Nim/lib/pure/bitops.nim

#
#
#            Nim's Runtime Library
#        (c) Copyright 2017 Nim Authors
#
#    See the file "copying.txt", included in this
#    distribution, for details about the copyright.
#

## This module implements a series of low level methods for bit manipulation.
##
## By default, compiler intrinsics are used where possible to improve performance
## on supported compilers: `GCC`, `LLVM_GCC`, `CLANG`, `VCC`, `ICC`.
##
## The module will fallback to pure nim procs in case the backend is not supported.
## You can also use the flag `noIntrinsicsBitOpts` to disable compiler intrinsics.
##
## This module is also compatible with other backends: `JavaScript`, `NimScript`
## as well as the `compiletime VM`.
##
## As a result of using optimized functions/intrinsics, some functions can return
## undefined results if the input is invalid. You can use the flag `noUndefinedBitOpts`
## to force predictable behaviour for all input, causing a small performance hit.
##
## At this time only `fastLog2`, `firstSetBit`, `countLeadingZeroBits` and `countTrailingZeroBits`
## may return undefined and/or platform dependent values if given invalid input.

import macros
import std/private/since
from std/private/bitops_utils import forwardImpl, castToUnsigned

func bitnot*[T: SomeInteger](x: T): T {.magic: "BitnotI".}
  ## Computes the `bitwise complement` of the integer `x`.

func internalBitand[T: SomeInteger](x, y: T): T {.magic: "BitandI".}

func internalBitor[T: SomeInteger](x, y: T): T {.magic: "BitorI".}

func internalBitxor[T: SomeInteger](x, y: T): T {.magic: "BitxorI".}

macro bitand*[T: SomeInteger](x, y: T; z: varargs[T]): T =
  ## Computes the `bitwise and` of all arguments collectively.
  let fn = bindSym("internalBitand")
  result = newCall(fn, x, y)
  for extra in z:
    result = newCall(fn, result, extra)

macro bitor*[T: SomeInteger](x, y: T; z: varargs[T]): T =
  ## Computes the `bitwise or` of all arguments collectively.
  let fn = bindSym("internalBitor")
  result = newCall(fn, x, y)
  for extra in z:
    result = newCall(fn, result, extra)

macro bitxor*[T: SomeInteger](x, y: T; z: varargs[T]): T =
  ## Computes the `bitwise xor` of all arguments collectively.
  let fn = bindSym("internalBitxor")
  result = newCall(fn, x, y)
  for extra in z:
    result = newCall(fn, result, extra)


type BitsRange*[T] = range[0..sizeof(T)*8-1]
  ## A range with all bit positions for type `T`.

func bitsliced*[T: SomeInteger](v: T; slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Returns an extracted (and shifted) slice of bits from `v`.
  runnableExamples:
    doAssert 0b10111.bitsliced(2 .. 4) == 0b101
    doAssert 0b11100.bitsliced(0 .. 2) == 0b100
    doAssert 0b11100.bitsliced(0 ..< 3) == 0b100

  let
    upmost = sizeof(T) * 8 - 1
    uv     = v.castToUnsigned
  (uv shl (upmost - slice.b) shr (upmost - slice.b + slice.a)).T

proc bitslice*[T: SomeInteger](v: var T; slice: Slice[int]) {.inline, since: (1, 3).} =
  ## Mutates `v` into an extracted (and shifted) slice of bits from `v`.
  runnableExamples:
    var x = 0b101110
    x.bitslice(2 .. 4)
    doAssert x == 0b011

  let
    upmost = sizeof(T) * 8 - 1
    uv     = v.castToUnsigned
  v = (uv shl (upmost - slice.b) shr (upmost - slice.b + slice.a)).T

func toMask*[T: SomeInteger](slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Creates a bitmask based on a slice of bits.
  runnableExamples:
    doAssert toMask[int32](1 .. 3) == 0b1110'i32
    doAssert toMask[int32](0 .. 3) == 0b1111'i32

  let
    upmost = sizeof(T) * 8 - 1
    bitmask = bitnot(0.T).castToUnsigned
  (bitmask shl (upmost - slice.b + slice.a) shr (upmost - slice.b)).T

proc masked*[T: SomeInteger](v, mask :T): T {.inline, since: (1, 3).} =
  ## Returns `v`, with only the `1` bits from `mask` matching those of
  ## `v` set to 1.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.masked(0b0000_1010'u8) == 0b0000_0010'u8

  bitand(v, mask)

func masked*[T: SomeInteger](v: T; slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Returns `v`, with only the `1` bits in the range of `slice`
  ## matching those of `v` set to 1.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_1011'u8
    doAssert v.masked(1 .. 3) == 0b0000_1010'u8

  bitand(v, toMask[T](slice))

