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() 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. And yet only if compiling
  61  * with a sufficiently recent gcc version to perform proper 64-bit constant
  62  * propagation.
  63  *
  64  * (It is unfortunate that gcc doesn't perform all this internally.)
  65  */
  66
  67 #ifndef __div64_const32_is_OK
  68 #define __div64_const32_is_OK (__GNUC__ >= 4)
  69 #endif
  70
  71 #define __div64_const32(n, ___b)                                        \
  72 ({                                                                      \
  73         /*                                                              \
  74          * Multiplication by reciprocal of b: n / b = n * (p / b) / p   \
  75          *                                                              \
  76          * We rely on the fact that most of this code gets optimized    \
  77          * away at compile time due to constant propagation and only    \
  78          * a few multiplication instructions should remain.             \
  79          * Hence this monstrous macro (static inline doesn't always     \
  80          * do the trick here).                                          \
  81          */                                                             \
  82         uint64_t ___res, ___x, ___t, ___m, ___n = (n);                  \
  83         uint32_t ___p, ___bias;                                         \
  84                                                                         \
  85         /* determine MSB of b */                                        \
  86         ___p = 1 << ilog2(___b);                                        \
  87                                                                         \
  88         /* compute m = ((p << 64) + b - 1) / b */                       \
  89         ___m = (~0ULL / ___b) * ___p;                                   \
  90         ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;        \
  91                                                                         \
  92         /* one less than the dividend with highest result */            \
  93         ___x = ~0ULL / ___b * ___b - 1;                                 \
  94                                                                         \
  95         /* test our ___m with res = m * x / (p << 64) */                \
  96         ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32;     \
  97         ___t = ___res += (___m & 0xffffffff) * (___x >> 32);            \
  98         ___res += (___x & 0xffffffff) * (___m >> 32);                   \
  99         ___t = (___res < ___t) ? (1ULL << 32) : 0;                      \
 100         ___res = (___res >> 32) + ___t;                                 \
 101         ___res += (___m >> 32) * (___x >> 32);                          \
 102         ___res /= ___p;                                                 \
 103                                                                         \
 104         /* Now sanitize and optimize what we've got. */                 \
 105         if (~0ULL % (___b / (___b & -___b)) == 0) {                     \
 106                 /* special case, can be simplified to ... */            \
 107                 ___n /= (___b & -___b);                                 \
 108                 ___m = ~0ULL / (___b / (___b & -___b));                 \
 109                 ___p = 1;                                               \
 110                 ___bias = 1;                                            \
 111         } else if (___res != ___x / ___b) {                             \
 112                 /*                                                      \
 113                  * We can't get away without a bias to compensate       \
 114                  * for bit truncation errors.  To avoid it we'd need an \
 115                  * additional bit to represent m which would overflow   \
 116                  * a 64-bit variable.                                   \
 117                  *                                                      \
 118                  * Instead we do m = p / b and n / b = (n * m + m) / p. \
 119                  */                                                     \
 120                 ___bias = 1;                                            \
 121                 /* Compute m = (p << 64) / b */                         \
 122                 ___m = (~0ULL / ___b) * ___p;                           \
 123                 ___m += ((~0ULL % ___b + 1) * ___p) / ___b;             \
 124         } else {                                                        \
 125                 /*                                                      \
 126                  * Reduce m / p, and try to clear bit 31 of m when      \
 127                  * possible, otherwise that'll need extra overflow      \
 128                  * handling later.                                      \
 129                  */                                                     \
 130                 uint32_t ___bits = -(___m & -___m);                     \
 131                 ___bits |= ___m >> 32;                                  \
 132                 ___bits = (~___bits) << 1;                              \
 133                 /*                                                      \
 134                  * If ___bits == 0 then setting bit 31 is  unavoidable. \
 135                  * Simply apply the maximum possible reduction in that  \
 136                  * case. Otherwise the MSB of ___bits indicates the     \
 137                  * best reduction we should apply.                      \
 138                  */                                                     \
 139                 if (!___bits) {                                         \
 140                         ___p /= (___m & -___m);                         \
 141                         ___m /= (___m & -___m);                         \
 142                 } else {                                                \
 143                         ___p >>= ilog2(___bits);                        \
 144                         ___m >>= ilog2(___bits);                        \
 145                 }                                                       \
 146                 /* No bias needed. */                                   \
 147                 ___bias = 0;                                            \
 148         }                                                               \
 149                                                                         \
 150         /*                                                              \
 151          * Now we have a combination of 2 conditions:                   \
 152          *                                                              \
 153          * 1) whether or not we need to apply a bias, and               \
 154          *                                                              \
 155          * 2) whether or not there might be an overflow in the cross    \
 156          *    product determined by (___m & ((1 << 63) | (1 << 31))).   \
 157          *                                                              \
 158          * Select the best way to do (m_bias + m * n) / (1 << 64).      \
 159          * From now on there will be actual runtime code generated.     \
 160          */                                                             \
 161         ___res = __arch_xprod_64(___m, ___n, ___bias);                  \
 162                                                                         \
 163         ___res /= ___p;                                                 \
 164 })
 165
 166 #ifndef __arch_xprod_64
 167 /*
 168  * Default C implementation for __arch_xprod_64()
 169  *
 170  * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 171  * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
 172  *
 173  * The product is a 128-bit value, scaled down to 64 bits.
