div64.h (7437B)
1/* SPDX-License-Identifier: GPL-2.0 */ 2#ifndef _ASM_GENERIC_DIV64_H 3#define _ASM_GENERIC_DIV64_H 4/* 5 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com> 6 * Based on former asm-ppc/div64.h and asm-m68knommu/div64.h 7 * 8 * Optimization for constant divisors on 32-bit machines: 9 * Copyright (C) 2006-2015 Nicolas Pitre 10 * 11 * The semantics of do_div() is, in C++ notation, observing that the name 12 * is a function-like macro and the n parameter has the semantics of a C++ 13 * reference: 14 * 15 * uint32_t do_div(uint64_t &n, uint32_t base) 16 * { 17 * uint32_t remainder = n % base; 18 * n = n / base; 19 * return remainder; 20 * } 21 * 22 * NOTE: macro parameter n is evaluated multiple times, 23 * beware of side effects! 24 */ 25 26#include <linux/types.h> 27#include <linux/compiler.h> 28 29#if BITS_PER_LONG == 64 30 31/** 32 * do_div - returns 2 values: calculate remainder and update new dividend 33 * @n: uint64_t dividend (will be updated) 34 * @base: uint32_t divisor 35 * 36 * Summary: 37 * ``uint32_t remainder = n % base;`` 38 * ``n = n / base;`` 39 * 40 * Return: (uint32_t)remainder 41 * 42 * NOTE: macro parameter @n is evaluated multiple times, 43 * beware of side effects! 44 */ 45# define do_div(n,base) ({ \ 46 uint32_t __base = (base); \ 47 uint32_t __rem; \ 48 __rem = ((uint64_t)(n)) % __base; \ 49 (n) = ((uint64_t)(n)) / __base; \ 50 __rem; \ 51 }) 52 53#elif BITS_PER_LONG == 32 54 55#include <linux/log2.h> 56 57/* 58 * If the divisor happens to be constant, we determine the appropriate 59 * inverse at compile time to turn the division into a few inline 60 * multiplications which ought to be much faster. 61 * 62 * (It is unfortunate that gcc doesn't perform all this internally.) 63 */ 64 65#define __div64_const32(n, ___b) \ 66({ \ 67 /* \ 68 * Multiplication by reciprocal of b: n / b = n * (p / b) / p \ 69 * \ 70 * We rely on the fact that most of this code gets optimized \ 71 * away at compile time due to constant propagation and only \ 72 * a few multiplication instructions should remain. \ 73 * Hence this monstrous macro (static inline doesn't always \ 74 * do the trick here). \ 75 */ \ 76 uint64_t ___res, ___x, ___t, ___m, ___n = (n); \ 77 uint32_t ___p, ___bias; \ 78 \ 79 /* determine MSB of b */ \ 80 ___p = 1 << ilog2(___b); \ 81 \ 82 /* compute m = ((p << 64) + b - 1) / b */ \ 83 ___m = (~0ULL / ___b) * ___p; \ 84 ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b; \ 85 \ 86 /* one less than the dividend with highest result */ \ 87 ___x = ~0ULL / ___b * ___b - 1; \ 88 \ 89 /* test our ___m with res = m * x / (p << 64) */ \ 90 ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32; \ 91 ___t = ___res += (___m & 0xffffffff) * (___x >> 32); \ 92 ___res += (___x & 0xffffffff) * (___m >> 32); \ 93 ___t = (___res < ___t) ? (1ULL << 32) : 0; \ 94 ___res = (___res >> 32) + ___t; \ 95 ___res += (___m >> 32) * (___x >> 32); \ 96 ___res /= ___p; \ 97 \ 98 /* Now sanitize and optimize what we've got. */ \ 99 if (~0ULL % (___b / (___b & -___b)) == 0) { \ 100 /* special case, can be simplified to ... */ \ 101 ___n /= (___b & -___b); \ 102 ___m = ~0ULL / (___b / (___b & -___b)); \ 103 ___p = 1; \ 104 ___bias = 1; \ 105 } else if (___res != ___x / ___b) { \ 106 /* \ 107 * We can't get away without a bias to compensate \ 108 * for bit truncation errors. To avoid it we'd need an \ 109 * additional bit to represent m which would overflow \ 110 * a 64-bit variable. \ 111 * \ 112 * Instead we do m = p / b and n / b = (n * m + m) / p. \ 113 */ \ 114 ___bias = 1; \ 115 /* Compute m = (p << 64) / b */ \ 116 ___m = (~0ULL / ___b) * ___p; \ 117 ___m += ((~0ULL % ___b + 1) * ___p) / ___b; \ 118 } else { \ 119 /* \ 120 * Reduce m / p, and try to clear bit 31 of m when \ 121 * possible, otherwise that'll need extra overflow \ 122 * handling later. \ 123 */ \ 124 uint32_t ___bits = -(___m & -___m); \ 125 ___bits |= ___m >> 32; \ 126 ___bits = (~___bits) << 1; \ 127 /* \ 128 * If ___bits == 0 then setting bit 31 is unavoidable. \ 129 * Simply apply the maximum possible reduction in that \ 130 * case. Otherwise the MSB of ___bits indicates the \ 131 * best reduction we should apply. \ 132 */ \ 133 if (!