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nim-stint
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Rename the library to Stint (#26)

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Mamy Ratsimbazafy 2018-04-25 12:52:00 +02:00 committed by GitHub
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22 changed files with 252 additions and 243 deletions
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27
README.md
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@ -1,20 +1,29 @@
# Mpint (Multi-precision integers)
# Stint (Stack-based multiprecision integers)
[![Build Status (Travis)](https://img.shields.io/travis/status-im/mpint/master.svg?label=Linux%20/%20macOS "Linux/macOS build status (Travis)")](https://travis-ci.org/status-im/mpint)
[![Build Status (Travis)](https://img.shields.io/travis/status-im/stint/master.svg?label=Linux%20/%20macOS "Linux/macOS build status (Travis)")](https://travis-ci.org/status-im/stint)
[![License: Apache](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://opensource.org/licenses/Apache-2.0)
[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
![Stability: experimental](https://img.shields.io/badge/stability-experimental-orange.svg)
A fast and portable multi-precision integer library in pure Nim
A fast and portable stack-based multi-precision integer library in pure Nim
Main focus:
- no heap/dynamic allocation
- uint256 for cryptographic and ethereum blockchain usage.
- ARM portability for usage on mobile phones
- Portability
- 32 and 64 bit arch
- ARM for usage on mobile phones
- Additionally RISC-V and MIPS for open hardware and low power IoT devices.
- Speed, library is carefully tuned to produce the best assembly given the current compilers.
However, the library itself does not resort to assembly for portability.
- No heap/dynamic allocation
- Ethereum applications
- Uint256/Int256 for Ethereum Virtual Machine usage.
- Uint2048 for Ethereum Bloom filters
- Ease of use:
- casting to and from array of bytes
- converting to and from Hex
- converting to and from decimal strings
- Use traditional `+`, `-`, `+=`, etc operators like on native types
- Representation of numbers in memory is the exact same as native types and endianness aware.
- In practice that means that interfacing with binary blobs representing numbers from cryptographic libraries can be done with a `cast` if it represents a Uint256, Uint512, Uint1024, Uint2048.
- converting to and from Hex
- converting to and from decimal strings
## License

6
benchmarks/bench_mod.nim
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@ -18,10 +18,10 @@ echo "Warmup: " & $(stop - start) & "s"
start = cpuTime()
block:
var foo = 123.initMpUint(256)
var foo = 123.u(256)
for i in 0 ..< 10_000_000:
foo += i.initMpUint(256) * i.initMpUint(256) mod 456.initMpUint(256)
foo = foo mod 789.initMpUint(256)
foo += i.u(256) * i.u(256) mod 456.u(256)
foo = foo mod 789.u(256)
stop = cpuTime()
echo "Library: " & $(stop - start) & "s"

2
src/debug/debugutils.nim
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@ -27,7 +27,7 @@ func tohexBE*[T: uint8 or uint16 or uint32 or uint64](x: T): string =
for i in 0 ..< T.sizeof:
result.add toHex(bytes[i])
func tohexBE*(x: MpUintImpl): string =
func tohexBE*(x: UintImpl): string =
## Stringify an uint to hex, Most significant byte on the left
## i.e. a (2.uint128)^64 + 1 will be 0000000100000001

8
src/private/as_words.nim
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@ -60,7 +60,7 @@ proc isUint(x: NimNode): static[bool] =
elif eqIdent(x, "uint8"): true
else: false
macro asWords*[T](n: MpUintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
macro asWords*[T](n: UintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
## Iterates over n, as an array of words.
## Input:
## - n: The Multiprecision int
@ -96,7 +96,7 @@ macro asWords*[T](n: MpUintImpl[T], ignoreEndianness: static[bool], loopBody: un
else:
assert false, "Not implemented"
macro asWordsZip*[T](x, y: MpUintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
macro asWordsZip*[T](x, y: UintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
## Iterates over x and y, as an array of words.
## Input:
## - x, y: The multiprecision ints
@ -155,7 +155,7 @@ macro asWordsZip*[T](x, y: MpUintImpl[T], ignoreEndianness: static[bool], loopBo
for `idx` in countdown(`inner_x`[].len - 1, 0):
`replacedAST`
macro m_asWordsZip*[T](m: var MpUintImpl[T], x: MpUintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
macro m_asWordsZip*[T](m: var UintImpl[T], x: UintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
## Iterates over a mutable int m and x as an array of words.
## returning a !! Pointer !! of the proper type to m.
## Input:
@ -217,7 +217,7 @@ macro m_asWordsZip*[T](m: var MpUintImpl[T], x: MpUintImpl[T], ignoreEndianness:
`replacedAST`
macro m_asWordsZip*[T](m: var MpUintImpl[T], x, y: MpUintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
macro m_asWordsZip*[T](m: var UintImpl[T], x, y: UintImpl[T], ignoreEndianness: static[bool], loopBody: untyped): untyped =
## Iterates over a mutable int m and x as an array of words.
## returning a !! Pointer !! of the proper type to m.
## Input:

2
src/private/bithacks.nim
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@ -14,7 +14,7 @@ export stdlib_bitops
# MpInt rely on no undefined behaviour as often we scan 0. (if 1 is stored in a uint128 for example)
# Also countLeadingZeroBits must return the size of the type and not 0 like in the stdlib
func countLeadingZeroBits*(n: MpUintImpl): int {.inline.} =
func countLeadingZeroBits*(n: UintImpl): int {.inline.} =
## Returns the number of leading zero bits in integer.
const maxHalfRepr = getSize(n) div 2

