lib/math/div64.c

   1 // SPDX-License-Identifier: GPL-2.0
   2 /*
   3  * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
   4  *
   5  * Based on former do_div() implementation from asm-parisc/div64.h:
   6  *      Copyright (C) 1999 Hewlett-Packard Co
   7  *      Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
   8  *
   9  *
  10  * Generic C version of 64bit/32bit division and modulo, with
  11  * 64bit result and 32bit remainder.
  12  *
  13  * The fast case for (n>>32 == 0) is handled inline by do_div().
  14  *
  15  * Code generated for this function might be very inefficient
  16  * for some CPUs. __div64_32() can be overridden by linking arch-specific
  17  * assembly versions such as arch/ppc/lib/div64.S and arch/sh/lib/div64.S
  18  * or by defining a preprocessor macro in arch/include/asm/div64.h.
  19  */
  20
  21 #include <linux/bitops.h>
  22 #include <linux/export.h>
  23 #include <linux/math.h>
  24 #include <linux/math64.h>
  25 #include <linux/log2.h>
  26
  27 /* Not needed on 64bit architectures */
  28 #if BITS_PER_LONG == 32
  29
  30 #ifndef __div64_32
  31 uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
  32 {
  33         uint64_t rem = *n;
  34         uint64_t b = base;
  35         uint64_t res, d = 1;
  36         uint32_t high = rem >> 32;
  37
  38         /* Reduce the thing a bit first */
  39         res = 0;
  40         if (high >= base) {
  41                 high /= base;
  42                 res = (uint64_t) high << 32;
  43                 rem -= (uint64_t) (high*base) << 32;
  44         }
  45
  46         while ((int64_t)b > 0 && b < rem) {
  47                 b = b+b;
  48                 d = d+d;
  49         }
  50
  51         do {
  52                 if (rem >= b) {
  53                         rem -= b;
  54                         res += d;
  55                 }
  56                 b >>= 1;
  57                 d >>= 1;
  58         } while (d);
  59
  60         *n = res;
  61         return rem;
  62 }
  63 EXPORT_SYMBOL(__div64_32);
  64 #endif
  65
  66 /**
  67  * div_s64_rem - signed 64bit divide with 64bit divisor and remainder
  68  * @dividend:   64bit dividend
  69  * @divisor:    64bit divisor
  70  * @remainder:  64bit remainder
  71  */
  72 #ifndef div_s64_rem
  73 s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
  74 {
  75         u64 quotient;
  76
  77         if (dividend < 0) {
  78                 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
  79                 *remainder = -*remainder;
  80                 if (divisor > 0)
  81                         quotient = -quotient;
  82         } else {
  83                 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
  84                 if (divisor < 0)
  85                         quotient = -quotient;
  86         }
  87         return quotient;
  88 }
  89 EXPORT_SYMBOL(div_s64_rem);
  90 #endif
  91
  92 /**
  93  * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
  94  * @dividend:   64bit dividend
  95  * @divisor:    64bit divisor
  96  * @remainder:  64bit remainder
  97  *
  98  * This implementation is a comparable to algorithm used by div64_u64.
  99  * But this operation, which includes math for calculating the remainder,
 100  * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
 101  * systems.
 102  */
 103 #ifndef div64_u64_rem
 104 u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
 105 {
 106         u32 high = divisor >> 32;
 107         u64 quot;
 108
 109         if (high == 0) {
 110                 u32 rem32;
 111                 quot = div_u64_rem(dividend, divisor, &rem32);
 112                 *remainder = rem32;
 113         } else {
 114                 int n = fls(high);
 115                 quot = div_u64(dividend >> n, divisor >> n);
 116
 117                 if (quot != 0)
 118                         quot--;
 119
 120                 *remainder = dividend - quot * divisor;
 121                 if (*remainder >= divisor) {
 122                         quot++;
 123                         *remainder -= divisor;
 124                 }
 125         }
 126
 127         return quot;
 128 }
 129 EXPORT_SYMBOL(div64_u64_rem);
 130 #endif
 131
 132 /**
 133  * div64_u64 - unsigned 64bit divide with 64bit divisor
 134  * @dividend:   64bit dividend
 135  * @divisor:    64bit divisor
 136  *
 137  * This implementation is a modified version of the algorithm proposed
 138  * by the book 'Hacker's Delight'.  The original source and full proof
 139  * can be found here and is available for use without restriction.
 140  *
 141  * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
 142  */
 143 #ifndef div64_u64
 144 u64 div64_u64(u64 dividend, u64 divisor)
 145 {
 146         u32 high = divisor >> 32;
 147         u64 quot;
 148
 149         if (high == 0) {
 150                 quot = div_u64(dividend, divisor);
 151         } else {
 152                 int n = fls(high);
 153                 quot = div_u64(dividend >> n, divisor >> n);
 154
 155                 if (quot != 0)
 156                         quot--;
 157                 if ((dividend - quot * divisor) >= divisor)
 158                         quot++;
 159         }
 160
 161         return quot;
 162 }
 163 EXPORT_SYMBOL(div64_u64);
 164 #endif
 165
 166 /**
 167  * div64_s64 - signed 64bit divide with 64bit divisor
 168  * @dividend:   64bit dividend
 169  * @divisor:    64bit divisor
 170  */
 171 #ifndef div64_s64
 172 s64 div64_s64(s64 dividend, s64 divisor)
 173 {
 174         s64 quot, t;
 175
 176         quot = div64_u64(abs(dividend), abs(divisor));
 177         t = (dividend ^ divisor) >> 63;
 178
 179         return (quot ^ t) - t;
 180 }
 181 EXPORT_SYMBOL(div64_s64);
 182 #endif
 183
 184 #endif /* BITS_PER_LONG == 32 */
 185
 186 /*
 187  * Iterative div/mod for use when dividend is not expected to be much
 188  * bigger than divisor.
 189  */
 190 u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
 191 {
 192         return __iter_div_u64_rem(dividend, divisor, remainder);
 193 }
 194 EXPORT_SYMBOL(iter_div_u64_rem);
 195
 196 #ifndef mul_u64_u64_div_u64
 197 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
 198 {
 199         u64 res = 0, div, rem;
 200         int shift;
 201
 202         /* can a * b overflow ? */
 203         if (ilog2(a) + ilog2(b) > 62) {
 204                 /*
 205                  * (b * a) / c is equal to
 206                  *
 207                  *      (b / c) * a +
 208                  *      (b % c) * a / c
 209                  *
 210                  * if nothing overflows. Can the 1st multiplication
 211                  * overflow? Yes, but we do not care: this can only
 212                  * happen if the end result can't fit in u64 anyway.
 213                  *
 214                  * So the code below does
 215                  *
 216                  *      res = (b / c) * a;
 217                  *      b = b % c;
 218                  */
 219                 div = div64_u64_rem(b, c, &rem);
 220                 res = div * a;
 221                 b = rem;
 222
 223                 shift = ilog2(a) + ilog2(b) - 62;
 224                 if (shift > 0) {
 225                         /* drop precision */
 226                         b >>= shift;
 227                         c >>= shift;
 228                         if (!c)
 229                                 return res;
 230                 }
 231         }
 232
 233         return res + div64_u64(a * b, c);
 234 }
 235 #endif