#ifndef RECIPROCAL_DIV_H
#define RECIPROCAL_DIV_H
#include "div64.h"
#include "bitops.h"
/*
* This algorithm is based on the paper "Division by Invariant
* Integers Using Multiplication" by Torbjörn Granlund and Peter
* L. Montgomery.
*
* The assembler implementation from Agner Fog, which this code is
* based on, can be found here:
* http://www.agner.org/optimize/asmlib.zip
*
* This optimization for A/B is helpful if the divisor B is mostly
* runtime invariant. The reciprocal of B is calculated in the
* slow-path with reciprocal_value(). The fast-path can then just use
* a much faster multiplication operation with a variable dividend A
* to calculate the division A/B.
*/
struct reciprocal_value {
u32 m;
u8 sh1, sh2;
};
struct reciprocal_value reciprocal_value(u32 d)
{
struct reciprocal_value R;
u64 m;
int l;
l = fls(d - 1);
m = ((1ULL << 32) * ((1ULL << l) - d));
do_div(m, d);
++m;
R.m = (u32)m;
R.sh1 = min(l, 1);
R.sh2 = max(l - 1, 0);
return R;
}
static inline u32 reciprocal_divide(u32 a, struct reciprocal_value R)
{
u32 t = (u32)(((u64)a * R.m) >> 32);
return (t + ((a - t) >> R.sh1)) >> R.sh2;
}
#endif /* RECIPROCAL_DIV_H */