26
src/private/conversion.nim
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@ -10,7 +10,7 @@
import ./uint_type,
macros, typetraits
func initMpUintImpl*[InType, OutType](x: InType, _: typedesc[OutType]): OutType {.inline.} =
func initUintImpl*[InType, OutType](x: InType, _: typedesc[OutType]): OutType {.inline.} =
const
size_in = getSize(x)
@ -27,12 +27,12 @@ func initMpUintImpl*[InType, OutType](x: InType, _: typedesc[OutType]): OutType
elif size_in == size_out:
result = cast[type result](x)
else:
result.lo = initMpUintImpl(x, type result.lo)
result.lo = initUintImpl(x, type result.lo)
func toSubtype*[T: SomeInteger](b: bool, _: typedesc[T]): T {.inline.}=
b.T
func toSubtype*[T: MpUintImpl](b: bool, _: typedesc[T]): T {.inline.}=
func toSubtype*[T: UintImpl](b: bool, _: typedesc[T]): T {.inline.}=
type SubTy = type result.lo
result.lo = toSubtype(b, SubTy)
@ -49,12 +49,12 @@ func one*[T: BaseUint](_: typedesc[T]): T {.inline.}=
else:
r_ptr[r_ptr[].len - 1] = 1
func toUint*(n: MpUIntImpl): auto {.inline.}=
func toUint*(n: UintImpl): auto {.inline.}=
## Casts a multiprecision integer to an uint of the same size
# TODO: uint128 support
when n.sizeof > 8:
raise newException("Unreachable. You are trying to cast a MpUint with more than 64-bit of precision")
raise newException("Unreachable. You are trying to cast a StUint with more than 64-bit of precision")
elif n.sizeof == 8:
cast[uint64](n)
elif n.sizeof == 4:
@ -62,14 +62,14 @@ func toUint*(n: MpUIntImpl): auto {.inline.}=
elif n.sizeof == 2:
cast[uint16](n)
else:
raise newException("Unreachable. MpUInt must be 16-bit minimum and a power of 2")
raise newException("Unreachable. StUint must be 16-bit minimum and a power of 2")
func toUint*(n: SomeUnsignedInt): SomeUnsignedInt {.inline.}=
## No-op overload of multi-precision int casting
n
func asDoubleUint*(n: BaseUint): auto {.inline.} =
## Convert an integer or MpUint to an uint with double the size
## Convert an integer or StUint to an uint with double the size
type Double = (
when n.sizeof == 4: uint64
@ -80,17 +80,17 @@ func asDoubleUint*(n: BaseUint): auto {.inline.} =
n.toUint.Double
func toMpUintImpl*(n: uint16|uint32|uint64): auto {.inline.} =
## Cast an integer to the corresponding size MpUintImpl
func toUintImpl*(n: uint16|uint32|uint64): auto {.inline.} =
## Cast an integer to the corresponding size UintImpl
# Sometimes direct casting doesn't work and we must cast through a pointer
when n is uint64:
return (cast[ptr [MpUintImpl[uint32]]](unsafeAddr n))[]
return (cast[ptr [UintImpl[uint32]]](unsafeAddr n))[]
elif n is uint32:
return (cast[ptr [MpUintImpl[uint16]]](unsafeAddr n))[]
return (cast[ptr [UintImpl[uint16]]](unsafeAddr n))[]
elif n is uint16:
return (cast[ptr [MpUintImpl[uint8]]](unsafeAddr n))[]
return (cast[ptr [UintImpl[uint8]]](unsafeAddr n))[]
func toMpUintImpl*(n: MpUintImpl): MpUintImpl {.inline.} =
func toUintImpl*(n: UintImpl): UintImpl {.inline.} =
## No op
n

8
src/private/uint_addsub.nim
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@ -14,25 +14,25 @@ import ./bithacks, ./conversion,
# ############ Addition & Substraction ############ #
proc `+=`*(x: var MpUintImpl, y: MpUintImpl) {.noSideEffect, inline.}=
proc `+=`*(x: var UintImpl, y: UintImpl) {.noSideEffect, inline.}=
## In-place addition for multi-precision unsigned int
type SubTy = type x.lo
x.lo += y.lo
x.hi += (x.lo < y.lo).toSubtype(SubTy) + y.hi
proc `+`*(x, y: MpUintImpl): MpUintImpl {.noSideEffect, noInit, inline.}=
proc `+`*(x, y: UintImpl): UintImpl {.noSideEffect, noInit, inline.}=
# Addition for multi-precision unsigned int
result = x
result += y
proc `-`*(x, y: MpUintImpl): MpUintImpl {.noSideEffect, noInit, inline.}=
proc `-`*(x, y: UintImpl): UintImpl {.noSideEffect, noInit, inline.}=
# Substraction for multi-precision unsigned int
type SubTy = type x.lo
result.lo = x.lo - y.lo
result.hi = x.hi - y.hi - (x.lo < y.lo).toSubtype(SubTy)
proc `-=`*(x: var MpUintImpl, y: MpUintImpl) {.noSideEffect, inline.}=
proc `-=`*(x: var UintImpl, y: UintImpl) {.noSideEffect, inline.}=
## In-place substraction for multi-precision unsigned int
x = x - y

