linux/include/asm-generic/div64.h
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   1#ifndef _ASM_GENERIC_DIV64_H
   2#define _ASM_GENERIC_DIV64_H
   3/*
   4 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
   5 * Based on former asm-ppc/div64.h and asm-m68knommu/div64.h
   6 *
   7 * Optimization for constant divisors on 32-bit machines:
   8 * Copyright (C) 2006-2015 Nicolas Pitre
   9 *
  10 * The semantics of do_div() are:
  11 *
  12 * uint32_t do_div(uint64_t *n, uint32_t base)
  13 * {
  14 *      uint32_t remainder = *n % base;
  15 *      *n = *n / base;
  16 *      return remainder;
  17 * }
  18 *
  19 * NOTE: macro parameter n is evaluated multiple times,
  20 *       beware of side effects!
  21 */
  22
  23#include <linux/types.h>
  24#include <linux/compiler.h>
  25
  26#if BITS_PER_LONG == 64
  27
  28# define do_div(n,base) ({                                      \
  29        uint32_t __base = (base);                               \
  30        uint32_t __rem;                                         \
  31        __rem = ((uint64_t)(n)) % __base;                       \
  32        (n) = ((uint64_t)(n)) / __base;                         \
  33        __rem;                                                  \
  34 })
  35
  36#elif BITS_PER_LONG == 32
  37
  38#include <linux/log2.h>
  39
  40/*
  41 * If the divisor happens to be constant, we determine the appropriate
  42 * inverse at compile time to turn the division into a few inline
  43 * multiplications which ought to be much faster. And yet only if compiling
  44 * with a sufficiently recent gcc version to perform proper 64-bit constant
  45 * propagation.
  46 *
  47 * (It is unfortunate that gcc doesn't perform all this internally.)
  48 */
  49
  50#ifndef __div64_const32_is_OK
  51#define __div64_const32_is_OK (__GNUC__ >= 4)
  52#endif
  53
  54#define __div64_const32(n, ___b)                                        \
  55({                                                                      \
  56        /*                                                              \
  57         * Multiplication by reciprocal of b: n / b = n * (p / b) / p   \
  58         *                                                              \
  59         * We rely on the fact that most of this code gets optimized    \
  60         * away at compile time due to constant propagation and only    \
  61         * a few multiplication instructions should remain.             \
  62         * Hence this monstrous macro (static inline doesn't always     \
  63         * do the trick here).                                          \
  64         */                                                             \
  65        uint64_t ___res, ___x, ___t, ___m, ___n = (n);                  \
  66        uint32_t ___p, ___bias;                                         \
  67                                                                        \
  68        /* determine MSB of b */                                        \
  69        ___p = 1 << ilog2(___b);                                        \
  70                                                                        \
  71        /* compute m = ((p << 64) + b - 1) / b */                       \
  72        ___m = (~0ULL / ___b) * ___p;                                   \
  73        ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;        \
  74                                                                        \
  75        /* one less than the dividend with highest result */            \
  76        ___x = ~0ULL / ___b * ___b - 1;                                 \
  77                                                                        \
  78        /* test our ___m with res = m * x / (p << 64) */                \
  79        ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32;     \
  80        ___t = ___res += (___m & 0xffffffff) * (___x >> 32);            \
  81        ___res += (___x & 0xffffffff) * (___m >> 32);                   \
  82        ___t = (___res < ___t) ? (1ULL << 32) : 0;                      \
  83        ___res = (___res >> 32) + ___t;                                 \
  84        ___res += (___m >> 32) * (___x >> 32);                          \
  85        ___res /= ___p;                                                 \
  86                                                                        \
  87        /* Now sanitize and optimize what we've got. */                 \
  88        if (~0ULL % (___b / (___b & -___b)) == 0) {                     \
  89                /* special case, can be simplified to ... */            \
  90                ___n /= (___b & -___b);                                 \
  91                ___m = ~0ULL / (___b / (___b & -___b));                 \
  92                ___p = 1;                                               \
  93                ___bias = 1;                                            \
  94        } else if (___res != ___x / ___b) {                             \
  95                /*                                                      \
  96                 * We can't get away without a bias to compensate       \
  97                 * for bit truncation errors.  To avoid it we'd need an \
  98                 * additional bit to represent m which would overflow   \
  99                 * a 64-bit variable.                                   \
 100                 *                                                      \
 101                 * Instead we do m = p / b and n / b = (n * m + m) / p. \
 102                 */                                                     \
 103                ___bias = 1;                                            \
 104                /* Compute m = (p << 64) / b */                         \
 105                ___m = (~0ULL / ___b) * ___p;                           \
 106                ___m += ((~0ULL % ___b + 1) * ___p) / ___b;             \
 107        } else {                                                        \
 108                /*                                                      \
 109                 * Reduce m / p, and try to clear bit 31 of m when      \
 110                 * possible, otherwise that'll need extra overflow      \