proc mask*[T: SomeInteger](v: var T; mask: T) {.inline, since: (1, 3).} =
  ## Mutates `v`, with only the `1` bits from `mask` matching those of
  ## `v` set to 1.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.mask(0b0000_1010'u8)
    doAssert v == 0b0000_0010'u8

  v = bitand(v, mask)

proc mask*[T: SomeInteger](v: var T; slice: Slice[int]) {.inline, since: (1, 3).} =
  ## Mutates `v`, with only the `1` bits in the range of `slice`
  ## matching those of `v` set to 1.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_1011'u8
    v.mask(1 .. 3)
    doAssert v == 0b0000_1010'u8

  v = bitand(v, toMask[T](slice))

func setMasked*[T: SomeInteger](v, mask :T): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits from `mask` set to 1.
  ##
  ## Effectively maps to a `bitor <#bitor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.setMasked(0b0000_1010'u8) == 0b0000_1011'u8

  bitor(v, mask)

func setMasked*[T: SomeInteger](v: T; slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits in the range of `slice` set to 1.
  ##
  ## Effectively maps to a `bitor <#bitor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.setMasked(2 .. 3) == 0b0000_1111'u8

  bitor(v, toMask[T](slice))

proc setMask*[T: SomeInteger](v: var T; mask: T) {.inline.} =
  ## Mutates `v`, with all the `1` bits from `mask` set to 1.
  ##
  ## Effectively maps to a `bitor <#bitor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.setMask(0b0000_1010'u8)
    doAssert v == 0b0000_1011'u8

  v = bitor(v, mask)

proc setMask*[T: SomeInteger](v: var T; slice: Slice[int]) {.inline, since: (1, 3).} =
  ## Mutates `v`, with all the `1` bits in the range of `slice` set to 1.
  ##
  ## Effectively maps to a `bitor <#bitor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.setMask(2 .. 3)
    doAssert v == 0b0000_1111'u8

  v = bitor(v, toMask[T](slice))

func clearMasked*[T: SomeInteger](v, mask :T): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits from `mask` set to 0.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation
  ## with an *inverted mask*.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.clearMasked(0b0000_1010'u8) == 0b0000_0001'u8

  bitand(v, bitnot(mask))

func clearMasked*[T: SomeInteger](v: T; slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits in the range of `slice` set to 0.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation
  ## with an *inverted mask*.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.clearMasked(1 .. 3) == 0b0000_0001'u8

  bitand(v, bitnot(toMask[T](slice)))

proc clearMask*[T: SomeInteger](v: var T; mask: T) {.inline.} =
  ## Mutates `v`, with all the `1` bits from `mask` set to 0.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation
  ## with an *inverted mask*.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.clearMask(0b0000_1010'u8)
    doAssert v == 0b0000_0001'u8

  v = bitand(v, bitnot(mask))

proc clearMask*[T: SomeInteger](v: var T; slice: Slice[int]) {.inline, since: (1, 3).} =
  ## Mutates `v`, with all the `1` bits in the range of `slice` set to 0.
  ##
  ## Effectively maps to a `bitand <#bitand.m,T,T,varargs[T]>`_ operation
  ## with an *inverted mask*.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.clearMask(1 .. 3)
    doAssert v == 0b0000_0001'u8

  v = bitand(v, bitnot(toMask[T](slice)))

func flipMasked*[T: SomeInteger](v, mask :T): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits from `mask` flipped.
  ##
  ## Effectively maps to a `bitxor <#bitxor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.flipMasked(0b0000_1010'u8) == 0b0000_1001'u8

  bitxor(v, mask)

func flipMasked*[T: SomeInteger](v: T; slice: Slice[int]): T {.inline, since: (1, 3).} =
  ## Returns `v`, with all the `1` bits in the range of `slice` flipped.
  ##
  ## Effectively maps to a `bitxor <#bitxor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    let v = 0b0000_0011'u8
    doAssert v.flipMasked(1 .. 3) == 0b0000_1101'u8

  bitxor(v, toMask[T](slice))

proc flipMask*[T: SomeInteger](v: var T; mask: T) {.inline.} =
  ## Mutates `v`, with all the `1` bits from `mask` flipped.
  ##
  ## Effectively maps to a `bitxor <#bitxor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.flipMask(0b0000_1010'u8)
    doAssert v == 0b0000_1001'u8

  v = bitxor(v, mask)

proc flipMask*[T: SomeInteger](v: var T; slice: Slice[int]) {.inline, since: (1, 3).} =
  ## Mutates `v`, with all the `1` bits in the range of `slice` flipped.
  ##
  ## Effectively maps to a `bitxor <#bitxor.m,T,T,varargs[T]>`_ operation.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.flipMask(1 .. 3)
    doAssert v == 0b0000_1101'u8

  v = bitxor(v, toMask[T](slice))

proc setBit*[T: SomeInteger](v: var T; bit: BitsRange[T]) {.inline.} =
  ## Mutates `v`, with the bit at position `bit` set to 1.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.setBit(5'u8)
    doAssert v == 0b0010_0011'u8

