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Nim/lib/pure/bitops.nim

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#
#
# 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, this module use compiler intrinsics where possible to improve performance
## on supported compilers: ``GCC``, ``LLVM_GCC``, ``CLANG``, ``VCC``, ``ICC``.
##
## The module will fallback to pure nim procs incase 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 function/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`, `countTrailingZeroBits`
## may return undefined and/or platform dependant value if given invalid input.
proc bitnot*[T: SomeInteger](x: T): T {.magic: "BitnotI", noSideEffect.}
## Computes the `bitwise complement` of the integer `x`.
proc bitand*[T: SomeInteger](x, y: T): T {.magic: "BitandI", noSideEffect.}
## Computes the `bitwise and` of numbers `x` and `y`.
proc bitor*[T: SomeInteger](x, y: T): T {.magic: "BitorI", noSideEffect.}
## Computes the `bitwise or` of numbers `x` and `y`.
proc bitxor*[T: SomeInteger](x, y: T): T {.magic: "BitxorI", noSideEffect.}
## Computes the `bitwise xor` of numbers `x` and `y`.
const useBuiltins = not defined(noIntrinsicsBitOpts)
const noUndefined = defined(noUndefinedBitOpts)
const useGCC_builtins = (defined(gcc) or defined(llvm_gcc) or defined(clang)) and useBuiltins
const useICC_builtins = defined(icc) and useBuiltins
const useVCC_builtins = defined(vcc) and useBuiltins
const arch64 = sizeof(int) == 8
template toUnsigned(x: int8): uint8 = cast[uint8](x)
template toUnsigned(x: int16): uint16 = cast[uint16](x)
template toUnsigned(x: int32): uint32 = cast[uint32](x)
template toUnsigned(x: int64): uint64 = cast[uint64](x)
template toUnsigned(x: int): uint = cast[uint](x)
template forwardImpl(impl, arg) {.dirty.} =
when sizeof(x) <= 4:
when x is SomeSignedInt:
impl(cast[uint32](x.int32))
else:
impl(x.uint32)
else:
when x is SomeSignedInt:
impl(cast[uint64](x.int64))
else:
impl(x.uint64)
when defined(nimHasalignOf):
import macros
type BitsRange*[T] = range[0..sizeof(T)*8-1]
## Returns a range with all bit positions for type ``T``
proc setMask*[T: SomeInteger](v: var T, mask: T) {.inline.} =
## Returns ``v``, with all the ``1`` bits from ``mask`` set to 1
v = v or mask
proc clearMask*[T: SomeInteger](v: var T, mask: T) {.inline.} =
## Returns ``v``, with all the ``1`` bits from ``mask`` set to 0
v = v and not mask
proc flipMask*[T: SomeInteger](v: var T, mask: T) {.inline.} =
## Returns ``v``, with all the ``1`` bits from ``mask`` flipped
v = v xor mask
proc setBit*[T: SomeInteger](v: var T, bit: BitsRange[T]) {.inline.} =
## Returns ``v``, with the bit at position ``bit`` set to 1
v.setMask(1.T shl bit)
proc clearBit*[T: SomeInteger](v: var T, bit: BitsRange[T]) {.inline.} =
## Returns ``v``, with the bit at position ``bit`` set to 0
v.clearMask(1.T shl bit)
proc flipBit*[T: SomeInteger](v: var T, bit: BitsRange[T]) {.inline.} =
## Returns ``v``, with the bit at position ``bit`` flipped
v.flipMask(1.T shl bit)
macro setBits*(v: typed, bits: varargs[typed]): untyped =
## Returns ``v``, with the bits at positions ``bits`` set to 1
bits.expectKind(nnkBracket)
result = newStmtList()
for bit in bits:
result.add newCall("setBit", v, bit)
macro clearBits*(v: typed, bits: varargs[typed]): untyped =
## Returns ``v``, with the bits at positions ``bits`` set to 0
bits.expectKind(nnkBracket)
result = newStmtList()
for bit in bits:
result.add newCall("clearBit", v, bit)
macro flipBits*(v: typed, bits: varargs[typed]): untyped =
## Returns ``v``, with the bits at positions ``bits`` set to 0
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
let mask = 1.T shl bit
return (v and mask) == mask
# #### Pure Nim version ####
proc firstSetBitNim(x: uint32): int {.inline, noSideEffect.} =
## 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]
var v = x.uint32
var 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
proc firstSetBitNim(x: uint64): int {.inline, noSideEffect.} =
## 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
var v = uint64(x)
var k = uint32(v and 0xFFFFFFFF'u32)
if k == 0:
k = uint32(v shr 32'u32) and 0xFFFFFFFF'u32
result = 32
result += firstSetBitNim(k)
proc fastlog2Nim(x: uint32): int {.inline, noSideEffect.} =
## 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
proc fastlog2Nim(x: uint64): int {.inline, noSideEffect.} =
## 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
# sets.nim cannot import bitops, but bitops can use include
# system/sets to eleminate code duplication. sets.nim defines defines
# countBits32 and countBits64.
include system/sets
template countSetBitsNim(n: uint32): int = countBits32(n)
template countSetBitsNim(n: uint64): int = countBits64(n)
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 number of set 1-bits in value.
