gno.land/p/moul/xmath/v1⧉

1package xmath23import "math/bits"45// maxInt64 is the largest int64. Unexported and spelled out because xmath6// already exports MaxInt64 as the max-of-two helper, and a constant sharing7// that name would shadow it.8const maxInt64 = int64(9223372036854775807)910// MulDiv returns a*b/c computed through a 128-bit intermediate, so the product11// does not have to fit in an int64. It is the proportional-share calculation:12// "this account's cut of the pot", "this stake's slice of the rewards".13//14// The naive a*b/c silently wraps when a*b exceeds an int64, and it wraps to a15// plausible-looking number rather than to an obvious one, which is how a payout16// split leaks money without anything failing. Ten realms deployed on gnoland-117// carry their own copy of this function for exactly that reason, and every one18// of them reaches for math/bits the same way.19//20// MulDiv panics rather than returning a wrong number:21//22//   - a or b negative, or c at or below zero: the domain is unsigned ratios,23//     and a negative share is a caller bug, not a value to propagate.24//   - the quotient not fitting in an int64.25//26// Rounding is toward zero, like integer division. See [MulDivUp] when the27// remainder must favour the payer instead.28func MulDiv(a, b, c int64) int64 {29	if a < 0 || b < 0 {30		panic("xmath: MulDiv on a negative operand")31	}32	if c <= 0 {33		panic("xmath: MulDiv by a non-positive denominator")34	}35	hi, lo := bits.Mul64(uint64(a), uint64(b))36	if hi >= uint64(c) {37		panic("xmath: MulDiv quotient overflows int64")38	}39	q, _ := bits.Div64(hi, lo, uint64(c))40	if q > uint64(maxInt64) {41		panic("xmath: MulDiv quotient overflows int64")42	}43	return int64(q)44}4546// MulDivUp is [MulDiv] rounding away from zero when the division is not exact.47//48// Which way to round is a money question, not a style one: rounding a fee down49// and a payout up is how a pool pays out more than it holds. Use MulDiv for50// what someone receives and MulDivUp for what someone owes.51func MulDivUp(a, b, c int64) int64 {52	q := MulDiv(a, b, c)53	hi, lo := bits.Mul64(uint64(a), uint64(b))54	_, rem := bits.Div64(hi, lo, uint64(c))55	if rem != 0 {56		if q == maxInt64 {57			panic("xmath: MulDivUp quotient overflows int64")58		}59		q++60	}61	return q62}6364