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linux/include/asm-generic/div64.h

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/* SPDX-License-Identifier: GPL-2.0 */
#ifndef _ASM_GENERIC_DIV64_H
#define _ASM_GENERIC_DIV64_H
/*
* Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
* Based on former asm-ppc/div64.h and asm-m68knommu/div64.h
*
* Optimization for constant divisors on 32-bit machines:
* Copyright (C) 2006-2015 Nicolas Pitre
*
* The semantics of do_div() is, in C++ notation, observing that the name
* is a function-like macro and the n parameter has the semantics of a C++
* reference:
*
* uint32_t do_div(uint64_t &n, uint32_t base)
* {
* uint32_t remainder = n % base;
* n = n / base;
* return remainder;
* }
*
* NOTE: macro parameter n is evaluated multiple times,
* beware of side effects!
*/
#include <linux/types.h>
#include <linux/compiler.h>
#if BITS_PER_LONG == 64
/**
* do_div - returns 2 values: calculate remainder and update new dividend
* @n: uint64_t dividend (will be updated)
* @base: uint32_t divisor
*
* Summary:
* ``uint32_t remainder = n % base;``
* ``n = n / base;``
*
* Return: (uint32_t)remainder
*
* NOTE: macro parameter @n is evaluated multiple times,
* beware of side effects!
*/
# define do_div(n,base) ({ \
uint32_t __base = (base); \
uint32_t __rem; \
__rem = ((uint64_t)(n)) % __base; \
(n) = ((uint64_t)(n)) / __base; \
__rem; \
})
#elif BITS_PER_LONG == 32
#include <linux/log2.h>
/*
* If the divisor happens to be constant, we determine the appropriate
* inverse at compile time to turn the division into a few inline
* multiplications which ought to be much faster. And yet only if compiling
* with a sufficiently recent gcc version to perform proper 64-bit constant
* propagation.
*
* (It is unfortunate that gcc doesn't perform all this internally.)
*/
#ifndef __div64_const32_is_OK
#define __div64_const32_is_OK (__GNUC__ >= 4)
#endif
#define __div64_const32(n, ___b) \
({ \
/* \
* Multiplication by reciprocal of b: n / b = n * (p / b) / p \
* \
* We rely on the fact that most of this code gets optimized \
* away at compile time due to constant propagation and only \
* a few multiplication instructions should remain. \
* Hence this monstrous macro (static inline doesn't always \
* do the trick here). \
*/ \
uint64_t ___res, ___x, ___t, ___m, ___n = (n); \
uint32_t ___p, ___bias; \
\
/* determine MSB of b */ \
___p = 1 << ilog2(___b); \
\
/* compute m = ((p << 64) + b - 1) / b */ \
___m = (~0ULL / ___b) * ___p; \
___m += (((~0ULL % ___b + 1) * ___p) + ___b - 1) / ___b; \
\
/* one less than the dividend with highest result */ \
___x = ~0ULL / ___b * ___b - 1; \
\
/* test our ___m with res = m * x / (p << 64) */ \
___res = ((___m & 0xffffffff) * (___x & 0xffffffff)) >> 32; \
___t = ___res += (___m & 0xffffffff) * (___x >> 32); \
___res += (___x & 0xffffffff) * (___m >> 32); \
___t = (___res < ___t) ? (1ULL << 32) : 0; \
___res = (___res >> 32) + ___t; \
___res += (___m >> 32) * (___x >> 32); \
___res /= ___p; \
\
/* Now sanitize and optimize what we've got. */ \
if (~0ULL % (___b / (___b & -___b)) == 0) { \
/* special case, can be simplified to ... */ \
___n /= (___b & -___b); \
___m = ~0ULL / (___b / (___b & -___b)); \
___p = 1; \
___bias = 1; \
} else if (___res != ___x / ___b) { \
/* \
* We can't get away without a bias to compensate \
* for bit truncation errors. To avoid it we'd need an \
* additional bit to represent m which would overflow \
* a 64-bit variable. \
* \
* Instead we do m = p / b and n / b = (n * m + m) / p. \
*/ \