___bits) { \ 134 ___p /= (___m & -___m); \ 135 ___m /= (___m & -___m); \ 136 } else { \ 137 ___p >>= ilog2(___bits); \ 138 ___m >>= ilog2(___bits); \ 139 } \ 140 /* No bias needed. */ \ 141 ___bias = 0; \ 142 } \ 143 \ 144 /* \ 145 * Now we have a combination of 2 conditions: \ 146 * \ 147 * 1) whether or not we need to apply a bias, and \ 148 * \ 149 * 2) whether or not there might be an overflow in the cross \ 150 * product determined by (___m & ((1 << 63) | (1 << 31))). \ 151 * \ 152 * Select the best way to do (m_bias + m * n) / (1 << 64). \ 153 * From now on there will be actual runtime code generated. \ 154 */ \ 155 ___res = __arch_xprod_64(___m, ___n, ___bias); \ 156 \ 157 ___res /= ___p; \ 158}) 159 160#ifndef __arch_xprod_64 161/* 162 * Default C implementation for __arch_xprod_64() 163 * 164 * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias) 165 * Semantic: retval = ((bias ? m : 0) + m * n) >> 64 166 * 167 * The product is a 128-bit value, scaled down to 64 bits. 168 * Assuming constant propagation to optimize away unused conditional code. 169 * Architectures may provide their own optimized assembly implementation. 170 */ 171static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias) 172{ 173 uint32_t m_lo = m; 174 uint32_t m_hi = m >> 32; 175 uint32_t n_lo = n; 176 uint32_t n_hi = n >> 32; 177 uint64_t res; 178 uint32_t res_lo, res_hi, tmp; 179 180 if (!bias) { 181 res = ((uint64_t)m_lo * n_lo) >> 32; 182 } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) { 183 /* there can't be any overflow here */ 184 res = (m + (uint64_t)m_lo * n_lo) >> 32; 185 } else { 186 res = m + (uint64_t)m_lo * n_lo; 187 res_lo = res >> 32; 188 res_hi = (res_lo < m_hi); 189 res = res_lo | ((uint64_t)res_hi << 32); 190 } 191 192 if (!(m & ((1ULL << 63) | (1ULL << 31)))) { 193 /* there can't be any overflow here */ 194 res += (uint64_t)m_lo * n_hi; 195 res += (uint64_t)m_hi * n_lo; 196 res >>= 32; 197 } else { 198 res += (uint64_t)m_lo * n_hi; 199 tmp = res >> 32; 200 res += (uint64_t)m_hi * n_lo; 201 res_lo = res >> 32; 202 res_hi = (res_lo < tmp); 203 res = res_lo | ((uint64_t)res_hi << 32); 204 } 205 206 res += (uint64_t)m_hi * n_hi; 207 208 return res; 209} 210#endif 211 212#ifndef __div64_32 213extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor); 214#endif 215 216/* The unnecessary pointer compare is there 217 * to check for type safety (n must be 64bit) 218 */ 219# define do_div(n,base) ({ \ 220 uint32_t __base = (base); \ 221 uint32_t __rem; \ 222 (void)(((typeof((n)) *)0) == ((uint64_t *)0)); \ 223 if (__builtin_constant_p(__base) && \ 224 is_power_of_2(__base)) { \ 225 __rem = (n) & (__base - 1); \ 226 (n) >>= ilog2(__base); \ 227 } else if (__builtin_constant_p(__base) && \ 228 __base != 0) { \ 229 uint32_t __res_lo, __n_lo = (n); \ 230 (n) = __div64_const32(n, __base); \ 231 /* the remainder can be computed with 32-bit regs */ \ 232 __res_lo = (n); \ 233 __rem = __n_lo - __res_lo * __base; \ 234 } else if (likely(((n) >> 32) == 0)) { \ 235 __rem = (uint32_t)(n) % __base; \ 236 (n) = (uint32_t)(n) / __base; \ 237 } else { \ 238 __rem = __div64_32(&(n), __base); \ 239 } \ 240 __rem; \ 241 }) 242 243#else /* BITS_PER_LONG == ?? */ 244 245# error do_div() does not yet support the C64 246 247#endif /* BITS_PER_LONG */ 248 249#endif /* _ASM_GENERIC_DIV64_H */