alias_test.go

Documentation: math/big

     1  // Copyright 2019 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package big_test
     6  
     7  import (
     8  	cryptorand "crypto/rand"
     9  	"math/big"
    10  	"math/rand"
    11  	"reflect"
    12  	"testing"
    13  	"testing/quick"
    14  )
    15  
    16  func equal(z, x *big.Int) bool {
    17  	return z.Cmp(x) == 0
    18  }
    19  
    20  type bigInt struct {
    21  	*big.Int
    22  }
    23  
    24  func generatePositiveInt(rand *rand.Rand, size int) *big.Int {
    25  	n := big.NewInt(1)
    26  	n.Lsh(n, uint(rand.Intn(size*8)))
    27  	n.Rand(rand, n)
    28  	return n
    29  }
    30  
    31  func (bigInt) Generate(rand *rand.Rand, size int) reflect.Value {
    32  	n := generatePositiveInt(rand, size)
    33  	if rand.Intn(4) == 0 {
    34  		n.Neg(n)
    35  	}
    36  	return reflect.ValueOf(bigInt{n})
    37  }
    38  
    39  type notZeroInt struct {
    40  	*big.Int
    41  }
    42  
    43  func (notZeroInt) Generate(rand *rand.Rand, size int) reflect.Value {
    44  	n := generatePositiveInt(rand, size)
    45  	if rand.Intn(4) == 0 {
    46  		n.Neg(n)
    47  	}
    48  	if n.Sign() == 0 {
    49  		n.SetInt64(1)
    50  	}
    51  	return reflect.ValueOf(notZeroInt{n})
    52  }
    53  
    54  type positiveInt struct {
    55  	*big.Int
    56  }
    57  
    58  func (positiveInt) Generate(rand *rand.Rand, size int) reflect.Value {
    59  	n := generatePositiveInt(rand, size)
    60  	return reflect.ValueOf(positiveInt{n})
    61  }
    62  
    63  type prime struct {
    64  	*big.Int
    65  }
    66  
    67  func (prime) Generate(r *rand.Rand, size int) reflect.Value {
    68  	n, err := cryptorand.Prime(r, r.Intn(size*8-2)+2)
    69  	if err != nil {
    70  		panic(err)
    71  	}
    72  	return reflect.ValueOf(prime{n})
    73  }
    74  
    75  type zeroOrOne struct {
    76  	uint
    77  }
    78  
    79  func (zeroOrOne) Generate(rand *rand.Rand, size int) reflect.Value {
    80  	return reflect.ValueOf(zeroOrOne{uint(rand.Intn(2))})
    81  }
    82  
    83  type smallUint struct {
    84  	uint
    85  }
    86  
    87  func (smallUint) Generate(rand *rand.Rand, size int) reflect.Value {
    88  	return reflect.ValueOf(smallUint{uint(rand.Intn(1024))})
    89  }
    90  
    91  // checkAliasingOneArg checks if f returns a correct result when v and x alias.
    92  //
    93  // f is a function that takes x as an argument, doesn't modify it, sets v to the
    94  // result, and returns v. It is the function signature of unbound methods like
    95  //
    96  //	func (v *big.Int) m(x *big.Int) *big.Int
    97  //
    98  // v and x are two random Int values. v is randomized even if it will be
    99  // overwritten to test for improper buffer reuse.
   100  func checkAliasingOneArg(t *testing.T, f func(v, x *big.Int) *big.Int, v, x *big.Int) bool {
   101  	x1, v1 := new(big.Int).Set(x), new(big.Int).Set(x)
   102  
   103  	// Calculate a reference f(x) without aliasing.
   104  	if out := f(v, x); out != v {
   105  		return false
   106  	}
   107  
   108  	// Test aliasing the argument and the receiver.
   109  	if out := f(v1, v1); out != v1 || !equal(v1, v) {
   110  		t.Logf("f(v, x) != f(x, x)")
   111  		return false
   112  	}
   113  
   114  	// Ensure the arguments was not modified.
   115  	return equal(x, x1)
   116  }
   117  
   118  // checkAliasingTwoArgs checks if f returns a correct result when any
   119  // combination of v, x and y alias.
   120  //
   121  // f is a function that takes x and y as arguments, doesn't modify them, sets v
   122  // to the result, and returns v. It is the function signature of unbound methods
   123  // like
   124  //
   125  //	func (v *big.Int) m(x, y *big.Int) *big.Int
   126  //
   127  // v, x and y are random Int values. v is randomized even if it will be
   128  // overwritten to test for improper buffer reuse.
   129  func checkAliasingTwoArgs(t *testing.T, f func(v, x, y *big.Int) *big.Int, v, x, y *big.Int) bool {
   130  	x1, y1, v1 := new(big.Int).Set(x), new(big.Int).Set(y), new(big.Int).Set(v)
   131  
   132  	// Calculate a reference f(x, y) without aliasing.
