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https://github.com/nim-lang/Nim.git
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8a19ac2070
* fixes #21393 and misc style changes * progress --------- Co-authored-by: ringabout <43030857+ringabout@users.noreply.github.com>
575 lines
16 KiB
Nim
575 lines
16 KiB
Nim
## This module is for compiler internal use only. For reliable error
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## messages and range checks, the compiler needs a data type that can
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## hold all from `low(BiggestInt)` to `high(BiggestUInt)`, This
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## type is for that purpose.
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from math import trunc
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when defined(nimPreviewSlimSystem):
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import std/assertions
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type
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Int128* = object
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udata: array[4, uint32]
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template sdata(arg: Int128, idx: int): int32 =
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# udata and sdata was supposed to be in a union, but unions are
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# handled incorrectly in the VM.
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cast[ptr int32](arg.udata[idx].unsafeAddr)[]
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# encoding least significant int first (like LittleEndian)
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const
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Zero* = Int128(udata: [0'u32, 0, 0, 0])
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One* = Int128(udata: [1'u32, 0, 0, 0])
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Ten* = Int128(udata: [10'u32, 0, 0, 0])
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Min = Int128(udata: [0'u32, 0, 0, 0x80000000'u32])
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Max = Int128(udata: [high(uint32), high(uint32), high(uint32), uint32(high(int32))])
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NegOne* = Int128(udata: [0xffffffff'u32, 0xffffffff'u32, 0xffffffff'u32, 0xffffffff'u32])
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template low*(t: typedesc[Int128]): Int128 = Min
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template high*(t: typedesc[Int128]): Int128 = Max
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proc `$`*(a: Int128): string
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proc toInt128*[T: SomeInteger | bool](arg: T): Int128 =
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{.noSideEffect.}:
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when T is bool: result.sdata(0) = int32(arg)
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elif T is SomeUnsignedInt:
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when sizeof(arg) <= 4:
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result.udata[0] = uint32(arg)
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else:
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result.udata[0] = uint32(arg and T(0xffffffff))
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result.udata[1] = uint32(arg shr 32)
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elif sizeof(arg) <= 4:
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result.sdata(0) = int32(arg)
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if arg < 0: # sign extend
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result.sdata(1) = -1
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result.sdata(2) = -1
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result.sdata(3) = -1
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else:
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let tmp = int64(arg)
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result.udata[0] = uint32(tmp and 0xffffffff)
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result.sdata(1) = int32(tmp shr 32)
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if arg < 0: # sign extend
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result.sdata(2) = -1
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result.sdata(3) = -1
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template isNegative(arg: Int128): bool =
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arg.sdata(3) < 0
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proc bitconcat(a, b: uint32): uint64 =
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(uint64(a) shl 32) or uint64(b)
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proc toInt64*(arg: Int128): int64 =
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if isNegative(arg):
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assert(arg.sdata(3) == -1, "out of range")
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assert(arg.sdata(2) == -1, "out of range")
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else:
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assert(arg.sdata(3) == 0, "out of range")
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assert(arg.sdata(2) == 0, "out of range")
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cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
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proc toInt64Checked*(arg: Int128; onError: int64): int64 =
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if isNegative(arg):
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if arg.sdata(3) != -1 or arg.sdata(2) != -1:
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return onError
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else:
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if arg.sdata(3) != 0 or arg.sdata(2) != 0:
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return onError
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return cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
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proc toInt32*(arg: Int128): int32 =
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if isNegative(arg):
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assert(arg.sdata(3) == -1, "out of range")
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assert(arg.sdata(2) == -1, "out of range")
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assert(arg.sdata(1) == -1, "out of range")
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else:
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assert(arg.sdata(3) == 0, "out of range")
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assert(arg.sdata(2) == 0, "out of range")
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assert(arg.sdata(1) == 0, "out of range")
