367 lines
8.3 KiB
Go
367 lines
8.3 KiB
Go
package main
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import (
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"fmt"
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"math"
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"math/big"
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"encoding/hex"
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"github.com/obscuren/sha3"
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"testing"
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"strconv"
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)
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//For use in benchmarking
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const tree_depth = 5
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const tape_width = 32 //int(math.Pow(2,tree_depth)) < would be nice, but go won't recognize as const
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const tape_depth = 100
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//Number of operations that are drawn from to form the tape and the tree
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const num_ops = 9
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//This is the number of times the PoW algorithm is run
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const sample_size = 100
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func Bytes2Hex(d []byte) string {
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return hex.EncodeToString(d)
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}
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func Hex2Bytes(str string) []byte {
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h, _ := hex.DecodeString(str)
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return h
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}
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func plus(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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var lim big.Int
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lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0))
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z.Add(x,y)
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return z.Mod(z,&lim)
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}
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func times(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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var lim, x1, y1 big.Int
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lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0))
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x1.Set(x)
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y1.Set(y)
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z.Mul(x,y)
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z.Mod(z,&lim)
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return z
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}
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func mod(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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if (x.Cmp(big.NewInt(0)) == 0 || y.Cmp(big.NewInt(0)) == 0) {
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return big.NewInt(0)
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}
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if x.Cmp(y) == -1 { //if x < y
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z.Mod(y,x)
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} else if x.Cmp(y) == 1 { //if x > y
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z.Mod(x,y)
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}
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return z
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}
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func xor(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.Xor(x,y)}
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func nxor(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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z.Xor(x,y)
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return z.Not(z)
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}
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func and(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.And(x,y)}
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func not(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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_ = y
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return z.Not(x)
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}
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func or(z *big.Int, x *big.Int, y *big.Int) *big.Int {return z.Or(x,y)}
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func rshift(z *big.Int, x *big.Int, y *big.Int) *big.Int {
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var lim big.Int
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lim.Exp(big.NewInt(2),big.NewInt(256), big.NewInt(0))
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z.Rsh(x,7)
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return z.Mod(z,&lim)
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}
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func GetOp(i int) func(z *big.Int, x *big.Int, y *big.Int) *big.Int{
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switch i {
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case 0:
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return plus
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case 1:
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return xor
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case 2:
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return not
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case 3:
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return times
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case 4:
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return mod
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case 5:
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return rshift
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case 6:
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return or
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case 7:
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return and
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case 8:
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return nxor
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}
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return plus
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}
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//the tapelink is used to t
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type Tapelink struct {
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I int64
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J int64
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op func(z *big.Int, x *big.Int, y *big.Int) *big.Int
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}
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func Sha3Bin(data []byte) []byte {
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d := sha3.NewKeccak256()
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d.Write(data)
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return d.Sum(nil)
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}
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func BenchmarkSha3Bin(b *testing.B){
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for i:= 0; i < b.N; i++ {
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Sha3Bin([]byte(string(i)))
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}
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}
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//generates a tape of operations that is w*d long
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func gen_tape(seed int64, w int, d int) []Tapelink {
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var X = big.NewInt(0)
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var Y = big.NewInt(0)
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Y.Exp(big.NewInt(2),big.NewInt(80), nil)
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var M = big.NewInt(0)
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var T []Tapelink
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for i := 0; i < w*d; i++{
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// add empty link to tape
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T = append(T, *new(Tapelink))
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// generate new entropy as needed
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if (int64(X.Cmp(Y)) == -1) {X.SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i), 10))))}
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// Pick random index I
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T[i].I = M.Mod(X,big.NewInt(int64(w))).Int64()
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M = big.NewInt(int64(w))
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X = X.Div(X,M)
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// Pick random index J
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mm := big.NewInt(M.Mod(X,big.NewInt(int64(w-1))).Int64() + int64(1) + T[i].I)
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T[i].J = M.Mod(mm, big.NewInt(int64(w))).Int64()
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M = big.NewInt(int64(w-1))
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X = X.Div(X,M)
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// Pick random operation
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T[i].op = GetOp(int(M.Mod(X, big.NewInt(int64(num_ops))).Int64()))
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M = big.NewInt(int64(num_ops))
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X = X.Div(X,M)
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}
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return T
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}
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func BenchmarkGen_tape(b *testing.B){
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var X big.Int
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var s int64
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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X.SetBytes(Sha3Bin([]byte(string(i))))
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s = X.Int64()
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b.StartTimer()
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gen_tape(s, tape_width, tape_depth)
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}
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}
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func gen_inputs(seed int64, w int) []big.Int {
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var A []big.Int
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for i := 0; i < w; i++ {
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A = append(A, *new(big.Int))
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if (i % 256 == 0) {