14
src/private/uint_bitwise_ops.nim
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@ -10,30 +10,30 @@
import ./uint_type, ./as_words
func `not`*(x: MpUintImpl): MpUintImpl {.noInit, inline.}=
func `not`*(x: UintImpl): UintImpl {.noInit, inline.}=
## Bitwise complement of unsigned integer x
m_asWordsZip(result, x, ignoreEndianness = true):
result = not x
func `or`*(x, y: MpUintImpl): MpUintImpl {.noInit, inline.}=
func `or`*(x, y: UintImpl): UintImpl {.noInit, inline.}=
## `Bitwise or` of numbers x and y
m_asWordsZip(result, x, y, ignoreEndianness = true):
result = x or y
func `and`*(x, y: MpUintImpl): MpUintImpl {.noInit, inline.}=
func `and`*(x, y: UintImpl): UintImpl {.noInit, inline.}=
## `Bitwise and` of numbers x and y
m_asWordsZip(result, x, y, ignoreEndianness = true):
result = x and y
func `xor`*(x, y: MpUintImpl): MpUintImpl {.noInit, inline.}=
func `xor`*(x, y: UintImpl): UintImpl {.noInit, inline.}=
## `Bitwise xor` of numbers x and y
m_asWordsZip(result, x, y, ignoreEndianness = true):
result = x xor y
func `shr`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.inline.}
func `shr`*(x: UintImpl, y: SomeInteger): UintImpl {.inline.}
# Forward declaration
func `shl`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.inline.}=
func `shl`*(x: UintImpl, y: SomeInteger): UintImpl {.inline.}=
## Compute the `shift left` operation of x and y
# Note: inlining this poses codegen/aliasing issue when doing `x = x shl 1`
@ -51,7 +51,7 @@ func `shl`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.inline.}=
else:
result.hi = x.lo shl (y - halfSize)
func `shr`*(x: MpUintImpl, y: SomeInteger): MpUintImpl {.inline.}=
func `shr`*(x: UintImpl, y: SomeInteger): UintImpl {.inline.}=
## Compute the `shift right` operation of x and y
const halfSize = getSize(x) div 2

8
src/private/uint_comparison.nim
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@ -12,27 +12,27 @@ import ./uint_type, ./as_words
func isZero*(n: SomeUnsignedInt): bool {.inline.} =
n == 0
func isZero*(n: MpUintImpl): bool {.inline.} =
func isZero*(n: UintImpl): bool {.inline.} =
asWords(n, ignoreEndianness = true):
if n != 0:
return false
return true
func `<`*(x, y: MpUintImpl): bool {.inline.}=
func `<`*(x, y: UintImpl): bool {.inline.}=
# Lower comparison for multi-precision integers
asWordsZip(x, y, ignoreEndianness = false):
if x != y:
return x < y
return false # they're equal
func `==`*(x, y: MpUintImpl): bool {.inline.}=
func `==`*(x, y: UintImpl): bool {.inline.}=
# Equal comparison for multi-precision integers
asWordsZip(x, y, ignoreEndianness = true):
if x != y:
return false
return true # they're equal
func `<=`*(x, y: MpUintImpl): bool {.inline.}=
func `<=`*(x, y: UintImpl): bool {.inline.}=
# Lower or equal comparison for multi-precision integers
asWordsZip(x, y, ignoreEndianness = false):
if x != y:

