371 lines
8.6 KiB
Nim
371 lines
8.6 KiB
Nim
# Stint
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# Copyright 2018-2023 Status Research & Development GmbH
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# Licensed under either of
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#
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# * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
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# * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
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#
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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import
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./private/datatypes,
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./private/uint_bitwise,
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./private/uint_shift,
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./private/uint_addsub,
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./private/uint_div,
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./uintops
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export StInt
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const
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signMask = 1.Word shl (WordBitWidth - 1)
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clearSignMask = not signMask
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# Signedness
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func sign*(a: StInt): int =
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## get the sign of `a`
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## either -1, 0, or 1
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if a.impl.isZero: return 0
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if a.limbs[^1] < signMask: 1
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else: -1
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func isNegative*(a: StInt): bool =
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a.limbs[^1] >= signMask
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func isPositive*(a: StInt): bool =
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a.limbs[^1] < signMask
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func clearMSB(a: var StInt) =
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a.limbs[^1] = a.limbs[^1] and clearSignMask
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func setMSB(a: var StInt) =
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a.limbs[^1] = a.limbs[^1] or signMask
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func negate*(a: var StInt) =
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## two complement negation
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a.impl.bitnot(a.impl)
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a.impl.inc
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func neg*(a: StInt): StInt =
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## two complement negation
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result.impl.bitnot(a.impl)
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result.impl.inc
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func abs*(a: StInt): StInt =
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## Returns the positive value of Stint
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if a.isNegative:
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a.neg
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else:
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a
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func `-`*(a: StInt): StInt =
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## two complement negation
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a.neg
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{.pop.}
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# Initialization
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func setZero*(a: var StInt) =
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## Set ``a`` to 0
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a.impl.setZero
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func setOne*(a: var StInt) =
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## Set ``a`` to 1
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a.impl.setOne
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func zero*[bits: static[int]](T: typedesc[StInt[bits]]): T =
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## Returns the zero of the input type
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result.setZero
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func one*[bits: static[int]](T: typedesc[StInt[bits]]): T =
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## Returns the one of the input type
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result.setOne
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func high*[bits](_: typedesc[StInt[bits]]): StInt[bits] =
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## Returns the highest value of Stint
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# The highest signed int has representation
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# 0b0111_1111_1111_1111 ....
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# so we only have to unset the most significant bit.
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for i in 0 ..< result.limbs.len:
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result[i] = high(Word)
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result.clearMSB
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func low*[bits](_: typedesc[StInt[bits]]): StInt[bits] =
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## Returns the lowest value of Stint
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# The lowest signed int has representation
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# 0b1000_0000_0000_0000 ....
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# so we only have to set the most significant bit.
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result.setZero
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result.setMSB
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{.pop.}
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# Comparisons
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func isZero*(a: StInt): bool =
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a.impl.isZero
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func isOne*(a: StInt): bool =
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a.impl.isOne
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func `==`*(a, b: StInt): bool =
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## Signed int `equal` comparison
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a.impl == b.impl
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func `<`*(a, b: StInt): bool =
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## Signed int `less than` comparison
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let
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aNeg = a.isNegative
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bNeg = b.isNegative
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if aNeg xor bNeg:
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return aNeg
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a.impl < b.impl
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func `<=`*(a, b: StInt): bool =
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## Signed int `less or equal` comparison
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not(b < a)
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func isOdd*(a: StInt): bool =
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## Returns true if input is odd
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## false otherwise
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bool(a[0] and 1)
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func isEven*(a: StInt): bool =
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## Returns true if input is zero
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## false otherwise
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not a.isOdd()
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{.pop.}
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# Bitwise operations
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func `not`*(a: StInt): StInt =
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## Bitwise complement of signed integer a
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## i.e. flips all bits of the input
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result.impl.bitnot(a.impl)
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func `or`*(a, b: StInt): StInt =
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## `Bitwise or` of numbers a and b
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result.impl.bitor(a.impl, b.impl)
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func `and`*(a, b: StInt): StInt =
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## `Bitwise and` of numbers a and b
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result.impl.bitand(a.impl, b.impl)
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func `xor`*(a, b: StInt): StInt =
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## `Bitwise xor` of numbers x and y
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result.impl.bitxor(a.impl, b.impl)
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{.pop.} # End noInit
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{.push raises: [], inline, gcsafe.}
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func `shr`*(a: StInt, k: SomeInteger): StInt =
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## Shift right by k bits, arithmetically
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## value < 0 ? ~(~value >> amount) : value >> amount
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if a.isNegative:
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var tmp: type a
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result.impl.bitnot(a.impl)
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tmp.impl.shiftRight(result.impl, k)
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result.impl.bitnot(tmp.impl)
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else:
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result.impl.shiftRight(a.impl, k)
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func `shl`*(a: StInt, k: SomeInteger): StInt =
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## Shift left by k bits
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result.impl.shiftLeft(a.impl, k)
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func setBit*(a: var StInt, k: Natural) =
