1 // Copyright 2009 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.
18 func isNormalized(x
*Int
) bool {
23 return x
.abs
[len(x
.abs
)-1] != 0
26 type funZZ
func(z
, x
, y
*Int
) *Int
32 {NewInt(0), NewInt(0), NewInt(0)},
33 {NewInt(1), NewInt(1), NewInt(0)},
34 {NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
35 {NewInt(-1), NewInt(-1), NewInt(0)},
36 {NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
37 {NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
41 {NewInt(0), NewInt(0), NewInt(0)},
42 {NewInt(0), NewInt(1), NewInt(0)},
43 {NewInt(1), NewInt(1), NewInt(1)},
44 {NewInt(-991 * 991), NewInt(991), NewInt(-991)},
45 // TODO(gri) add larger products
48 func TestSignZ(t
*testing
.T
) {
50 for _
, a
:= range sumZZ
{
54 t
.Errorf("got %d; want %d for z = %v", s
, e
, a
.z
)
59 func TestSetZ(t
*testing
.T
) {
60 for _
, a
:= range sumZZ
{
63 if !isNormalized(&z
) {
64 t
.Errorf("%v is not normalized", z
)
66 if (&z
).Cmp(a
.z
) != 0 {
67 t
.Errorf("got z = %v; want %v", z
, a
.z
)
72 func TestAbsZ(t
*testing
.T
) {
74 for _
, a
:= range sumZZ
{
83 t
.Errorf("got z = %v; want %v", z
, e
)
88 func testFunZZ(t
*testing
.T
, msg
string, f funZZ
, a argZZ
) {
91 if !isNormalized(&z
) {
92 t
.Errorf("%s%v is not normalized", msg
, z
)
94 if (&z
).Cmp(a
.z
) != 0 {
95 t
.Errorf("%s%+v\n\tgot z = %v; want %v", msg
, a
, &z
, a
.z
)
99 func TestSumZZ(t
*testing
.T
) {
100 AddZZ
:= func(z
, x
, y
*Int
) *Int
{ return z
.Add(x
, y
) }
101 SubZZ
:= func(z
, x
, y
*Int
) *Int
{ return z
.Sub(x
, y
) }
102 for _
, a
:= range sumZZ
{
104 testFunZZ(t
, "AddZZ", AddZZ
, arg
)
106 arg
= argZZ
{a
.z
, a
.y
, a
.x
}
107 testFunZZ(t
, "AddZZ symmetric", AddZZ
, arg
)
109 arg
= argZZ
{a
.x
, a
.z
, a
.y
}
110 testFunZZ(t
, "SubZZ", SubZZ
, arg
)
112 arg
= argZZ
{a
.y
, a
.z
, a
.x
}
113 testFunZZ(t
, "SubZZ symmetric", SubZZ
, arg
)
117 func TestProdZZ(t
*testing
.T
) {
118 MulZZ
:= func(z
, x
, y
*Int
) *Int
{ return z
.Mul(x
, y
) }
119 for _
, a
:= range prodZZ
{
121 testFunZZ(t
, "MulZZ", MulZZ
, arg
)
123 arg
= argZZ
{a
.z
, a
.y
, a
.x
}
124 testFunZZ(t
, "MulZZ symmetric", MulZZ
, arg
)
128 // mulBytes returns x*y via grade school multiplication. Both inputs
129 // and the result are assumed to be in big-endian representation (to
130 // match the semantics of Int.Bytes and Int.SetBytes).
131 func mulBytes(x
, y
[]byte) []byte {
132 z
:= make([]byte, len(x
)+len(y
))
136 for j
:= len(y
) - 1; j
>= 0; j
-- {
141 for i
:= len(x
) - 1; i
>= 0; i
-- {
142 t
:= int(z
[k
]) + int(x
[i
])*d
+ carry
143 z
[k
], carry
= byte(t
), t
>>8
151 // normalize (remove leading 0's)
153 for i
< len(z
) && z
[i
] == 0 {
160 func checkMul(a
, b
[]byte) bool {
167 z2
.SetBytes(mulBytes(a
, b
))
169 return z1
.Cmp(&z2
) == 0
172 func TestMul(t
*testing
.T
) {
173 if err
:= quick
.Check(checkMul
, nil); err
!= nil {
178 var mulRangesZ
= []struct {
182 // entirely positive ranges are covered by mulRangesN
189 {0, -1, "1"}, // empty range
190 {-1, -100, "1"}, // empty range
191 {-1, 1, "0"}, // range includes 0
192 {-1e9
, 0, "0"}, // range includes 0
193 {-1e9
, 1e9
, "0"}, // range includes 0
194 {-10, -1, "3628800"}, // 10!
