Source file src/cmd/compile/internal/ssacompile/magic_test.go

     1  // Copyright 2017 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 ssacompile
     6  
     7  import (
     8  	"math/big"
     9  	"testing"
    10  
    11  	"cmd/compile/internal/ssa"
    12  )
    13  
    14  func TestMagicExhaustive8(t *testing.T) {
    15  	testMagicExhaustive(t, 8)
    16  }
    17  func TestMagicExhaustive8U(t *testing.T) {
    18  	testMagicExhaustiveU(t, 8)
    19  }
    20  func TestMagicExhaustive16(t *testing.T) {
    21  	if testing.Short() {
    22  		t.Skip("slow test; skipping")
    23  	}
    24  	testMagicExhaustive(t, 16)
    25  }
    26  func TestMagicExhaustive16U(t *testing.T) {
    27  	if testing.Short() {
    28  		t.Skip("slow test; skipping")
    29  	}
    30  	testMagicExhaustiveU(t, 16)
    31  }
    32  
    33  // exhaustive test of magic for n bits
    34  func testMagicExhaustive(t *testing.T, n uint) {
    35  	min := -int64(1) << (n - 1)
    36  	max := int64(1) << (n - 1)
    37  	for c := int64(1); c < max; c++ {
    38  		if !ssa.SmagicOK(n, c) {
    39  			continue
    40  		}
    41  		m := int64(ssa.Smagic(n, c).M)
    42  		s := ssa.Smagic(n, c).S
    43  		for i := min; i < max; i++ {
    44  			want := i / c
    45  			got := (i * m) >> (n + uint(s))
    46  			if i < 0 {
    47  				got++
    48  			}
    49  			if want != got {
    50  				t.Errorf("signed magic wrong for %d / %d: got %d, want %d (m=%d,s=%d)\n", i, c, got, want, m, s)
    51  			}
    52  		}
    53  	}
    54  }
    55  func testMagicExhaustiveU(t *testing.T, n uint) {
    56  	max := uint64(1) << n
    57  	for c := uint64(1); c < max; c++ {
    58  		if !umagicOK(n, int64(c)) {
    59  			continue
    60  		}
    61  		m := ssa.Umagic(n, int64(c)).M
    62  		s := ssa.Umagic(n, int64(c)).S
    63  		for i := uint64(0); i < max; i++ {
    64  			want := i / c
    65  			got := (i * (max + m)) >> (n + uint(s))
    66  			if want != got {
    67  				t.Errorf("unsigned magic wrong for %d / %d: got %d, want %d (m=%d,s=%d)\n", i, c, got, want, m, s)
    68  			}
    69  		}
    70  	}
    71  }
    72  
    73  func TestMagicUnsigned(t *testing.T) {
    74  	One := new(big.Int).SetUint64(1)
    75  	for _, n := range [...]uint{8, 16, 32, 64} {
    76  		TwoN := new(big.Int).Lsh(One, n)
    77  		Max := new(big.Int).Sub(TwoN, One)
    78  		for _, c := range [...]uint64{
    79  			3,
    80  			5,
    81  			6,
    82  			7,
    83  			9,
    84  			10,
    85  			11,
    86  			12,
    87  			13,
    88  			14,
    89  			15,
    90  			17,
    91  			1<<8 - 1,
    92  			1<<8 + 1,
    93  			1<<16 - 1,
    94  			1<<16 + 1,
    95  			1<<32 - 1,
    96  			1<<32 + 1,
    97  			1<<64 - 1,
    98  		} {
    99  			if c>>n != 0 {
   100  				continue // not appropriate for the given n.
   101  			}
   102  			if !umagicOK(n, int64(c)) {
   103  				t.Errorf("expected n=%d c=%d to pass\n", n, c)
   104  			}
   105  			m := ssa.Umagic(n, int64(c)).M
   106  			s := ssa.Umagic(n, int64(c)).S
   107  
   108  			C := new(big.Int).SetUint64(c)
   109  			M := new(big.Int).SetUint64(m)
   110  			M.Add(M, TwoN)
   111  
   112  			// Find largest multiple of c.
