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# Source file src/math/big/rat_test.go

## Documentation: math/big

```     1  // Copyright 2010 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  package big
6
7  import (
8  	"math"
9  	"testing"
10  )
11
12  func TestZeroRat(t *testing.T) {
13  	var x, y, z Rat
14  	y.SetFrac64(0, 42)
15
16  	if x.Cmp(&y) != 0 {
17  		t.Errorf("x and y should be both equal and zero")
18  	}
19
20  	if s := x.String(); s != "0/1" {
21  		t.Errorf("got x = %s, want 0/1", s)
22  	}
23
24  	if s := x.RatString(); s != "0" {
25  		t.Errorf("got x = %s, want 0", s)
26  	}
27
29  	if s := z.RatString(); s != "0" {
30  		t.Errorf("got x+y = %s, want 0", s)
31  	}
32
33  	z.Sub(&x, &y)
34  	if s := z.RatString(); s != "0" {
35  		t.Errorf("got x-y = %s, want 0", s)
36  	}
37
38  	z.Mul(&x, &y)
39  	if s := z.RatString(); s != "0" {
40  		t.Errorf("got x*y = %s, want 0", s)
41  	}
42
43  	// check for division by zero
44  	defer func() {
45  		if s := recover(); s == nil || s.(string) != "division by zero" {
46  			panic(s)
47  		}
48  	}()
49  	z.Quo(&x, &y)
50  }
51
52  func TestRatSign(t *testing.T) {
53  	zero := NewRat(0, 1)
54  	for _, a := range setStringTests {
55  		x, ok := new(Rat).SetString(a.in)
56  		if !ok {
57  			continue
58  		}
59  		s := x.Sign()
60  		e := x.Cmp(zero)
61  		if s != e {
62  			t.Errorf("got %d; want %d for z = %v", s, e, &x)
63  		}
64  	}
65  }
66
67  var ratCmpTests = []struct {
68  	rat1, rat2 string
69  	out        int
70  }{
71  	{"0", "0/1", 0},
72  	{"1/1", "1", 0},
73  	{"-1", "-2/2", 0},
74  	{"1", "0", 1},
75  	{"0/1", "1/1", -1},
76  	{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
77  	{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
78  	{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
79  	{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
80  }
81
82  func TestRatCmp(t *testing.T) {
83  	for i, test := range ratCmpTests {
84  		x, _ := new(Rat).SetString(test.rat1)
85  		y, _ := new(Rat).SetString(test.rat2)
86
87  		out := x.Cmp(y)
88  		if out != test.out {
89  			t.Errorf("#%d got out = %v; want %v", i, out, test.out)
90  		}
91  	}
92  }
93
94  func TestIsInt(t *testing.T) {
95  	one := NewInt(1)
96  	for _, a := range setStringTests {
97  		x, ok := new(Rat).SetString(a.in)
98  		if !ok {
99  			continue
100  		}
101  		i := x.IsInt()
102  		e := x.Denom().Cmp(one) == 0
103  		if i != e {
104  			t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
105  		}
106  	}
107  }
108
109  func TestRatAbs(t *testing.T) {
110  	zero := new(Rat)
111  	for _, a := range setStringTests {
112  		x, ok := new(Rat).SetString(a.in)
113  		if !ok {
114  			continue
115  		}
116  		e := new(Rat).Set(x)
117  		if e.Cmp(zero) < 0 {
118  			e.Sub(zero, e)
119  		}
120  		z := new(Rat).Abs(x)
121  		if z.Cmp(e) != 0 {
122  			t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
123  		}
124  	}
125  }
126
127  func TestRatNeg(t *testing.T) {
128  	zero := new(Rat)
129  	for _, a := range setStringTests {
130  		x, ok := new(Rat).SetString(a.in)
131  		if !ok {
132  			continue
133  		}
134  		e := new(Rat).Sub(zero, x)
135  		z := new(Rat).Neg(x)
136  		if z.Cmp(e) != 0 {
137  			t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
138  		}
