chk, "FFFF", "3", "5555", 32)
chkDiv(chk, "0F", "FFFFFFFF", "FFFFFFF1", 32)
chkDiv(chk, "FFFFFFFF", "FFFFFFFF", "1", 32)
chkDiv(chk, "0", "3", "0", 64)
chkDiv(chk, "1", "3", "0", 64)
chkDiv(chk, "3", "3", "1", 64)
chkDiv(chk, "3", "1", "3", 64)
chkDiv(chk, "FF", "3", "55", 64)
chkDiv(chk, "0F", "FF", "0", 64)
chkDiv(chk, "FF", "FF", "1", 64)
chkDiv(chk, "FFFF", "3", "5555", 64)
chkDiv(chk, "0F", "FFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFF1", 64)
chkDiv(chk, "FFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFF", "1", 64)
chkDiv(chk, "0", "3", "0", 128)
chkDiv(chk, "1", "3", "0", 128)
chkDiv(chk, "3", "3", "1", 128)
chkDiv(chk, "3", "1", "3", 128)
chkDiv(chk, "FF", "3", "55", 128)
chkDiv(chk, "0F", "FF", "0", 128)
chkDiv(chk, "FF", "FF", "1", 128)
chkDiv(chk, "FFFF", "3", "5555", 128)
chkDiv(chk, "0F", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF1", 128)
chkDiv(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "1", 128)
tst "operator `mod`":
chkMod(chk, "0", "3", "0", 8)
chkMod(chk, "1", "3", "1", 8)
chkMod(chk, "3", "3", "0", 8)
chkMod(chk, "3", "1", "0", 8)
chkMod(chk, "FF", "3", "FF", 8)
chkMod(chk, "FF", "4", "FF", 8)
chkMod(chk, "FF", "FF", "0", 8)
chkMod(chk, "0F", "FC", "3", 8)
chkMod(chk, "0", "3", "0", 16)
chkMod(chk, "1", "3", "1", 16)
chkMod(chk, "3", "3", "0", 16)
chkMod(chk, "3", "1", "0", 16)
chkMod(chk, "FFFF", "3", "FFFF", 16)
chkMod(chk, "FFFF", "4", "FFFF", 16)
chkMod(chk, "FFFF", "FFFF", "0", 16)
chkMod(chk, "0F", "FFFC", "3", 16)
chkMod(chk, "0", "3", "0", 32)
chkMod(chk, "1", "3", "1", 32)
chkMod(chk, "3", "3", "0", 32)
chkMod(chk, "3", "1", "0", 32)
chkMod(chk, "FFFFFFFF", "3", "FFFFFFFF", 32)
chkMod(chk, "FFFFFFFF", "4", "FFFFFFFF", 32)
chkMod(chk, "FFFFFFFF", "FFFFFFFF", "0", 32)
chkMod(chk, "0F", "FFFFFFFC", "3", 32)
chkMod(chk, "0", "3", "0", 64)
chkMod(chk, "1", "3", "1", 64)
chkMod(chk, "3", "3", "0", 64)
chkMod(chk, "3", "1", "0", 64)
chkMod(chk, "FFFFFFFFFFFFFFFF", "3", "FFFFFFFFFFFFFFFF", 64)
chkMod(chk, "FFFFFFFFFFFFFFFF", "4", "FFFFFFFFFFFFFFFF", 64)
chkMod(chk, "FFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFF", "0", 64)
chkMod(chk, "0F", "FFFFFFFFFFFFFFFC", "3", 64)
chkMod(chk, "0", "3", "0", 128)
chkMod(chk, "1", "3", "1", 128)
chkMod(chk, "3", "3", "0", 128)
chkMod(chk, "3", "1", "0", 128)
chkMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "3", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 128)
chkMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "4", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 128)
chkMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "0", 128)
chkMod(chk, "0F", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", "3", 128)
tst "operator `divmod`":
chkDivMod(chk, "0", "3", "0", "0", 8)
chkDivMod(chk, "1", "3", "0", "1", 8)
chkDivMod(chk, "3", "3", "1", "0", 8)
chkDivMod(chk, "3", "1", "3", "0", 8)
chkDivMod(chk, "FF", "3", "0", "FF", 8)
chkDivMod(chk, "FF", "4", "0", "FF", 8)
chkDivMod(chk, "FF", "FF", "1", "0", 8)
chkDivMod(chk, "0F", "FC", "FD", "3", 8)
chkDivMod(chk, "0", "3", "0", "0", 16)
chkDivMod(chk, "1", "3", "0", "1", 16)
chkDivMod(chk, "3", "3", "1", "0", 16)
chkDivMod(chk, "3", "1", "3", "0", 16)
chkDivMod(chk, "FFFF", "3", "0", "FFFF", 16)
chkDivMod(chk, "FFFF", "4", "0", "FFFF", 16)
chkDivMod(chk, "FFFF", "FFFF", "1", "0", 16)
chkDivMod(chk, "0F", "FFFC", "FFFD", "3", 16)
chkDivMod(chk, "0", "3", "0", "0", 32)
chkDivMod(chk, "1", "3", "0", "1", 32)
chkDivMod(chk, "3", "3", "1", "0", 32)
chkDivMod(chk, "3", "1", "3", "0", 32)
chkDivMod(chk, "FFFFFFFF", "3", "0", "FFFFFFFF", 32)
chkDivMod(chk, "FFFFFFFF", "4", "0", "FFFFFFFF", 32)
chkDivMod(chk, "FFFFFFFF", "FFFFFFFF", "1", "0", 32)
chkDivMod(chk, "0F", "FFFFFFFC", "FFFFFFFD", "3", 32)
chkDivMod(chk, "0", "3", "0", "0", 64)
chkDivMod(chk, "1", "3", "0", "1", 64)
chkDivMod(chk, "3", "3", "1", "0", 64)
chkDivMod(chk, "3", "1", "3", "0", 64)
chkDivMod(chk, "FFFFFFFFFFFFFFFF", "3", "0", "FFFFFFFFFFFFFFFF", 64)
chkDivMod(chk, "FFFFFFFFFFFFFFFF", "4", "0", "FFFFFFFFFFFFFFFF", 64)