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arg.sdata(0)
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proc toInt16*(arg: Int128): int16 =
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if isNegative(arg):
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assert(arg.sdata(3) == -1, "out of range")
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assert(arg.sdata(2) == -1, "out of range")
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assert(arg.sdata(1) == -1, "out of range")
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else:
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assert(arg.sdata(3) == 0, "out of range")
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assert(arg.sdata(2) == 0, "out of range")
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assert(arg.sdata(1) == 0, "out of range")
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int16(arg.sdata(0))
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proc toInt8*(arg: Int128): int8 =
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if isNegative(arg):
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assert(arg.sdata(3) == -1, "out of range")
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assert(arg.sdata(2) == -1, "out of range")
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assert(arg.sdata(1) == -1, "out of range")
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else:
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assert(arg.sdata(3) == 0, "out of range")
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assert(arg.sdata(2) == 0, "out of range")
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assert(arg.sdata(1) == 0, "out of range")
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int8(arg.sdata(0))
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proc toInt*(arg: Int128): int =
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when sizeof(int) == 4:
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cast[int](toInt32(arg))
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else:
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cast[int](toInt64(arg))
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proc toUInt64*(arg: Int128): uint64 =
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assert(arg.udata[3] == 0)
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assert(arg.udata[2] == 0)
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bitconcat(arg.udata[1], arg.udata[0])
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proc toUInt32*(arg: Int128): uint32 =
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assert(arg.udata[3] == 0)
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assert(arg.udata[2] == 0)
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assert(arg.udata[1] == 0)
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arg.udata[0]
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proc toUInt16*(arg: Int128): uint16 =
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assert(arg.udata[3] == 0)
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assert(arg.udata[2] == 0)
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assert(arg.udata[1] == 0)
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uint16(arg.udata[0])
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proc toUInt8*(arg: Int128): uint8 =
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assert(arg.udata[3] == 0)
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assert(arg.udata[2] == 0)
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assert(arg.udata[1] == 0)
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uint8(arg.udata[0])
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proc toUInt*(arg: Int128): uint =
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when sizeof(int) == 4:
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cast[uint](toInt32(arg))
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else:
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cast[uint](toInt64(arg))
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proc castToInt64*(arg: Int128): int64 =
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## Conversion to int64 without range check.
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cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
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proc castToUInt64*(arg: Int128): uint64 =
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## Conversion to uint64 without range check.
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cast[uint64](bitconcat(arg.udata[1], arg.udata[0]))
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proc addToHex(result: var string; arg: uint32) =
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for i in 0..<8:
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let idx = (arg shr ((7-i) * 4)) and 0xf
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result.add "0123456789abcdef"[idx]
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proc addToHex*(result: var string; arg: Int128) =
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var i = 3
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while i >= 0:
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result.addToHex(arg.udata[i])
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i -= 1
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proc toHex*(arg: Int128): string =
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result.addToHex(arg)
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proc inc*(a: var Int128, y: uint32 = 1) =
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a.udata[0] += y
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if unlikely(a.udata[0] < y):
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a.udata[1].inc
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if unlikely(a.udata[1] == 0):
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a.udata[2].inc
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if unlikely(a.udata[2] == 0):
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a.udata[3].inc
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doAssert(a.sdata(3) != low(int32), "overflow")
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proc cmp*(a, b: Int128): int =
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let tmp1 = cmp(a.sdata(3), b.sdata(3))
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if tmp1 != 0: return tmp1
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let tmp2 = cmp(a.udata[2], b.udata[2])
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if tmp2 != 0: return tmp2
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let tmp3 = cmp(a.udata[1], b.udata[1])
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if tmp3 != 0: return tmp3
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let tmp4 = cmp(a.udata[0], b.udata[0])