44
src/private/uint_div.nim
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@ -45,24 +45,24 @@ import ./bithacks, ./conversion,
###################################################################################################################
func div2n1n[T: SomeunsignedInt](q, r: var T, n_hi, n_lo, d: T)
func div2n1n(q, r: var MpUintImpl, ah, al, b: MpUintImpl)
func div2n1n(q, r: var UintImpl, ah, al, b: UintImpl)
# Forward declaration
proc divmod*(x, y: SomeInteger): tuple[quot, rem: SomeInteger] {.noSideEffect, inline.}=
# hopefully the compiler fuse that in a single op
(x div y, x mod y)
func divmod*[T](x, y: MpUintImpl[T]): tuple[quot, rem: MpUintImpl[T]]
func divmod*[T](x, y: UintImpl[T]): tuple[quot, rem: UintImpl[T]]
# Forward declaration
func div3n2n[T]( q: var MpUintImpl[T],
r: var MpUintImpl[MpUintImpl[T]],
a2, a1, a0: MpUintImpl[T],
b: MpUintImpl[MpUintImpl[T]]) =
func div3n2n[T]( q: var UintImpl[T],
r: var UintImpl[UintImpl[T]],
a2, a1, a0: UintImpl[T],
b: UintImpl[UintImpl[T]]) =
var
c: MpUintImpl[T]
d: MpUintImpl[MpUintImpl[T]]
c: UintImpl[T]
d: UintImpl[UintImpl[T]]
carry: bool
if a2 < b.hi:
@ -74,7 +74,7 @@ func div3n2n[T]( q: var MpUintImpl[T],
carry = true
extPrecMul[T](d, q, b.lo)
let ca0 = MpUintImpl[type c](hi: c, lo: a0)
let ca0 = UintImpl[type c](hi: c, lo: a0)
r = ca0 - d
@ -89,13 +89,13 @@ func div3n2n[T]( q: var MpUintImpl[T],
proc div3n2n[T: SomeUnsignedInt](
q: var T,
r: var MpUintImpl[T],
r: var UintImpl[T],
a2, a1, a0: T,
b: MpUintImpl[T]) =
b: UintImpl[T]) =
var
c: T
d: MpUintImpl[T]
d: UintImpl[T]
carry: bool
if a2 < b.hi:
@ -108,7 +108,7 @@ proc div3n2n[T: SomeUnsignedInt](
carry = true
extPrecMul[T](d, q, b.lo)
let ca0 = MpUintImpl[T](hi: c, lo: a0)
let ca0 = UintImpl[T](hi: c, lo: a0)
r = ca0 - d
if (not carry) and d > ca0:
@ -120,11 +120,11 @@ proc div3n2n[T: SomeUnsignedInt](
dec q
r += b
func div2n1n(q, r: var MpUintImpl, ah, al, b: MpUintImpl) =
func div2n1n(q, r: var UintImpl, ah, al, b: UintImpl) =
# assert countLeadingZeroBits(b) == 0, "Divisor was not normalized"
var s: MpUintImpl
var s: UintImpl
div3n2n(q.hi, s, ah.hi, ah.lo, al.hi, b)
div3n2n(q.lo, r, s.hi, s.lo, al.lo, b)
@ -168,7 +168,7 @@ func div2n1n[T: SomeunsignedInt](q, r: var T, n_hi, n_lo, d: T) =
q = (q1 shl halfSize) or q2
r = r2
func divmodBZ[T](x, y: MpUintImpl[T], q, r: var MpUintImpl[T])=
func divmodBZ[T](x, y: UintImpl[T], q, r: var UintImpl[T])=
assert y.isZero.not() # This should be checked on release mode in the divmod caller proc
@ -209,7 +209,7 @@ func divmodBZ[T](x, y: MpUintImpl[T], q, r: var MpUintImpl[T])=
let clz = countLeadingZeroBits(y)
let
xx = MpUintImpl[type x](lo: x) shl clz
xx = UintImpl[type x](lo: x) shl clz
yy = y shl clz
# Compute
@ -218,7 +218,7 @@ func divmodBZ[T](x, y: MpUintImpl[T], q, r: var MpUintImpl[T])=
# Undo normalization
r = r shr clz
func divmodBS(x, y: MpUintImpl, q, r: var MpuintImpl) =
func divmodBS(x, y: UintImpl, q, r: var UintImpl) =
## Division for multi-precision unsigned uint
## Implementation through binary shift division
@ -244,7 +244,7 @@ func divmodBS(x, y: MpUintImpl, q, r: var MpuintImpl) =
const BinaryShiftThreshold = 8 # If the difference in bit-length is below 8
# binary shift is probably faster
func divmod*[T](x, y: MpUintImpl[T]): tuple[quot, rem: MpUintImpl[T]]=
func divmod*[T](x, y: UintImpl[T]): tuple[quot, rem: UintImpl[T]]=
let x_clz = x.countLeadingZeroBits
let y_clz = y.countLeadingZeroBits
@ -266,7 +266,7 @@ func divmod*[T](x, y: MpUintImpl[T]): tuple[quot, rem: MpUintImpl[T]]=
# It is a bit tricky with recursive types. An empty n.lo means 0 or sizeof(n.lo)
let y_ctz = getSize(y) - y_clz - 1
result.quot = x shr y_ctz
result.rem = y_ctz.initMpUintImpl(MpUintImpl[T])
result.rem = y_ctz.initUintImpl(UintImpl[T])
result.rem = result.rem and x
elif x == y:
result.quot.lo = one(T)
@ -277,11 +277,11 @@ func divmod*[T](x, y: MpUintImpl[T]): tuple[quot, rem: MpUintImpl[T]]=
else:
divmodBZ(x, y, result.quot, result.rem)
func `div`*(x, y: MpUintImpl): MpUintImpl {.inline.} =
func `div`*(x, y: UintImpl): UintImpl {.inline.} =
## Division operation for multi-precision unsigned uint
divmod(x,y).quot
func `mod`*(x, y: MpUintImpl): MpUintImpl {.inline.} =
func `mod`*(x, y: UintImpl): UintImpl {.inline.} =
## Division operation for multi-precision unsigned uint
divmod(x,y).rem

24
src/private/uint_mul.nim
View File

@ -26,24 +26,24 @@ func hi[T:SomeUnsignedInt](x: T): T {.inline.} =
p = T.sizeof * 8 div 2
result = x shr p
# No generic, somehow Nim is given ambiguous call with the T: MpUintImpl overload
func extPrecMul*(result: var MpUintImpl[uint8], x, y: uint8) =
# No generic, somehow Nim is given ambiguous call with the T: UintImpl overload
func extPrecMul*(result: var UintImpl[uint8], x, y: uint8) =
## Extended precision multiplication
result = cast[type result](x.asDoubleUint * y.asDoubleUint)
func extPrecMul*(result: var MpUintImpl[uint16], x, y: uint16) =
func extPrecMul*(result: var UintImpl[uint16], x, y: uint16) =
## Extended precision multiplication
result = cast[type result](x.asDoubleUint * y.asDoubleUint)
func extPrecMul*(result: var MpUintImpl[uint32], x, y: uint32) =
func extPrecMul*(result: var UintImpl[uint32], x, y: uint32) =
## Extended precision multiplication
result = cast[type result](x.asDoubleUint * y.asDoubleUint)
func extPrecAddMul[T: uint8 or uint16 or uint32](result: var MpUintImpl[T], x, y: T) =
func extPrecAddMul[T: uint8 or uint16 or uint32](result: var UintImpl[T], x, y: T) =
## Extended precision fused in-place addition & multiplication
result += cast[type result](x.asDoubleUint * y.asDoubleUint)
template extPrecMulImpl(result: var MpUintImpl[uint64], op: untyped, u, v: uint64) =
template extPrecMulImpl(result: var UintImpl[uint64], op: untyped, u, v: uint64) =
const
p = 64 div 2
base = 1 shl p
@ -70,15 +70,15 @@ template extPrecMulImpl(result: var MpUintImpl[uint64], op: untyped, u, v: uint6
op(result.hi, x3 + x1.hi)
op(result.lo, (x1 shl p) or x0.lo)
func extPrecMul*(result: var MpUintImpl[uint64], u, v: uint64) =
func extPrecMul*(result: var UintImpl[uint64], u, v: uint64) =
## Extended precision multiplication
extPrecMulImpl(result, `=`, u, v)
func extPrecAddMul(result: var MpUintImpl[uint64], u, v: uint64) =
func extPrecAddMul(result: var UintImpl[uint64], u, v: uint64) =
## Extended precision fused in-place addition & multiplication
extPrecMulImpl(result, `+=`, u, v)
func extPrecMul*[T](result: var MpUintImpl[MpUintImpl[T]], x, y: MpUintImpl[T]) =
func extPrecMul*[T](result: var UintImpl[UintImpl[T]], x, y: UintImpl[T]) =
# See details at
# https://en.wikipedia.org/wiki/Karatsuba_algorithm
# https://locklessinc.com/articles/256bit_arithmetic/
@ -93,7 +93,7 @@ func extPrecMul*[T](result: var MpUintImpl[MpUintImpl[T]], x, y: MpUintImpl[T])
# and introduce branching
# - More total operations means more register moves
var z1: MpUintImpl[T]
var z1: UintImpl[T]
# Low part - z0
extPrecMul(result.lo, x.lo, y.lo)
@ -112,9 +112,9 @@ func extPrecMul*[T](result: var MpUintImpl[MpUintImpl[T]], x, y: MpUintImpl[T])
# Finalize low part
result.lo.hi += z1.lo
if result.lo.hi < z1.lo:
result.hi += one(MpUintImpl[T])
result.hi += one(UintImpl[T])
func `*`*[T](x, y: MpUintImpl[T]): MpUintImpl[T] {.inline.}=
func `*`*[T](x, y: UintImpl[T]): UintImpl[T] {.inline.}=
## Multiplication for multi-precision unsigned uint
#
# For our representation, it is similar to school grade multiplication

