# [llvm-dev] proposal for optimization method

Craig Topper via llvm-dev llvm-dev at lists.llvm.org
Wed Feb 20 21:27:12 PST 2019

```It looks like gcc already does something like this.
https://godbolt.org/z/JWljkL

~Craig

On Wed, Feb 20, 2019 at 8:45 PM or dv via llvm-dev <llvm-dev at lists.llvm.org>
wrote:

> 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
>         if (bits == 64)
>         else
>         {
>         }
>         uint64_t result=1, state=x, ctz=0;
>         while(state!=1ULL)
>         {
>                 ctz=__builtin_ctzll(state^1);
>                 result|=1ULL<<ctz;
>                 state+=x<<ctz;
>         }
>         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.
>
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> llvm-dev at lists.llvm.org
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>
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