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return tmp4
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proc `<`*(a, b: Int128): bool =
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cmp(a, b) < 0
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proc `<=`*(a, b: Int128): bool =
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cmp(a, b) <= 0
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proc `==`*(a, b: Int128): bool =
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if a.udata[0] != b.udata[0]: return false
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if a.udata[1] != b.udata[1]: return false
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if a.udata[2] != b.udata[2]: return false
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if a.udata[3] != b.udata[3]: return false
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return true
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proc bitnot*(a: Int128): Int128 =
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result.udata[0] = not a.udata[0]
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result.udata[1] = not a.udata[1]
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result.udata[2] = not a.udata[2]
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result.udata[3] = not a.udata[3]
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proc bitand*(a, b: Int128): Int128 =
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result.udata[0] = a.udata[0] and b.udata[0]
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result.udata[1] = a.udata[1] and b.udata[1]
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result.udata[2] = a.udata[2] and b.udata[2]
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result.udata[3] = a.udata[3] and b.udata[3]
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proc bitor*(a, b: Int128): Int128 =
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result.udata[0] = a.udata[0] or b.udata[0]
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result.udata[1] = a.udata[1] or b.udata[1]
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result.udata[2] = a.udata[2] or b.udata[2]
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result.udata[3] = a.udata[3] or b.udata[3]
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proc bitxor*(a, b: Int128): Int128 =
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result.udata[0] = a.udata[0] xor b.udata[0]
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result.udata[1] = a.udata[1] xor b.udata[1]
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result.udata[2] = a.udata[2] xor b.udata[2]
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result.udata[3] = a.udata[3] xor b.udata[3]
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proc `shr`*(a: Int128, b: int): Int128 =
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let b = b and 127
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if b < 32:
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result.sdata(3) = a.sdata(3) shr b
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result.udata[2] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr b)
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result.udata[1] = cast[uint32](bitconcat(a.udata[2], a.udata[1]) shr b)
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result.udata[0] = cast[uint32](bitconcat(a.udata[1], a.udata[0]) shr b)
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elif b < 64:
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if isNegative(a):
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result.sdata(3) = -1
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result.sdata(2) = a.sdata(3) shr (b and 31)
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result.udata[1] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr (b and 31))
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result.udata[0] = cast[uint32](bitconcat(a.udata[2], a.udata[1]) shr (b and 31))
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elif b < 96:
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if isNegative(a):
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result.sdata(3) = -1
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result.sdata(2) = -1
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result.sdata(1) = a.sdata(3) shr (b and 31)
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result.udata[0] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr (b and 31))
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else: # b < 128
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if isNegative(a):
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result.sdata(3) = -1
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result.sdata(2) = -1
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result.sdata(1) = -1
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result.sdata(0) = a.sdata(3) shr (b and 31)
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proc `shl`*(a: Int128, b: int): Int128 =
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let b = b and 127
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if b < 32:
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result.udata[0] = a.udata[0] shl b
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result.udata[1] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl b) shr 32)
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result.udata[2] = cast[uint32]((bitconcat(a.udata[2], a.udata[1]) shl b) shr 32)
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result.udata[3] = cast[uint32]((bitconcat(a.udata[3], a.udata[2]) shl b) shr 32)
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elif b < 64:
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result.udata[0] = 0
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result.udata[1] = a.udata[0] shl (b and 31)
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result.udata[2] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl (b and 31)) shr 32)
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result.udata[3] = cast[uint32]((bitconcat(a.udata[2], a.udata[1]) shl (b and 31)) shr 32)
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elif b < 96:
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result.udata[0] = 0
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result.udata[1] = 0
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result.udata[2] = a.udata[0] shl (b and 31)
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result.udata[3] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl (b and 31)) shr 32)
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else:
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result.udata[0] = 0
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result.udata[1] = 0
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result.udata[2] = 0
