On Mon, 25 Nov 2024 at 05:12, Eric Biggers <ebiggers@xxxxxxxxxx> wrote:
>
> From: Eric Biggers <ebiggers@xxxxxxxxxx>
>
> Add a Python script that generates constants for computing the given CRC
> variant(s) using x86's pclmulqdq or vpclmulqdq instructions.
>
There is nothing x86 specific about this, right? Except perhaps the
choice of fold distances?
> It can also generate the traditional byte-at-a-time tables.
>
> Only small changes should be needed for this script to also work to
> generate the constants needed for CRC computation on other architectures
> with a carryless multiplication instruction, such as arm64.
>
> Signed-off-by: Eric Biggers <ebiggers@xxxxxxxxxx>
> ---
> scripts/crc/gen-crc-consts.py | 207 ++++++++++++++++++++++++++++++++++
> 1 file changed, 207 insertions(+)
> create mode 100755 scripts/crc/gen-crc-consts.py
>
> diff --git a/scripts/crc/gen-crc-consts.py b/scripts/crc/gen-crc-consts.py
> new file mode 100755
> index 0000000000000..84f0902e1cd7b
> --- /dev/null
> +++ b/scripts/crc/gen-crc-consts.py
> @@ -0,0 +1,207 @@
> +#!/usr/bin/env python3
> +# SPDX-License-Identifier: GPL-2.0-or-later
> +#
> +# Script that generates constants for computing the given CRC variant(s).
> +#
> +# Copyright 2024 Google LLC
> +#
> +# Author: Eric Biggers <ebiggers@xxxxxxxxxx>
> +
> +import sys
> +
> +# XOR (add) an iterable of polynomials.
> +def xor(iterable):
> + res = 0
> + for val in iterable:
> + res ^= val
> + return res
> +
> +# Multiply two polynomials.
> +def clmul(a, b):
> + return xor(a << i for i in range(b.bit_length()) if (b & (1 << i)) != 0)
> +
> +# Polynomial division floor(a / b).
> +def div(a, b):
> + q = 0
> + while a.bit_length() >= b.bit_length():
> + q ^= 1 << (a.bit_length() - b.bit_length())
> + a ^= b << (a.bit_length() - b.bit_length())
> + return q
> +
> +# Reduce the polynomial 'a' modulo the polynomial 'b'.
> +def reduce(a, b):
> + return a ^ clmul(div(a, b), b)
> +
> +# Pretty-print a polynomial.
> +def pprint_poly(prefix, poly):
> + terms = ['1' if i == 0 else 'x' if i == 1 else f'x^{i}'
> + for i in reversed(range(poly.bit_length()))
> + if (poly & (1 << i)) != 0]
> + j = 0
> + while j < len(terms):
> + s = prefix + terms[j] + (' +' if j < len(terms) - 1 else '')
> + j += 1
> + while j < len(terms) and len(s) < 72:
> + s += ' ' + terms[j] + (' +' if j < len(terms) - 1 else '')
> + j += 1
> + print(s)
> + prefix = ' * ' + (' ' * (len(prefix) - 3))
> +
> +# Reverse the bits of a polynomial.
> +def bitreverse(poly, num_bits):
> + return xor(1 << (num_bits - 1 - i) for i in range(num_bits)
> + if (poly & (1 << i)) != 0)
> +
> +# Format a polynomial as hex. Bit-reflect it if the CRC is LSB-first.
> +def fmt_poly(variant, poly, num_bits):
> + if variant.lsb:
> + poly = bitreverse(poly, num_bits)
> + return f'0x{poly:0{2*num_bits//8}x}'
> +
> +# Print a comment describing constants generated for the given CRC variant.
> +def print_header(variant, what):
> + print('/*')
> + s = f'{"least" if variant.lsb else "most"}-significant-bit-first CRC-{variant.bits}'
> + print(f' * {what} generated for {s} using')
> + pprint_poly(' * G(x) = ', variant.G)
> + print(' */')
> +
> +# Print a polynomial as hex, but drop a term if needed to keep it in 64 bits.
> +def print_poly_truncate65thbit(variant, poly, num_bits, desc):
> + if num_bits > 64:
> + assert num_bits == 65
> + if variant.lsb:
> + assert (poly & 1) != 0
> + poly >>= 1
> + desc += ' - 1'
> + else:
> + poly ^= 1 << 64
> + desc += ' - x^64'
> + num_bits = 64
> + print(f'\t\t{fmt_poly(variant, poly, num_bits)},\t/* {desc} */')
> +
> +class CrcVariant:
> + def __init__(self, bits, generator_poly, bit_order):
> + self.bits = bits
> + if bit_order not in ['lsb', 'msb']:
> + raise ValueError('Invalid value for bit_order')
> + self.lsb = bit_order == 'lsb'
> + self.name = f'crc{bits}_{bit_order}_0x{generator_poly:0{(2*bits+7)//8}x}'
> + if self.lsb:
> + generator_poly = bitreverse(generator_poly, bits)
> + self.G = generator_poly ^ (1 << bits)
> +
> +# Generate tables for byte-at-a-time CRC computation.