   133  	if out := f(v, x, y); out == nil {
   134  		// Certain functions like ModInverse return nil for certain inputs.
   135  		// Check that receiver and arguments were unchanged and move on.
   136  		return equal(x, x1) && equal(y, y1) && equal(v, v1)
   137  	} else if out != v {
   138  		return false
   139  	}
   140  
   141  	// Test aliasing the first argument and the receiver.
   142  	v1.Set(x)
   143  	if out := f(v1, v1, y); out != v1 || !equal(v1, v) {
   144  		t.Logf("f(v, x, y) != f(x, x, y)")
   145  		return false
   146  	}
   147  	// Test aliasing the second argument and the receiver.
   148  	v1.Set(y)
   149  	if out := f(v1, x, v1); out != v1 || !equal(v1, v) {
   150  		t.Logf("f(v, x, y) != f(y, x, y)")
   151  		return false
   152  	}
   153  
   154  	// Calculate a reference f(y, y) without aliasing.
   155  	// We use y because it's the one that commonly has restrictions
   156  	// like being prime or non-zero.
   157  	v1.Set(v)
   158  	y2 := new(big.Int).Set(y)
   159  	if out := f(v, y, y2); out == nil {
   160  		return equal(y, y1) && equal(y2, y1) && equal(v, v1)
   161  	} else if out != v {
   162  		return false
   163  	}
   164  
   165  	// Test aliasing the two arguments.
   166  	if out := f(v1, y, y); out != v1 || !equal(v1, v) {
   167  		t.Logf("f(v, y1, y2) != f(v, y, y)")
   168  		return false
   169  	}
   170  	// Test aliasing the two arguments and the receiver.
   171  	v1.Set(y)
   172  	if out := f(v1, v1, v1); out != v1 || !equal(v1, v) {
   173  		t.Logf("f(v, y1, y2) != f(y, y, y)")
   174  		return false
   175  	}
   176  
   177  	// Ensure the arguments were not modified.
   178  	return equal(x, x1) && equal(y, y1)
   179  }
   180  
   181  func TestAliasing(t *testing.T) {
   182  	for name, f := range map[string]interface{}{
   183  		"Abs": func(v, x bigInt) bool {
   184  			return checkAliasingOneArg(t, (*big.Int).Abs, v.Int, x.Int)
   185  		},
   186  		"Add": func(v, x, y bigInt) bool {
   187  			return checkAliasingTwoArgs(t, (*big.Int).Add, v.Int, x.Int, y.Int)
   188  		},
   189  		"And": func(v, x, y bigInt) bool {
   190  			return checkAliasingTwoArgs(t, (*big.Int).And, v.Int, x.Int, y.Int)
   191  		},
   192  		"AndNot": func(v, x, y bigInt) bool {
   193  			return checkAliasingTwoArgs(t, (*big.Int).AndNot, v.Int, x.Int, y.Int)
   194  		},
   195  		"Div": func(v, x bigInt, y notZeroInt) bool {
   196  			return checkAliasingTwoArgs(t, (*big.Int).Div, v.Int, x.Int, y.Int)
   197  		},
   198  		"Exp-XY": func(v, x, y bigInt, z notZeroInt) bool {
   199  			return checkAliasingTwoArgs(t, func(v, x, y *big.Int) *big.Int {
   200  				return v.Exp(x, y, z.Int)
   201  			}, v.Int, x.Int, y.Int)
   202  		},
   203  		"Exp-XZ": func(v, x, y bigInt, z notZeroInt) bool {
   204  			return checkAliasingTwoArgs(t, func(v, x, z *big.Int) *big.Int {
   205  				return v.Exp(x, y.Int, z)
   206  			}, v.Int, x.Int, z.Int)
   207  		},
   208  		"Exp-YZ": func(v, x, y bigInt, z notZeroInt) bool {
   209  			return checkAliasingTwoArgs(t, func(v, y, z *big.Int) *big.Int {
   210  				return v.Exp(x.Int, y, z)
   211  			}, v.Int, y.Int, z.Int)
   212  		},
   213  		"GCD": func(v, x, y bigInt) bool {
   214  			return checkAliasingTwoArgs(t, func(v, x, y *big.Int) *big.Int {
   215  				return v.GCD(nil, nil, x, y)
   216  			}, v.Int, x.Int, y.Int)
   217  		},
   218  		"GCD-X": func(v, x, y bigInt) bool {
   219  			a, b := new(big.Int), new(big.Int)
   220  			return checkAliasingTwoArgs(t, func(v, x, y *big.Int) *big.Int {
   221  				a.GCD(v, b, x, y)
   222  				return v