34
src/private/uint_type.nim
View File

@ -12,34 +12,34 @@
import macros
# The macro getMpUintImpl must be exported
# The macro getUintImpl must be exported
when defined(mpint_test):
macro getMpUintImpl*(bits: static[int]): untyped =
# Test version, mpuint[64] = 2 uint32. Test the logic of the library
macro getUintImpl*(bits: static[int]): untyped =
# Test version, StUint[64] = 2 uint32. Test the logic of the library
assert (bits and (bits-1)) == 0, $bits & " is not a power of 2"
assert bits >= 16, "The number of bits in a should be greater or equal to 16"
if bits >= 128:
let inner = getAST(getMpUintImpl(bits div 2))
result = newTree(nnkBracketExpr, ident("MpUintImpl"), inner)
let inner = getAST(getUintImpl(bits div 2))
result = newTree(nnkBracketExpr, ident("UintImpl"), inner)
elif bits == 64:
result = newTree(nnkBracketExpr, ident("MpUintImpl"), ident("uint32"))
result = newTree(nnkBracketExpr, ident("UintImpl"), ident("uint32"))
elif bits == 32:
result = newTree(nnkBracketExpr, ident("MpUintImpl"), ident("uint16"))
result = newTree(nnkBracketExpr, ident("UintImpl"), ident("uint16"))
elif bits == 16:
result = newTree(nnkBracketExpr, ident("MpUintImpl"), ident("uint8"))
result = newTree(nnkBracketExpr, ident("UintImpl"), ident("uint8"))
else:
error "Fatal: unreachable"
else:
macro getMpUintImpl*(bits: static[int]): untyped =
# Release version, mpuint[64] = uint64.
macro getUintImpl*(bits: static[int]): untyped =
# Release version, StUint[64] = uint64.
assert (bits and (bits-1)) == 0, $bits & " is not a power of 2"
assert bits >= 8, "The number of bits in a should be greater or equal to 8"
if bits >= 128:
let inner = getAST(getMpUintImpl(bits div 2))
result = newTree(nnkBracketExpr, ident("MpUintImpl"), inner)
let inner = getAST(getUintImpl(bits div 2))
result = newTree(nnkBracketExpr, ident("UintImpl"), inner)
elif bits == 64:
result = ident("uint64")
elif bits == 32:
@ -59,7 +59,7 @@ proc getSize*(x: NimNode): static[int] =
var node = x.getTypeInst
while node.kind == nnkBracketExpr:
assert eqIdent(node[0], "MpuintImpl")
assert eqIdent(node[0], "UintImpl")
multiplier *= 2
node = node[1]
@ -86,15 +86,15 @@ type
# ### Private ### #
# If this is not in the same type section
# the compiler has trouble
BaseUint* = MpUintImpl or SomeUnsignedInt
BaseUint* = UintImpl or SomeUnsignedInt
MpUintImpl*[Baseuint] = object
UintImpl*[Baseuint] = object
when system.cpuEndian == littleEndian:
lo*, hi*: BaseUint
else:
hi*, lo*: BaseUint
# ### Private ### #
MpUint*[bits: static[int]] = object
data*: getMpUintImpl(bits)
StUint*[bits: static[int]] = object
data*: getUintImpl(bits)
# wrapped in object to avoid recursive calls

8
src/uint_init.nim
View File

@ -13,17 +13,17 @@ import ./private/uint_type
import typetraits
func initMpUint*[T: SomeInteger](n: T, bits: static[int]): MpUint[bits] {.inline.}=
func u*[T: SomeInteger](n: T, bits: static[int]): StUint[bits] {.inline.}=
assert n >= 0.T
when result.data is MpuintImpl:
when result.data is UintImpl:
when getSize(n) > bits:
# To avoid a costly runtime check, we refuse storing into MpUint types smaller
# To avoid a costly runtime check, we refuse storing into StUint types smaller
# than the input type.
raise newException(ValueError, "Input " & $n & " (" & $T &
") cannot be stored in a multi-precision " &
$bits & "-bit integer." &
"\nUse a smaller input type instead. This is a compile-time check" &
" to avoid a costly run-time bit_length check at each MpUint initialization.")
" to avoid a costly run-time bit_length check at each StUint initialization.")
else:
let r_ptr = cast[ptr array[bits div (sizeof(T) * 8), T]](result.addr)
when system.cpuEndian == littleEndian:

46
src/uint_public.nim
View File

@ -8,55 +8,55 @@
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import ./private/uint_type, macros
export MpUint, MpUintImpl, getMpUintImpl # TODO remove the need to export MpUintImpl and this macro
export StUint, UintImpl, getUintImpl # TODO remove the need to export UintImpl and this macro
type
UInt128* = MpUint[128]
UInt256* = MpUint[256]
UInt128* = StUint[128]
UInt256* = StUint[256]
template make_conv(conv_name: untyped, size: int): untyped =
func `convname`*(n: SomeInteger): MpUint[size] {.inline, noInit.}=
n.initMpUint(size)
func `convname`*(n: SomeInteger): StUint[size] {.inline, noInit.}=
n.u(size)
make_conv(u128, 128)
make_conv(u256, 256)
template make_unary(op, ResultTy): untyped =
func `op`*(x: MpUint): ResultTy {.noInit, inline.} =
when ResultTy is MpUint:
func `op`*(x: StUint): ResultTy {.noInit, inline.} =
when ResultTy is StUint:
result.data = op(x.data)
else:
op(x.data)
export op
template make_binary(op, ResultTy): untyped =
func `op`*(x, y: MpUint): ResultTy {.noInit, inline.} =
when ResultTy is MpUint:
func `op`*(x, y: StUint): ResultTy {.noInit, inline.} =
when ResultTy is StUint:
result.data = op(x.data, y.data)
else:
op(x.data, y.data)
export `op`
template make_binary_inplace(op): untyped =
func `op`*(x: var MpUint, y: MpUint) {.inline.} =
func `op`*(x: var StUint, y: StUint) {.inline.} =
op(x.data, y.data)
export op
import ./private/uint_addsub
make_binary(`+`, MpUint)
make_binary(`+`, StUint)
make_binary_inplace(`+=`)
make_binary(`-`, MpUint)
make_binary(`-`, StUint)
make_binary_inplace(`-=`)
import ./private/uint_mul
make_binary(`*`, MpUint)
make_binary(`*`, StUint)
import ./private/uint_div
make_binary(`div`, MpUint)
make_binary(`mod`, MpUint)
func divmod*(x, y: MpUint): tuple[quot, rem: MpUint] {.noInit, inline.} =
make_binary(`div`, StUint)
make_binary(`mod`, StUint)
func divmod*(x, y: StUint): tuple[quot, rem: StUint] {.noInit, inline.} =
(result.quot.data, result.rem.data) = divmod(x.data, y.data)
import ./private/uint_comparison
@ -64,15 +64,15 @@ import ./private/uint_comparison
make_binary(`<`, bool)
make_binary(`<=`, bool)
make_binary(`==`, bool)
func isZero*(x: MpUint): bool {.inline.} = isZero x.data
func isZero*(x: StUint): bool {.inline.} = isZero x.data
import ./private/uint_bitwise_ops
make_unary(`not`, MpUint)
make_binary(`or`, MpUint)
make_binary(`and`, MpUint)
make_binary(`xor`, MpUint)
proc `shr`*(x: Mpuint, y: SomeInteger): MpUint {.noInit, inline, noSideEffect.} =
make_unary(`not`, StUint)
make_binary(`or`, StUint)
make_binary(`and`, StUint)
make_binary(`xor`, StUint)
proc `shr`*(x: StUint, y: SomeInteger): StUint {.noInit, inline, noSideEffect.} =
result.data = x.data shr y
proc `shl`*(x: Mpuint, y: SomeInteger): MpUint {.noInit, inline, noSideEffect.} =
proc `shl`*(x: StUint, y: SomeInteger): StUint {.noInit, inline, noSideEffect.} =
result.data = x.data shl y

12
mpint.nimble → stint.nimble
View File

@ -1,7 +1,7 @@
packageName = "mpint"
packageName = "stint"
version = "0.0.1"
author = "Status Research & Development GmbH"
description = "Efficient multiprecision int in Nim"
description = "Efficient stack-based multiprecision int in Nim"
license = "Apache License 2.0 or MIT"
srcDir = "src"
@ -20,19 +20,19 @@ proc test(name: string, lang: string = "c") =
switch("out", ("./build/" & name))
setCommand lang, "tests/" & name & ".nim"
task test_debug, "Run all tests - test implementation (MpUint[64] = 2x uint32":
task test_debug, "Run all tests - test implementation (StUint[64] = 2x uint32":
switch("define", "mpint_test")
test "all_tests"
task test_release, "Run all tests - prod implementation (MpUint[64] = uint64":
task test_release, "Run all tests - prod implementation (StUint[64] = uint64":
test "all_tests"
task test_property_debug, "Run random tests (normal mode) - test implementation (MpUint[64] = 2x uint32)":
task test_property_debug, "Run random tests (normal mode) - test implementation (StUint[64] = 2x uint32)":
requires "quicktest > 0.0.8"
switch("define", "mpint_test")
test "property_based"
task test_property_release, "Run random tests (release mode) - test implementation (MpUint[64] = 2x uint32)":
task test_property_release, "Run random tests (release mode) - test implementation (StUint[64] = 2x uint32)":
requires "quicktest > 0.0.8"
switch("define", "mpint_test")
switch("define", "release")