 174  * Assuming constant propagation to optimize away unused conditional code.
 175  * Architectures may provide their own optimized assembly implementation.
 176  */
 177 static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 178 {
 179         uint32_t m_lo = m;
 180         uint32_t m_hi = m >> 32;
 181         uint32_t n_lo = n;
 182         uint32_t n_hi = n >> 32;
 183         uint64_t res;
 184         uint32_t res_lo, res_hi, tmp;
 185
 186         if (!bias) {
 187                 res = ((uint64_t)m_lo * n_lo) >> 32;
 188         } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 189                 /* there can't be any overflow here */
 190                 res = (m + (uint64_t)m_lo * n_lo) >> 32;
 191         } else {
 192                 res = m + (uint64_t)m_lo * n_lo;
 193                 res_lo = res >> 32;
 194                 res_hi = (res_lo < m_hi);
 195                 res = res_lo | ((uint64_t)res_hi << 32);
 196         }
 197
 198         if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 199                 /* there can't be any overflow here */
 200                 res += (uint64_t)m_lo * n_hi;
 201                 res += (uint64_t)m_hi * n_lo;
 202                 res >>= 32;
 203         } else {
 204                 res += (uint64_t)m_lo * n_hi;
 205                 tmp = res >> 32;
 206                 res += (uint64_t)m_hi * n_lo;
 207                 res_lo = res >> 32;
 208                 res_hi = (res_lo < tmp);
 209                 res = res_lo | ((uint64_t)res_hi << 32);
 210         }
 211
 212         res += (uint64_t)m_hi * n_hi;
 213
 214         return res;
 215 }
 216 #endif
 217
 218 #ifndef __div64_32
 219 extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
 220 #endif
 221
 222 /* The unnecessary pointer compare is there
 223  * to check for type safety (n must be 64bit)
 224  */
 225 # define do_div(n,base) ({                              \
 226         uint32_t __base = (base);                       \
 227         uint32_t __rem;                                 \
 228         (void)(((typeof((n)) *)0) == ((uint64_t *)0));  \
 229         if (__builtin_constant_p(__base) &&             \
 230             is_power_of_2(__base)) {                    \
 231                 __rem = (n) & (__base - 1);             \
 232                 (n) >>= ilog2(__base);                  \
 233         } else if (__div64_const32_is_OK &&             \
 234                    __builtin_constant_p(__base) &&      \
 235                    __base != 0) {                       \
 236                 uint32_t __res_lo, __n_lo = (n);        \
 237                 (n) = __div64_const32(n, __base);       \
 238                 /* the remainder can be computed with 32-bit regs */ \
 239                 __res_lo = (n);                         \
 240                 __rem = __n_lo - __res_lo * __base;     \
 241         } else if (likely(((n) >> 32) == 0)) {          \
 242                 __rem = (uint32_t)(n) % __base;         \
 243                 (n) = (uint32_t)(n) / __base;           \
 244         } else                                          \
 245                 __rem = __div64_32(&(n), __base);       \
 246         __rem;                                          \
 247  })
 248
 249 #else /* BITS_PER_LONG == ?? */
 250
 251 # error do_div() does not yet support the C64
 252
 253 #endif /* BITS_PER_LONG */
 254
 255 #endif /* _ASM_GENERIC_DIV64_H */