292 lines
12 KiB
Python
Executable File
292 lines
12 KiB
Python
Executable File
#!/usr/bin/env python3
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# SPDX-License-Identifier: GPL-2.0-or-later
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#
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# Script that generates constants for computing the given CRC variant(s).
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#
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# Copyright 2025 Google LLC
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#
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# Author: Eric Biggers <ebiggers@google.com>
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import sys
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# XOR (add) an iterable of polynomials.
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def xor(iterable):
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res = 0
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for val in iterable:
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res ^= val
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return res
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# Multiply two polynomials.
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def clmul(a, b):
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return xor(a << i for i in range(b.bit_length()) if (b & (1 << i)) != 0)
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# Polynomial division floor(a / b).
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def div(a, b):
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q = 0
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while a.bit_length() >= b.bit_length():
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q ^= 1 << (a.bit_length() - b.bit_length())
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a ^= b << (a.bit_length() - b.bit_length())
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return q
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# Reduce the polynomial 'a' modulo the polynomial 'b'.
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def reduce(a, b):
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return a ^ clmul(div(a, b), b)
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# Reflect the bits of a polynomial.
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def bitreflect(poly, num_bits):
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assert poly.bit_length() <= num_bits
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return xor(((poly >> i) & 1) << (num_bits - 1 - i) for i in range(num_bits))
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# Format a polynomial as hex. Bit-reflect it if the CRC is lsb-first.
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def fmt_poly(variant, poly, num_bits):
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if variant.lsb:
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poly = bitreflect(poly, num_bits)
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return f'0x{poly:0{2*num_bits//8}x}'
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# Print a pair of 64-bit polynomial multipliers. They are always passed in the
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# order [HI64_TERMS, LO64_TERMS] but will be printed in the appropriate order.
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def print_mult_pair(variant, mults):
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mults = list(mults if variant.lsb else reversed(mults))
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terms = ['HI64_TERMS', 'LO64_TERMS'] if variant.lsb else ['LO64_TERMS', 'HI64_TERMS']
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for i in range(2):
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print(f'\t\t{fmt_poly(variant, mults[i]["val"], 64)},\t/* {terms[i]}: {mults[i]["desc"]} */')
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# Pretty-print a polynomial.
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def pprint_poly(prefix, poly):
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terms = [f'x^{i}' for i in reversed(range(poly.bit_length()))
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if (poly & (1 << i)) != 0]
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j = 0
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while j < len(terms):
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s = prefix + terms[j] + (' +' if j < len(terms) - 1 else '')
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j += 1
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while j < len(terms) and len(s) < 73:
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s += ' ' + terms[j] + (' +' if j < len(terms) - 1 else '')
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j += 1
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print(s)
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prefix = ' * ' + (' ' * (len(prefix) - 3))
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# Print a comment describing constants generated for the given CRC variant.
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def print_header(variant, what):
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print('/*')
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s = f'{"least" if variant.lsb else "most"}-significant-bit-first CRC-{variant.bits}'
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print(f' * {what} generated for {s} using')
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pprint_poly(' * G(x) = ', variant.G)
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print(' */')
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class CrcVariant:
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def __init__(self, bits, generator_poly, bit_order):
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self.bits = bits
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if bit_order not in ['lsb', 'msb']:
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raise ValueError('Invalid value for bit_order')
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self.lsb = bit_order == 'lsb'
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self.name = f'crc{bits}_{bit_order}_0x{generator_poly:0{(2*bits+7)//8}x}'
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if self.lsb:
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generator_poly = bitreflect(generator_poly, bits)
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self.G = generator_poly ^ (1 << bits)
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# Generate tables for CRC computation using the "slice-by-N" method.
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# N=1 corresponds to the traditional byte-at-a-time table.
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def gen_slicebyN_tables(variants, n):
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for v in variants:
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print('')
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print_header(v, f'Slice-by-{n} CRC table')
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print(f'static const u{v.bits} __maybe_unused {v.name}_table[{256*n}] = {{')
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s = ''
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for i in range(256 * n):
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# The i'th table entry is the CRC of the message consisting of byte
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# i % 256 followed by i // 256 zero bytes.