195 {-20, -2, "-2432902008176640000"}, // -20!
197 "-933262154439441526816992388562667004907159682643816214685929" +
198 "638952175999932299156089414639761565182862536979208272237582" +
199 "511852109168640000000000000000000000", // -99!
203 func TestMulRangeZ(t
*testing
.T
) {
205 // test entirely positive ranges
206 for i
, r
:= range mulRangesN
{
207 prod
:= tmp
.MulRange(int64(r
.a
), int64(r
.b
)).String()
209 t
.Errorf("#%da: got %s; want %s", i
, prod
, r
.prod
)
213 for i
, r
:= range mulRangesZ
{
214 prod
:= tmp
.MulRange(r
.a
, r
.b
).String()
216 t
.Errorf("#%db: got %s; want %s", i
, prod
, r
.prod
)
221 var stringTests
= []struct {
229 {in
: "a", ok
: false},
230 {in
: "z", ok
: false},
231 {in
: "+", ok
: false},
232 {in
: "-", ok
: false},
233 {in
: "0b", ok
: false},
234 {in
: "0x", ok
: false},
235 {in
: "2", base
: 2, ok
: false},
236 {in
: "0b2", base
: 0, ok
: false},
237 {in
: "08", ok
: false},
238 {in
: "8", base
: 8, ok
: false},
239 {in
: "0xg", base
: 0, ok
: false},
240 {in
: "g", base
: 16, ok
: false},
241 {"0", "0", 0, 0, true},
242 {"0", "0", 10, 0, true},
243 {"0", "0", 16, 0, true},
244 {"+0", "0", 0, 0, true},
245 {"-0", "0", 0, 0, true},
246 {"10", "10", 0, 10, true},
247 {"10", "10", 10, 10, true},
248 {"10", "10", 16, 16, true},
249 {"-10", "-10", 16, -16, true},
250 {"+10", "10", 16, 16, true},
251 {"0x10", "16", 0, 16, true},
252 {in
: "0x10", base
: 16, ok
: false},
253 {"-0x10", "-16", 0, -16, true},
254 {"+0x10", "16", 0, 16, true},
255 {"00", "0", 0, 0, true},
256 {"0", "0", 8, 0, true},
257 {"07", "7", 0, 7, true},
258 {"7", "7", 8, 7, true},
259 {"023", "19", 0, 19, true},
260 {"23", "23", 8, 19, true},
261 {"cafebabe", "cafebabe", 16, 0xcafebabe, true},
262 {"0b0", "0", 0, 0, true},
263 {"-111", "-111", 2, -7, true},
264 {"-0b111", "-7", 0, -7, true},
265 {"0b1001010111", "599", 0, 0x257, true},
266 {"1001010111", "1001010111", 2, 0x257, true},
269 func format(base
int) string {
281 func TestGetString(t
*testing
.T
) {
283 for i
, test
:= range stringTests
{
292 t
.Errorf("#%da got %s; want %s", i
, s
, test
.out
)
296 s
:= fmt
.Sprintf(format(test
.base
), z
)
298 t
.Errorf("#%db got %s; want %s", i
, s
, test
.out
)
303 func TestSetString(t
*testing
.T
) {
305 for i
, test
:= range stringTests
{
306 // initialize to a non-zero value so that issues with parsing
308 tmp
.SetInt64(1234567890)
309 n1
, ok1
:= new(Int
).SetString(test
.in
, test
.base
)
310 n2
, ok2
:= tmp
.SetString(test
.in
, test
.base
)
311 expected
:= NewInt(test
.val
)
312 if ok1
!= test
.ok || ok2
!= test
.ok
{
313 t
.Errorf("#%d (input '%s') ok incorrect (should be %t)", i
, test
.in
, test
.ok
)
318 t
.Errorf("#%d (input '%s') n1 != nil", i
, test
.in
)
324 t
.Errorf("#%d (input '%s') n2 != nil", i
, test
.in
)
329 if ok1
&& !isNormalized(n1
) {
330 t
