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/minmax.h>
  26 #include <linux/log2.h>
  27
  28 /* Not needed on 64bit architectures */
  29 #if BITS_PER_LONG == 32
  30
  31 #ifndef __div64_32
  32 uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
  33 {
  34         uint64_t rem = *n;
  35         uint64_t b = base;
  36         uint64_t res, d = 1;
  37         uint32_t high = rem >> 32;
  38
  39         /* Reduce the thing a bit first */
  40         res = 0;
  41         if (high >= base) {
  42                 high /= base;
  43                 res = (uint64_t) high << 32;
  44                 rem -= (uint64_t) (high*base) << 32;
  45         }
  46
  47         while ((int64_t)b > 0 && b < rem) {
  48                 b = b+b;
  49                 d = d+d;
  50         }
  51
  52         do {
  53                 if (rem >= b) {
  54                         rem -= b;
  55                         res += d;
  56                 }
  57                 b >>= 1;
  58                 d >>= 1;
  59         } while (d);
  60
  61         *n = res;
  62         return rem;
  63 }
  64 EXPORT_SYMBOL(__div64_32);
  65 #endif
  66
  67 #ifndef div_s64_rem
  68 s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
  69 {
  70         u64 quotient;
  71
  72         if (dividend < 0) {
  73                 quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
  74                 *remainder = -*remainder;
  75                 if (divisor > 0)
  76                         quotient = -quotient;
  77         } else {
  78                 quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
  79                 if (divisor < 0)
  80                         quotient = -quotient;
  81         }
  82         return quotient;
  83 }
  84 EXPORT_SYMBOL(div_s64_rem);
  85 #endif
  86
  87 /*
  88  * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
  89  * @dividend:   64bit dividend
  90  * @divisor:    64bit divisor
  91  * @remainder:  64bit remainder
  92  *
  93  * This implementation is a comparable to algorithm used by div64_u64.
  94  * But this operation, which includes math for calculating the remainder,
  95  * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
  96  * systems.
  97  */
  98 #ifndef div64_u64_rem
  99 u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
 100 {
 101         u32 high = divisor >> 32;
 102         u64 quot;
 103
 104         if (high == 0) {
 105                 u32 rem32;
 106                 quot = div_u64_rem(dividend, divisor, &rem32);
 107                 *remainder = rem32;
 108         } else {
 109                 int n = fls(high);
 110                 quot = div_u64(dividend >> n, divisor >> n);
 111
 112                 if (quot != 0)
 113                         quot--;
 114
 115                 *remainder = dividend - quot * divisor;
 116                 if (*remainder >= divisor) {
 117                         quot++;
 118                         *remainder -= divisor;
 119                 }
 120         }
 121
 122         return quot;
 123 }
 124 EXPORT_SYMBOL(div64_u64_rem);
 125 #endif
 126
 127 /*
 128  * div64_u64 - unsigned 64bit divide with 64bit divisor
 129  * @dividend:   64bit dividend
 130  * @divisor:    64bit divisor
 131  *
 132  * This implementation is a modified version of the algorithm proposed
 133  * by the book 'Hacker's Delight'.  The original source and full proof
 134  * can be found here and is available for use without restriction.
 135  *
 136  * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
 137  */
 138 #ifndef div64_u64
 139 u64 div64_u64(u64 dividend, u64 divisor)
 140 {
 141         u32 high = divisor >> 32;
 142         u64 quot;
 143
 144         if (high == 0) {
 145                 quot = div_u64(dividend, divisor);
 146         } else {
 147                 int n = fls(high);
 148                 quot = div_u64(dividend >> n, divisor >> n);
 149
 150                 if (quot != 0)
 151                         quot--;
 152                 if ((dividend - quot * divisor) >= divisor)
 153                         quot++;
 154         }
 155
 156         return quot;
 157 }
 158 EXPORT_SYMBOL(div64_u64);
 159 #endif
 160
 161 #ifndef div64_s64
 162 s64 div64_s64(s64 dividend, s64 divisor)
 163 {
 164         s64 quot, t;
 165
 166         quot = div64_u64(abs(dividend), abs(divisor));
 167         t = (dividend ^ divisor) >> 63;
 168
 169         return (quot ^ t) - t;
 170 }
 171 EXPORT_SYMBOL(div64_s64);
 172 #endif
 173
 174 #endif /* BITS_PER_LONG == 32 */
 175
 176 /*
 177  * Iterative div/mod for use when dividend is not expected to be much
 178  * bigger than divisor.