   113  			Mul := new(big.Int).Div(Max, C)
   114  			Mul.Mul(Mul, C)
   115  			mul := Mul.Uint64()
   116  
   117  			// Try some input values, mostly around multiples of c.
   118  			for _, x := range [...]uint64{0, 1,
   119  				c - 1, c, c + 1,
   120  				2*c - 1, 2 * c, 2*c + 1,
   121  				mul - 1, mul, mul + 1,
   122  				uint64(1)<<n - 1,
   123  			} {
   124  				X := new(big.Int).SetUint64(x)
   125  				if X.Cmp(Max) > 0 {
   126  					continue
   127  				}
   128  				Want := new(big.Int).Quo(X, C)
   129  				Got := new(big.Int).Mul(X, M)
   130  				Got.Rsh(Got, n+uint(s))
   131  				if Want.Cmp(Got) != 0 {
   132  					t.Errorf("umagic for %d/%d n=%d doesn't work, got=%s, want %s\n", x, c, n, Got, Want)
   133  				}
   134  			}
   135  		}
   136  	}
   137  }
   138  
   139  func TestMagicSigned(t *testing.T) {
   140  	One := new(big.Int).SetInt64(1)
   141  	for _, n := range [...]uint{8, 16, 32, 64} {
   142  		TwoNMinusOne := new(big.Int).Lsh(One, n-1)
   143  		Max := new(big.Int).Sub(TwoNMinusOne, One)
   144  		Min := new(big.Int).Neg(TwoNMinusOne)
   145  		for _, c := range [...]int64{
   146  			3,
   147  			5,
   148  			6,
   149  			7,
   150  			9,
   151  			10,
   152  			11,
   153  			12,
   154  			13,
   155  			14,
   156  			15,
   157  			17,
   158  			1<<7 - 1,
   159  			1<<7 + 1,
   160  			1<<15 - 1,
   161  			1<<15 + 1,
   162  			1<<31 - 1,
   163  			1<<31 + 1,
   164  			1<<63 - 1,
   165  		} {
   166  			if c>>(n-1) != 0 {
   167  				continue // not appropriate for the given n.
   168  			}
   169  			if !ssa.SmagicOK(n, c) {
   170  				t.Errorf("expected n=%d c=%d to pass\n", n, c)
   171  			}
   172  			m := ssa.Smagic(n, c).M
   173  			s := ssa.Smagic(n, c).S
   174  
   175  			C := new(big.Int).SetInt64(c)
   176  			M := new(big.Int).SetUint64(m)
   177  
   178  			// Find largest multiple of c.
   179  			Mul := new(big.Int).Div(Max, C)
   180  			Mul.Mul(Mul, C)
   181  			mul := Mul.Int64()
   182  
   183  			// Try some input values, mostly around multiples of c.
   184  			for _, x := range [...]int64{
   185  				-1, 1,
   186  				-c - 1, -c, -c + 1, c - 1, c, c + 1,
   187  				-2*c - 1, -2 * c, -2*c + 1, 2*c - 1, 2 * c, 2*c + 1,
   188  				-mul - 1, -mul, -mul + 1, mul - 1, mul, mul + 1,
   189  				int64(1)<<(n-1) - 1, -int64(1) << (n - 1),
   190  			} {
   191  				X := new(big.Int).SetInt64(x)
   192  				if X.Cmp(Min) < 0 || X.Cmp(Max) > 0 {
   193  					continue
   194  				}
   195  				Want := new(big.Int).Quo(X, C)
   196  				Got := new(big.Int).Mul(X, M)
   197  				Got.Rsh(Got, n+uint(s))
   198  				if x < 0 {