139  	}
140  }
141
142  func TestRatInv(t *testing.T) {
143  	zero := new(Rat)
144  	for _, a := range setStringTests {
145  		x, ok := new(Rat).SetString(a.in)
146  		if !ok {
147  			continue
148  		}
149  		if x.Cmp(zero) == 0 {
150  			continue // avoid division by zero
151  		}
152  		e := new(Rat).SetFrac(x.Denom(), x.Num())
153  		z := new(Rat).Inv(x)
154  		if z.Cmp(e) != 0 {
155  			t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
156  		}
157  	}
158  }
159
160  type ratBinFun func(z, x, y *Rat) *Rat
161  type ratBinArg struct {
162  	x, y, z string
163  }
164
165  func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
166  	x, _ := new(Rat).SetString(a.x)
167  	y, _ := new(Rat).SetString(a.y)
168  	z, _ := new(Rat).SetString(a.z)
169  	out := f(new(Rat), x, y)
170
171  	if out.Cmp(z) != 0 {
172  		t.Errorf("%s #%d got %s want %s", name, i, out, z)
173  	}
174  }
175
176  var ratBinTests = []struct {
177  	x, y      string
178  	sum, prod string
179  }{
180  	{"0", "0", "0", "0"},
181  	{"0", "1", "1", "0"},
182  	{"-1", "0", "-1", "0"},
183  	{"-1", "1", "0", "-1"},
184  	{"1", "1", "2", "1"},
185  	{"1/2", "1/2", "1", "1/4"},
186  	{"1/4", "1/3", "7/12", "1/12"},
187  	{"2/5", "-14/3", "-64/15", "-28/15"},
188  	{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
189  	{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
190  	{"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
191  	{"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
192  	{"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
193  	{"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
194  	{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
195  	{"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
196  	{"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
197  	{"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
198  }
199
200  func TestRatBin(t *testing.T) {
201  	for i, test := range ratBinTests {
202  		arg := ratBinArg{test.x, test.y, test.sum}
204
205  		arg = ratBinArg{test.y, test.x, test.sum}
207
208  		arg = ratBinArg{test.sum, test.x, test.y}
209  		testRatBin(t, i, "Sub", (*Rat).Sub, arg)
210
211  		arg = ratBinArg{test.sum, test.y, test.x}
212  		testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
213
214  		arg = ratBinArg{test.x, test.y, test.prod}
215  		testRatBin(t, i, "Mul", (*Rat).Mul, arg)
216
217  		arg = ratBinArg{test.y, test.x, test.prod}
218  		testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
219
220  		if test.x != "0" {
221  			arg = ratBinArg{test.prod, test.x, test.y}
222  			testRatBin(t, i, "Quo", (*Rat).Quo, arg)
223  		}
224
225  		if test.y != "0" {
226  			arg = ratBinArg{test.prod, test.y, test.x}
227  			testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
228  		}
229  	}
230  }
231
232  func TestIssue820(t *testing.T) {
233  	x := NewRat(3, 1)
234  	y := NewRat(2, 1)
235  	z := y.Quo(x, y)
236  	q := NewRat(3, 2)
237  	if z.Cmp(q) != 0 {
238  		t.Errorf("got %s want %s", z, q)
239  	}
240
241  	y = NewRat(3, 1)
242  	x = NewRat(2, 1)
243  	z = y.Quo(x, y)
244  	q = NewRat(2, 3)
245  	if z.Cmp(q) != 0 {
246  		t.Errorf("got %s want %s", z, q)
247  	}
248
249  	x = NewRat(3, 1)
250  	z = x.Quo(x, x)
251  	q = NewRat(3, 3)
252  	if z.Cmp(q) != 0 {
253  		t.Errorf("got %s want %s", z, q)