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result.udata[3] = a.udata[0] shl (b and 31)
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proc `+`*(a, b: Int128): Int128 =
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let tmp0 = uint64(a.udata[0]) + uint64(b.udata[0])
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result.udata[0] = cast[uint32](tmp0)
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let tmp1 = uint64(a.udata[1]) + uint64(b.udata[1]) + (tmp0 shr 32)
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result.udata[1] = cast[uint32](tmp1)
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let tmp2 = uint64(a.udata[2]) + uint64(b.udata[2]) + (tmp1 shr 32)
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result.udata[2] = cast[uint32](tmp2)
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let tmp3 = uint64(a.udata[3]) + uint64(b.udata[3]) + (tmp2 shr 32)
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result.udata[3] = cast[uint32](tmp3)
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proc `+=`*(a: var Int128, b: Int128) =
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a = a + b
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proc `-`*(a: Int128): Int128 =
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result = bitnot(a)
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result.inc
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proc `-`*(a, b: Int128): Int128 =
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a + (-b)
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proc `-=`*(a: var Int128, b: Int128) =
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a = a - b
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proc abs*(a: Int128): Int128 =
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if isNegative(a):
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-a
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else:
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a
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proc abs(a: int32): int =
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if a < 0: -a else: a
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proc `*`(a: Int128, b: uint32): Int128 =
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let tmp0 = uint64(a.udata[0]) * uint64(b)
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let tmp1 = uint64(a.udata[1]) * uint64(b)
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let tmp2 = uint64(a.udata[2]) * uint64(b)
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let tmp3 = uint64(a.udata[3]) * uint64(b)
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if unlikely(tmp3 > uint64(high(int32))):
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assert(false, "overflow")
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result.udata[0] = cast[uint32](tmp0)
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result.udata[1] = cast[uint32](tmp1) + cast[uint32](tmp0 shr 32)
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result.udata[2] = cast[uint32](tmp2) + cast[uint32](tmp1 shr 32)
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result.udata[3] = cast[uint32](tmp3) + cast[uint32](tmp2 shr 32)
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proc `*`*(a: Int128, b: int32): Int128 =
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result = a * cast[uint32](abs(b))
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if b < 0:
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result = -result
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proc `*=`*(a: var Int128, b: int32): Int128 =
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result = result * b
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proc makeInt128(high, low: uint64): Int128 =
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result.udata[0] = cast[uint32](low)
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result.udata[1] = cast[uint32](low shr 32)
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result.udata[2] = cast[uint32](high)
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result.udata[3] = cast[uint32](high shr 32)
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proc high64(a: Int128): uint64 =
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bitconcat(a.udata[3], a.udata[2])
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proc low64(a: Int128): uint64 =
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bitconcat(a.udata[1], a.udata[0])
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proc `*`*(lhs, rhs: Int128): Int128 =
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let a32 = uint64(lhs.udata[1])
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let a00 = uint64(lhs.udata[0])
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let b32 = uint64(rhs.udata[1])
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let b00 = uint64(rhs.udata[0])
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result = makeInt128(high64(lhs) * low64(rhs) + low64(lhs) * high64(rhs) + a32 * b32, a00 * b00)
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result += toInt128(a32 * b00) shl 32
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result += toInt128(a00 * b32) shl 32
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proc `*=`*(a: var Int128, b: Int128) =
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a = a * b
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import bitops
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proc fastLog2*(a: Int128): int =
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if a.udata[3] != 0:
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return 96 + fastLog2(a.udata[3])
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if a.udata[2] != 0:
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return 64 + fastLog2(a.udata[2])
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if a.udata[1] != 0:
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return 32 + fastLog2(a.udata[1])
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if a.udata[0] != 0:
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return fastLog2(a.udata[0])
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proc divMod*(dividend, divisor: Int128): tuple[quotient, remainder: Int128] =
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assert(divisor != Zero)
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let isNegativeA = isNegative(dividend)
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let isNegativeB = isNegative(divisor)
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var dividend = abs(dividend)
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let divisor = abs(divisor)
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if divisor > dividend:
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result.quotient = Zero
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if isNegativeA:
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result.remainder = -dividend
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else:
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result.remainder = dividend
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return
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if divisor == dividend:
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if isNegativeA xor isNegativeB:
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result.quotient = NegOne
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else:
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result.quotient = One
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result.remainder = Zero
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return
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var denominator = divisor
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var quotient = Zero
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# Left aligns the MSB of the denominator and the dividend.
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let shift = fastLog2(dividend) - fastLog2(denominator)
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denominator = denominator shl shift
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# Uses shift-subtract algorithm to divide dividend by denominator. The
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# remainder will be left in dividend.
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for i in 0..shift:
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quotient = quotient shl 1
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if dividend >= denominator:
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dividend -= denominator
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quotient = bitor(quotient, One)
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denominator = denominator shr 1
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if isNegativeA xor isNegativeB:
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result.quotient = -quotient
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else:
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result.quotient = quotient
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if isNegativeA:
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result.remainder = -dividend
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else:
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result.remainder = dividend
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proc `div`*(a, b: Int128): Int128 =
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let (a, _) = divMod(a, b)
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return a
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proc `mod`*(a, b: Int128): Int128 =
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let (_, b) = divMod(a, b)
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return b
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proc addInt128*(result: var string; value: Int128) =
|
|
let initialSize = result.len
|
|
if value == Zero:
|
|
result.add '0'
|
|
elif value == low(Int128):
|
|
result.add "-170141183460469231731687303715884105728"
|
|
else:
|
|
let isNegative = isNegative(value)
|
|
var value = abs(value)
|
|
while value > Zero:
|
|
let (quot, rem) = divMod(value, Ten)
|
|
result.add "0123456789"[rem.toInt64]
|
|
value = quot
|
|
if isNegative:
|
|
result.add '-'
|
|
|
|
var i = initialSize
|
|
var j = high(result)
|
|
while i < j:
|
|
swap(result[i], result[j])
|
|
i += 1
|
|
j -= 1
|
|
|
|
proc `$`*(a: Int128): string =
|
|
# "-170141183460469231731687303715884105728".len == 41
|
|
result = newStringOfCap(41)
|
|
result.addInt128(a)
|
|
|
|
proc parseDecimalInt128*(arg: string, pos: int = 0): Int128 =
|
|
assert(pos < arg.len)
|
|
assert(arg[pos] in {'-', '0'..'9'})
|
|
|
|
var isNegative = false
|
|
var pos = pos
|
|
if arg[pos] == '-':
|
|
isNegative = true
|
|
pos += 1
|
|
|
|
result = Zero
|
|
while pos < arg.len and arg[pos] in '0'..'9':
|
|
result = result * Ten
|
|
result.inc(uint32(arg[pos]) - uint32('0'))
|
|
pos += 1
|
|
|
|
if isNegative:
|
|
result = -result
|
|
|
|
# fluff
|
|
|
|
proc `<`*(a: Int128, b: BiggestInt): bool =
|
|
cmp(a, toInt128(b)) < 0
|
|
|
|
proc `<`*(a: BiggestInt, b: Int128): bool =
|
|
cmp(toInt128(a), b) < 0
|
|
|
|
proc `<=`*(a: Int128, b: BiggestInt): bool =
|
|
cmp(a, toInt128(b)) <= 0
|
|
|
|
proc `<=`*(a: BiggestInt, b: Int128): bool =
|
|
cmp(toInt128(a), b) <= 0
|
|
|
|
proc `==`*(a: Int128, b: BiggestInt): bool =
|
|
a == toInt128(b)
|
|
|
|
proc `==`*(a: BiggestInt, b: Int128): bool =
|
|
toInt128(a) == b
|
|
|
|
proc `-`*(a: BiggestInt, b: Int128): Int128 =
|
|
toInt128(a) - b
|
|
|
|
proc `-`*(a: Int128, b: BiggestInt): Int128 =
|
|
a - toInt128(b)
|
|
|
|
proc `+`*(a: BiggestInt, b: Int128): Int128 =
|
|
toInt128(a) + b
|
|
|
|
proc `+`*(a: Int128, b: BiggestInt): Int128 =
|
|
a + toInt128(b)
|
|
|
|
proc toFloat64*(arg: Int128): float64 =
|
|
let isNegative = isNegative(arg)
|
|
let arg = abs(arg)
|
|
|
|
let a = float64(bitconcat(arg.udata[1], arg.udata[0]))
|
|
let b = float64(bitconcat(arg.udata[3], arg.udata[2]))
|
|
|
|
result = a + 18446744073709551616'f64 * b # a + 2^64 * b
|
|
if isNegative:
|
|
result = -result
|
|
|
|
proc ldexp(x: float64, exp: cint): float64 {.importc: "ldexp", header: "<math.h>".}
|
|
|
|
template bitor(a, b, c: Int128): Int128 = bitor(bitor(a, b), c)
|
|
|
|
proc toInt128*(arg: float64): Int128 =
|
|
let isNegative = arg < 0
|
|
let v0 = ldexp(abs(arg), -100)
|
|
let w0 = uint64(trunc(v0))
|
|
let v1 = ldexp(v0 - float64(w0), 50)
|
|
let w1 = uint64(trunc(v1))
|
|
let v2 = ldexp(v1 - float64(w1), 50)
|
|
let w2 = uint64(trunc(v2))
|
|
|
|
let res = bitor(toInt128(w0) shl 100, toInt128(w1) shl 50, toInt128(w2))
|
|
if isNegative:
|
|
return -res
|
|
else:
|
|
return res
|
|
|
|
proc maskUInt64*(arg: Int128): Int128 {.noinit, inline.} =
|
|
result.udata[0] = arg.udata[0]
|
|
result.udata[1] = arg.udata[1]
|
|
result.udata[2] = 0
|
|
result.udata[3] = 0
|
|
|
|
proc maskUInt32*(arg: Int128): Int128 {.noinit, inline.} =
|
|
result.udata[0] = arg.udata[0]
|
|
result.udata[1] = 0
|
|
result.udata[2] = 0
|
|
result.udata[3] = 0
|
|
|
|
proc maskUInt16*(arg: Int128): Int128 {.noinit, inline.} =
|
|
result.udata[0] = arg.udata[0] and 0xffff
|
|
result.udata[1] = 0
|
|
result.udata[2] = 0
|
|
result.udata[3] = 0
|
|
|
|
proc maskUInt8*(arg: Int128): Int128 {.noinit, inline.} =
|
|
result.udata[0] = arg.udata[0] and 0xff
|
|
result.udata[1] = 0
|
|
result.udata[2] = 0
|
|
result.udata[3] = 0
|
|
|
|
proc maskBytes*(arg: Int128, numbytes: int): Int128 {.noinit.} =
|
|
case numbytes
|
|
of 1:
|
|
return maskUInt8(arg)
|
|
of 2:
|
|
return maskUInt16(arg)
|
|
of 4:
|
|
return maskUInt32(arg)
|
|
of 8:
|
|
return maskUInt64(arg)
|
|
else:
|
|
assert(false, "masking only implemented for 1, 2, 4 and 8 bytes")
|