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 <[email protected]>
   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.
  61  *
  62  * (It is unfortunate that gcc doesn't perform all this internally.)
  63  */
  64
  65 #define __div64_const32(n, ___b)                                        \
  66 ({                                                                      \
  67         /*                                                              \
  68          * Multiplication by reciprocal of b: n / b = n * (p / b) / p   \
  69          *                                                              \
  70          * We rely on the fact that most of this code gets optimized    \
  71          * away at compile time due to constant propagation and only    \
  72          * a few multiplication instructions should remain.             \
  73          * Hence this monstrous macro (static inline doesn't always     \
  74          * do the trick here).                                          \
  75          */                                                             \
  76         uint64_t ___res, ___x, ___t, ___m, ___n = (n);                  \
  77         uint32_t ___p;                                                  \
  78         bool ___bias = false;                                           \
  79                                                                         \
  80         /* determine MSB of b */                                        \
  81         ___p = 1 << ilog2(___b);                                        \
  82                                                                         \
  83         /* compute m = ((p << 64) + b - 1) / b */                       \
  84         ___m = (~0ULL / ___b) * ___p;                                   \
  85         ___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b;        \
  86                                                                         \
  87         /* one less than the dividend with highest result */            \
  88         ___x = ~0ULL / ___b * ___b - 1;                                 \
  89                                                                         \
  90         /* test our ___m with res = m * x / (p << 64) */                \
  91         ___res = (___m & 0xffffffff) * (___x & 0xffffffff);             \
  92         ___t = (___m & 0xffffffff) * (___x >> 32) + (___res >> 32);     \
  93         ___res = (___m >> 32) * (___x >> 32) + (___t >> 32);            \
  94         ___t = (___m >> 32) * (___x & 0xffffffff) + (___t & 0xffffffff);\
  95         ___res = (___res + (___t >> 32)) / ___p;                        \
  96                                                                         \
  97         /* Now validate what we've got. */                              \
  98         if (___res != ___x / ___b) {                                    \
  99                 /*                                                      \
 100                  * We can't get away without a bias to compensate       \
 101                  * for bit truncation errors.  To avoid it we'd need an \
 102                  * additional bit to represent m which would overflow   \
 103                  * a 64-bit variable.                                   \
 104                  *                                                      \
 105                  * Instead we do m = p / b and n / b = (n * m + m) / p. \
 106                  */                                                     \
 107                 ___bias = true;                                         \
 108                 /* Compute m = (p << 64) / b */                         \
 109                 ___m = (~0ULL / ___b) * ___p;                           \
 110                 ___m += ((~0ULL % ___b + 1) * ___p) / ___b;             \
 111         }                                                               \
 112                                                                         \
 113         /* Reduce m / p to help avoid overflow handling later. */       \
 114         ___p /= (___m & -___m);                                         \
 115         ___m /= (___m & -___m);                                         \
 116                                                                         \
 117         /*                                                              \
 118          * Perform (m_bias + m * n) / (1 << 64).                        \
 119          * From now on there will be actual runtime code generated.     \
 120          */                                                             \
 121         ___res = __arch_xprod_64(___m, ___n, ___bias);                  \
 122                                                                         \
 123         ___res /= ___p;                                                 \
 124 })
 125
 126 #ifndef __arch_xprod_64
 127 /*
 128  * Default C implementation for __arch_xprod_64()
 129  *
 130  * Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 131  * Semantic:  retval = ((bias ? m : 0) + m * n) >> 64
 132  *
 133  * The product is a 128-bit value, scaled down to 64 bits.
 134  * Hoping for compile-time optimization of  conditional code.
 135  * Architectures may provide their own optimized assembly implementation.
 136  */
 137 #ifdef CONFIG_CC_OPTIMIZE_FOR_PERFORMANCE
 138 static __always_inline
 139 #else
 140 static inline
 141 #endif
 142 uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
 143 {
 144         uint32_t m_lo = m;
 145         uint32_t m_hi = m >> 32;
 146         uint32_t n_lo = n;
 147         uint32_t n_hi = n >> 32;
 148         uint64_t x, y;
 149
 150         /* Determine if overflow handling can be dispensed with. */
 151         bool no_ovf = __builtin_constant_p(m) &&
 152                       ((m >> 32) + (m & 0xffffffff) < 0x100000000);
 153
 154         if (no_ovf) {
 155                 x = (uint64_t)m_lo * n_lo + (bias ? m : 0);
 156                 x >>= 32;
 157                 x += (uint64_t)m_lo * n_hi;
 158                 x += (uint64_t)m_hi * n_lo;
 159                 x >>= 32;
 160                 x += (uint64_t)m_hi * n_hi;
 161         } else {
 162                 x = (uint64_t)m_lo * n_lo + (bias ? m_lo : 0);
 163                 y = (uint64_t)m_lo * n_hi + (uint32_t)(x >> 32) + (bias ? m_hi : 0);
 164                 x = (uint64_t)m_hi * n_hi + (uint32_t)(y >> 32);
 165                 y = (uint64_t)m_hi * n_lo + (uint32_t)y;
 166                 x += (uint32_t)(y >> 32);
 167         }
 168
 169         return x;
 170 }
 171 #endif
 172
 173 #ifndef __div64_32
 174 extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
 175 #endif
 176
 177 /* The unnecessary pointer compare is there
 178  * to check for type safety (n must be 64bit)
 179  */
 180 # define do_div(n,base) ({                              \
 181         uint32_t __base = (base);                       \
 182         uint32_t __rem;                                 \
 183         (void)(((typeof((n)) *)0) == ((uint64_t *)0));  \
 184         if (__builtin_constant_p(__base) &&             \
 185             is_power_of_2(__base)) {                    \
 186                 __rem = (n) & (__base - 1);             \
 187                 (n) >>= ilog2(__base);                  \
 188         } else if (__builtin_constant_p(__base) &&      \
 189                    __base != 0) {                       \
 190                 uint32_t __res_lo, __n_lo = (n);        \
 191                 (n) = __div64_const32(n, __base);       \
 192                 /* the remainder can be computed with 32-bit regs */ \
 193                 __res_lo = (n);                         \
 194                 __rem = __n_lo - __res_lo * __base;     \
 195         } else if (likely(((n) >> 32) == 0)) {          \
 196                 __rem = (uint32_t)(n) % __base;         \
 197                 (n) = (uint32_t)(n) / __base;           \
 198         } else {                                        \
 199                 __rem = __div64_32(&(n), __base);       \
 200         }                                               \
 201         __rem;                                          \
 202  })
 203
 204 #else /* BITS_PER_LONG == ?? */
 205
 206 # error do_div() does not yet support the C64
 207
 208 #endif /* BITS_PER_LONG */
 209
 210 #endif /* _ASM_GENERIC_DIV64_H */