.Errorf("#%d (input '%s'): %v is not normalized", i
, test
.in
, *n1
)
332 if ok2
&& !isNormalized(n2
) {
333 t
.Errorf("#%d (input '%s'): %v is not normalized", i
, test
.in
, *n2
)
336 if n1
.Cmp(expected
) != 0 {
337 t
.Errorf("#%d (input '%s') got: %s want: %d", i
, test
.in
, n1
, test
.val
)
339 if n2
.Cmp(expected
) != 0 {
340 t
.Errorf("#%d (input '%s') got: %s want: %d", i
, test
.in
, n2
, test
.val
)
345 var formatTests
= []struct {
350 {"<nil>", "%x", "<nil>"},
351 {"<nil>", "%#x", "<nil>"},
352 {"<nil>", "%#y", "%!y(big.Int=<nil>)"},
354 {"10", "%b", "1010"},
361 {"10", "%y", "%!y(big.Int=10)"},
362 {"-10", "%y", "%!y(big.Int=-10)"},
364 {"10", "%#b", "1010"},
365 {"10", "%#o", "012"},
368 {"10", "%#x", "0xa"},
369 {"10", "%#X", "0XA"},
370 {"-10", "%#X", "-0XA"},
371 {"10", "%#y", "%!y(big.Int=10)"},
372 {"-10", "%#y", "%!y(big.Int=-10)"},
374 {"1234", "%d", "1234"},
375 {"1234", "%3d", "1234"},
376 {"1234", "%4d", "1234"},
377 {"-1234", "%d", "-1234"},
378 {"1234", "% 5d", " 1234"},
379 {"1234", "%+5d", "+1234"},
380 {"1234", "%-5d", "1234 "},
381 {"1234", "%x", "4d2"},
382 {"1234", "%X", "4D2"},
383 {"-1234", "%3x", "-4d2"},
384 {"-1234", "%4x", "-4d2"},
385 {"-1234", "%5x", " -4d2"},
386 {"-1234", "%-5x", "-4d2 "},
387 {"1234", "%03d", "1234"},
388 {"1234", "%04d", "1234"},
389 {"1234", "%05d", "01234"},
390 {"1234", "%06d", "001234"},
391 {"-1234", "%06d", "-01234"},
392 {"1234", "%+06d", "+01234"},
393 {"1234", "% 06d", " 01234"},
394 {"1234", "%-6d", "1234 "},
395 {"1234", "%-06d", "1234 "},
396 {"-1234", "%-06d", "-1234 "},
398 {"1234", "%.3d", "1234"},
399 {"1234", "%.4d", "1234"},
400 {"1234", "%.5d", "01234"},
401 {"1234", "%.6d", "001234"},
402 {"-1234", "%.3d", "-1234"},
403 {"-1234", "%.4d", "-1234"},
404 {"-1234", "%.5d", "-01234"},
405 {"-1234", "%.6d", "-001234"},
407 {"1234", "%8.3d", " 1234"},
408 {"1234", "%8.4d", " 1234"},
409 {"1234", "%8.5d", " 01234"},
410 {"1234", "%8.6d", " 001234"},
411 {"-1234", "%8.3d", " -1234"},
412 {"-1234", "%8.4d", " -1234"},
413 {"-1234", "%8.5d", " -01234"},
414 {"-1234", "%8.6d", " -001234"},
416 {"1234", "%+8.3d", " +1234"},
417 {"1234", "%+8.4d", " +1234"},
418 {"1234", "%+8.5d", " +01234"},
419 {"1234", "%+8.6d", " +001234"},
420 {"-1234", "%+8.3d", " -1234"},
421 {"-1234", "%+8.4d", " -1234"},
422 {"-1234", "%+8.5d", " -01234"},
423 {"-1234", "%+8.6d", " -001234"},
425 {"1234", "% 8.3d", " 1234"},
426 {"1234", "% 8.4d", " 1234"},
427 {"1234", "% 8.5d", " 01234"},
428 {"1234", "% 8.6d", " 001234"},
429 {"-1234", "% 8.3d", " -1234"},
430 {"-1234", "% 8.4d", " -1234"},
431 {"-1234", "% 8.5d", " -01234"},
432 {"-1234", "% 8.6d", " -001234"},
434 {"1234", "%.3x", "4d2"},
435 {"1234", "%.4x", "04d2"},
436 {"1234", "%.5x", "004d2"},
437 {"1234", "%.6x", "0004d2"},
438 {"-1234", "%.3x", "-4d2"},
439 {"-1234", "%.4x", "-04d2"},