92
tests/property_based.nim
View File

@ -24,13 +24,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx or ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx or ty
@ -41,13 +41,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx and ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx and ty
check(cast[uint](tz) == (x and y))
@ -56,13 +56,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx xor ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx xor ty
check(cast[uint](tz) == (x xor y))
@ -71,11 +71,11 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
tx = cast[StUint[64]](x)
tz = not tx
else:
let
tx = cast[MpUint[32]](x)
tx = cast[StUint[32]](x)
tz = not tx
check(cast[uint](tz) == (not x))
@ -84,13 +84,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx < ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx < ty
check(tz == (x < y))
@ -100,13 +100,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx <= ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx <= ty
check(tz == (x <= y))
@ -115,13 +115,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx + ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx + ty
check(cast[uint](tz) == x+y)
@ -131,13 +131,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx - ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx - ty
check(cast[uint](tz) == x-y)
@ -146,13 +146,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx * ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx * ty
check(cast[uint](tz) == x*y)
@ -161,11 +161,11 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
tx = cast[StUint[64]](x)
tz = tx shl y
else:
let
tx = cast[MpUint[32]](x)
tx = cast[StUint[32]](x)
tz = tx shl y
check(cast[uint](tz) == x shl y)
@ -174,11 +174,11 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
tx = cast[StUint[64]](x)
tz = tx shr y
else:
let
tx = cast[MpUint[32]](x)
tx = cast[StUint[32]](x)
tz = tx shr y
check(cast[uint](tz) == x shr y)
@ -187,13 +187,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx mod ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx mod ty
check(cast[uint](tz) == x mod y)
@ -202,13 +202,13 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
when sizeof(int) == 8:
let
tx = cast[MpUint[64]](x)
ty = cast[MpUint[64]](y)
tx = cast[StUint[64]](x)
ty = cast[StUint[64]](y)
tz = tx div ty
else:
let
tx = cast[MpUint[32]](x)
ty = cast[MpUint[32]](y)
tx = cast[StUint[32]](x)
ty = cast[StUint[32]](y)
tz = tx div ty
check(cast[uint](tz) == x div y)

46
tests/property_based_uint256.nim
View File

@ -35,8 +35,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x or ttm_y
@ -60,8 +60,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x and ttm_y
@ -84,8 +84,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x xor ttm_y
@ -104,7 +104,7 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
# y = [y0, y1, y2, y3]
# ttm_x = cast[ttmath.UInt256](x)
# mp_x = cast[MpUint[256]](x)
# mp_x = cast[StUint[256]](x)
# let
# ttm_z = not ttm_x
@ -127,8 +127,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x < ttm_y
@ -152,8 +152,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x <= ttm_y
@ -176,8 +176,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x + ttm_y
@ -200,8 +200,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x - ttm_y
@ -224,8 +224,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x * ttm_y
@ -243,7 +243,7 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
x = [x0, x1, x2, x3]
ttm_x = cast[ttmath.UInt256](x)
mp_x = cast[MpUint[256]](x)
mp_x = cast[StUint[256]](x)
let
ttm_z = ttm_x shl y
@ -261,7 +261,7 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
x = [x0, x1, x2, x3]
ttm_x = cast[ttmath.UInt256](x)
mp_x = cast[MpUint[256]](x)
mp_x = cast[StUint[256]](x)
let
ttm_z = ttm_x shr y
@ -284,8 +284,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x mod ttm_y
@ -306,8 +306,8 @@ suite "Property-based testing (testing with random inputs) - uint64 on 64-bit /
ttm_x = cast[ttmath.UInt256](x)
ttm_y = cast[ttmath.UInt256](y)
mp_x = cast[MpUint[256]](x)
mp_y = cast[MpUint[256]](y)
mp_x = cast[StUint[256]](x)
mp_y = cast[StUint[256]](y)
let
ttm_z = ttm_x div ttm_y

30
tests/test_addsub.nim
View File

@ -12,8 +12,8 @@ import ../src/mpint, unittest
suite "Testing addition implementation":
test "In-place addition gives expected result":
var a = 20182018.initMpUint(64)
let b = 20172017.initMpUint(64)
var a = 20182018.u(64)
let b = 20172017.u(64)
a += b
@ -21,23 +21,23 @@ suite "Testing addition implementation":
test "Addition gives expected result":
let a = 20182018.initMpUint(64)
let b = 20172017.initMpUint(64)
let a = 20182018.u(64)
let b = 20172017.u(64)
check: cast[uint64](a+b) == 20182018'u64 + 20172017'u64
test "When the low half overflows, it is properly carried":
# uint8 (low half) overflow at 255
let a = 100'u16.initMpUint(16)
let b = 100'u16.initMpUint(16)
let a = 100'u16.u(16)
let b = 100'u16.u(16)
check: cast[uint16](a+b) == 200
test "Full overflow is handled like native unsigned types":
# uint16 overflows after 65535
let a = 100'u16.initMpUint(16)
var z = 0'u16.initMpUint(16)
let o = 36'u16.initMpUint(16)
let a = 100'u16.u(16)
var z = 0'u16.u(16)
let o = 36'u16.u(16)
for _ in 0 ..< 655:
z += a
@ -54,8 +54,8 @@ suite "Testing addition implementation":
suite "Testing substraction implementation":
test "In-place substraction gives expected result":
var a = 20182018.initMpUint(64)
let b = 20172017.initMpUint(64)
var a = 20182018.u(64)
let b = 20172017.u(64)
a -= b
@ -63,14 +63,14 @@ suite "Testing substraction implementation":
test "Substraction gives expected result":
let a = 20182018.initMpUint(64)
let b = 20172017.initMpUint(64)
let a = 20182018.u(64)
let b = 20172017.u(64)
check: cast[uint64](a-b) == 20182018'u64 - 20172017'u64
test "Full overflow is handled like native unsigned types":
# uint16 overflows after 65535
let a = 100'u16.initMpUint(16)
let b = 101'u16.initMpUint(16)
let a = 100'u16.u(16)
let b = 101'u16.u(16)
check: cast[uint16](a-b) == high(uint16)

