include/asm-generic/div64.h

   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 /**
  29  * do_div - returns 2 values: calculate remainder and update new dividend
  30  * @n: pointer to uint64_t dividend (will be updated)
  31  * @base: uint32_t divisor
  32  *
  33  * Summary:
  34  * ``uint32_t remainder = *n % base;``
  35  * ``*n = *n / base;``
  36  *
  37  * Return: (uint32_t)remainder
  38  *
  39  * NOTE: macro parameter @n is evaluated multiple times,
  40  * beware of side effects!
  41  */
  42 # define do_div(n,base) ({                                      \
  43         uint32_t __base = (base);                               \
  44         uint32_t __rem;                                         \
  45         __rem = ((uint64_t)(n)) % __base;                       \
  46         (n) = ((uint64_t)(n)) / __base;                         \
  47         __rem;                                                  \
  48  })
  49
  50 #elif BITS_PER_LONG == 32
  51
  52 #include <linux/log2.h>
  53
  54 /*
  55  * If the divisor happens to be constant, we determine the appropriate
  56  * inverse at compile time to turn the division into a few inline
  57  * multiplications which ought to be much faster. And yet only if compiling
  58  * with a sufficiently recent gcc version to perform proper 64-bit constant
  59  * propagation.
  60  *
  61  * (It is unfortunate that gcc doesn't perform all this internally.)
  62  */
  63
  64 #ifndef __div64_const32_is_OK
  65 #define __div64_const32_is_OK (__GNUC__ >= 4)
  66 #endif
  67
  68 #define __div64_const32(n, ___b)                                        \
  69 ({                                                                      \
  70         /*                                                              \
  71          * Multiplication by reciprocal of b: n / b = n * (p / b) / p   \
  72          *                                                              \
  73          * We rely on the fact that most of this code gets optimized    \
  74          * away at compile time due to constant propagation and only    \
  75          * a few multiplication instructions should remain.             \
  76          * Hence this monstrous macro (static inline doesn't always     \
  77          * do the trick here).                                          \
  78          */                                                             \
  79         uint64_t ___res, ___x, ___t, ___m, ___n = (n);                  \
  80         uint32_t ___p, ___bias;                                         \
  81                                                                         \
  82         /* determine MSB of b */                                        \
  83         ___p = 1 << ilog2(___b);                                        \
  84                                                                         \
  85         /* compute m = ((p << 64) + b - 1) / b */                       \
  86         ___m = (~0ULL / ___b) * ___p;                                   \
  87         ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;        \
  88                                                                         \
  89         /* one less than the dividend with highest result */            \
  90         ___x = ~0ULL / ___b * ___b - 1;                                 \
  91                                                                         \
  92         /* test our ___m with res = m * x / (p << 64) */                \
  93         ___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32;     \
  94         ___t = ___res += (___m & 0xffffffff) * (___x >> 32);            \
  95         ___res += (___x & 0xffffffff) * (___m >> 32);                   \
  96         ___t = (___res < ___t) ? (1ULL << 32) : 0;                      \
  97         ___res = (___res >> 32) + ___t;                                 \
  98         ___res += (___m >> 32) * (___x >> 32);                          \
  99         ___res /= ___p;                                                 \
 100                                                                         \
 101         /* Now sanitize and optimize what we've got. */                 \
 102         if (~0ULL % (___b / (___b & -___b)) == 0) {                     \
 103                 /* special case, can be simplified to ... */            \
 104                 ___n /= (___b & -___b);                                 \
 105                 ___m = ~0ULL / (___b / (___b & -___b));                 \
 106                 ___p = 1;                                               \
 107                 ___bias = 1;                                            \
 108         } else if (___res != ___x / ___b) {                             \
 109                 /*                                                      \
 110                  * We can't get away without a bias to compensate       \
 111                  * for bit truncation errors.  To avoid it we'd need an \
 112                  * additional bit to represent m which would overflow   \
 113                  * a 64-bit variable.                                   \
 114                  *                                                      \
 115                  * Instead we do m = p / b and n / b = (n * m + m) / p. \
 116                  */                                                     \
 117                 ___bias = 1;                                            \
 118                 /* Compute m = (p << 64) / b */                         \
 119                 ___m = (~0ULL / ___b) * ___p;                           \
 120                 ___m += ((~0ULL % ___b + 1) * ___p) / ___b;             \
 121         } else {                                                        \
 122                 /*                                                      \