440 {"-1234", "%.5x", "-004d2"},
441 {"-1234", "%.6x", "-0004d2"},
443 {"1234", "%8.3x", " 4d2"},
444 {"1234", "%8.4x", " 04d2"},
445 {"1234", "%8.5x", " 004d2"},
446 {"1234", "%8.6x", " 0004d2"},
447 {"-1234", "%8.3x", " -4d2"},
448 {"-1234", "%8.4x", " -04d2"},
449 {"-1234", "%8.5x", " -004d2"},
450 {"-1234", "%8.6x", " -0004d2"},
452 {"1234", "%+8.3x", " +4d2"},
453 {"1234", "%+8.4x", " +04d2"},
454 {"1234", "%+8.5x", " +004d2"},
455 {"1234", "%+8.6x", " +0004d2"},
456 {"-1234", "%+8.3x", " -4d2"},
457 {"-1234", "%+8.4x", " -04d2"},
458 {"-1234", "%+8.5x", " -004d2"},
459 {"-1234", "%+8.6x", " -0004d2"},
461 {"1234", "% 8.3x", " 4d2"},
462 {"1234", "% 8.4x", " 04d2"},
463 {"1234", "% 8.5x", " 004d2"},
464 {"1234", "% 8.6x", " 0004d2"},
465 {"1234", "% 8.7x", " 00004d2"},
466 {"1234", "% 8.8x", " 000004d2"},
467 {"-1234", "% 8.3x", " -4d2"},
468 {"-1234", "% 8.4x", " -04d2"},
469 {"-1234", "% 8.5x", " -004d2"},
470 {"-1234", "% 8.6x", " -0004d2"},
471 {"-1234", "% 8.7x", "-00004d2"},
472 {"-1234", "% 8.8x", "-000004d2"},
474 {"1234", "%-8.3d", "1234 "},
475 {"1234", "%-8.4d", "1234 "},
476 {"1234", "%-8.5d", "01234 "},
477 {"1234", "%-8.6d", "001234 "},
478 {"1234", "%-8.7d", "0001234 "},
479 {"1234", "%-8.8d", "00001234"},
480 {"-1234", "%-8.3d", "-1234 "},
481 {"-1234", "%-8.4d", "-1234 "},
482 {"-1234", "%-8.5d", "-01234 "},
483 {"-1234", "%-8.6d", "-001234 "},
484 {"-1234", "%-8.7d", "-0001234"},
485 {"-1234", "%-8.8d", "-00001234"},
487 {"16777215", "%b", "111111111111111111111111"}, // 2**24 - 1
494 func TestFormat(t
*testing
.T
) {
495 for i
, test
:= range formatTests
{
497 if test
.input
!= "<nil>" {
499 x
, ok
= new(Int
).SetString(test
.input
, 0)
501 t
.Errorf("#%d failed reading input %s", i
, test
.input
)
504 output
:= fmt
.Sprintf(test
.format
, x
)
505 if output
!= test
.output
{
506 t
.Errorf("#%d got %q; want %q, {%q, %q, %q}", i
, output
, test
.output
, test
.input
, test
.format
, test
.output
)
511 var scanTests
= []struct {
517 {"1010", "%b", "10", 0},
518 {"0b1010", "%v", "10", 0},
519 {"12", "%o", "10", 0},
520 {"012", "%v", "10", 0},
521 {"10", "%d", "10", 0},
522 {"10", "%v", "10", 0},
523 {"a", "%x", "10", 0},
524 {"0xa", "%v", "10", 0},
525 {"A", "%X", "10", 0},
526 {"-A", "%X", "-10", 0},
527 {"+0b1011001", "%v", "89", 0},
528 {"0xA", "%v", "10", 0},
529 {"0 ", "%v", "0", 1},
530 {"2+3", "%v", "2", 2},
531 {"0XABC 12", "%v", "2748", 3},
534 func TestScan(t
*testing
.T
) {
536 for i
, test
:= range scanTests
{
539 buf
.WriteString(test
.input
)
540 if _
, err
:= fmt
.Fscanf(&buf
, test
.format
, x
); err
!= nil {
541 t
.Errorf("#%d error: %s", i
, err
)
543 if x
.String() != test
.output
{
544 t
.Errorf("#%d got %s; want %s", i
, x
.String(), test
.output
)
546 if buf
.Len() != test
.remaining
{
547 t
.Errorf("#%d got %d bytes remaining; want %d", i
, buf
