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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 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.
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
# #### Pure Nim version ####
proc firstSetBit_nim(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 firstSetBit_nim(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 += firstSetBit_nim(k)
proc fastlog2_nim(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 fastlog2_nim(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
proc countSetBits_nim(n: uint32): int {.inline, noSideEffect.} =
## Counts the set bits in integer. (also called Hamming weight.)
# generic formula is from: https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
var v = uint32(n)
v = v - ((v shr 1) and 0x55555555)
v = (v and 0x33333333) + ((v shr 2) and 0x33333333)
result = (((v + (v shr 4) and 0xF0F0F0F) * 0x1010101) shr 24).int
proc countSetBits_nim(n: uint64): int {.inline, noSideEffect.} =
## Counts the set bits in integer. (also called Hamming weight.)
# generic formula is from: https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
var v = uint64(n)
v = v - ((v shr 1'u64) and 0x5555555555555555'u64)
v = (v and 0x3333333333333333'u64) + ((v shr 2'u64) and 0x3333333333333333'u64)
v = (v + (v shr 4'u64) and 0x0F0F0F0F0F0F0F0F'u64)
result = ((v * 0x0101010101010101'u64) shr 56'u64).int
template parity_impl[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.)
# TODO: figure out if ICC support _popcnt32/_popcnt64 on platform without POPCNT.
# like GCC and MSVC
when nimvm:
when sizeof(x) <= 4: result = countSetBits_nim(x.uint32)
else: result = countSetBits_nim(x.uint64)
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 = countSetBits_nim(x.uint32)
else: result = countSetBits_nim(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 nimvm:
when sizeof(x) <= 4: result = parity_impl(x.uint32)
else: result = parity_impl(x.uint64)
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 = parity_impl(x.uint32)
else: result = parity_impl(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 nimvm:
when noUndefined:
if x == 0:
return 0
when sizeof(x) <= 4: result = firstSetBit_nim(x.uint32)
else: result = firstSetBit_nim(x.uint64)
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 = firstSetBit_nim(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 = firstSetBit_nim(x.uint64)
else:
when sizeof(x) <= 4: result = firstSetBit_nim(x.uint32)
else: result = firstSetBit_nim(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 noUndefined:
if x == 0:
return -1
when nimvm:
when sizeof(x) <= 4: result = fastlog2_nim(x.uint32)
else: result = fastlog2_nim(x.uint64)
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 = fastlog2_nim(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 = fastlog2_nim(x.uint64)
else:
when sizeof(x) <= 4: result = fastlog2_nim(x.uint32)
else: result = fastlog2_nim(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 noUndefined:
if x == 0:
return 0
when nimvm:
when sizeof(x) <= 4: result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint32)
else: result = sizeof(x)*8 - 1 - fastlog2_nim(x.uint64)
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 - fastlog2_nim(x.uint32)
else: result = sizeof(x)*8 - 1 - fastlog2_nim(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 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))
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