   223  			}, v.Int, x.Int, y.Int)
   224  		},
   225  		"GCD-Y": func(v, x, y bigInt) bool {
   226  			a, b := new(big.Int), new(big.Int)
   227  			return checkAliasingTwoArgs(t, func(v, x, y *big.Int) *big.Int {
   228  				a.GCD(b, v, x, y)
   229  				return v
   230  			}, v.Int, x.Int, y.Int)
   231  		},
   232  		"Lsh": func(v, x bigInt, n smallUint) bool {
   233  			return checkAliasingOneArg(t, func(v, x *big.Int) *big.Int {
   234  				return v.Lsh(x, n.uint)
   235  			}, v.Int, x.Int)
   236  		},
   237  		"Mod": func(v, x bigInt, y notZeroInt) bool {
   238  			return checkAliasingTwoArgs(t, (*big.Int).Mod, v.Int, x.Int, y.Int)
   239  		},
   240  		"ModInverse": func(v, x bigInt, y notZeroInt) bool {
   241  			return checkAliasingTwoArgs(t, (*big.Int).ModInverse, v.Int, x.Int, y.Int)
   242  		},
   243  		"ModSqrt": func(v, x bigInt, p prime) bool {
   244  			return checkAliasingTwoArgs(t, (*big.Int).ModSqrt, v.Int, x.Int, p.Int)
   245  		},
   246  		"Mul": func(v, x, y bigInt) bool {
   247  			return checkAliasingTwoArgs(t, (*big.Int).Mul, v.Int, x.Int, y.Int)
   248  		},
   249  		"Neg": func(v, x bigInt) bool {
   250  			return checkAliasingOneArg(t, (*big.Int).Neg, v.Int, x.Int)
   251  		},
   252  		"Not": func(v, x bigInt) bool {
   253  			return checkAliasingOneArg(t, (*big.Int).Not, v.Int, x.Int)
   254  		},
   255  		"Or": func(v, x, y bigInt) bool {
   256  			return checkAliasingTwoArgs(t, (*big.Int).Or, v.Int, x.Int, y.Int)
   257  		},
   258  		"Quo": func(v, x bigInt, y notZeroInt) bool {
   259  			return checkAliasingTwoArgs(t, (*big.Int).Quo, v.Int, x.Int, y.Int)
   260  		},
   261  		"Rand": func(v, x bigInt, seed int64) bool {
   262  			return checkAliasingOneArg(t, func(v, x *big.Int) *big.Int {
   263  				rnd := rand.New(rand.NewSource(seed))
   264  				return v.Rand(rnd, x)
   265  			}, v.Int, x.Int)
   266  		},
   267  		"Rem": func(v, x bigInt, y notZeroInt) bool {
   268  			return checkAliasingTwoArgs(t, (*big.Int).Rem, v.Int, x.Int, y.Int)
   269  		},
   270  		"Rsh": func(v, x bigInt, n smallUint) bool {
   271  			return checkAliasingOneArg(t, func(v, x *big.Int) *big.Int {
   272  				return v.Rsh(x, n.uint)
   273  			}, v.Int, x.Int)
   274  		},
   275  		"Set": func(v, x bigInt) bool {
   276  			return checkAliasingOneArg(t, (*big.Int).Set, v.Int, x.Int)
   277  		},
   278  		"SetBit": func(v, x bigInt, i smallUint, b zeroOrOne) bool {
   279  			return checkAliasingOneArg(t, func(v, x *big.Int) *big.Int {
   280  				return v.SetBit(x, int(i.uint), b.uint)
   281  			}, v.Int, x.Int)
   282  		},
   283  		"Sqrt": func(v bigInt, x positiveInt) bool {
   284  			return checkAliasingOneArg(t, (*big.Int).Sqrt, v.Int, x.Int)
   285  		},
   286  		"Sub": func(v, x, y bigInt) bool {
   287  			return checkAliasingTwoArgs(t, (*big.Int).Sub, v.Int, x.Int, y.Int)
   288  		},
   289  		"Xor": func(v, x, y bigInt) bool {
   290  			return checkAliasingTwoArgs(t, (*big.Int).Xor, v.Int, x.Int, y.Int)
   291  		},
   292  	} {
   293  		t.Run(name, func(t *testing.T) {
   294  			scale := 1.0
   295  			switch name {
   296  			case "ModInverse", "GCD-Y", "GCD-X":
   297  				scale /= 5
   298  			case "Rand":
   299  				scale /= 10
   300  			case "Exp-XZ", "Exp-XY", "Exp-YZ":
   301  				scale /= 50
   302  			case "ModSqrt":
   303  				scale /= 500
   304  			}
   305  			if err := quick.Check(f, &quick.Config{
   306  				MaxCountScale: scale,
   307  			}); err != nil {
   308  				t.Error(err)
   309  			}
   310  		})
   311  	}
   312  }
   313
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