linux/lib/math/div64.c

// SPDX-License-Identifier: GPL-2.0
/*
 * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
 *
 * Based on former do_div() implementation from asm-parisc/div64.h:
 *	Copyright (C) 1999 Hewlett-Packard Co
 *	Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
 *
 *
 * Generic C version of 64bit/32bit division and modulo, with
 * 64bit result and 32bit remainder.
 *
 * The fast case for (n>>32 == 0) is handled inline by do_div().
 *
 * Code generated for this function might be very inefficient
 * for some CPUs. __div64_32() can be overridden by linking arch-specific
 * assembly versions such as arch/ppc/lib/div64.S and arch/sh/lib/div64.S
 * or by defining a preprocessor macro in arch/include/asm/div64.h.
 */

#include <linux/bitops.h>
#include <linux/export.h>
#include <linux/math.h>
#include <linux/math64.h>
#include <linux/minmax.h>
#include <linux/log2.h>

/* Not needed on 64bit architectures */
#if BITS_PER_LONG == 32

#ifndef __div64_32
uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
{
	uint64_t rem = *n;
	uint64_t b = base;
	uint64_t res, d = 1;
	uint32_t high = rem >> 32;

	/* Reduce the thing a bit first */
	res = 0;
	if (high >= base) {
		high /= base;
		res = (uint64_t) high << 32;
		rem -= (uint64_t) (high*base) << 32;
	}

	while ((int64_t)b > 0 && b < rem) {
		b = b+b;
		d = d+d;
	}

	do {
		if (rem >= b) {
			rem -= b;
			res += d;
		}
		b >>= 1;
		d >>= 1;
	} while (d);

	*n = res;
	return rem;
}
EXPORT_SYMBOL(__div64_32);
#endif

#ifndef div_s64_rem
s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
{
	u64 quotient;

	if (dividend < 0) {
		quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
		*remainder = -*remainder;
		if (divisor > 0)
			quotient = -quotient;
	} else {
		quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
		if (divisor < 0)
			quotient = -quotient;
	}
	return quotient;
}
EXPORT_SYMBOL(div_s64_rem);
#endif

/*
 * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
 * @dividend:	64bit dividend
 * @divisor:	64bit divisor
 * @remainder:  64bit remainder
 *
 * This implementation is a comparable to algorithm used by div64_u64.
 * But this operation, which includes math for calculating the remainder,
 * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
 * systems.
 */
#ifndef div64_u64_rem
u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
{
	u32 high = divisor >> 32;
	u64 quot;

	if (high == 0) {
		u32 rem32;
		quot = div_u64_rem(dividend, divisor, &rem32);
		*remainder = rem32;
	} else {
		int n = fls(high);
		quot = div_u64(dividend >> n, divisor >> n);

		if (quot != 0)
			quot--;

		*remainder = dividend - quot * divisor;
		if (*remainder >= divisor) {
			quot++;
			*remainder -= divisor;
		}
	}

	return quot;
}
EXPORT_SYMBOL(div64_u64_rem);
#endif

/*
 * div64_u64 - unsigned 64bit divide with 64bit divisor
 * @dividend:	64bit dividend
 * @divisor:	64bit divisor
 *
 * This implementation is a modified version of the algorithm proposed
 * by the book 'Hacker's Delight'.  The original source and full proof
 * can be found here and is available for use without restriction.
 *
 * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
 */
#ifndef div64_u64
u64 div64_u64(u64 dividend, u64 divisor)
{
	u32 high = divisor >> 32;
	u64 quot;

	if (high == 0) {
		quot = div_u64(dividend, divisor);
	} else {
		int n = fls(high);
		quot = div_u64(dividend >> n, divisor >> n);

		if (quot != 0)
			quot--;
		if ((dividend - quot * divisor) >= divisor)
			quot++;
	}

	return quot;
}
EXPORT_SYMBOL(div64_u64);
#endif

#ifndef div64_s64
s64 div64_s64(s64 dividend, s64 divisor)
{
	s64 quot, t;

	quot = div64_u64(abs(dividend), abs(divisor));
	t = (dividend ^ divisor) >> 63;

	return (quot ^ t) - t;
}
EXPORT_SYMBOL(div64_s64);
#endif

#endif /* BITS_PER_LONG == 32 */

/*
 * Iterative div/mod for use when dividend is not expected to be much
 * bigger than divisor.
 */
u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
{
	return __iter_div_u64_rem(dividend, divisor, remainder);
}
EXPORT_SYMBOL(iter_div_u64_rem);

#ifndef mul_u64_u64_div_u64
u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
{
	u64 res = 0, div, rem;
	int shift;

	/* can a * b overflow ? */
	if (ilog2(a) + ilog2(b) > 62) {
		/*
		 * Note that the algorithm after the if block below might lose
		 * some precision and the result is more exact for b > a. So
		 * exchange a and b if a is bigger than b.
		 *
		 * For example with a = 43980465100800, b = 100000000, c = 1000000000
		 * the below calculation doesn't modify b at all because div == 0
		 * and then shift becomes 45 + 26 - 62 = 9 and so the result
		 * becomes 4398035251080. However with a and b swapped the exact
		 * result is calculated (i.e. 4398046510080).
		 */
		if (a > b)
			swap(a, b);

		/*
		 * (b * a) / c is equal to
		 *
		 *      (b / c) * a +
		 *      (b % c) * a / c
		 *
		 * if nothing overflows. Can the 1st multiplication
		 * overflow? Yes, but we do not care: this can only
		 * happen if the end result can't fit in u64 anyway.
		 *
		 * So the code below does
		 *
		 *      res = (b / c) * a;
		 *      b = b % c;
		 */
		div = div64_u64_rem(b, c, &rem);
		res = div * a;
		b = rem;

		shift = ilog2(a) + ilog2(b) - 62;
		if (shift > 0) {
			/* drop precision */
			b >>= shift;
			c >>= shift;
			if (!c)
				return res;
		}
	}

	return res + div64_u64(a * b, c);
}
EXPORT_SYMBOL(mul_u64_u64_div_u64);
#endif