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#ifndef HEX_FASTDIV_H
#define HEX_FASTDIV_H
// See https://gmplib.org/~tege/divcnst-pldi94.pdf figure 4.1.
// Precompute mp (m' in the paper) and L such that division
// can be computed using a multiply (high 32b of 64b result)
// and a shift:
//
// n/d = (mulhi(n, mp) + n) >> L;
struct fastdiv_values {
uint32_t mp;
uint32_t l;
};
static inline struct fastdiv_values init_fastdiv_values(uint32_t d) {
struct fastdiv_values result = { 0, 0 };
// compute L = ceil(log2(d));
while (result.l < 32 && ((uint32_t) 1 << result.l) < d) {
++(result.l);
}
result.mp = (uint32_t) (((uint64_t) 1 << 32) * (((uint64_t) 1 << result.l) - d) / d + 1);
return result;
}
static inline uint32_t fastdiv(uint32_t n, const struct fastdiv_values * vals) {
// Compute high 32 bits of n * mp
const uint32_t hi = (uint32_t) (((uint64_t) n * vals->mp) >> 32); // mulhi(n, mp)
// add n, apply bit shift
return (hi + n) >> vals->l;
}
static inline uint32_t fastmodulo(uint32_t n, uint32_t d, const struct fastdiv_values * vals) {
return n - fastdiv(n, vals) * d;
}
#endif /* HEX_FASTDIV_H */
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