   199  					Got.Add(Got, One)
   200  				}
   201  				if Want.Cmp(Got) != 0 {
   202  					t.Errorf("smagic for %d/%d n=%d doesn't work, got=%s, want %s\n", x, c, n, Got, Want)
   203  				}
   204  			}
   205  		}
   206  	}
   207  }
   208  
   209  func testDivisibleExhaustiveU(t *testing.T, n uint) {
   210  	maxU := uint64(1) << n
   211  	for c := uint64(1); c < maxU; c++ {
   212  		if !ssa.UdivisibleOK(n, int64(c)) {
   213  			continue
   214  		}
   215  		k := ssa.Udivisible(n, int64(c)).K
   216  		m := ssa.Udivisible(n, int64(c)).M
   217  		max := ssa.Udivisible(n, int64(c)).Max
   218  		mask := ^uint64(0) >> (64 - n)
   219  		for i := uint64(0); i < maxU; i++ {
   220  			want := i%c == 0
   221  			mul := (i * m) & mask
   222  			rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
   223  			got := rot <= max
   224  			if want != got {
   225  				t.Errorf("unsigned divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,max=%d)\n", i, c, got, want, k, m, max)
   226  			}
   227  		}
   228  	}
   229  }
   230  
   231  func TestDivisibleExhaustive8U(t *testing.T) {
   232  	testDivisibleExhaustiveU(t, 8)
   233  }
   234  
   235  func TestDivisibleExhaustive16U(t *testing.T) {
   236  	if testing.Short() {
   237  		t.Skip("slow test; skipping")
   238  	}
   239  	testDivisibleExhaustiveU(t, 16)
   240  }
   241  
   242  func TestDivisibleUnsigned(t *testing.T) {
   243  	One := new(big.Int).SetUint64(1)
   244  	for _, n := range [...]uint{8, 16, 32, 64} {
   245  		TwoN := new(big.Int).Lsh(One, n)
   246  		Max := new(big.Int).Sub(TwoN, One)
   247  		for _, c := range [...]uint64{
   248  			3,
   249  			5,
   250  			6,
   251  			7,
   252  			9,
   253  			10,
   254  			11,
   255  			12,
   256  			13,
   257  			14,
   258  			15,
   259  			17,
   260  			1<<8 - 1,
   261  			1<<8 + 1,
   262  			1<<16 - 1,
   263  			1<<16 + 1,
   264  			1<<32 - 1,
   265  			1<<32 + 1,
   266  			1<<64 - 1,
   267  		} {
   268  			if c>>n != 0 {
   269  				continue // c too large for the given n.
   270  			}
   271  			if !ssa.UdivisibleOK(n, int64(c)) {
   272  				t.Errorf("expected n=%d c=%d to pass\n", n, c)
   273  			}
   274  			k := ssa.Udivisible(n, int64(c)).K
   275  			m := ssa.Udivisible(n, int64(c)).M
   276  			max := ssa.Udivisible(n, int64(c)).Max
   277  			mask := ^uint64(0) >> (64 - n)
   278  
   279  			C := new(big.Int).SetUint64(c)
   280  
   281  			// Find largest multiple of c.
   282  			Mul := new(big.Int).Div(Max, C)
   283  			Mul.Mul(Mul, C)
   284  			mul := Mul.Uint64()
   285  
   286  			// Try some input values, mostly around multiples of c.
