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Source file test/peano.go

Documentation: test

     1  // run
     2  
     3  // Copyright 2009 The Go Authors. All rights reserved.
     4  // Use of this source code is governed by a BSD-style
     5  // license that can be found in the LICENSE file.
     6  
     7  // Test that heavy recursion works. Simple torture test for
     8  // segmented stacks: do math in unary by recursion.
     9  
    10  package main
    11  
    12  type Number *Number
    13  
    14  // -------------------------------------
    15  // Peano primitives
    16  
    17  func zero() *Number {
    18  	return nil
    19  }
    20  
    21  func is_zero(x *Number) bool {
    22  	return x == nil
    23  }
    24  
    25  func add1(x *Number) *Number {
    26  	e := new(Number)
    27  	*e = x
    28  	return e
    29  }
    30  
    31  func sub1(x *Number) *Number {
    32  	return *x
    33  }
    34  
    35  func add(x, y *Number) *Number {
    36  	if is_zero(y) {
    37  		return x
    38  	}
    39  
    40  	return add(add1(x), sub1(y))
    41  }
    42  
    43  func mul(x, y *Number) *Number {
    44  	if is_zero(x) || is_zero(y) {
    45  		return zero()
    46  	}
    47  
    48  	return add(mul(x, sub1(y)), x)
    49  }
    50  
    51  func fact(n *Number) *Number {
    52  	if is_zero(n) {
    53  		return add1(zero())
    54  	}
    55  
    56  	return mul(fact(sub1(n)), n)
    57  }
    58  
    59  // -------------------------------------
    60  // Helpers to generate/count Peano integers
    61  
    62  func gen(n int) *Number {
    63  	if n > 0 {
    64  		return add1(gen(n - 1))
    65  	}
    66  
    67  	return zero()
    68  }
    69  
    70  func count(x *Number) int {
    71  	if is_zero(x) {
    72  		return 0
    73  	}
    74  
    75  	return count(sub1(x)) + 1
    76  }
    77  
    78  func check(x *Number, expected int) {
    79  	var c = count(x)
    80  	if c != expected {
    81  		print("error: found ", c, "; expected ", expected, "\n")
    82  		panic("fail")
    83  	}
    84  }
    85  
    86  // -------------------------------------
    87  // Test basic functionality
    88  
    89  func init() {
    90  	check(zero(), 0)
    91  	check(add1(zero()), 1)
    92  	check(gen(10), 10)
    93  
    94  	check(add(gen(3), zero()), 3)
    95  	check(add(zero(), gen(4)), 4)
    96  	check(add(gen(3), gen(4)), 7)
    97  
    98  	check(mul(zero(), zero()), 0)
    99  	check(mul(gen(3), zero()), 0)
   100  	check(mul(zero(), gen(4)), 0)
   101  	check(mul(gen(3), add1(zero())), 3)
   102  	check(mul(add1(zero()), gen(4)), 4)
   103  	check(mul(gen(3), gen(4)), 12)
   104  
   105  	check(fact(zero()), 1)
   106  	check(fact(add1(zero())), 1)
   107  	check(fact(gen(5)), 120)
   108  }
   109  
   110  // -------------------------------------
   111  // Factorial
   112  
   113  var results = [...]int{
   114  	1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800,
   115  	39916800, 479001600,
   116  }
   117  
   118  func main() {
   119  	for i := 0; i <= 9; i++ {
   120  		if f := count(fact(gen(i))); f != results[i] {
   121  			println("FAIL:", i, "!:", f, "!=", results[i])
   122  			panic(0)
   123  		}
   124  	}
   125  }
   126  

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