 111                 * handling later.                                      \
 112                 */                                                     \
 113                uint32_t ___bits = -(___m & -___m);                     \
 114                ___bits |= ___m >> 32;                                  \
 115                ___bits = (~___bits) << 1;                              \
 116                /*                                                      \
 117                 * If ___bits == 0 then setting bit 31 is  unavoidable. \
 118                 * Simply apply the maximum possible reduction in that  \
 119                 * case. Otherwise the MSB of ___bits indicates the     \
 120                 * best reduction we should apply.                      \
 121                 */                                                     \
 122                if (!___bits) {                                         \
 123                        ___p /= (___m & -___m);                         \
 124                        ___m /= (___m & -___m);                         \
 125                } else {                                                \
 126                        ___p >>= ilog2(___bits);                        \
 127                        ___m >>= ilog2(___bits);                        \
 128                }                                                       \
 129                /* No bias needed. */                                   \
 130                ___bias = 0;                                            \
 131        }                                                               \
 132                                                                        \
 133        /*                                                              \
 134         * Now we have a combination of 2 conditions:                   \
 135         *                                                              \
 136         * 1) whether or not we need to apply a bias, and               \
 137         *                                                              \
 138         * 2) whether or not there might be an overflow in the cross    \
 139         *    product determined by (___m & ((1 << 63) | (1 << 31))).   \
 140         *                                                              \
 141         * Select the best way to do (m_bias + m * n) / (1 << 64).      \
 142         * From now on there will be actual runtime code generated.     \
 143         */                                                             \
 144        ___res = __arch_xprod_64(___m, ___n, ___bias);                  \
 145                                                                        \
 146        ___res /= ___p;                                                 \
 147})
 148
 149#ifndef __arch_xprod_64
 150/*
 151 * Default C implementation for __arch_xprod_64()
 152 *
 153 * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 154 * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
 155 *
 156 * The product is a 128-bit value, scaled down to 64 bits.
 157 * Assuming constant propagation to optimize away unused conditional code.
 158 * Architectures may provide their own optimized assembly implementation.
 159 */
 160static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 161{
 162        uint32_t m_lo = m;
 163        uint32_t m_hi = m >> 32;
 164        uint32_t n_lo = n;
 165        uint32_t n_hi = n >> 32;
 166        uint64_t res, tmp;
 167
 168        if (!bias) {
 169                res = ((uint64_t)m_lo * n_lo) >> 32;
 170        } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 171                /* there can't be any overflow here */
 172                res = (m + (uint64_t)m_lo * n_lo) >> 32;
 173        } else {
 174                res = m + (uint64_t)m_lo * n_lo;
 175                tmp = (res < m) ? (1ULL << 32) : 0;
 176                res = (res >> 32) + tmp;
 177        }
 178
 179        if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 180                /* there can't be any overflow here */
 181                res += (uint64_t)m_lo * n_hi;
 182                res += (uint64_t)m_hi * n_lo;
 183                res >>= 32;
 184        } else {
 185                tmp = res += (uint64_t)m_lo * n_hi;
 186                res += (uint64_t)m_hi * n_lo;
 187                tmp = (res < tmp) ? (1ULL << 32) : 0;
 188                res = (res >> 32) + tmp;
 189        }
 190
 191        res += (uint64_t)m_hi * n_hi;
 192
 193        return res;
 194}
 195#endif
 196
 197#ifndef __div64_32
 198extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
 199#endif
 200
 201/* The unnecessary pointer compare is there
 202 * to check for type safety (n must be 64bit)
 203 */
 204# define do_div(n,base) ({                              \
 205        uint32_t __base = (base);                       \
 206        uint32_t __rem;                                 \
 207        (void)(((typeof((n)) *)0) == ((uint64_t *)0));  \
 208        if (__builtin_constant_p(__base) &&             \
 209            is_power_of_2(__base)) {                    \
 210                __rem = (n) & (__base - 1);             \
 211                (n) >>= ilog2(__base);                  \
 212        } else if (__div64_const32_is_OK &&             \
 213                   __builtin_constant_p(__base) &&      \
 214                   __base != 0) {                       \
 215                uint32_t __res_lo, __n_lo = (n);        \
 216                (n) = __div64_const32(n, __base);       \
 217                /* the remainder can be computed with 32-bit regs */ \
 218                __res_lo = (n);                         \
 219                __rem = __n_lo - __res_lo * __base;     \
 220        } else if (likely(((n) >> 32) == 0)) {          \
 221                __rem = (uint32_t)(n) % __base;         \
 222                (n) = (uint32_t)(n) / __base;           \
 223        } else                                          \
 224                __rem = __div64_32(&(n), __base);       \
 225        __rem;                                          \
 226 })
 227
 228#else /* BITS_PER_LONG == ?? */
 229
 230# error do_div() does not yet support the C64
 231
 232#endif /* BITS_PER_LONG */
 233
 234#endif /* _ASM_GENERIC_DIV64_H */
 235