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Address review comments

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This commit is contained in:
Riccardo Gerosa 2022-10-20 10:31:50 -07:00
parent 3de002725c
commit ed4d75a075
1 changed files with 25 additions and 22 deletions
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47
src/math/big/int.go
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@ -206,47 +206,50 @@ func (z *Int) MulRange(a, b int64) *Int {
}
// Binomial sets z to the binomial coefficient of (n, k) and returns z.
func (z *Int) Binomial(n, k int64) *Int {
if k > n {
func (z *Int) Binomial(n_, k_ int64) *Int {
if k_ > n_ {
return z.SetInt64(0)
}
// reduce the number of multiplications by reducing k
if k > n-k {
k = n - k // Binomial(n, k) == Binomial(n, n-k)
if k_ > n_-k_ {
k_ = n_ - k_ // Binomial(n, k) == Binomial(n, n-k)
}
// C(n, k) == n * (n-1) * ... * (n-k+1) / k * (k-1) * ... * 1
// == n * (n-1) * ... * (n-k+1) / 1 * (1+1) * ... * k
// using the multiplicative formula produces smaller values
// at each step, that require fewer allocations and computations:
//
// Using the multiplicative formula produces smaller values
// at each step, requiring fewer allocations and computations:
//
// z = 1
// for i := 0; i < k; i = i+1 {
// z *= n-i
// z /= i+1
// z *= n-i
// z /= i+1
// }
//
// finally to avoid computing i+1 twice per loop:
//
// z = 1
// i := 0
// for {
// if i == k {
// break
// }
// z *= n-i
// i++
// z /= i
// if i == k {
// break
// }
// z *= n-i
// i++
// z /= i
// }
var bN, bK, bI, bNMinusI Int
bN.SetInt64(n)
bK.SetInt64(k)
var n, k, i, d Int
n.SetInt64(n_)
k.SetInt64(k_)
z.Set(intOne)
for {
if bI.Cmp(&bK) == 0 {
if i.Cmp(&k) == 0 {
break
}
bNMinusI.Sub(&bN, &bI)
z.Mul(z, &bNMinusI)
bI.Add(&bI, intOne)
z.Quo(z, &bI)
d.Sub(&n, &i)
z.Mul(z, &d)
i.Add(&i, intOne)
z.Quo(z, &i)
}
return z
}