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![Jiong Wang](/assets/img/avatar_default.png)
The new added "reciprocal_value_adv" implements the advanced version of the algorithm described in Figure 4.2 of the paper except when "divisor > (1U << 31)" whose ceil(log2(d)) result will be 32 which then requires u128 divide on host. The exception case could be easily handled before calling "reciprocal_value_adv". The advanced version requires more complex calculation to get the reciprocal multiplier and other control variables, but then could reduce the required emulation operations. It makes no sense to use this advanced version for host divide emulation, those extra complexities for calculating multiplier etc could completely waive our saving on emulation operations. However, it makes sense to use it for JIT divide code generation (for example eBPF JIT backends) for which we are willing to trade performance of JITed code with that of host. As shown by the following pseudo code, the required emulation operations could go down from 6 (the basic version) to 3 or 4. To use the result of "reciprocal_value_adv", suppose we want to calculate n/d, the C-style pseudo code will be the following, it could be easily changed to real code generation for other JIT targets. struct reciprocal_value_adv rvalue; u8 pre_shift, exp; // handle exception case. if (d >= (1U << 31)) { result = n >= d; return; } rvalue = reciprocal_value_adv(d, 32) exp = rvalue.exp; if (rvalue.is_wide_m && !(d & 1)) { // floor(log2(d & (2^32 -d))) pre_shift = fls(d & -d) - 1; rvalue = reciprocal_value_adv(d >> pre_shift, 32 - pre_shift); } else { pre_shift = 0; } // code generation starts. if (imm == 1U << exp) { result = n >> exp; } else if (rvalue.is_wide_m) { // pre_shift must be zero when reached here. t = (n * rvalue.m) >> 32; result = n - t; result >>= 1; result += t; result >>= rvalue.sh - 1; } else { if (pre_shift) result = n >> pre_shift; result = ((u64)result * rvalue.m) >> 32; result >>= rvalue.sh; } Signed-off-by: Jiong Wang <jiong.wang@netronome.com> Reviewed-by: Jakub Kicinski <jakub.kicinski@netronome.com> Signed-off-by: Daniel Borkmann <daniel@iogearbox.net>
69 lines
1.4 KiB
C
69 lines
1.4 KiB
C
// SPDX-License-Identifier: GPL-2.0
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#include <linux/bug.h>
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#include <linux/kernel.h>
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#include <asm/div64.h>
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#include <linux/reciprocal_div.h>
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#include <linux/export.h>
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/*
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* For a description of the algorithm please have a look at
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* include/linux/reciprocal_div.h
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*/
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struct reciprocal_value reciprocal_value(u32 d)
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{
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struct reciprocal_value R;
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u64 m;
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int l;
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l = fls(d - 1);
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m = ((1ULL << 32) * ((1ULL << l) - d));
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do_div(m, d);
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++m;
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R.m = (u32)m;
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R.sh1 = min(l, 1);
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R.sh2 = max(l - 1, 0);
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return R;
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}
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EXPORT_SYMBOL(reciprocal_value);
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struct reciprocal_value_adv reciprocal_value_adv(u32 d, u8 prec)
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{
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struct reciprocal_value_adv R;
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u32 l, post_shift;
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u64 mhigh, mlow;
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/* ceil(log2(d)) */
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l = fls(d - 1);
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/* NOTE: mlow/mhigh could overflow u64 when l == 32. This case needs to
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* be handled before calling "reciprocal_value_adv", please see the
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* comment at include/linux/reciprocal_div.h.
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*/
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WARN(l == 32,
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"ceil(log2(0x%08x)) == 32, %s doesn't support such divisor",
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d, __func__);
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post_shift = l;
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mlow = 1ULL << (32 + l);
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do_div(mlow, d);
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mhigh = (1ULL << (32 + l)) + (1ULL << (32 + l - prec));
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do_div(mhigh, d);
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for (; post_shift > 0; post_shift--) {
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u64 lo = mlow >> 1, hi = mhigh >> 1;
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if (lo >= hi)
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break;
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mlow = lo;
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mhigh = hi;
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}
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R.m = (u32)mhigh;
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R.sh = post_shift;
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R.exp = l;
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R.is_wide_m = mhigh > U32_MAX;
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return R;
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}
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EXPORT_SYMBOL(reciprocal_value_adv);
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