include/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  * u32 do_div(u64 *n, u32 base)
  13  * {
  14  *      u32 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         u32 __base = (base);                            \
  30         u32 __rem;                                              \
  31         __rem = ((u64)(n)) % __base;                    \
  32         (n) = ((u64)(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         u64 ___res, ___x, ___t, ___m, ___n = (n);                       \
  66         u32 ___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                 u32 ___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: u64 __arch_xprod_64(const u64 m, u64 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  */
 160 static inline u64 __arch_xprod_64(const u64 m, u64 n, bool bias)
 161 {
 162         u32 m_lo = m;
 163         u32 m_hi = m >> 32;
 164         u32 n_lo = n;
 165         u32 n_hi = n >> 32;
 166         u64 res, tmp;
 167
 168         if (!bias) {
 169                 res = ((u64)m_lo * n_lo) >> 32;
 170         } else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
 171                 /* there can't be any overflow here */
 172                 res = (m + (u64)m_lo * n_lo) >> 32;
 173         } else {
 174                 res = m + (u64)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 += (u64)m_lo * n_hi;
 182                 res += (u64)m_hi * n_lo;
 183                 res >>= 32;
 184         } else {
 185                 tmp = res += (u64)m_lo * n_hi;
 186                 res += (u64)m_hi * n_lo;
 187                 tmp = (res < tmp) ? (1ULL << 32) : 0;
 188                 res = (res >> 32) + tmp;
 189         }
 190
 191         res += (u64)m_hi * n_hi;
 192
 193         return res;
 194 }
 195 #endif
 196
 197 #ifndef __div64_32
 198 extern u32 __div64_32(u64 *dividend, u32 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         u32 __base = (base);                    \
 206         u32 __rem;                                      \
 207         (void)(((typeof((n)) *)0) == ((u64 *)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                 u32 __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 = (u32)(n) % __base;              \
 222                 (n) = (u32)(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 /* Wrapper for do_div(). Doesn't modify dividend and returns
 235  * the result, not remainder.
 236  */
 237 static inline u64 lldiv(u64 dividend, u32 divisor)
 238 {
 239         u64 __res = dividend;
 240         do_div(__res, divisor);
 241         return(__res);
 242 }
 243
 244 #endif /* _ASM_GENERIC_DIV64_H */