 179  */
 180 u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
 181 {
 182         return __iter_div_u64_rem(dividend, divisor, remainder);
 183 }
 184 EXPORT_SYMBOL(iter_div_u64_rem);
 185
 186 #ifndef mul_u64_u64_div_u64
 187 u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
 188 {
 189         if (ilog2(a) + ilog2(b) <= 62)
 190                 return div64_u64(a * b, c);
 191
 192 #if defined(__SIZEOF_INT128__)
 193
 194         /* native 64x64=128 bits multiplication */
 195         u128 prod = (u128)a * b;
 196         u64 n_lo = prod, n_hi = prod >> 64;
 197
 198 #else
 199
 200         /* perform a 64x64=128 bits multiplication manually */
 201         u32 a_lo = a, a_hi = a >> 32, b_lo = b, b_hi = b >> 32;
 202         u64 x, y, z;
 203
 204         x = (u64)a_lo * b_lo;
 205         y = (u64)a_lo * b_hi + (u32)(x >> 32);
 206         z = (u64)a_hi * b_hi + (u32)(y >> 32);
 207         y = (u64)a_hi * b_lo + (u32)y;
 208         z += (u32)(y >> 32);
 209         x = (y << 32) + (u32)x;
 210
 211         u64 n_lo = x, n_hi = z;
 212
 213 #endif
 214
 215         /* make sure c is not zero, trigger exception otherwise */
 216 #pragma GCC diagnostic push
 217 #pragma GCC diagnostic ignored "-Wdiv-by-zero"
 218         if (unlikely(c == 0))
 219                 return 1/0;
 220 #pragma GCC diagnostic pop
 221
 222         int shift = __builtin_ctzll(c);
 223
 224         /* try reducing the fraction in case the dividend becomes <= 64 bits */
 225         if ((n_hi >> shift) == 0) {
 226                 u64 n = shift ? (n_lo >> shift) | (n_hi << (64 - shift)) : n_lo;
 227
 228                 return div64_u64(n, c >> shift);
 229                 /*
 230                  * The remainder value if needed would be:
 231                  *   res = div64_u64_rem(n, c >> shift, &rem);
 232                  *   rem = (rem << shift) + (n_lo - (n << shift));
 233                  */
 234         }
 235
 236         if (n_hi >= c) {
 237                 /* overflow: result is unrepresentable in a u64 */
 238                 return -1;
 239         }
 240
 241         /* Do the full 128 by 64 bits division */
 242
 243         shift = __builtin_clzll(c);
 244         c <<= shift;
 245
 246         int p = 64 + shift;
 247         u64 res = 0;
 248         bool carry;
 249
 250         do {
 251                 carry = n_hi >> 63;
 252                 shift = carry ? 1 : __builtin_clzll(n_hi);
 253                 if (p < shift)
 254                         break;
 255                 p -= shift;
 256                 n_hi <<= shift;
 257                 n_hi |= n_lo >> (64 - shift);
 258                 n_lo <<= shift;
 259                 if (carry || (n_hi >= c)) {
 260                         n_hi -= c;
 261                         res |= 1ULL << p;
 262                 }
 263         } while (n_hi);
 264         /* The remainder value if needed would be n_hi << p */
 265
 266         return res;
 267 }
 268 EXPORT_SYMBOL(mul_u64_u64_div_u64);
 269 #endif