254  	}
255  }
256
257  var setFrac64Tests = []struct {
258  	a, b int64
259  	out  string
260  }{
261  	{0, 1, "0"},
262  	{0, -1, "0"},
263  	{1, 1, "1"},
264  	{-1, 1, "-1"},
265  	{1, -1, "-1"},
266  	{-1, -1, "1"},
267  	{-9223372036854775808, -9223372036854775808, "1"},
268  }
269
270  func TestRatSetFrac64Rat(t *testing.T) {
271  	for i, test := range setFrac64Tests {
272  		x := new(Rat).SetFrac64(test.a, test.b)
273  		if x.RatString() != test.out {
274  			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
275  		}
276  	}
277  }
278
279  func TestIssue2379(t *testing.T) {
280  	// 1) no aliasing
281  	q := NewRat(3, 2)
282  	x := new(Rat)
283  	x.SetFrac(NewInt(3), NewInt(2))
284  	if x.Cmp(q) != 0 {
285  		t.Errorf("1) got %s want %s", x, q)
286  	}
287
288  	// 2) aliasing of numerator
289  	x = NewRat(2, 3)
290  	x.SetFrac(NewInt(3), x.Num())
291  	if x.Cmp(q) != 0 {
292  		t.Errorf("2) got %s want %s", x, q)
293  	}
294
295  	// 3) aliasing of denominator
296  	x = NewRat(2, 3)
297  	x.SetFrac(x.Denom(), NewInt(2))
298  	if x.Cmp(q) != 0 {
299  		t.Errorf("3) got %s want %s", x, q)
300  	}
301
302  	// 4) aliasing of numerator and denominator
303  	x = NewRat(2, 3)
304  	x.SetFrac(x.Denom(), x.Num())
305  	if x.Cmp(q) != 0 {
306  		t.Errorf("4) got %s want %s", x, q)
307  	}
308
309  	// 5) numerator and denominator are the same
310  	q = NewRat(1, 1)
311  	x = new(Rat)
312  	n := NewInt(7)
313  	x.SetFrac(n, n)
314  	if x.Cmp(q) != 0 {
315  		t.Errorf("5) got %s want %s", x, q)
316  	}
317  }
318
319  func TestIssue3521(t *testing.T) {
320  	a := new(Int)
321  	b := new(Int)
322  	a.SetString("64375784358435883458348587", 0)
323  	b.SetString("4789759874531", 0)
324
325  	// 0) a raw zero value has 1 as denominator
326  	zero := new(Rat)
327  	one := NewInt(1)
328  	if zero.Denom().Cmp(one) != 0 {
329  		t.Errorf("0) got %s want %s", zero.Denom(), one)
330  	}
331
332  	// 1a) a zero value remains zero independent of denominator
333  	x := new(Rat)
334  	x.Denom().Set(new(Int).Neg(b))
335  	if x.Cmp(zero) != 0 {
336  		t.Errorf("1a) got %s want %s", x, zero)
337  	}
338
339  	// 1b) a zero value may have a denominator != 0 and != 1
340  	x.Num().Set(a)
341  	qab := new(Rat).SetFrac(a, b)
342  	if x.Cmp(qab) != 0 {
343  		t.Errorf("1b) got %s want %s", x, qab)
344  	}
345
346  	// 2a) an integral value becomes a fraction depending on denominator
347  	x.SetFrac64(10, 2)
348  	x.Denom().SetInt64(3)
349  	q53 := NewRat(5, 3)
350  	if x.Cmp(q53) != 0 {
351  		t.Errorf("2a) got %s want %s", x, q53)
352  	}
353
354  	// 2b) an integral value becomes a fraction depending on denominator
355  	x = NewRat(10, 2)
356  	x.Denom().SetInt64(3)
357  	if x.Cmp(q53) != 0 {
358  		t.Errorf("2b) got %s want %s", x, q53)
359  	}
360
361  	// 3) changing the numerator/denominator of a Rat changes the Rat
362  	x.SetFrac(a, b)
363  	a = x.Num()
364  	b = x.Denom()
365  	a.SetInt64(5)
366  	b.SetInt64(3)
367  	if x.Cmp(q53) != 0 {
368  		t.Errorf("3) got %s want %s", x, q53)
369  	}
370  }
371
372  func TestFloat32Distribution(t *testing.T) {
373  	// Generate a distribution of (sign, mantissa, exp) values
374  	// broader than the float32 range, and check Rat.Float32()
375  	// always picks the closest float32 approximation.