  v.setMask(1.T shl bit)

proc clearBit*[T: SomeInteger](v: var T; bit: BitsRange[T]) {.inline.} =
  ## Mutates `v`, with the bit at position `bit` set to 0.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.clearBit(1'u8)
    doAssert v == 0b0000_0001'u8

  v.clearMask(1.T shl bit)

proc flipBit*[T: SomeInteger](v: var T; bit: BitsRange[T]) {.inline.} =
  ## Mutates `v`, with the bit at position `bit` flipped.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.flipBit(1'u8)
    doAssert v == 0b0000_0001'u8

    v = 0b0000_0011'u8
    v.flipBit(2'u8)
    doAssert v == 0b0000_0111'u8

  v.flipMask(1.T shl bit)

macro setBits*(v: typed; bits: varargs[typed]): untyped =
  ## Mutates `v`, with the bits at positions `bits` set to 1.
  runnableExamples:
    var v = 0b0000_0011'u8
    v.setBits(3, 5, 7)
    doAssert v == 0b1010_1011'u8

  bits.expectKind(nnkBracket)
  result = newStmtList()
  for bit in bits:
    result.add newCall("setBit", v, bit)

macro clearBits*(v: typed; bits: varargs[typed]): untyped =
  ## Mutates `v`, with the bits at positions `bits` set to 0.
  runnableExamples:
    var v = 0b1111_1111'u8
    v.clearBits(1, 3, 5, 7)
    doAssert v == 0b0101_0101'u8

  bits.expectKind(nnkBracket)
  result = newStmtList()
  for bit in bits:
    result.add newCall("clearBit", v, bit)

macro flipBits*(v: typed; bits: varargs[typed]): untyped =
  ## Mutates `v`, with the bits at positions `bits` set to 0.
  runnableExamples:
    var v = 0b0000_1111'u8
    v.flipBits(1, 3, 5, 7)
    doAssert v == 0b1010_0101'u8

  bits.expectKind(nnkBracket)
  result = newStmtList()
  for bit in bits:
    result.add newCall("flipBit", v, bit)


proc testBit*[T: SomeInteger](v: T; bit: BitsRange[T]): bool {.inline.} =
  ## Returns true if the bit in `v` at positions `bit` is set to 1.
  runnableExamples:
    let v = 0b0000_1111'u8
    doAssert v.testBit(0)
    doAssert not v.testBit(7)

  let mask = 1.T shl bit
  return (v and mask) == mask

# #### Pure Nim version ####

func firstSetBitNim(x: uint32): int {.inline.} =
  ## Returns the 1-based index of the least significant set bit of x, or if x is zero, returns zero.
  # https://graphics.stanford.edu/%7Eseander/bithacks.html#ZerosOnRightMultLookup
  const lookup: array[32, uint8] = [0'u8, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15,
    25, 17, 4, 8, 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9]
  let v = x.uint32
  let k = not v + 1 # get two's complement # cast[uint32](-cast[int32](v))
  result = 1 + lookup[uint32((v and k) * 0x077CB531'u32) shr 27].int

func firstSetBitNim(x: uint64): int {.inline.} =
  ## Returns the 1-based index of the least significant set bit of x, or if x is zero, returns zero.
  # https://graphics.stanford.edu/%7Eseander/bithacks.html#ZerosOnRightMultLookup
  let v = uint64(x)
  var k = uint32(v and 0xFFFFFFFF'u32)
  if k == 0:
    k = uint32(v shr 32'u32) and 0xFFFFFFFF'u32
    result = 32
  else:
    result = 0
  result += firstSetBitNim(k)

func fastlog2Nim(x: uint32): int {.inline.} =
  ## Quickly find the log base 2 of a 32-bit or less integer.
  # https://graphics.stanford.edu/%7Eseander/bithacks.html#IntegerLogDeBruijn
  # https://stackoverflow.com/questions/11376288/fast-computing-of-log2-for-64-bit-integers
  const lookup: array[32, uint8] = [0'u8, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18,
    22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31]
  var v = x.uint32
  v = v or v shr 1 # first round down to one less than a power of 2
  v = v or v shr 2
  v = v or v shr 4
  v = v or v shr 8
  v = v or v shr 16
  result = lookup[uint32(v * 0x07C4ACDD'u32) shr 27].int