proc builtin_popcount(x: cuint): cint {.importc: "__builtin_popcount", cdecl.}
proc builtin_popcountll(x: culonglong): cint {.importc: "__builtin_popcountll", cdecl.}
# 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:
# Counts the number of one bits (population count) in a 16-, 32-, or 64-byte unsigned integer.
proc builtin_popcnt16(a2: uint16): uint16 {.importc: "__popcnt16" header: "<intrin.h>", noSideEffect.}
proc builtin_popcnt32(a2: uint32): uint32 {.importc: "__popcnt" header: "<intrin.h>", noSideEffect.}
proc builtin_popcnt64(a2: uint64): uint64 {.importc: "__popcnt64" header: "<intrin.h>", noSideEffect.}
# Search the mask data from most significant bit (MSB) to least significant bit (LSB) for a set bit (1).
proc bitScanReverse(index: ptr culong, mask: culong): cuchar {.importc: "_BitScanReverse", header: "<intrin.h>", noSideEffect.}
proc bitScanReverse64(index: ptr culong, mask: uint64): cuchar {.importc: "_BitScanReverse64", header: "<intrin.h>", noSideEffect.}
# Search the mask data from least significant bit (LSB) to the most significant bit (MSB) for a set bit (1).
proc bitScanForward(index: ptr culong, mask: culong): cuchar {.importc: "_BitScanForward", header: "<intrin.h>", noSideEffect.}
proc bitScanForward64(index: ptr culong, mask: uint64): cuchar {.importc: "_BitScanForward64", header: "<intrin.h>", noSideEffect.}
template vcc_scan_impl(fnc: untyped; v: untyped): int =
var index: culong
discard fnc(index.addr, v)
index.int
elif useICC_builtins:
# Intel compiler intrinsics: http://fulla.fnal.gov/intel/compiler_c/main_cls/intref_cls/common/intref_allia_misc.htm
# see also: https://software.intel.com/en-us/node/523362
# Count the number of bits set to 1 in an integer a, and return that count in dst.
proc builtin_popcnt32(a: cint): cint {.importc: "_popcnt" header: "<immintrin.h>", noSideEffect.}
proc builtin_popcnt64(a: uint64): cint {.importc: "_popcnt64" header: "<immintrin.h>", noSideEffect.}
# 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 bitScanForward(p: ptr uint32, b: uint32): cuchar {.importc: "_BitScanForward", header: "<immintrin.h>", noSideEffect.}
proc bitScanForward64(p: ptr uint32, b: uint64): cuchar {.importc: "_BitScanForward64", header: "<immintrin.h>", noSideEffect.}
# 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 bitScanReverse(p: ptr uint32, b: uint32): cuchar {.importc: "_BitScanReverse", header: "<immintrin.h>", noSideEffect.}
proc bitScanReverse64(p: ptr uint32, b: uint64): cuchar {.importc: "_BitScanReverse64", header: "<immintrin.h>", noSideEffect.}
template icc_scan_impl(fnc: untyped; v: untyped): int =
var index: uint32
discard fnc(index.addr, v)
index.int
proc countSetBits*(x: SomeInteger): int {.inline, noSideEffect.} =
## Counts the set bits in integer. (also called `Hamming weight`:idx:.)
# TODO: figure out if ICC support _popcnt32/_popcnt64 on platform without POPCNT.
# like GCC and MSVC
when x is SomeSignedInt:
let x = x.toUnsigned
when nimvm:
result = forwardImpl(countSetBitsNim, x)
else:
when useGCC_builtins:
when sizeof(x) <= 4: result = builtin_popcount(x.cuint).int
else: result = builtin_popcountll(x.culonglong).int
elif useVCC_builtins:
when sizeof(x) <= 2: result = builtin_popcnt16(x.uint16).int
elif sizeof(x) <= 4: result = builtin_popcnt32(x.uint32).int
elif arch64: result = builtin_popcnt64(x.uint64).int
else: result = builtin_popcnt32((x.uint64 and 0xFFFFFFFF'u64).uint32 ).int +
builtin_popcnt32((x.uint64 shr 32'u64).uint32 ).int
elif useICC_builtins:
when sizeof(x) <= 4: result = builtin_popcnt32(x.cint).int
elif arch64: result = builtin_popcnt64(x.uint64).int
else: result = builtin_popcnt32((x.uint64 and 0xFFFFFFFF'u64).cint ).int +
builtin_popcnt32((x.uint64 shr 32'u64).cint ).int
else:
when sizeof(x) <= 4: result = countSetBitsNim(x.uint32)
else: result = countSetBitsNim(x.uint64)