 123                  * Reduce m / p, and try to clear bit 31 of m when      \
 124                  * possible, otherwise that'll need extra overflow      \
 125                  * handling later.                                      \
 126                  */                                                     \
 127                 uint32_t ___bits = -(___m & -___m);                     \
 128                 ___bits |= ___m >> 32;                                  \
 129                 ___bits = (~___bits) << 1;                              \
 130                 /*                                                      \
 131                  * If ___bits == 0 then setting bit 31 is  unavoidable. \
 132                  * Simply apply the maximum possible reduction in that  \
 133                  * case. Otherwise the MSB of ___bits indicates the     \
 134                  * best reduction we should apply.                      \
 135                  */                                                     \
 136                 if (!___bits) {                                         \
 137                         ___p /= (___m & -___m);                         \
 138                         ___m /= (___m & -___m);                         \
 139                 } else {                                                \
 140                         ___p >>= ilog2(___bits);                        \
 141                         ___m >>= ilog2(___bits);                        \
 142                 }                                                       \
 143                 /* No bias needed. */                                   \
 144                 ___bias = 0;                                            \
 145         }                                                               \
 146                                                                         \
 147         /*                                                              \
 148          * Now we have a combination of 2 conditions:                   \
 149          *                                                              \
 150          * 1) whether or not we need to apply a bias, and               \
 151          *                                                              \
 152          * 2) whether or not there might be an overflow in the cross    \
 153          *    product determined by (___m & ((1 << 63) | (1 << 31))).   \
 154          *                                                              \
 155          * Select the best way to do (m_bias + m * n) / (1 << 64).      \
 156          * From now on there will be actual runtime code generated.     \
 157          */                                                             \
 158         ___res = __arch_xprod_64(___m, ___n, ___bias);                  \
 159                                                                         \
 160         ___res /= ___p;                                                 \
 161 })
 162
 163 #ifndef __arch_xprod_64
 164 /*
 165  * Default C implementation for __arch_xprod_64()
 166  *
 167  * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 168  * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
 169  *
 170  * The product is a 128-bit value, scaled down to 64 bits.
 171  * Assuming constant propagation to optimize away unused conditional code.
 172  * Architectures may provide their own optimized assembly implementation.
 173  */
 174 static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 175 {
 176         uint32_t m_lo = m;
 177         uint32_t m_hi = m >> 32;
 178         uint32_t n_lo = n;
 179         uint32_t n_hi = n >> 32;
 180         uint64_t res, tmp;
 181
 182         if (!bias) {
 183                 res = ((uint64_t)m_lo * n_lo) >> 32;
 184         } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 185                 /* there can't be any overflow here */
 186                 res = (m + (uint64_t)m_lo * n_lo) >> 32;
 187         } else {
 188                 res = m + (uint64_t)m_lo * n_lo;
 189                 tmp = (res < m) ? (1ULL << 32) : 0;
 190                 res = (res >> 32) + tmp;
 191         }
 192
 193         if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 194                 /* there can't be any overflow here */
 195                 res += (uint64_t)m_lo * n_hi;
 196                 res += (uint64_t)m_hi * n_lo;
 197                 res >>= 32;
 198         } else {
 199                 tmp = res += (uint64_t)m_lo * n_hi;
 200                 res += (uint64_t)m_hi * n_lo;
 201                 tmp = (res < tmp) ? (1ULL << 32) : 0;
 202                 res = (res >> 32) + tmp;
 203         }
 204
 205         res += (uint64_t)m_hi * n_hi;
 206
 207         return res;
 208 }
 209 #endif
 210
 211 #ifndef __div64_32
 212 extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
 213 #endif
 214
 215 /* The unnecessary pointer compare is there
 216  * to check for type safety (n must be 64bit)
 217  */
 218 # define do_div(n,base) ({                              \
 219         uint32_t __base = (base);                       \
 220         uint32_t __rem;                                 \
 221         (void)(((typeof((n)) *)0) == ((uint64_t *)0));  \
 222         if (__builtin_constant_p(__base) &&             \
 223             is_power_of_2(__base)) {                    \
 224                 __rem = (n) & (__base - 1);             \
 225                 (n) >>= ilog2(__base);                  \
 226         } else if (__div64_const32_is_OK &&             \
 227                    __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         __rem;                                          \
 240  })
 241
 242 #else /* BITS_PER_LONG == ?? */
 243
 244 # error do_div() does not yet support the C64
 245
 246 #endif /* BITS_PER_LONG */
 247
 248 #endif /* _ASM_GENERIC_DIV64_H */