func fastlog2Nim(x: uint64): int {.inline.} =
  ## Quickly find the log base 2 of a 64-bit integer.
  # https://graphics.stanford.edu/%7Eseander/bithacks.html#IntegerLogDeBruijn
  # https://stackoverflow.com/questions/11376288/fast-computing-of-log2-for-64-bit-integers
  const lookup: array[64, uint8] = [0'u8, 58, 1, 59, 47, 53, 2, 60, 39, 48, 27, 54,
    33, 42, 3, 61, 51, 37, 40, 49, 18, 28, 20, 55, 30, 34, 11, 43, 14, 22, 4, 62,
    57, 46, 52, 38, 26, 32, 41, 50, 36, 17, 19, 29, 10, 13, 21, 56, 45, 25, 31,
    35, 16, 9, 12, 44, 24, 15, 8, 23, 7, 6, 5, 63]
  var v = x.uint64
  v = v or v shr 1 # first round down to one less than a power of 2
  v = v or v shr 2
  v = v or v shr 4
  v = v or v shr 8
  v = v or v shr 16
  v = v or v shr 32
  result = lookup[(v * 0x03F6EAF2CD271461'u64) shr 58].int

import system/countbits_impl

const useBuiltinsRotate = (defined(amd64) or defined(i386)) and
                          (defined(gcc) or defined(clang) or defined(vcc) or
                           (defined(icl) and not defined(cpp))) and useBuiltins

template parityImpl[T](value: T): int =
  # formula id from: https://graphics.stanford.edu/%7Eseander/bithacks.html#ParityParallel
  var v = value
  when sizeof(T) == 8:
    v = v xor (v shr 32)
  when sizeof(T) >= 4:
    v = v xor (v shr 16)
  when sizeof(T) >= 2:
    v = v xor (v shr 8)
  v = v xor (v shr 4)
  v = v and 0xf
  ((0x6996'u shr v) and 1).int


when useGCC_builtins:
  # Returns the bit parity in value
  proc builtin_parity(x: cuint): cint {.importc: "__builtin_parity", cdecl.}
  proc builtin_parityll(x: culonglong): cint {.importc: "__builtin_parityll", cdecl.}

  # Returns one plus the index of the least significant 1-bit of x, or if x is zero, returns zero.
  proc builtin_ffs(x: cint): cint {.importc: "__builtin_ffs", cdecl.}
  proc builtin_ffsll(x: clonglong): cint {.importc: "__builtin_ffsll", cdecl.}

  # Returns the number of leading 0-bits in x, starting at the most significant bit position. If x is 0, the result is undefined.
  proc builtin_clz(x: cuint): cint {.importc: "__builtin_clz", cdecl.}
  proc builtin_clzll(x: culonglong): cint {.importc: "__builtin_clzll", cdecl.}

  # Returns the number of trailing 0-bits in x, starting at the least significant bit position. If x is 0, the result is undefined.
  proc builtin_ctz(x: cuint): cint {.importc: "__builtin_ctz", cdecl.}
  proc builtin_ctzll(x: culonglong): cint {.importc: "__builtin_ctzll", cdecl.}

elif useVCC_builtins:
  # Search the mask data from most significant bit (MSB) to least significant bit (LSB) for a set bit (1).
  func bitScanReverse(index: ptr culong, mask: culong): uint8 {.
      importc: "_BitScanReverse", header: "<intrin.h>".}
  func bitScanReverse64(index: ptr culong, mask: uint64): uint8 {.
      importc: "_BitScanReverse64", header: "<intrin.h>".}

  # Search the mask data from least significant bit (LSB) to the most significant bit (MSB) for a set bit (1).
  func bitScanForward(index: ptr culong, mask: culong): uint8 {.
      importc: "_BitScanForward", header: "<intrin.h>".}
  func bitScanForward64(index: ptr culong, mask: uint64): uint8 {.
      importc: "_BitScanForward64", header: "<intrin.h>".}

  template vcc_scan_impl(fnc: untyped; v: untyped): int =
    var index: culong
    discard fnc(index.addr, v)
    index.int

elif useICC_builtins:
  # Returns the number of trailing 0-bits in x, starting at the least significant bit position. If x is 0, the result is undefined.
  func bitScanForward(p: ptr uint32, b: uint32): uint8 {.
      importc: "_BitScanForward", header: "<immintrin.h>".}
  func bitScanForward64(p: ptr uint32, b: uint64): uint8 {.
      importc: "_BitScanForward64", header: "<immintrin.h>".}

  # Returns the number of leading 0-bits in x, starting at the most significant bit position. If x is 0, the result is undefined.
  func bitScanReverse(p: ptr uint32, b: uint32): uint8 {.
      importc: "_BitScanReverse", header: "<immintrin.h>".}
  func bitScanReverse64(p: ptr uint32, b: uint64): uint8 {.
      importc: "_BitScanReverse64", header: "<immintrin.h>".}

  template icc_scan_impl(fnc: untyped; v: untyped): int =
    var index: uint32
    discard fnc(index.addr, v)
    index.int

func countSetBits*(x: SomeInteger): int {.inline.} =
  ## Counts the set bits in an integer (also called `Hamming weight`:idx:).
  runnableExamples:
    doAssert countSetBits(0b0000_0011'u8) == 2
    doAssert countSetBits(0b1010_1010'u8) == 4

  result = countSetBitsImpl(x)

func popcount*(x: SomeInteger): int {.inline.} =
  ## Alias for `countSetBits <#countSetBits,SomeInteger>`_ (Hamming weight).
  result = countSetBits(x)

func parityBits*(x: SomeInteger): int {.inline.} =
  ## Calculate the bit parity in an integer. If the number of 1-bits
  ## is odd, the parity is 1, otherwise 0.
  runnableExamples:
    doAssert parityBits(0b0000_0000'u8) == 0
    doAssert parityBits(0b0101_0001'u8) == 1
    doAssert parityBits(0b0110_1001'u8) == 0
    doAssert parityBits(0b0111_1111'u8) == 1