377  		0,
378  		1,
379  		3,
380  		5,
381  		7,
382  		9,
383  		11,
384  	}
385  	var winc, einc = uint64(5), 15 // quick test (~60ms on x86-64)
386  	if *long {
387  		winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
388  	}
389
390  	for _, sign := range "+-" {
391  		for _, a := range add {
392  			for wid := uint64(0); wid < 30; wid += winc {
393  				b := 1<<wid + a
394  				if sign == '-' {
395  					b = -b
396  				}
397  				for exp := -150; exp < 150; exp += einc {
398  					num, den := NewInt(b), NewInt(1)
399  					if exp > 0 {
400  						num.Lsh(num, uint(exp))
401  					} else {
402  						den.Lsh(den, uint(-exp))
403  					}
404  					r := new(Rat).SetFrac(num, den)
405  					f, _ := r.Float32()
406
407  					if !checkIsBestApprox32(t, f, r) {
408  						// Append context information.
409  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
410  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
411  					}
412
413  					checkNonLossyRoundtrip32(t, f)
414  				}
415  			}
416  		}
417  	}
418  }
419
420  func TestFloat64Distribution(t *testing.T) {
421  	// Generate a distribution of (sign, mantissa, exp) values
422  	// broader than the float64 range, and check Rat.Float64()
423  	// always picks the closest float64 approximation.
425  		0,
426  		1,
427  		3,
428  		5,
429  		7,
430  		9,
431  		11,
432  	}
433  	var winc, einc = uint64(10), 500 // quick test (~12ms on x86-64)
434  	if *long {
435  		winc, einc = uint64(1), 1 // soak test (~75s on x86-64)
436  	}
437
438  	for _, sign := range "+-" {
439  		for _, a := range add {
440  			for wid := uint64(0); wid < 60; wid += winc {
441  				b := 1<<wid + a
442  				if sign == '-' {
443  					b = -b
444  				}
445  				for exp := -1100; exp < 1100; exp += einc {
446  					num, den := NewInt(b), NewInt(1)
447  					if exp > 0 {
448  						num.Lsh(num, uint(exp))
449  					} else {
450  						den.Lsh(den, uint(-exp))
451  					}
452  					r := new(Rat).SetFrac(num, den)
453  					f, _ := r.Float64()
454
455  					if !checkIsBestApprox64(t, f, r) {
456  						// Append context information.
457  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
458  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
459  					}
460
461  					checkNonLossyRoundtrip64(t, f)
462  				}
463  			}
464  		}
465  	}
466  }
467
468  // TestSetFloat64NonFinite checks that SetFloat64 of a non-finite value
469  // returns nil.
470  func TestSetFloat64NonFinite(t *testing.T) {
471  	for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
472  		var r Rat
473  		if r2 := r.SetFloat64(f); r2 != nil {
474  			t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
475  		}
476  	}
477  }
478
479  // checkNonLossyRoundtrip32 checks that a float->Rat->float roundtrip is
480  // non-lossy for finite f.
481  func checkNonLossyRoundtrip32(t *testing.T, f float32) {
482  	if !isFinite(float64(f)) {
483  		return
484  	}
485  	r := new(Rat).SetFloat64(float64(f))
486  	if r == nil {
487  		t.Errorf("Rat.SetFloat64(float64(%g) (%b)) == nil", f, f)
488  		return
489  	}
490  	f2, exact := r.Float32()
491  	if f != f2 || !exact {
492  		t.Errorf("Rat.SetFloat64(float64(%g)).Float32() = %g (%b), %v, want %g (%b), %v; delta = %b",
493  			f, f2, f2, exact, f, f, true, f2-f)
494  	}
495  }
496
497  // checkNonLossyRoundtrip64 checks that a float->Rat->float roundtrip is
498  // non-lossy for finite f.