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poly = (bitreflect(i % 256, 8) if v.lsb else i % 256) << (v.bits + 8*(i//256))
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next_entry = fmt_poly(v, reduce(poly, v.G), v.bits) + ','
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if len(s + next_entry) > 71:
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print(f'\t{s}')
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s = ''
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s += (' ' if s else '') + next_entry
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if s:
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print(f'\t{s}')
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print('};')
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def print_riscv_const(v, bits_per_long, name, val, desc):
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print(f'\t.{name} = {fmt_poly(v, val, bits_per_long)}, /* {desc} */')
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def do_gen_riscv_clmul_consts(v, bits_per_long):
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(G, n, lsb) = (v.G, v.bits, v.lsb)
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pow_of_x = 3 * bits_per_long - (1 if lsb else 0)
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print_riscv_const(v, bits_per_long, 'fold_across_2_longs_const_hi',
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reduce(1 << pow_of_x, G), f'x^{pow_of_x} mod G')
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pow_of_x = 2 * bits_per_long - (1 if lsb else 0)
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print_riscv_const(v, bits_per_long, 'fold_across_2_longs_const_lo',
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reduce(1 << pow_of_x, G), f'x^{pow_of_x} mod G')
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pow_of_x = bits_per_long - 1 + n
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print_riscv_const(v, bits_per_long, 'barrett_reduction_const_1',
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div(1 << pow_of_x, G), f'floor(x^{pow_of_x} / G)')
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val = G - (1 << n)
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desc = f'G - x^{n}'
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if lsb:
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val <<= bits_per_long - n
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desc = f'({desc}) * x^{bits_per_long - n}'
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print_riscv_const(v, bits_per_long, 'barrett_reduction_const_2', val, desc)
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def gen_riscv_clmul_consts(variants):
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print('')
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print('struct crc_clmul_consts {');
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print('\tunsigned long fold_across_2_longs_const_hi;');
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print('\tunsigned long fold_across_2_longs_const_lo;');
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print('\tunsigned long barrett_reduction_const_1;');
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print('\tunsigned long barrett_reduction_const_2;');
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print('};');
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for v in variants:
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print('');
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if v.bits > 32:
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print_header(v, 'Constants')
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print('#ifdef CONFIG_64BIT')
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print(f'static const struct crc_clmul_consts {v.name}_consts __maybe_unused = {{')
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do_gen_riscv_clmul_consts(v, 64)
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print('};')
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print('#endif')
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else:
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print_header(v, 'Constants')
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print(f'static const struct crc_clmul_consts {v.name}_consts __maybe_unused = {{')
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print('#ifdef CONFIG_64BIT')
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do_gen_riscv_clmul_consts(v, 64)
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print('#else')
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do_gen_riscv_clmul_consts(v, 32)
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print('#endif')
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print('};')
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# Generate constants for carryless multiplication based CRC computation.
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def gen_x86_pclmul_consts(variants):
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# These are the distances, in bits, to generate folding constants for.
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FOLD_DISTANCES = [2048, 1024, 512, 256, 128]
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for v in variants:
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(G, n, lsb) = (v.G, v.bits, v.lsb)
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print('')
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print_header(v, 'CRC folding constants')
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print('static const struct {')
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if not lsb:
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print('\tu8 bswap_mask[16];')
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for i in FOLD_DISTANCES:
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print(f'\tu64 fold_across_{i}_bits_consts[2];')
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print('\tu8 shuf_table[48];')
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print('\tu64 barrett_reduction_consts[2];')
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print(f'}} {v.name}_consts ____cacheline_aligned __maybe_unused = {{')
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# Byte-reflection mask, needed for msb-first CRCs
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if not lsb:
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print('\t.bswap_mask = {' + ', '.join(str(i) for i in reversed(range(16))) + '},')
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# Fold constants for all distances down to 128 bits
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for i in FOLD_DISTANCES:
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print(f'\t.fold_across_{i}_bits_consts = {{')
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# Given 64x64 => 128 bit carryless multiplication instructions, two
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# 64-bit fold constants are needed per "fold distance" i: one for
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# HI64_TERMS that is basically x^(i+64) mod G and one for LO64_TERMS
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# that is basically x^i mod G. The exact values however undergo a
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# couple adjustments, described below.
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mults = []
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for j in [64, 0]:
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pow_of_x = i + j
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if lsb:
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# Each 64x64 => 128 bit carryless multiplication instruction
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# actually generates a 127-bit product in physical bits 0
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# through 126, which in the lsb-first case represent the
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# coefficients of x^1 through x^127, not x^0 through x^126.