  # Can be used a base if creating ASM version.
  # https://stackoverflow.com/questions/21617970/how-to-check-if-value-has-even-parity-of-bits-or-odd
  let x = x.castToUnsigned
  when nimvm:
    result = forwardImpl(parityImpl, x)
  else:
    when useGCC_builtins:
      when sizeof(x) <= 4: result = builtin_parity(x.uint32).int
      else: result = builtin_parityll(x.uint64).int
    else:
      when sizeof(x) <= 4: result = parityImpl(x.uint32)
      else: result = parityImpl(x.uint64)

func firstSetBit*(x: SomeInteger): int {.inline.} =
  ## Returns the 1-based index of the least significant set bit of `x`.
  ## If `x` is zero, when `noUndefinedBitOpts` is set, the result is 0,
  ## otherwise the result is undefined.
  runnableExamples:
    doAssert firstSetBit(0b0000_0001'u8) == 1
    doAssert firstSetBit(0b0000_0010'u8) == 2
    doAssert firstSetBit(0b0000_0100'u8) == 3
    doAssert firstSetBit(0b0000_1000'u8) == 4
    doAssert firstSetBit(0b0000_1111'u8) == 1

  # GCC builtin 'builtin_ffs' already handle zero input.
  let x = x.castToUnsigned
  when nimvm:
    when noUndefined:
      if x == 0:
        return 0
    result = forwardImpl(firstSetBitNim, x)
  else:
    when noUndefined and not useGCC_builtins:
      if x == 0:
        return 0
    when useGCC_builtins:
      when sizeof(x) <= 4: result = builtin_ffs(cast[cint](x.cuint)).int
      else: result = builtin_ffsll(cast[clonglong](x.culonglong)).int
    elif useVCC_builtins:
      when sizeof(x) <= 4:
        result = 1 + vcc_scan_impl(bitScanForward, x.culong)
      elif arch64:
        result = 1 + vcc_scan_impl(bitScanForward64, x.uint64)
      else:
        result = firstSetBitNim(x.uint64)
    elif useICC_builtins:
      when sizeof(x) <= 4:
        result = 1 + icc_scan_impl(bitScanForward, x.uint32)
      elif arch64:
        result = 1 + icc_scan_impl(bitScanForward64, x.uint64)
      else:
        result = firstSetBitNim(x.uint64)
    else:
      when sizeof(x) <= 4: result = firstSetBitNim(x.uint32)
      else: result = firstSetBitNim(x.uint64)

func fastLog2*(x: SomeInteger): int {.inline.} =
  ## Quickly find the log base 2 of an integer.
  ## If `x` is zero, when `noUndefinedBitOpts` is set, the result is -1,
  ## otherwise the result is undefined.
  runnableExamples:
    doAssert fastLog2(0b0000_0001'u8) == 0
    doAssert fastLog2(0b0000_0010'u8) == 1
    doAssert fastLog2(0b0000_0100'u8) == 2
    doAssert fastLog2(0b0000_1000'u8) == 3
    doAssert fastLog2(0b0000_1111'u8) == 3

  let x = x.castToUnsigned
  when noUndefined:
    if x == 0:
      return -1
  when nimvm:
    result = forwardImpl(fastlog2Nim, x)
  else:
    when useGCC_builtins:
      when sizeof(x) <= 4: result = 31 - builtin_clz(x.uint32).int
      else: result = 63 - builtin_clzll(x.uint64).int
    elif useVCC_builtins:
      when sizeof(x) <= 4:
        result = vcc_scan_impl(bitScanReverse, x.culong)
      elif arch64:
        result = vcc_scan_impl(bitScanReverse64, x.uint64)
      else:
        result = fastlog2Nim(x.uint64)
    elif useICC_builtins:
      when sizeof(x) <= 4:
        result = icc_scan_impl(bitScanReverse, x.uint32)
      elif arch64:
        result = icc_scan_impl(bitScanReverse64, x.uint64)
      else:
        result = fastlog2Nim(x.uint64)
    else:
      when sizeof(x) <= 4: result = fastlog2Nim(x.uint32)
      else: result = fastlog2Nim(x.uint64)

