func TestLog2(t *testing.T) {
for _, tc := range s {
u := uint(tc)
u >>= u & 0x1f
if u == 0 {
continue // not interesting
}
l := xmath.Log2(u)
s := u >> l
if s != 1 {
t.Fatalf("Log2(%d) returned %x", u, l)
}
}
}
func init() {
// singletons
Binary = func(n uint) uint {
return n / 2
}
CoBinary = func(n uint) uint {
return (n + 1) / 2
}
Dichotomic = func(n uint) uint {
return n / (1 << ((xmath.Log2(n) + 1) / 2))
}
// non-singletons
Total = func(n uint) []uint {
s := make([]uint, n-2)
for i := range s {
s[i] = uint(i + 2)
}
// fmt.Printf(indent+" Total(%d) = %v\n", n, s)
return s
}
Dyadic = func(n uint) []uint {
s := make([]uint, xmath.Log2(n)-1)
for i := range s {
s[i] = n / (uint(1) << uint(len(s)-i))
}
// fmt.Printf(indent+" Dyadic(%d) = %v\n", n, s)
return s
}
Fermat = func(n uint) []uint {
s := make([]uint, 1+xmath.Log2(xmath.Log2(n)-1))
for i := range s {
s[i] = n / (uint(1) << (uint(1) << uint(len(s)-1-i)))
}
// fmt.Printf(indent+" Fermat(%d) = %v\n", n, s)
return s
}
}
// Chain computes an addition chain, returning it in StarChain form.
func (γ SingletonStrategy) Chain(n uint) StarChain {
// This is the function minChain as described in the paper.
switch a := xmath.Log2(n); {
case n == 1<<a:
r := make(StarChain, a)
for i := range r {
r[i] = i
}
return r
case n == 3:
return StarChain{0, 0}
}
s, _ := γ.chain1(n, γ(n))
return s
}
// Factorial computes n!, leaving result in z and returning z.
func Factorial(z *big.Int, n uint) *big.Int {
currentN := int64(1)
var product func(*big.Int, uint) *big.Int
product = func(z *big.Int, n uint) *big.Int {
switch n {
case 1:
currentN += 2
return z.SetInt64(currentN)
case 2:
currentN += 2
r := currentN
currentN += 2
r *= currentN
return z.SetInt64(r)
}
m := n / 2
var r big.Int
return z.Mul(product(z, m), product(&r, n-m))
}
var p, pr big.Int
p.SetInt64(1)
z.SetInt64(1)
var h, shift uint
var high uint = 1
log2n := xmath.Log2(n)
for h != n {
shift += h
h = n >> log2n
log2n--
length := high
high = (h - 1) | 1
length = (high - length) / 2
if length > 0 {
z.Mul(z, p.Mul(&p, product(&pr, length)))
}
}
return z.Lsh(z, shift)
}
// minChain returns a chain that is stored in the map.
func (cc *cm) minChain(n uint) StarChain {
// fmt.Println(indent, "minChain(", n, ")")
ns := indent
indent += " "
defer func() { indent = ns }()
if s, ok := cc.m[n]; ok {
// fmt.Println(indent, "memoized")
return s
}
// This is the function minChain as described in the paper.
switch a := xmath.Log2(n); {
case n == 1<<a:
r := make(StarChain, a)
for i := range r {
r[i] = i
}
cc.m[n] = r
// fmt.Println(indent, "It's a power of 2. Returning", r.AddChain())
return r
// case n == 3:
// // fmt.Println(indent, "It's 3. Returning", StarChain{0, 0}.AddChain())
// return StarChain{0, 0}
}
min := int(n)
var minS StarChain
// var bestk uint
// fmt.Println(indent, "Considering some possibilities...")
for _, k := range cc.γ(n) {
s, _ := cc.chain1(n, k)
if len(s) < min {
// fmt.Println(indent, "oh,", k, "was a good one")
// bestk = k
min = len(s)
minS = s
}
}
cc.m[n] = minS
// fmt.Println(indent, "yeah,", bestk, "was best. Returning", minS.AddChain())
return minS
}