___bias = 1; \
/* Compute m = (p << 64) / b */ \
___m = (~0ULL / ___b) * ___p; \
___m += ((~0ULL % ___b + 1) * ___p) / ___b; \
} else { \
/* \
* Reduce m / p, and try to clear bit 31 of m when \
* possible, otherwise that'll need extra overflow \
* handling later. \
*/ \
uint32_t ___bits = -(___m & -___m); \
___bits |= ___m >> 32; \
___bits = (~___bits) << 1; \
/* \
* If ___bits == 0 then setting bit 31 is unavoidable. \
* Simply apply the maximum possible reduction in that \
* case. Otherwise the MSB of ___bits indicates the \
* best reduction we should apply. \
*/ \
if (!___bits) { \
___p /= (___m & -___m); \
___m /= (___m & -___m); \
} else { \
___p >>= ilog2(___bits); \
___m >>= ilog2(___bits); \
} \
/* No bias needed. */ \
___bias = 0; \
} \
\
/* \
* Now we have a combination of 2 conditions: \
* \
* 1) whether or not we need to apply a bias, and \
* \
* 2) whether or not there might be an overflow in the cross \
* product determined by (___m & ((1 << 63) | (1 << 31))). \
* \
* Select the best way to do (m_bias + m * n) / (1 << 64). \
* From now on there will be actual runtime code generated. \
*/ \
___res = __arch_xprod_64(___m, ___n, ___bias); \
\
___res /= ___p; \
})
#ifndef __arch_xprod_64
/*
* Default C implementation for __arch_xprod_64()
*
* Prototype: uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
* Semantic: retval = ((bias ? m : 0) + m * n) >> 64
*
* The product is a 128-bit value, scaled down to 64 bits.
* Assuming constant propagation to optimize away unused conditional code.
* Architectures may provide their own optimized assembly implementation.
*/
static inline uint64_t __arch_xprod_64(const uint64_t m, uint64_t n, bool bias)
{
uint32_t m_lo = m;
uint32_t m_hi = m >> 32;
uint32_t n_lo = n;
uint32_t n_hi = n >> 32;
uint64_t res;
uint32_t res_lo, res_hi, tmp;
if (!bias) {
res = ((uint64_t)m_lo * n_lo) >> 32;
} else if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
/* there can't be any overflow here */
res = (m + (uint64_t)m_lo * n_lo) >> 32;
} else {
res = m + (uint64_t)m_lo * n_lo;
res_lo = res >> 32;
res_hi = (res_lo < m_hi);
res = res_lo | ((uint64_t)res_hi << 32);
}
if (!(m & ((1ULL << 63) | (1ULL << 31)))) {
/* there can't be any overflow here */
res += (uint64_t)m_lo * n_hi;
res += (uint64_t)m_hi * n_lo;
res >>= 32;
} else {
res += (uint64_t)m_lo * n_hi;
tmp = res >> 32;
res += (uint64_t)m_hi * n_lo;
res_lo = res >> 32;
res_hi = (res_lo < tmp);
res = res_lo | ((uint64_t)res_hi << 32);
}
res += (uint64_t)m_hi * n_hi;
return res;
}
#endif
#ifndef __div64_32
extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
#endif
/* The unnecessary pointer compare is there
* to check for type safety (n must be 64bit)
*/
# define do_div(n,base) ({ \
uint32_t __base = (base); \
uint32_t __rem; \
(void)(((typeof((n)) *)0) == ((uint64_t *)0)); \
if (__builtin_constant_p(__base) && \
is_power_of_2(__base)) { \
__rem = (n) & (__base - 1); \
(n) >>= ilog2(__base); \
} else if (__div64_const32_is_OK && \
__builtin_constant_p(__base) && \
__base != 0) { \
uint32_t __res_lo, __n_lo = (n); \
(n) = __div64_const32(n, __base); \
/* the remainder can be computed with 32-bit regs */ \
__res_lo = (n); \
__rem = __n_lo - __res_lo * __base; \
} else if (likely(((n) >> 32) == 0)) { \
__rem = (uint32_t)(n) % __base; \
(n) = (uint32_t)(n) / __base; \
} else \
__rem = __div64_32(&(n), __base); \
__rem; \
})
#else /* BITS_PER_LONG == ?? */
# error do_div() does not yet support the C64
#endif /* BITS_PER_LONG */
#endif /* _ASM_GENERIC_DIV64_H */
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