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## set bit at position `k`
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## k = 0..a.bits-1
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a.impl.setBit(k)
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func clearBit*(a: var StInt, k: Natural) =
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## set bit at position `k`
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## k = 0..a.bits-1
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a.impl.clearBit(k)
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func getBit*(a: StInt, k: Natural): bool =
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## set bit at position `k`
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## k = 0..a.bits-1
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a.impl.getBit(k)
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{.pop.}
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# Addsub
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func `+`*(a, b: StInt): StInt =
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## Addition for multi-precision signed int
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result.impl.sum(a.impl, b.impl)
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func `+=`*(a: var StInt, b: StInt) =
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## In-place addition for multi-precision signed int
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a.impl.sum(a.impl, b.impl)
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func `-`*(a, b: StInt): StInt =
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## Substraction for multi-precision signed int
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result.impl.diff(a.impl, b.impl)
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func `-=`*(a: var StInt, b: StInt) =
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## In-place substraction for multi-precision signed int
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a.impl.diff(a.impl, b.impl)
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func inc*(a: var StInt, w: Word = 1) =
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a.impl.inc(w)
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func `+`*(a: StInt, b: SomeUnsignedInt): StInt =
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## Addition for multi-precision signed int
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## with an unsigned integer
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result.impl.sum(a.impl, Word(b))
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func `+=`*(a: var StInt, b: SomeUnsignedInt) =
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## In-place addition for multi-precision signed int
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## with an unsigned integer
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a.impl.inc(Word(b))
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{.pop.}
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# Exponentiation
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# --------------------------------------------------------
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{.push raises: [], noinit, gcsafe.}
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func isOdd(x: Natural): bool =
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bool(x and 1)
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func pow*(a: StInt, e: Natural): StInt =
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## Compute ``a`` to the power of ``e``,
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## ``e`` must be non-negative
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if a.isNegative:
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let base = a.neg
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result.impl = base.impl.pow(e)
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if e.isOdd:
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result.negate
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else:
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result.impl = a.impl.pow(e)
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func pow*[aBits, eBits](a: StInt[aBits], e: StInt[eBits]): StInt[aBits] =
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## Compute ``x`` to the power of ``y``,
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## ``x`` must be non-negative
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doAssert e.isNegative.not, "exponent must be non-negative"
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if a.isNegative:
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let base = a.neg
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result.impl = base.impl.pow(e.impl)
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if e.isOdd:
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result.negate
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else:
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result.impl = a.impl.pow(e.impl)
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{.pop.}
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# Division & Modulo
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func `div`*(n, d: StInt): StInt =
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## Division operation for multi-precision signed uint
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var tmp{.noinit.}: StInt
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if n.isPositive:
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if d.isPositive:
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# pos / pos
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result.impl = n.impl div d.impl
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return
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else:
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# pos / neg
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tmp = d.neg
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result.impl = n.impl div tmp.impl
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result.negate
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return
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let nneg = n.neg
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if d.isNegative:
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# neg / neg
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tmp = d.neg
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result.impl = nneg.impl div tmp.impl
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return
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# neg / pos
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result.impl = nneg.impl div d.impl
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result.negate
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func `mod`*(x, y: StInt): StInt =
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## Remainder operation for multi-precision signed uint
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## The behavior is similar to Nim's `mod` operator
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## The sign of the remainder will follow the sign of left operand
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let
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xIn = x.abs
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yIn = y.abs
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result.impl = xIn.impl mod yIn.impl
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if x.isNegative:
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result.negate
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func divmodI(x, y: StInt): tuple[quot, rem: StInt] =
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## Division and remainder operations for multi-precision uint
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## with StInt operands
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divRem(result.quot.limbs, result.rem.limbs, x.limbs, y.limbs)
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func divmod*(n, d: StInt): tuple[quot, rem: StInt] =
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## Division and remainder operations for multi-precision signed uint
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## The sign of the remainder will follow the sign of left operand
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var tmp{.noinit.}: StInt
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if n.isPositive:
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if d.isPositive:
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# pos / pos
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return divmodI(n, d)
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else:
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# pos / neg
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tmp = d.neg
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result = divmodI(n, tmp)
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result.quot.negate
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return
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let nneg = n.neg
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if d.isNegative:
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# neg / neg
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tmp = d.neg
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result = divmodI(nneg, tmp)
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result.rem.negate
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return
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# neg / pos
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result = divmodI(nneg, d)
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result.quot.negate
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result.rem.negate
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{.pop.}
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# Multiplication
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# --------------------------------------------------------
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{.push raises: [], inline, noinit, gcsafe.}
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func `*`*(a, b: StInt): StInt =
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## Signed integer multiplication
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let
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av = a.abs
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bv = b.abs
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result.impl = av.impl * bv.impl
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if a.isNegative xor b.isNegative:
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result.negate
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{.pop.}
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