.Len(), test
.remaining
)
552 // Examples from the Go Language Spec, section "Arithmetic operators"
553 var divisionSignsTests
= []struct {
555 q
, r
int64 // T-division
556 d
, m
int64 // Euclidian division
559 {-5, 3, -1, -2, -2, 1},
560 {5, -3, -1, 2, -1, 2},
561 {-5, -3, 1, -2, 2, 1},
566 func TestDivisionSigns(t
*testing
.T
) {
567 for i
, test
:= range divisionSignsTests
{
575 q1
:= new(Int
).Quo(x
, y
)
576 r1
:= new(Int
).Rem(x
, y
)
577 if !isNormalized(q1
) {
578 t
.Errorf("#%d Quo: %v is not normalized", i
, *q1
)
580 if !isNormalized(r1
) {
581 t
.Errorf("#%d Rem: %v is not normalized", i
, *r1
)
583 if q1
.Cmp(q
) != 0 || r1
.Cmp(r
) != 0 {
584 t
.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i
, q1
, r1
, q
, r
)
587 q2
, r2
:= new(Int
).QuoRem(x
, y
, new(Int
))
588 if !isNormalized(q2
) {
589 t
.Errorf("#%d Quo: %v is not normalized", i
, *q2
)
591 if !isNormalized(r2
) {
592 t
.Errorf("#%d Rem: %v is not normalized", i
, *r2
)
594 if q2
.Cmp(q
) != 0 || r2
.Cmp(r
) != 0 {
595 t
.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i
, q2
, r2
, q
, r
)
598 d1
:= new(Int
).Div(x
, y
)
599 m1
:= new(Int
).Mod(x
, y
)
600 if !isNormalized(d1
) {
601 t
.Errorf("#%d Div: %v is not normalized", i
, *d1
)
603 if !isNormalized(m1
) {
604 t
.Errorf("#%d Mod: %v is not normalized", i
, *m1
)
606 if d1
.Cmp(d
) != 0 || m1
.Cmp(m
) != 0 {
607 t
.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i
, d1
, m1
, d
, m
)
610 d2
, m2
:= new(Int
).DivMod(x
, y
, new(Int
))
611 if !isNormalized(d2
) {
612 t
.Errorf("#%d Div: %v is not normalized", i
, *d2
)
614 if !isNormalized(m2
) {
615 t
.Errorf("#%d Mod: %v is not normalized", i
, *m2
)
617 if d2
.Cmp(d
) != 0 || m2
.Cmp(m
) != 0 {
618 t
.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i
, d2
, m2
, d
, m
)
623 func checkSetBytes(b
[]byte) bool {
624 hex1
:= hex
.EncodeToString(new(Int
).SetBytes(b
).Bytes())
625 hex2
:= hex
.EncodeToString(b
)
627 for len(hex1
) < len(hex2
) {
631 for len(hex1
) > len(hex2
) {
638 func TestSetBytes(t
*testing
.T
) {
639 if err
:= quick
.Check(checkSetBytes
, nil); err
!= nil {
644 func checkBytes(b
[]byte) bool {
645 b2
:= new(Int
).SetBytes(b
).Bytes()
646 return bytes
.Equal(b
, b2
)
649 func TestBytes(t
*testing
.T
) {
650 if err
:= quick
.Check(checkSetBytes
, nil); err
!= nil {
655 func checkQuo(x
, y
[]byte) bool {
656 u
:= new(Int
).SetBytes(x
)
657 v
:= new(Int
).SetBytes(y
)
664 q
, r
:= new(Int
).QuoRem(u
, v
, r
)
670 uprime
:= new(Int
).Set(q
)
671 uprime
.Mul(uprime
, v
)
672 uprime
.Add(uprime
, r
)
674 return uprime
.Cmp(u
) == 0
677 var quoTests
= []struct {
682 "476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
683 "9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
688 "11510768301994997771168",
689 "1328165573307167369775",
691 "885443715537658812968",
