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// $G $F.go && $L $F.$A && ./$A.out
// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package main
import (
"fmt"
"runtime"
"time"
)
type Number struct {
next *Number
}
// -------------------------------------
// Peano primitives
func zero() *Number { return nil }
func is_zero(x *Number) bool { return x == nil }
func add1(x *Number) *Number {
e := new(Number)
e.next = x
return e
}
func sub1(x *Number) *Number { return x.next }
func add(x, y *Number) *Number {
if is_zero(y) {
return x
}
return add(add1(x), sub1(y))
}
func mul(x, y *Number) *Number {
if is_zero(x) || is_zero(y) {
return zero()
}
return add(mul(x, sub1(y)), x)
}
func fact(n *Number) *Number {
if is_zero(n) {
return add1(zero())
}
return mul(fact(sub1(n)), n)
}
// -------------------------------------
// Helpers to generate/count Peano integers
func gen(n int) *Number {
if n > 0 {
return add1(gen(n - 1))
}
return zero()
}
func count(x *Number) int {
if is_zero(x) {
return 0
}
return count(sub1(x)) + 1
}
func check(x *Number, expected int) {
var c = count(x)
if c != expected {
panic(fmt.Sprintf("error: found %d; expected %d", c, expected))
}
}
// -------------------------------------
// Test basic functionality
func verify() {
check(zero(), 0)
check(add1(zero()), 1)
check(gen(10), 10)
check(add(gen(3), zero()), 3)
check(add(zero(), gen(4)), 4)
check(add(gen(3), gen(4)), 7)
check(mul(zero(), zero()), 0)
check(mul(gen(3), zero()), 0)
check(mul(zero(), gen(4)), 0)
check(mul(gen(3), add1(zero())), 3)
check(mul(add1(zero()), gen(4)), 4)
check(mul(gen(3), gen(4)), 12)
check(fact(zero()), 1)
check(fact(add1(zero())), 1)
check(fact(gen(5)), 120)
}
// -------------------------------------
// Factorial
func main() {
st := &runtime.MemStats
t0 := time.Nanoseconds()
verify()
for i := 0; i <= 9; i++ {
print(i, "! = ", count(fact(gen(i))), "\n")
}
runtime.GC()
t1 := time.Nanoseconds()
fmt.Printf("garbage.BenchmarkPeano 1 %d ns/op\n", t1-t0)
fmt.Printf("garbage.BenchmarkPeanoPause %d %d ns/op\n", st.NumGC, int64(st.PauseNs)/int64(st.NumGC))
}
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