func countLeadingZeroBits*(x: SomeInteger): int {.inline.} =
  ## Returns the number of leading zero bits in an integer.
  ## If `x` is zero, when `noUndefinedBitOpts` is set, the result is 0,
  ## otherwise the result is undefined.
  ##
  ## **See also:**
  ## * `countTrailingZeroBits proc <#countTrailingZeroBits,SomeInteger>`_
  runnableExamples:
    doAssert countLeadingZeroBits(0b0000_0001'u8) == 7
    doAssert countLeadingZeroBits(0b0000_0010'u8) == 6
    doAssert countLeadingZeroBits(0b0000_0100'u8) == 5
    doAssert countLeadingZeroBits(0b0000_1000'u8) == 4
    doAssert countLeadingZeroBits(0b0000_1111'u8) == 4

  let x = x.castToUnsigned
  when noUndefined:
    if x == 0:
      return 0
  when nimvm:
    result = sizeof(x)*8 - 1 - forwardImpl(fastlog2Nim, x)
  else:
    when useGCC_builtins:
      when sizeof(x) <= 4: result = builtin_clz(x.uint32).int - (32 - sizeof(x)*8)
      else: result = builtin_clzll(x.uint64).int
    else:
      when sizeof(x) <= 4: result = sizeof(x)*8 - 1 - fastlog2Nim(x.uint32)
      else: result = sizeof(x)*8 - 1 - fastlog2Nim(x.uint64)

func countTrailingZeroBits*(x: SomeInteger): int {.inline.} =
  ## Returns the number of trailing zeros in an integer.
  ## If `x` is zero, when `noUndefinedBitOpts` is set, the result is 0,
  ## otherwise the result is undefined.
  ##
  ## **See also:**
  ## * `countLeadingZeroBits proc <#countLeadingZeroBits,SomeInteger>`_
  runnableExamples:
    doAssert countTrailingZeroBits(0b0000_0001'u8) == 0
    doAssert countTrailingZeroBits(0b0000_0010'u8) == 1
    doAssert countTrailingZeroBits(0b0000_0100'u8) == 2
    doAssert countTrailingZeroBits(0b0000_1000'u8) == 3
    doAssert countTrailingZeroBits(0b0000_1111'u8) == 0

  let x = x.castToUnsigned
  when noUndefined:
    if x == 0:
      return 0
  when nimvm:
    result = firstSetBit(x) - 1
  else:
    when useGCC_builtins:
      when sizeof(x) <= 4: result = builtin_ctz(x.uint32).int
      else: result = builtin_ctzll(x.uint64).int
    else:
      result = firstSetBit(x) - 1

when useBuiltinsRotate:
  when defined(gcc):
    # GCC was tested until version 4.8.1 and intrinsics were present. Not tested
    # in previous versions.
    func builtin_rotl8(value: uint8, shift: cint): uint8
                      {.importc: "__rolb", header: "<x86intrin.h>".}
    func builtin_rotl16(value: cushort, shift: cint): cushort
                       {.importc: "__rolw", header: "<x86intrin.h>".}
    func builtin_rotl32(value: cuint, shift: cint): cuint
                       {.importc: "__rold", header: "<x86intrin.h>".}
    when defined(amd64):
      func builtin_rotl64(value: culonglong, shift: cint): culonglong
                         {.importc: "__rolq", header: "<x86intrin.h>".}

    func builtin_rotr8(value: uint8, shift: cint): uint8
                      {.importc: "__rorb", header: "<x86intrin.h>".}
    func builtin_rotr16(value: cushort, shift: cint): cushort
                       {.importc: "__rorw", header: "<x86intrin.h>".}
    func builtin_rotr32(value: cuint, shift: cint): cuint
                       {.importc: "__rord", header: "<x86intrin.h>".}
    when defined(amd64):
      func builtin_rotr64(value: culonglong, shift: cint): culonglong
                         {.importc: "__rorq", header: "<x86intrin.h>".}
  elif defined(clang):
    # In CLANG, builtins have been present since version 8.0.0 and intrinsics
    # since version 9.0.0. This implementation chose the builtins, as they have
    # been around for longer.
    # https://releases.llvm.org/8.0.0/tools/clang/docs/ReleaseNotes.html#non-comprehensive-list-of-changes-in-this-release
    # https://releases.llvm.org/8.0.0/tools/clang/docs/LanguageExtensions.html#builtin-rotateleft
    # source for correct declarations: https://github.com/llvm/llvm-project/blob/main/clang/include/clang/Basic/Builtins.def
    func builtin_rotl8(value: uint8, shift: uint8): uint8
                      {.importc: "__builtin_rotateleft8", nodecl.}
    func builtin_rotl16(value: cushort, shift: cushort): cushort
                       {.importc: "__builtin_rotateleft16", nodecl.}
    func builtin_rotl32(value: cuint, shift: cuint): cuint
                       {.importc: "__builtin_rotateleft32", nodecl.}
    when defined(amd64):
      func builtin_rotl64(value: culonglong, shift: culonglong): culonglong
                         {.importc: "__builtin_rotateleft64", nodecl.}