   287  			for _, x := range [...]uint64{0, 1,
   288  				c - 1, c, c + 1,
   289  				2*c - 1, 2 * c, 2*c + 1,
   290  				mul - 1, mul, mul + 1,
   291  				uint64(1)<<n - 1,
   292  			} {
   293  				X := new(big.Int).SetUint64(x)
   294  				if X.Cmp(Max) > 0 {
   295  					continue
   296  				}
   297  				want := x%c == 0
   298  				mul := (x * m) & mask
   299  				rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
   300  				got := rot <= max
   301  				if want != got {
   302  					t.Errorf("unsigned divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,max=%d)\n", x, c, got, want, k, m, max)
   303  				}
   304  			}
   305  		}
   306  	}
   307  }
   308  
   309  func testDivisibleExhaustive(t *testing.T, n uint) {
   310  	minI := -int64(1) << (n - 1)
   311  	maxI := int64(1) << (n - 1)
   312  	for c := int64(1); c < maxI; c++ {
   313  		if !ssa.SdivisibleOK(n, c) {
   314  			continue
   315  		}
   316  		k := ssa.Sdivisible(n, c).K
   317  		m := ssa.Sdivisible(n, c).M
   318  		a := ssa.Sdivisible(n, c).A
   319  		max := ssa.Sdivisible(n, c).Max
   320  		mask := ^uint64(0) >> (64 - n)
   321  		for i := minI; i < maxI; i++ {
   322  			want := i%c == 0
   323  			mul := (uint64(i)*m + a) & mask
   324  			rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
   325  			got := rot <= max
   326  			if want != got {
   327  				t.Errorf("signed divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,a=%d,max=%d)\n", i, c, got, want, k, m, a, max)
   328  			}
   329  		}
   330  	}
   331  }
   332  
   333  func TestDivisibleExhaustive8(t *testing.T) {
   334  	testDivisibleExhaustive(t, 8)
   335  }
   336  
   337  func TestDivisibleExhaustive16(t *testing.T) {
   338  	if testing.Short() {
   339  		t.Skip("slow test; skipping")
   340  	}
   341  	testDivisibleExhaustive(t, 16)
   342  }
   343  
   344  func TestDivisibleSigned(t *testing.T) {
   345  	One := new(big.Int).SetInt64(1)
   346  	for _, n := range [...]uint{8, 16, 32, 64} {
   347  		TwoNMinusOne := new(big.Int).Lsh(One, n-1)
   348  		Max := new(big.Int).Sub(TwoNMinusOne, One)
   349  		Min := new(big.Int).Neg(TwoNMinusOne)
   350  		for _, c := range [...]int64{
   351  			3,
   352  			5,
   353  			6,
   354  			7,
   355  			9,
   356  			10,
   357  			11,
   358  			12,
   359  			13,
   360  			14,
   361  			15,
   362  			17,
   363  			1<<7 - 1,
   364  			1<<7 + 1,
   365  			1<<15 - 1,
   366  			1<<15 + 1,
   367  			1<<31 - 1,
   368  			1<<31 + 1,
   369  			1<<63 - 1,
   370  		} {
   371  			if c>>(n-1) != 0 {
   372  				continue // not appropriate for the given n.
   373  			}
   374  			if !ssa.SdivisibleOK(n, c) {
   375  				t.Errorf("expected n=%d c=%d to pass\n", n, c)
   376  			}
   377  			k := ssa.Sdivisible(n, c).K
   378  			m := ssa.Sdivisible(n, c).M
   379  			a := ssa.Sdivisible(n, c).A
   380  			max := ssa.Sdivisible(n, c).Max
   381  			mask := ^uint64(0) >> (64 - n)
   382  
   383  			C := new(big.Int).SetInt64(c)
   384  
   385  			// Find largest multiple of c.
   386  			Mul := new(big.Int).Div(Max, C)
   387  			Mul.Mul(Mul, C)
   388  			mul := Mul.Int64()
   389  
   390  			// Try some input values, mostly around multiples of c.
   391  			for _, x := range [...]int64{
   392  				-1, 1,
   393  				-c - 1, -c, -c + 1, c - 1, c, c + 1,
   394  				-2*c - 1, -2 * c, -2*c + 1, 2*c - 1, 2 * c, 2*c + 1,
   395  				-mul - 1, -mul, -mul + 1, mul - 1, mul, mul + 1,
   396  				int64(1)<<(n-1) - 1, -int64(1) << (n - 1),
   397  			} {
   398  				X := new(big.Int).SetInt64(x)
   399  				if X.Cmp(Min) < 0 || X.Cmp(Max) > 0 {
   400  					continue
   401  				}
   402  				want := x%c == 0
   403  				mul := (uint64(x)*m + a) & mask
   404  				rot := (mul>>uint(k) | mul<<(n-uint(k))) & mask
   405  				got := rot <= max
   406  				if want != got {
   407  					t.Errorf("signed divisible wrong for %d %% %d == 0: got %v, want %v (k=%d,m=%d,a=%d,max=%d)\n", x, c, got, want, k, m, a, max)
   408  				}
   409  			}
   410  		}
   411  	}
   412  }
   413  

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