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# Thus in the lsb-first case, each such instruction
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# implicitly adds an extra factor of x. The below removes a
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# factor of x from each constant to compensate for this.
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# For n < 64 the x could be removed from either the reduced
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# part or unreduced part, but for n == 64 the reduced part
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# is the only option. Just always use the reduced part.
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pow_of_x -= 1
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# Make a factor of x^(64-n) be applied unreduced rather than
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# reduced, to cause the product to use only the x^(64-n) and
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# higher terms and always be zero in the lower terms. Usually
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# this makes no difference as it does not affect the product's
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# congruence class mod G and the constant remains 64-bit, but
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# part of the final reduction from 128 bits does rely on this
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# property when it reuses one of the constants.
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pow_of_x -= 64 - n
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mults.append({ 'val': reduce(1 << pow_of_x, G) << (64 - n),
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'desc': f'(x^{pow_of_x} mod G) * x^{64-n}' })
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print_mult_pair(v, mults)
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print('\t},')
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# Shuffle table for handling 1..15 bytes at end
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print('\t.shuf_table = {')
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print('\t\t' + (16*'-1, ').rstrip())
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print('\t\t' + ''.join(f'{i:2}, ' for i in range(16)).rstrip())
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print('\t\t' + (16*'-1, ').rstrip())
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print('\t},')
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# Barrett reduction constants for reducing 128 bits to the final CRC
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print('\t.barrett_reduction_consts = {')
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mults = []
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val = div(1 << (63+n), G)
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desc = f'floor(x^{63+n} / G)'
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if not lsb:
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val = (val << 1) - (1 << 64)
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desc = f'({desc} * x) - x^64'
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mults.append({ 'val': val, 'desc': desc })
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val = G - (1 << n)
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desc = f'G - x^{n}'
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if lsb and n == 64:
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assert (val & 1) != 0 # The x^0 term should always be nonzero.
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val >>= 1
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desc = f'({desc} - x^0) / x'
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else:
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pow_of_x = 64 - n - (1 if lsb else 0)
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val <<= pow_of_x
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desc = f'({desc}) * x^{pow_of_x}'
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mults.append({ 'val': val, 'desc': desc })
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print_mult_pair(v, mults)
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print('\t},')
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print('};')
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def parse_crc_variants(vars_string):
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variants = []
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for var_string in vars_string.split(','):
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bits, bit_order, generator_poly = var_string.split('_')
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assert bits.startswith('crc')
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bits = int(bits.removeprefix('crc'))
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assert generator_poly.startswith('0x')
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generator_poly = generator_poly.removeprefix('0x')
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assert len(generator_poly) % 2 == 0
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generator_poly = int(generator_poly, 16)
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variants.append(CrcVariant(bits, generator_poly, bit_order))
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return variants
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if len(sys.argv) != 3:
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sys.stderr.write(f'Usage: {sys.argv[0]} CONSTS_TYPE[,CONSTS_TYPE]... CRC_VARIANT[,CRC_VARIANT]...\n')
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sys.stderr.write(' CONSTS_TYPE can be sliceby[1-8], riscv_clmul, or x86_pclmul\n')
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sys.stderr.write(' CRC_VARIANT is crc${num_bits}_${bit_order}_${generator_poly_as_hex}\n')
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sys.stderr.write(' E.g. crc16_msb_0x8bb7 or crc32_lsb_0xedb88320\n')
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sys.stderr.write(' Polynomial must use the given bit_order and exclude x^{num_bits}\n')
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sys.exit(1)
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print('/* SPDX-License-Identifier: GPL-2.0-or-later */')
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print('/*')
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print(' * CRC constants generated by:')
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print(' *')
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print(f' *\t{sys.argv[0]} {" ".join(sys.argv[1:])}')
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print(' *')
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print(' * Do not edit manually.')
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print(' */')
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consts_types = sys.argv[1].split(',')
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variants = parse_crc_variants(sys.argv[2])
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for consts_type in consts_types:
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if consts_type.startswith('sliceby'):
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gen_slicebyN_tables(variants, int(consts_type.removeprefix('sliceby')))
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elif consts_type == 'riscv_clmul':
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gen_riscv_clmul_consts(variants)
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elif consts_type == 'x86_pclmul':
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gen_x86_pclmul_consts(variants)
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else:
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raise ValueError(f'Unknown consts_type: {consts_type}')
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