chkDivMod(chk, "FFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFF", "1", "0", 64)
chkDivMod(chk, "0F", "FFFFFFFFFFFFFFFC", "FFFFFFFFFFFFFFFD", "3", 64)
chkDivMod(chk, "0", "3", "0", "0", 128)
chkDivMod(chk, "1", "3", "0", "1", 128)
chkDivMod(chk, "3", "3", "1", "0", 128)
chkDivMod(chk, "3", "1", "3", "0", 128)
chkDivMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "3", "0", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 128)
chkDivMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "4", "0", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", 128)
chkDivMod(chk, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "1", "0", 128)
chkDivMod(chk, "0F", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD", "3", 128)
tst "issues with Nim v1.0.2":
block:
let x = -2.stint(256)
let y = 3200566678774828.stint(256)
let z = -6401133357549656.stint(256)
chk x * y == z
chkMod(chk, -3, 7, -3, 64)
chkMod(chk, -3, 5, -3, 64)
chkMod(chk, -13, 5, -3, 64)
chkMod(chk, 7, 5, 2, 64)
chkMod(chk, -7, 5, -2, 64)
chkMod(chk, 7, -5, 2, 64)
chkMod(chk, -7, -5, -2, 64)
chkMod(chk, 2, 5, 2, 64)
chkMod(chk, -2, 5, -2, 64)
chkMod(chk, 2, -5, 2, 64)
chkMod(chk, -2, -5, -2, 64)
static:
testMuldiv(ctCheck, ctTest)
suite "Wider signed int muldiv coverage":
testMuldiv(check, test)
suite "Testing signed int multiplication implementation":
test "Multiplication with result fitting in low half":
let a = 10000.stint(64)
let b = 10000.stint(64)
check: cast[int64](a*b) == 100_000_000'i64 # need 27-bits
test "Multiplication with result overflowing low half":
let a = 1_000_000.stint(64)
let b = 1_000_000.stint(64)
check: cast[int64](a*b) == 1_000_000_000_000'i64 # need 40 bits
test "Multiplication with result fitting in low half - opposite signs":
let a = -10000.stint(64)
let b = 10000.stint(64)
check:
cast[int64](a*b) == -100_000_000'i64 # need 27-bits
cast[int64](b*a) == -100_000_000'i64
test "Multiplication with result overflowing low half - opposite signs":
let a = -1_000_000.stint(64)
let b = 1_000_000.stint(64)
check:
cast[int64](a*b) == -1_000_000_000_000'i64 # need 40 bits
cast[int64](b*a) == -1_000_000_000_000'i64
test "Multiplication with result fitting in low half - both negative":
let a = -10000.stint(64)
let b = -10000.stint(64)
check: cast[int64](a*b) == 100_000_000'i64 # need 27-bits
test "Multiplication with result overflowing low half - both negative":
let a = -1_000_000.stint(64)
let b = -1_000_000.stint(64)
check: cast[int64](a*b) == 1_000_000_000_000'i64 # need 40 bits
suite "Testing signed int division and modulo implementation":
test "Divmod(100, 13) returns the correct result":
let a = 100.stint(64)
let b = 13.stint(64)
let qr = divmod(a, b)
check: cast[int64](qr.quot) == 7'i64
check: cast[int64](qr.rem) == 9'i64
test "Divmod(-100, 13) returns the correct result":
let a = -100.stint(64)
let b = 13.stint(64)
let qr = divmod(a, b)
check: cast[int64](qr.quot) == -100'i64 div 13
check: cast[int64](qr.rem) == -100'i64 mod 13
test "Divmod(100, -13) returns the correct result":
let a = 100.stint(64)
let b = -13.stint(64)
let qr = divmod(a, b)
check: cast[int64](qr.quot) == 100'i64 div -13
check: cast[int64](qr.rem) == 100'i64 mod -13
test "Divmod(-100, -13) returns the correct result":
let a = -100.stint(64)
let b = -13.stint(64)
let qr = divmod(a, b)
check: cast[int64](qr.quot) == -100'i64 div -13
check: cast[int64](qr.rem) == -100'i64 mod -13
# test "Divmod(2^64, 3) returns the correct result":
# let a = 1.stint(128) shl 64
# let b = 3.stint(128)
# let qr = divmod(a, b)
# let q = cast[UintImpl[uint64]](qr.quot)
# let r = cast[UintImpl[uint64]](qr.rem)
# check: q.lo == 6148914691236517205'u64
# check: q.hi == 0'u64
# check: r.lo == 1'u64
# check: r.hi == 0'u64
test "Divmod(1234567891234567890, 10) returns the correct result":
let a = cast[StInt[64]](1234567891234567890'i64)
let b = cast[StInt[64]](10'i64)
let qr = divmod(a, b)
let q = cast[int64](qr.quot)
let r = cast[int64](qr.rem)
check: q == 123456789123456789'i64
check: r == 0'i64
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