[llvm-dev] proposal for optimization method (original) (raw)

or dv via llvm-dev llvm-dev at lists.llvm.org
Wed Feb 20 04:08:59 PST 2019

Hello everyone, I discovered a way to perform optimization on the following code (I gave an example that uses 32bit integer, but it works with any size.):

const uint32 d,r;//d is an odd number //d is the divisor, r is the remainder bool check_remainder(uint32 x) { return x%d==r; }

if we know d and r at compile time, and d is an odd integer, we can use modular multiplicative inverse to bypass the division operation. I wrote the following code to calculate the M.M.I of a number over 2^b. I give anyone the permission to use it (unlicensed).

uint64_t find_mod_mul_inverse(uint64_t x, uint64_t bits) { if (bits > 64 || ((x&1)==0)) return 0;// invalid parameters uint64_t mask; if (bits == 64) mask = -1; else { mask = 1; mask<<=bits; mask--; } x&=mask; uint64_t result=1, state=x, ctz=0; while(state!=1ULL) { ctz=__builtin_ctzll(state^1); result|=1ULL<<ctz; state+=x<<ctz; state&=mask; } return result; }

now consider the following steps: from the 2 constants (d and r) we create 3 constants (with the same bit length): constants uint32 s,u,mmi; mmi = find_mod_mul_inverse(d,32); s = (r*mmi); u = (UINT32_MAX-r)/d; // UINT32_MAX corresponds to pow(2,32)-1. the idea behind these constants is the following formula: mmi_of(d)*x=x/d+(x%d)*mmi_of(d)

now after we generated the constants, we will just emit the following code instead of the former: bool check_remainder(uint32 x) { return ((x*mmi)-s)<=u; }

Anyway, I looked at the file IntegerDivision.cpp, it seems to me that this new optimization is more effective then the optimization used there. However, I have no experience with compiler development, so I can just give you my idea. if further explanation is needed, just ask. I tested my method and it gives the correct results. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20190220/9e9e5aec/attachment.html>

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