499  func checkNonLossyRoundtrip64(t *testing.T, f float64) {
500  	if !isFinite(f) {
501  		return
502  	}
503  	r := new(Rat).SetFloat64(f)
504  	if r == nil {
505  		t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
506  		return
507  	}
508  	f2, exact := r.Float64()
509  	if f != f2 || !exact {
510  		t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
511  			f, f2, f2, exact, f, f, true, f2-f)
512  	}
513  }
514
515  // delta returns the absolute difference between r and f.
516  func delta(r *Rat, f float64) *Rat {
517  	d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
518  	return d.Abs(d)
519  }
520
521  // checkIsBestApprox32 checks that f is the best possible float32
522  // approximation of r.
523  // Returns true on success.
524  func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
525  	if math.Abs(float64(f)) >= math.MaxFloat32 {
526  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
527  		// But we have tests for these special cases.
528  		return true
529  	}
530
531  	// r must be strictly between f0 and f1, the floats bracketing f.
532  	f0 := math.Nextafter32(f, float32(math.Inf(-1)))
533  	f1 := math.Nextafter32(f, float32(math.Inf(+1)))
534
535  	// For f to be correct, r must be closer to f than to f0 or f1.
536  	df := delta(r, float64(f))
537  	df0 := delta(r, float64(f0))
538  	df1 := delta(r, float64(f1))
539  	if df.Cmp(df0) > 0 {
540  		t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
541  		return false
542  	}
543  	if df.Cmp(df1) > 0 {
544  		t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
545  		return false
546  	}
547  	if df.Cmp(df0) == 0 && !isEven32(f) {
548  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
549  		return false
550  	}
551  	if df.Cmp(df1) == 0 && !isEven32(f) {
552  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
553  		return false
554  	}
555  	return true
556  }
557
558  // checkIsBestApprox64 checks that f is the best possible float64
559  // approximation of r.
560  // Returns true on success.
561  func checkIsBestApprox64(t *testing.T, f float64, r *Rat) bool {
562  	if math.Abs(f) >= math.MaxFloat64 {
563  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
564  		// But we have tests for these special cases.
565  		return true
566  	}
567
568  	// r must be strictly between f0 and f1, the floats bracketing f.
569  	f0 := math.Nextafter(f, math.Inf(-1))
570  	f1 := math.Nextafter(f, math.Inf(+1))
571
572  	// For f to be correct, r must be closer to f than to f0 or f1.
573  	df := delta(r, f)
574  	df0 := delta(r, f0)
575  	df1 := delta(r, f1)
576  	if df.Cmp(df0) > 0 {
577  		t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
578  		return false
579  	}
580  	if df.Cmp(df1) > 0 {
581  		t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
582  		return false
583  	}
584  	if df.Cmp(df0) == 0 && !isEven64(f) {
585  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
586  		return false
587  	}
588  	if df.Cmp(df1) == 0 && !isEven64(f) {
589  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
590  		return false
591  	}
592  	return true
593  }
594
595  func isEven32(f float32) bool { return math.Float32bits(f)&1 == 0 }
596  func isEven64(f float64) bool { return math.Float64bits(f)&1 == 0 }
597
598  func TestIsFinite(t *testing.T) {
599  	finites := []float64{
600  		1.0 / 3,
601  		4891559871276714924261e+222,
602  		math.MaxFloat64,
603  		math.SmallestNonzeroFloat64,
604  		-math.MaxFloat64,
605  		-math.SmallestNonzeroFloat64,
606  	}
607  	for _, f := range finites {
608  		if !isFinite(f) {
609  			t.Errorf("!IsFinite(%g (%b))", f, f)
610  		}
611  	}
612  	nonfinites := []float64{
613  		math.NaN(),
614  		math.Inf(-1),
615  		math.Inf(+1),
616  	}
617  	for _, f := range nonfinites {
618  		if isFinite(f) {
619  			t.Errorf("IsFinite(%g, (%b))", f, f)
620  		}
621  	}
622  }
623
```

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