include/asm-generic/div64.h

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