proc popcount*(x: SomeInteger): int {.inline, noSideEffect.} =
## Alias for for countSetBits (Hamming weight.)
result = countSetBits(x)
proc parityBits*(x: SomeInteger): int {.inline, noSideEffect.} =
## Calculate the bit parity in integer. If number of 1-bit
## is odd parity is 1, otherwise 0.
# 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
when x is SomeSignedInt:
let x = x.toUnsigned
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)
proc firstSetBit*(x: SomeInteger): int {.inline, noSideEffect.} =
## Returns the 1-based index of the least significant set bit of x.
## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is 0,
## otherwise result is undefined.
# GCC builtin 'builtin_ffs' already handle zero input.
when x is SomeSignedInt:
let x = x.toUnsigned
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)
proc fastLog2*(x: SomeInteger): int {.inline, noSideEffect.} =
## Quickly find the log base 2 of an integer.
## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is -1,
## otherwise result is undefined.
when x is SomeSignedInt:
let x = x.toUnsigned
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)
proc countLeadingZeroBits*(x: SomeInteger): int {.inline, noSideEffect.} =
## Returns the number of leading zero bits in integer.
## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is 0,
## otherwise result is undefined.
when x is SomeSignedInt:
let x = x.toUnsigned
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)
proc countTrailingZeroBits*(x: SomeInteger): int {.inline, noSideEffect.} =
## Returns the number of trailing zeros in integer.
## If `x` is zero, when ``noUndefinedBitOpts`` is set, result is 0,
## otherwise result is undefined.
when x is SomeSignedInt:
let x = x.toUnsigned
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
proc rotateLeftBits*(value: uint8;
amount: range[0..8]): uint8 {.inline, noSideEffect.} =
## Left-rotate bits in a 8-bits value.
# using this form instead of the one below should handle any value
# out of range as well as negative values.
# result = (value shl amount) or (value shr (8 - amount))
# taken from: https://en.wikipedia.org/wiki/Circular_shift#Implementing_circular_shifts
let amount = amount and 7
result = (value shl amount) or (value shr ( (-amount) and 7))
proc rotateLeftBits*(value: uint16;
amount: range[0..16]): uint16 {.inline, noSideEffect.} =
## Left-rotate bits in a 16-bits value.
let amount = amount and 15
result = (value shl amount) or (value shr ( (-amount) and 15))
proc rotateLeftBits*(value: uint32;
amount: range[0..32]): uint32 {.inline, noSideEffect.} =
## Left-rotate bits in a 32-bits value.
let amount = amount and 31
result = (value shl amount) or (value shr ( (-amount) and 31))
proc rotateLeftBits*(value: uint64;
amount: range[0..64]): uint64 {.inline, noSideEffect.} =
## Left-rotate bits in a 64-bits value.
let amount = amount and 63
result = (value shl amount) or (value shr ( (-amount) and 63))
proc rotateRightBits*(value: uint8;
amount: range[0..8]): uint8 {.inline, noSideEffect.} =
## Right-rotate bits in a 8-bits value.
let amount = amount and 7
result = (value shr amount) or (value shl ( (-amount) and 7))
proc rotateRightBits*(value: uint16;
amount: range[0..16]): uint16 {.inline, noSideEffect.} =
## Right-rotate bits in a 16-bits value.
let amount = amount and 15
result = (value shr amount) or (value shl ( (-amount) and 15))
proc rotateRightBits*(value: uint32;
amount: range[0..32]): uint32 {.inline, noSideEffect.} =
## Right-rotate bits in a 32-bits value.
let amount = amount and 31
result = (value shr amount) or (value shl ( (-amount) and 31))
proc rotateRightBits*(value: uint64;
amount: range[0..64]): uint64 {.inline, noSideEffect.} =
## Right-rotate bits in a 64-bits value.
let amount = amount and 63
result = (value shr amount) or (value shl ( (-amount) and 63))
proc repeatBits[T: SomeUnsignedInt](x: SomeUnsignedInt; retType: type[T]): T {.
noSideEffect.} =
result = x
var i = 1
while i != (sizeof(T) div sizeof(x)):
result = (result shl (sizeof(x)*8*i)) or result
i *= 2
proc reverseBits*[T: SomeUnsignedInt](x: T): T {.noSideEffect.} =
## 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)
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