12
tests/test_bitwise.nim
View File

@ -10,14 +10,14 @@
import ../src/mpint, unittest
suite "Testing bitwise operations":
let a = 100'i16.initMpUint(16)
let a = 100'i16.u(16)
let b = a * a
let z = 10000'u16
assert cast[uint16](b) == z, "Test cannot proceed, something is wrong with the multiplication implementation"
let u = 10000.initMpUint(64)
let u = 10000.u(64)
let v = 10000'u64
let clz = 30
@ -35,11 +35,11 @@ suite "Testing bitwise operations":
check: cast[uint16](b) == z # Sanity check
check: cast[uint16](b shl 8) == z shl 8
block: # Testing shl for nested MpUintImpl
let p2_64 = MpUintImpl[uint64](hi:1, lo:0)
let p = 1.initMpUint(128) shl 64
block: # Testing shl for nested UintImpl
let p2_64 = UintImpl[uint64](hi:1, lo:0)
let p = 1.u(128) shl 64
check: p == cast[MpUint[128]](p2_64)
check: p == cast[StUint[128]](p2_64)
test "Shift right - by less than half the size of the integer":
check: cast[uint16](b) == z # Sanity check

18
tests/test_comparison.nim
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@ -11,19 +11,19 @@ import ../src/mpint, unittest
suite "Testing comparison operators":
let
a = 10'i16.initMpUint(16)
b = 15'i16.initMpUint(16)
a = 10'i16.u(16)
b = 15'i16.u(16)
c = 150'u16
d = 4.initMpUint(128) shl 64
e = 4.initMpUint(128)
f = 4.initMpUint(128) shl 65
d = 4.u(128) shl 64
e = 4.u(128)
f = 4.u(128) shl 65
test "< operator":
check:
a < b
not (a + b < b)
not (a + a + a < b + b)
not (a * b < cast[MpUint[16]](c))
not (a * b < cast[StUint[16]](c))
e < d
d < f
@ -32,7 +32,7 @@ suite "Testing comparison operators":
a <= b
not (a + b <= b)
a + a + a <= b + b
a * b <= cast[MpUint[16]](c)
a * b <= cast[StUint[16]](c)
e <= d
d <= f
@ -41,7 +41,7 @@ suite "Testing comparison operators":
b > a
not (b > a + b)
not (b + b > a + a + a)
not (cast[Mpuint[16]](c) > a * b)
not (cast[StUint[16]](c) > a * b)
d > e
f > d
@ -50,6 +50,6 @@ suite "Testing comparison operators":
b >= a
not (b >= a + b)
b + b >= a + a + a
cast[MpUint[16]](c) >= a * b
cast[StUint[16]](c) >= a * b
d >= e
f >= d

2
tests/test_endianness.nim
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@ -11,7 +11,7 @@ import ../src/mpint, unittest
suite "Testing byte representation":
test "Byte representation conforms to the platform endianness":
let a = 20182018.initMpUint(64)
let a = 20182018.u(64)
let b = 20182018'u64
type AsBytes = array[8, byte]

26
tests/test_muldiv.nim
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@ -12,23 +12,23 @@ import ../src/mpint, unittest
suite "Testing multiplication implementation":
test "Multiplication with result fitting in low half":
let a = 10000.initMpUint(64)
let b = 10000.initMpUint(64)
let a = 10000.u(64)
let b = 10000.u(64)
check: cast[uint64](a*b) == 100_000_000'u64 # need 27-bits
test "Multiplication with result overflowing low half":
let a = 1_000_000.initMpUint(64)
let b = 1_000_000.initMpUint(64)
let a = 1_000_000.u(64)
let b = 1_000_000.u(64)
check: cast[uint64](a*b) == 1_000_000_000_000'u64 # need 40 bits
test "Full overflow is handled like native unsigned types":
let a = 1_000_000_000.initMpUint(64)
let b = 1_000_000_000.initMpUint(64)
let c = 1_000.initMpUint(64)
let a = 1_000_000_000.u(64)
let b = 1_000_000_000.u(64)
let c = 1_000.u(64)
check: cast[uint64](a*b*c) == 1_000_000_000_000_000_000_000'u64 # need 70-bits
@ -36,21 +36,21 @@ suite "Testing multiplication implementation":
suite "Testing division and modulo implementation":
test "Divmod(100, 13) returns the correct result":
let a = 100.initMpUint(64)
let b = 13.initMpUint(64)
let a = 100.u(64)
let b = 13.u(64)
let qr = divmod(a, b)
check: cast[uint64](qr.quot) == 7'u64
check: cast[uint64](qr.rem) == 9'u64
test "Divmod(2^64, 3) returns the correct result":
let a = 1.initMpUint(128) shl 64
let b = 3.initMpUint(128)
let a = 1.u(128) shl 64
let b = 3.u(128)
let qr = divmod(a, b)
let q = cast[MpUintImpl[uint64]](qr.quot)
let r = cast[MpUintImpl[uint64]](qr.rem)
let q = cast[UintImpl[uint64]](qr.quot)
let r = cast[UintImpl[uint64]](qr.rem)
check: q.lo == 6148914691236517205'u64
check: q.hi == 0'u64