    func builtin_rotr8(value: uint8, shift: uint8): uint8
                      {.importc: "__builtin_rotateright8", nodecl.}
    func builtin_rotr16(value: cushort, shift: cushort): cushort
                       {.importc: "__builtin_rotateright16", nodecl.}
    func builtin_rotr32(value: cuint, shift: cuint): cuint
                       {.importc: "__builtin_rotateright32", nodecl.}
    when defined(amd64):
      # shift is unsigned, refs https://github.com/llvm-mirror/clang/commit/892de415b7fde609dafc4e6c1643b7eaa0150a4d
      func builtin_rotr64(value: culonglong, shift: culonglong): culonglong
                         {.importc: "__builtin_rotateright64", nodecl.}
  elif defined(vcc):
    # Tested on Microsoft (R) C/C++ Optimizing Compiler 19.28.29335 x64 and x86.
    # Not tested in previous versions.
    # https://docs.microsoft.com/en-us/cpp/intrinsics/rotl8-rotl16?view=msvc-160
    # https://docs.microsoft.com/en-us/cpp/intrinsics/rotr8-rotr16?view=msvc-160
    # https://docs.microsoft.com/en-us/cpp/c-runtime-library/reference/rotl-rotl64-rotr-rotr64?view=msvc-160
    func builtin_rotl8(value: uint8, shift: uint8): uint8
                      {.importc: "_rotl8", header: "<intrin.h>".}
    func builtin_rotl16(value: cushort, shift: uint8): cushort
                       {.importc: "_rotl16", header: "<intrin.h>".}
    func builtin_rotl32(value: cuint, shift: cint): cuint
                       {.importc: "_rotl", header: "<stdlib.h>".}
    when defined(amd64):
      func builtin_rotl64(value: culonglong, shift: cint): culonglong
                         {.importc: "_rotl64", header: "<stdlib.h>".}

    func builtin_rotr8(value: uint8, shift: uint8): uint8
                      {.importc: "_rotr8", header: "<intrin.h>".}
    func builtin_rotr16(value: cushort, shift: uint8): cushort
                       {.importc: "_rotr16", header: "<intrin.h>".}
    func builtin_rotr32(value: cuint, shift: cint): cuint
                       {.importc: "_rotr", header: "<stdlib.h>".}
    when defined(amd64):
      func builtin_rotr64(value: culonglong, shift: cint): culonglong
                         {.importc: "_rotr64", header: "<stdlib.h>".}
  elif defined(icl):
    # Tested on Intel(R) C++ Intel(R) 64 Compiler Classic Version 2021.1.2 Build
    # 20201208_000000 x64 and x86. Not tested in previous versions.
    func builtin_rotl8(value: uint8, shift: cint): uint8
                      {.importc: "__rolb", header: "<immintrin.h>".}
    func builtin_rotl16(value: cushort, shift: cint): cushort
                       {.importc: "__rolw", header: "<immintrin.h>".}
    func builtin_rotl32(value: cuint, shift: cint): cuint
                       {.importc: "__rold", header: "<immintrin.h>".}
    when defined(amd64):
      func builtin_rotl64(value: culonglong, shift: cint): culonglong
                         {.importc: "__rolq", header: "<immintrin.h>".}

    func builtin_rotr8(value: uint8, shift: cint): uint8
                      {.importc: "__rorb", header: "<immintrin.h>".}
    func builtin_rotr16(value: cushort, shift: cint): cushort
                       {.importc: "__rorw", header: "<immintrin.h>".}
    func builtin_rotr32(value: cuint, shift: cint): cuint
                       {.importc: "__rord", header: "<immintrin.h>".}
    when defined(amd64):
      func builtin_rotr64(value: culonglong, shift: cint): culonglong
                         {.importc: "__rorq", header: "<immintrin.h>".}

func rotl[T: SomeUnsignedInt](value: T, rot: int32): T {.inline.} =
  ## Left-rotate bits in a `value`.
  # https://stackoverflow.com/a/776523
  const mask = 8 * sizeof(value) - 1
  let rot = rot and mask
  (value shl rot) or (value shr ((-rot) and mask))

func rotr[T: SomeUnsignedInt](value: T, rot: int32): T {.inline.} =
  ## Right-rotate bits in a `value`.
  const mask = 8 * sizeof(value) - 1
  let rot = rot and mask
  (value shr rot) or (value shl ((-rot) and mask))

func shiftTypeTo(size: static int, shift: int): auto {.inline.} =
  ## Returns the `shift` for the rotation according to the compiler and the
  ## `size`.
  when (defined(vcc) and (size in [4, 8])) or defined(gcc) or defined(icl):
    cint(shift)
  elif (defined(vcc) and (size in [1, 2])) or (defined(clang) and size == 1):
    uint8(shift)
  elif defined(clang):
    when size == 2:
      cushort(shift)
    elif size == 4:
      cuint(shift)
    elif size == 8:
      culonglong(shift)