695 func TestQuo(t
*testing
.T
) {
696 if err
:= quick
.Check(checkQuo
, nil); err
!= nil {
700 for i
, test
:= range quoTests
{
701 x
, _
:= new(Int
).SetString(test
.x
, 10)
702 y
, _
:= new(Int
).SetString(test
.y
, 10)
703 expectedQ
, _
:= new(Int
).SetString(test
.q
, 10)
704 expectedR
, _
:= new(Int
).SetString(test
.r
, 10)
707 q
, r
:= new(Int
).QuoRem(x
, y
, r
)
709 if q
.Cmp(expectedQ
) != 0 || r
.Cmp(expectedR
) != 0 {
710 t
.Errorf("#%d got (%s, %s) want (%s, %s)", i
, q
, r
, expectedQ
, expectedR
)
715 func TestQuoStepD6(t
*testing
.T
) {
716 // See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises
717 // a code path which only triggers 1 in 10^{-19} cases.
719 u
:= &Int
{false, nat
{0, 0, 1 + 1<<(_W
-1), _M
^ (1 << (_W
- 1))}}
720 v
:= &Int
{false, nat
{5, 2 + 1<<(_W
-1), 1 << (_W
- 1)}}
723 q
, r
:= new(Int
).QuoRem(u
, v
, r
)
724 const expectedQ64
= "18446744073709551613"
725 const expectedR64
= "3138550867693340382088035895064302439801311770021610913807"
726 const expectedQ32
= "4294967293"
727 const expectedR32
= "39614081266355540837921718287"
728 if q
.String() != expectedQ64
&& q
.String() != expectedQ32 ||
729 r
.String() != expectedR64
&& r
.String() != expectedR32
{
730 t
.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q
, r
, expectedQ64
, expectedR64
, expectedQ32
, expectedR32
)
734 var bitLenTests
= []struct {
746 {"0x800000000000", 48},
747 {"0x8000000000000000", 64},
748 {"0x80000000000000000000", 80},
749 {"-0x4000000000000000000000", 87},
752 func TestBitLen(t
*testing
.T
) {
753 for i
, test
:= range bitLenTests
{
754 x
, ok
:= new(Int
).SetString(test
.in
, 0)
756 t
.Errorf("#%d test input invalid: %s", i
, test
.in
)
760 if n
:= x
.BitLen(); n
!= test
.out
{
761 t
.Errorf("#%d got %d want %d", i
, n
, test
.out
)
766 var expTests
= []struct {
770 {"5", "-7", "", "1"},
771 {"-5", "-7", "", "1"},
773 {"-5", "0", "", "1"},
775 {"-5", "1", "", "-5"},
776 {"-2", "3", "2", "0"},
777 {"5", "2", "", "25"},
778 {"1", "65537", "2", "1"},
779 {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
780 {"0x8000000000000000", "2", "6719", "4944"},
781 {"0x8000000000000000", "3", "6719", "5447"},
782 {"0x8000000000000000", "1000", "6719", "1603"},
783 {"0x8000000000000000", "1000000", "6719", "3199"},
784 {"0x8000000000000000", "-1000000", "6719", "1"},
786 "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
787 "298472983472983471903246121093472394872319615612417471234712061",
788 "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
789 "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
793 func TestExp(t
*testing
.T
) {
794 for i
, test
:= range expTests
{
795 x
, ok1
:= new(Int
).SetString(test
.x
, 0)
796 y
, ok2
:= new(Int
).SetString(test
.y
, 0)
797 out
, ok3
:= new(Int
).SetString(test
.out
, 0)
802 if len(test
.m
) == 0 {
805 m
, ok4