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A[i].SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i), 10))))
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} else {
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A[i].Lsh(&A[i-1], 1)
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}
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}
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return A
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}
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func BenchmarkGen_inputs(b *testing.B){
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var X big.Int
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var s int64
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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X.SetBytes(Sha3Bin([]byte(string(i))))
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s = X.Int64()
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b.StartTimer()
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gen_inputs(s, tape_width)
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}
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}
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//this changes the inputs as it goes through a tape with d links
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func run_tape(tape []Tapelink, inputs []big.Int, d int) {
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var X *big.Int
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X = big.NewInt(0)
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for i := 0; i < d; i++ {
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X = tape[i].op(X, &inputs[tape[i].I], &inputs[tape[i].J])
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inputs[tape[i].I].Set(X)
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}
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}
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func BenchmarkRun_tape(b *testing.B){
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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T := gen_tape(int64(i), tape_width, tape_depth)
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I := gen_inputs(int64(i), tape_width)
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b.StartTimer()
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run_tape(T,I,tape_width*tape_depth)
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}
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}
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//returns a 2^d - 1 length tape of operations (no I or J's in the Tapelinks)
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func gen_tree(seed int64, d int) []Tapelink {
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M := big.NewInt(0) // dummy variable
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X := big.NewInt(0) // entropy variable
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Y := big.NewInt(0) // entropy buffer size
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Y.Exp(big.NewInt(2),big.NewInt(80), nil)
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var T []Tapelink // the tree will be stored here
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for i := 0; i < int(math.Pow(2, float64(d))) - 1; i++{
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T = append(T, *new(Tapelink))
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//giving it more entropy, if X < 2^32
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if (X.Cmp(Y) == -1) {X.SetBytes(Sha3Bin([]byte(strconv.FormatInt(seed + int64(i),10))))}
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//filling the tape with random ops
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T[i].op = GetOp(int(M.Mod(X, big.NewInt(num_ops)).Int64()))
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M = big.NewInt(num_ops)
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X = X.Div(X,M)
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}
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return T
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}
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func BenchmarkGen_tree(b *testing.B) {
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var X big.Int
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var s int64
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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X.SetBytes(Sha3Bin([]byte(string(i))))
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s = X.Int64()
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b.StartTimer()
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gen_tree(s, tree_depth)
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}
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}
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//there should be 2^d inputs and 2^d - 1 links in the tape. not complying is an unhandled exception
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func run_tree(inputs []big.Int, tree []Tapelink, d int) *big.Int {
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X := big.NewInt(0)
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counter := 0
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for j := 0; j < d; j++ {
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for i := 0; i < int(math.Pow(2,float64(d - j - 1))); i++ {
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X = tree[counter].op(X, &inputs[2*i], &inputs[2*i + 1])
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inputs[i].Set(X)
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counter += 1
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}
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}
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return &inputs[0]
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}
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func BenchmarkRun_tree(b *testing.B) {
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var X big.Int
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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var inputs []big.Int
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for j := 0; j < tape_width; j++ {
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X.SetBytes(Sha3Bin([]byte(string(j + i*tape_width))))
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inputs = append(inputs, X)
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}
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tree := gen_tree(X.Int64(), tree_depth)
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b.StartTimer()
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run_tree(inputs, tree, tree_depth)
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}
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}
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func sha_cap(s []string, n int) []byte{
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var feed string
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feed = ""
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for i := 0; i < n; i++ {
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feed += s[i]
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}
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return Sha3Bin([]byte(feed))
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}
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func BenchmarkSha_cap(b *testing.B){
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var X big.Int
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var s []string
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b.ResetTimer()
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for i := 0; i < b.N; i++ {
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b.StopTimer()
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X.SetBytes(Sha3Bin([]byte(string(i))))
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s = append(s, X.String())
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b.StartTimer()
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sha_cap(s,1)
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}
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}
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func main(){
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var seed int64
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var sample []big.Int
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seed = int64(13300331)
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for i := 0; i < sample_size; i++ {
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Tape := gen_tape(seed, tape_width, tape_depth)
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Tree := gen_tree(seed, tree_depth)
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seed += int64(i*i)
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if i%10 == 0 {
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fmt.Printf("i: %d\n",i)
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}
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I := gen_inputs(seed, tape_width)
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run_tape(Tape, I, tape_depth*tape_width)
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output := *run_tree(I, Tree, tree_depth)
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if output.Cmp(big.NewInt(0)) == 0 {
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fmt.Printf("We have a zero from the tree, form operation: \n")
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fmt.Println(Tree[len(Tree)-1])
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}
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var blockhashes []string
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blockhashes = append(blockhashes, output.String())
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sample = append(sample, output)
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H := sha_cap(blockhashes, 1)
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output.SetBytes(H)
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//sample = append(sample, output)
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}
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var collisions int = 0
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for i := 0; i < sample_size; i++ {
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//fmt.Println(sample[i])
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for j:=0; j < i; j++ {
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//if sample[i] == sample[j] {
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if sample[i].Cmp(&sample[j]) == 0 {
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collisions += 1
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//fmt.Printf("collision on i, j: %d, %d", i, j)
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//fmt.Println(sample[i])
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}
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}
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}
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fmt.Printf("number of outputs with same value: %d out of %d\n", (1+int(math.Pow(float64(1+8*collisions),0.5)))/2, sample_size)
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}
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