narrowTotalForPair()

bool fl::anonymous_namespace{white_allocation.cpp.hpp}::narrowTotalForPair	(	const SplitBound &	lower,
		const SplitBound &	upper,
		i64 *	low,
		i64 *	high )

The totals at which lower <= upper holds, narrowed into [*low, *high].

Returns false when the pair excludes every total, which is the one case the caller cannot express as a narrowed interval.

Cross-multiplied rather than divided first: with positive denominators the inequality

(nL + mL*s) / qL  <=  (nU + mU*s) / qU

is s * (qU*mL - qL*mU) <= qL*nU - qU*nL, one linear inequality in s whose coefficients are exact in i64.

Definition at line 332 of file white_allocation.cpp.hpp.

                                                {
    const i64 slope = static_cast<i64>(upper.denominator) * lower.slope -
                      static_cast<i64>(lower.denominator) * upper.slope;
    const i64 constant = static_cast<i64>(lower.denominator) * upper.numerator -
                         static_cast<i64>(upper.denominator) * lower.numerator;
    if (slope == 0) {
        // No s makes this pair better or worse; it either always holds or
        // never does.
        return constant >= 0;
    }
    const i64 bound = (constant * 65536) / slope;
    if (slope > 0) {
        if (bound < *high) {
            *high = bound;
        }
    } else if (bound > *low) {
        *low = bound;
    }
    return true;
}

References fl::FL_NO_EXCEPT, and narrowTotalForPair().

Referenced by narrowTotalForPair().

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