105 строки
3.3 KiB
C
105 строки
3.3 KiB
C
/* SPDX-License-Identifier: GPL-2.0 */
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#ifndef _LINUX_RECIPROCAL_DIV_H
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#define _LINUX_RECIPROCAL_DIV_H
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#include <linux/types.h>
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/*
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* This algorithm is based on the paper "Division by Invariant
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* Integers Using Multiplication" by Torbjörn Granlund and Peter
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* L. Montgomery.
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*
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* The assembler implementation from Agner Fog, which this code is
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* based on, can be found here:
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* http://www.agner.org/optimize/asmlib.zip
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*
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* This optimization for A/B is helpful if the divisor B is mostly
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* runtime invariant. The reciprocal of B is calculated in the
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* slow-path with reciprocal_value(). The fast-path can then just use
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* a much faster multiplication operation with a variable dividend A
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* to calculate the division A/B.
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*/
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struct reciprocal_value {
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u32 m;
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u8 sh1, sh2;
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};
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/* "reciprocal_value" and "reciprocal_divide" together implement the basic
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* version of the algorithm described in Figure 4.1 of the paper.
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*/
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struct reciprocal_value reciprocal_value(u32 d);
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static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
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{
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u32 t = (u32)(((u64)a * R.m) >> 32);
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return (t + ((a - t) >> R.sh1)) >> R.sh2;
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}
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struct reciprocal_value_adv {
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u32 m;
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u8 sh, exp;
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bool is_wide_m;
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};
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/* "reciprocal_value_adv" implements the advanced version of the algorithm
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* described in Figure 4.2 of the paper except when "divisor > (1U << 31)" whose
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* ceil(log2(d)) result will be 32 which then requires u128 divide on host. The
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* exception case could be easily handled before calling "reciprocal_value_adv".
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*
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* The advanced version requires more complex calculation to get the reciprocal
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* multiplier and other control variables, but then could reduce the required
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* emulation operations.
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*
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* It makes no sense to use this advanced version for host divide emulation,
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* those extra complexities for calculating multiplier etc could completely
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* waive our saving on emulation operations.
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*
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* However, it makes sense to use it for JIT divide code generation for which
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* we are willing to trade performance of JITed code with that of host. As shown
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* by the following pseudo code, the required emulation operations could go down
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* from 6 (the basic version) to 3 or 4.
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*
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* To use the result of "reciprocal_value_adv", suppose we want to calculate
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* n/d, the pseudo C code will be:
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*
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* struct reciprocal_value_adv rvalue;
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* u8 pre_shift, exp;
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*
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* // handle exception case.
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* if (d >= (1U << 31)) {
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* result = n >= d;
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* return;
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* }
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*
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* rvalue = reciprocal_value_adv(d, 32)
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* exp = rvalue.exp;
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* if (rvalue.is_wide_m && !(d & 1)) {
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* // floor(log2(d & (2^32 -d)))
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* pre_shift = fls(d & -d) - 1;
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* rvalue = reciprocal_value_adv(d >> pre_shift, 32 - pre_shift);
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* } else {
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* pre_shift = 0;
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* }
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*
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* // code generation starts.
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* if (imm == 1U << exp) {
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* result = n >> exp;
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* } else if (rvalue.is_wide_m) {
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* // pre_shift must be zero when reached here.
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* t = (n * rvalue.m) >> 32;
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* result = n - t;
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* result >>= 1;
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* result += t;
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* result >>= rvalue.sh - 1;
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* } else {
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* if (pre_shift)
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* result = n >> pre_shift;
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* result = ((u64)result * rvalue.m) >> 32;
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* result >>= rvalue.sh;
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* }
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*/
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struct reciprocal_value_adv reciprocal_value_adv(u32 d, u8 prec);
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#endif /* _LINUX_RECIPROCAL_DIV_H */
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