[PATCH 2/6] scripts/crc: add gen-crc-consts.py

[Eric Biggers <ebiggers@kernel.org>]

From: Eric Biggers <ebiggers@google.com>

Add a Python script that generates constants for computing the given CRC
variant(s) using x86's pclmulqdq or vpclmulqdq instructions.

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@google.com>
---
 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@google.com>
+
+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 */')
+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