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linux/include/asm-generic/div64.h

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Linux-2.6.12-rc2 Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
2005-04-17 02:20:36 +04:00
#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
*
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
* Optimization for constant divisors on 32-bit machines:
* Copyright (C) 2006-2015 Nicolas Pitre
*
Linux-2.6.12-rc2 Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
2005-04-17 02:20:36 +04:00
* The semantics of do_div() are:
*
* 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
# 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
div64.h: optimize do_div() for power-of-two constant divisors Let's perform the obvious mask and shift operation in this case. On 32-bit targets, gcc is able to do the same thing with a constant divisor that happens to be a power of two i.e. it turns the division into an inline shift, but it doesn't hurt to be explicit. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-11-02 22:55:05 +03:00
#include <linux/log2.h>
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
/*
* 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); \
__div64_const32(): abstract out the actual 128-bit cross product code The default C implementation for the 128-bit cross product is abstracted into the __arch_xprod_64() macro that can be overridden to let architectures provide their own assembly optimized implementation. There are many advantages to an assembly version for this operation. Carry bit handling becomes trivial, and 32-bit shifts may be achieved simply by inverting register pairs on some architectures. This has the potential to be quite faster and use much fewer instructions. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-10-31 00:54:56 +03:00
uint32_t ___p, ___bias; \
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
\
/* 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))). \
* \
__div64_const32(): abstract out the actual 128-bit cross product code The default C implementation for the 128-bit cross product is abstracted into the __arch_xprod_64() macro that can be overridden to let architectures provide their own assembly optimized implementation. There are many advantages to an assembly version for this operation. Carry bit handling becomes trivial, and 32-bit shifts may be achieved simply by inverting register pairs on some architectures. This has the potential to be quite faster and use much fewer instructions. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-10-31 00:54:56 +03:00
* Select the best way to do (m_bias + m * n) / (1 << 64). \
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
* From now on there will be actual runtime code generated. \
*/ \
__div64_const32(): abstract out the actual 128-bit cross product code The default C implementation for the 128-bit cross product is abstracted into the __arch_xprod_64() macro that can be overridden to let architectures provide their own assembly optimized implementation. There are many advantages to an assembly version for this operation. Carry bit handling becomes trivial, and 32-bit shifts may be achieved simply by inverting register pairs on some architectures. This has the potential to be quite faster and use much fewer instructions. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-10-31 00:54:56 +03:00
___res = __arch_xprod_64(___m, ___n, ___bias); \
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
\
___res /= ___p; \
})
__div64_const32(): abstract out the actual 128-bit cross product code The default C implementation for the 128-bit cross product is abstracted into the __arch_xprod_64() macro that can be overridden to let architectures provide their own assembly optimized implementation. There are many advantages to an assembly version for this operation. Carry bit handling becomes trivial, and 32-bit shifts may be achieved simply by inverting register pairs on some architectures. This has the potential to be quite faster and use much fewer instructions. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-10-31 00:54:56 +03:00
#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, 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;
tmp = (res < m) ? (1ULL << 32) : 0;
res = (res >> 32) + tmp;
}
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 {
tmp = res += (uint64_t)m_lo * n_hi;
res += (uint64_t)m_hi * n_lo;
tmp = (res < tmp) ? (1ULL << 32) : 0;
res = (res >> 32) + tmp;
}
res += (uint64_t)m_hi * n_hi;
return res;
}
#endif
__div64_32(): make it overridable at compile time Some architectures may want to override the default implementation at compile time to do things inline. For example, ARM uses a non-standard calling convention for better efficiency in this case. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-11-02 21:02:46 +03:00
#ifndef __div64_32
Linux-2.6.12-rc2 Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
2005-04-17 02:20:36 +04:00
extern uint32_t __div64_32(uint64_t *dividend, uint32_t divisor);
__div64_32(): make it overridable at compile time Some architectures may want to override the default implementation at compile time to do things inline. For example, ARM uses a non-standard calling convention for better efficiency in this case. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-11-02 21:02:46 +03:00
#endif
Linux-2.6.12-rc2 Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
2005-04-17 02:20:36 +04:00
/* 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)); \
div64.h: optimize do_div() for power-of-two constant divisors Let's perform the obvious mask and shift operation in this case. On 32-bit targets, gcc is able to do the same thing with a constant divisor that happens to be a power of two i.e. it turns the division into an inline shift, but it doesn't hurt to be explicit. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-11-02 22:55:05 +03:00
if (__builtin_constant_p(__base) && \
is_power_of_2(__base)) { \
__rem = (n) & (__base - 1); \
(n) >>= ilog2(__base); \
do_div(): generic optimization for constant divisor on 32-bit machines 64-by-32-bit divisions are prominent in the kernel, even on 32-bit machines. Luckily, many of them use a constant divisor that allows for a much faster multiplication by the divisor's reciprocal. The compiler already performs this optimization when compiling a 32-by-32 division with a constant divisor. Unfortunately, on 32-bit machines, gcc does not optimize 64-by-32 divisions in that case, except for constant divisors that happen to be a power of 2. Let's avoid the slow path whenever the divisor is constant by manually computing the reciprocal ourselves and performing the multiplication inline. In most cases, this improves performance of 64-by-32 divisions by about two orders of magnitude compared to the __div64_32() fallback, especially on architectures lacking a native div instruction. The algorithm used here comes from the existing ARM code. The __div64_const32_is_OK macro can be predefined by architectures to disable this optimization in some cases. For example, some ancient gcc version on ARM would crash with an ICE when fed this code. Signed-off-by: Nicolas Pitre <nico@linaro.org> Acked-by: Alexey Brodkin <abrodkin@synopsys.com>
2015-10-30 22:36:39 +03:00
} 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; \
div64.h: optimize do_div() for power-of-two constant divisors Let's perform the obvious mask and shift operation in this case. On 32-bit targets, gcc is able to do the same thing with a constant divisor that happens to be a power of two i.e. it turns the division into an inline shift, but it doesn't hurt to be explicit. Signed-off-by: Nicolas Pitre <nico@linaro.org>
2015-11-02 22:55:05 +03:00
} else if (likely(((n) >> 32) == 0)) { \
Linux-2.6.12-rc2 Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
2005-04-17 02:20:36 +04:00
__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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