func rotateLeftBits*[T: SomeUnsignedInt](value: T, shift: range[0..(sizeof(T) * 8)]): T {.inline.} =
  ## Left-rotate bits in a `value`.
  runnableExamples:
    doAssert rotateLeftBits(0b0110_1001'u8, 4) == 0b1001_0110'u8
    doAssert rotateLeftBits(0b00111100_11000011'u16, 8) ==
      0b11000011_00111100'u16
    doAssert rotateLeftBits(0b0000111111110000_1111000000001111'u32, 16) ==
      0b1111000000001111_0000111111110000'u32
    doAssert rotateLeftBits(0b00000000111111111111111100000000_11111111000000000000000011111111'u64, 32) ==
      0b11111111000000000000000011111111_00000000111111111111111100000000'u64
  when nimvm:
    rotl(value, shift.int32)
  else:
    when useBuiltinsRotate:
      const size = sizeof(T)
      when size == 1:
        builtin_rotl8(value.uint8, shiftTypeTo(size, shift)).T
      elif size == 2:
        builtin_rotl16(value.cushort, shiftTypeTo(size, shift)).T
      elif size == 4:
        builtin_rotl32(value.cuint, shiftTypeTo(size, shift)).T
      elif size == 8 and arch64:
        builtin_rotl64(value.culonglong, shiftTypeTo(size, shift)).T
      else:
        rotl(value, shift.int32)
    else:
      rotl(value, shift.int32)

func rotateRightBits*[T: SomeUnsignedInt](value: T, shift: range[0..(sizeof(T) * 8)]): T {.inline.} =
  ## Right-rotate bits in a `value`.
  runnableExamples:
    doAssert rotateRightBits(0b0110_1001'u8, 4) == 0b1001_0110'u8
    doAssert rotateRightBits(0b00111100_11000011'u16, 8) ==
      0b11000011_00111100'u16
    doAssert rotateRightBits(0b0000111111110000_1111000000001111'u32, 16) ==
      0b1111000000001111_0000111111110000'u32
    doAssert rotateRightBits(0b00000000111111111111111100000000_11111111000000000000000011111111'u64, 32) ==
      0b11111111000000000000000011111111_00000000111111111111111100000000'u64
  when nimvm:
    rotr(value, shift.int32)
  else:
    when useBuiltinsRotate:
      const size = sizeof(T)
      when size == 1:
        builtin_rotr8(value.uint8, shiftTypeTo(size, shift)).T
      elif size == 2:
        builtin_rotr16(value.cushort, shiftTypeTo(size, shift)).T
      elif size == 4:
        builtin_rotr32(value.cuint, shiftTypeTo(size, shift)).T
      elif size == 8 and arch64:
        builtin_rotr64(value.culonglong, shiftTypeTo(size, shift)).T
      else:
        rotr(value, shift.int32)
    else:
      rotr(value, shift.int32)

func repeatBits[T: SomeUnsignedInt](x: SomeUnsignedInt; retType: type[T]): T  =
  result = x
  var i = 1
  while i != (sizeof(T) div sizeof(x)):
    result = (result shl (sizeof(x)*8*i)) or result
    i *= 2

func reverseBits*[T: SomeUnsignedInt](x: T): T =
  ## Return the bit reversal of x.
  runnableExamples:
    doAssert reverseBits(0b10100100'u8) == 0b00100101'u8
    doAssert reverseBits(0xdd'u8) == 0xbb'u8
    doAssert reverseBits(0xddbb'u16) == 0xddbb'u16
    doAssert reverseBits(0xdeadbeef'u32) == 0xf77db57b'u32

  template repeat(x: SomeUnsignedInt): T = repeatBits(x, T)

  result = x
  result =
    ((repeat(0x55u8) and result) shl 1) or
    ((repeat(0xaau8) and result) shr 1)
  result =
    ((repeat(0x33u8) and result) shl 2) or
    ((repeat(0xccu8) and result) shr 2)
  when sizeof(T) == 1:
    result = (result shl 4) or (result shr 4)
  when sizeof(T) >= 2:
    result =
      ((repeat(0x0fu8) and result) shl 4) or
      ((repeat(0xf0u8) and result) shr 4)
  when sizeof(T) == 2:
    result = (result shl 8) or (result shr 8)
  when sizeof(T) >= 4:
    result =
      ((repeat(0x00ffu16) and result) shl 8) or
      ((repeat(0xff00u16) and result) shr 8)
  when sizeof(T) == 4:
    result = (result shl 16) or (result shr 16)
  when sizeof(T) == 8:
    result =
      ((repeat(0x0000ffffu32) and result) shl 16) or
      ((repeat(0xffff0000u32) and result) shr 16)
    result = (result shl 32) or (result shr 32)