> +def gen_sliceby1_tables(variants):
> + for v in variants:
> + print('')
> + print_header(v, 'CRC table')
> + print(f'static const u{v.bits} __maybe_unused {v.name}_table[256] = {{')
> + s = ''
> + for i in range(256):
> + remainder = (bitreverse(i, 8) if v.lsb else i) << (v.bits - 8)
> + for _ in range(8):
> + remainder <<= 1
> + if (remainder & (1 << v.bits)) != 0:
> + remainder ^= v.G
> + next_entry = fmt_poly(v, remainder, v.bits) + ','
> + if len(s + next_entry) > 71:
> + print(f'\t{s}')
> + s = ''
> + s += (' ' if s else '') + next_entry
> + if s:
> + print(f'\t{s}')
> + print('};')
> +
> +# Generate constants for carryless multiplication based CRC computation.
> +def gen_x86_pclmul_consts(variants):
> + # These are the distances, in bits, to generate folding constants for.
> + FOLD_DISTANCES = [2048, 1024, 512, 256, 128]
> +
> + for v in variants:
> + print('')
> + print_header(v, 'CRC folding constants')
> + print('static const struct {')
> + if not v.lsb:
> + print('\tu8 bswap_mask[16];')
> + for i in FOLD_DISTANCES:
> + print(f'\tu64 fold_across_{i}_bits_consts[2];')
> + print('\tu8 shuf_table[48];')
> + print('\tu64 barrett_reduction_consts[2];')
> + if v.lsb and v.bits < 64:
> + print('\tu64 extract_crc_mask[2];')
> + print(f'}} {v.name}_consts __cacheline_aligned __maybe_unused = {{')
> +
> + # Byte-reflection mask, needed for MSB CRCs
> + if not v.lsb:
> + print('\t.bswap_mask = {' + ', '.join(str(i) for i in reversed(range(16))) + '},')
> +
> + # Fold constants for all distances down to 128 bits
> + k = v.bits - 65 if v.lsb else 0
> + for i in FOLD_DISTANCES:
> + print(f'\t.fold_across_{i}_bits_consts = {{')
> + for j in [64, 0] if v.lsb else [0, 64]:
> + const = reduce(1<<(i+j+k), v.G)
> + pow_desc = f'{i}{"+" if j >= 0 else "-"}{abs(j)}'
> + if k != 0:
> + pow_desc += f'{"+" if k >= 0 else "-"}{abs(k)}'
> + print(f'\t\t{fmt_poly(v, const, v.bits)},\t/* x^({pow_desc}) mod G(x) */')
> + print('\t},')
> +
> + # Shuffle table for handling 1..15 bytes at end
> + print('\t.shuf_table = {')
> + print('\t\t' + (16*'-1, ').rstrip())
> + print('\t\t' + ''.join(f'{i:2}, ' for i in range(16)).rstrip())
> + print('\t\t' + (16*'-1, ').rstrip())
> + print('\t},')
> +
> + # Barrett reduction constants for reducing 128 bits to the final CRC
> + m = 63 if v.lsb else 64
> + print('\t.barrett_reduction_consts = {')
> + print_poly_truncate65thbit(v, div(1<<(m+v.bits), v.G), m+1,
> + f'floor(x^{m+v.bits} / G(x))')
> + print_poly_truncate65thbit(v, v.G, v.bits+1, 'G(x)')
> + print('\t},')
> + if v.lsb and v.bits < 64:
> + print(f'\t.extract_crc_mask = {{0, 0x{(1<<(v.bits))-1:x}}},')
> +
> + print('};')
> +
> +def parse_crc_variants(vars_string):
> + variants = []
> + for var_string in vars_string.split(','):
> + bits, bit_order, generator_poly = var_string.split('_')
> + assert bits.startswith('crc')
> + bits = int(bits.removeprefix('crc'))
> + assert generator_poly.startswith('0x')
> + generator_poly = generator_poly.removeprefix('0x')
> + assert len(generator_poly) % 2 == 0
> + generator_poly = int(generator_poly, 16)
> + variants.append(CrcVariant(bits, generator_poly, bit_order))
> + return variants
> +
> +if len(sys.argv) != 3:
> + sys.stderr.write(f'Usage: {sys.argv[0]} CONSTS_TYPE[,CONSTS_TYPE]... CRC_VARIANT[,CRC_VARIANT]...\n')
> + sys.stderr.write(' CONSTS_TYPE can be sliceby1 or x86_pclmul\n')
> + sys.stderr.write(' CRC_VARIANT is crc${num_bits}_${bit_order}_${generator_poly_as_hex}\n')
> + sys.stderr.write(' E.g. crc16_msb_0x8bb7 or crc32_lsb_0xedb88320\n')
> + sys.stderr.write(' Polynomial must use the given bit_order and exclude x^{num_bits}\n')
> + sys.exit(1)
> +
> +print('/* SPDX-License-Identifier: GPL-2.0-or-later */')
Does it make sense to add a GPL header into a generated file?
> +print('/*')
> +print(' * CRC constants generated by:')
> +print(' *')
> +print(f' *\t{sys.argv[0]} {" ".join(sys.argv[1:])}')
> +print(' *')
> +print(' * Do not edit manually.')
> +print(' */')
> +consts_types = sys.argv[1].split(',')
> +variants = parse_crc_variants(sys.argv[2])
> +for consts_type in consts_types:
> + if consts_type == 'sliceby1':
> + gen_sliceby1_tables(variants)
> + elif consts_type == 'x86_pclmul':
> + gen_x86_pclmul_consts(variants)
> + else:
> + raise ValueError(f'Unknown consts_type: {consts_type}')
> --
> 2.47.0
>