= new(Int
).SetString(test
.m
, 0)
808 if !ok1 ||
!ok2 ||
!ok3 ||
!ok4
{
809 t
.Errorf("#%d: error in input", i
)
813 z1
:= new(Int
).Exp(x
, y
, m
)
814 if !isNormalized(z1
) {
815 t
.Errorf("#%d: %v is not normalized", i
, *z1
)
817 if z1
.Cmp(out
) != 0 {
818 t
.Errorf("#%d: got %s want %s", i
, z1
, out
)
822 // the result should be the same as for m == 0;
823 // specifically, there should be no div-zero panic
824 m
= &Int
{abs
: nat
{}} // m != nil && len(m.abs) == 0
825 z2
:= new(Int
).Exp(x
, y
, m
)
827 t
.Errorf("#%d: got %s want %s", i
, z1
, z2
)
833 func checkGcd(aBytes
, bBytes
[]byte) bool {
836 a
:= new(Int
).SetBytes(aBytes
)
837 b
:= new(Int
).SetBytes(bBytes
)
839 d
:= new(Int
).GCD(x
, y
, a
, b
)
847 var gcdTests
= []struct {
851 {"0", "0", "0", "0", "0"},
852 {"0", "0", "0", "0", "7"},
853 {"0", "0", "0", "11", "0"},
854 {"0", "0", "0", "-77", "35"},
855 {"0", "0", "0", "64515", "-24310"},
856 {"0", "0", "0", "-64515", "-24310"},
858 {"1", "-9", "47", "120", "23"},
859 {"7", "1", "-2", "77", "35"},
860 {"935", "-3", "8", "64515", "24310"},
861 {"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"},
862 {"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"},
864 // test early exit (after one Euclidean iteration) in binaryGCD
865 {"1", "", "", "1", "98920366548084643601728869055592650835572950932266967461790948584315647051443"},
868 func testGcd(t
*testing
.T
, d
, x
, y
, a
, b
*Int
) {
878 D
:= new(Int
).GCD(X
, Y
, a
, b
)
880 t
.Errorf("GCD(%s, %s): got d = %s, want %s", a
, b
, D
, d
)
882 if x
!= nil && X
.Cmp(x
) != 0 {
883 t
.Errorf("GCD(%s, %s): got x = %s, want %s", a
, b
, X
, x
)
885 if y
!= nil && Y
.Cmp(y
) != 0 {
886 t
.Errorf("GCD(%s, %s): got y = %s, want %s", a
, b
, Y
, y
)
889 // binaryGCD requires a > 0 && b > 0
890 if a
.Sign() <= 0 || b
.Sign() <= 0 {
896 t
.Errorf("binaryGcd(%s, %s): got d = %s, want %s", a
, b
, D
, d
)
900 func TestGcd(t
*testing
.T
) {
901 for _
, test
:= range gcdTests
{
902 d
, _
:= new(Int
).SetString(test
.d
, 0)
903 x
, _
:= new(Int
).SetString(test
.x
, 0)
904 y
, _
:= new(Int
).SetString(test
.y
, 0)
905 a
, _
:= new(Int
).SetString(test
.a
, 0)
906 b
, _
:= new(Int
).SetString(test
.b
, 0)
908 testGcd(t
, d
, nil, nil, a
, b
)
909 testGcd(t
, d
, x
, nil, a
, b
)
910 testGcd(t
, d
, nil, y
, a
, b
)
911 testGcd(t
, d
, x
, y
, a
, b
)
914 quick
.Check(checkGcd
, nil)
917 var primes
= []string{
924 "13756265695458089029",
925 "13496181268022124907",
926 "10953742525620032441",
927 "17908251027575790097",
929 // http://code.google.com/p/go/issues/detail?id=638
930 "18699199384836356663",
932 "98920366548084643601728869055592650835572950932266967461790948584315647051443",
933 "94560208308847015747498523884063394671606671904944666360068158221458669711639",
935 // http://primes.utm.edu/lists/small/small3.html
936 "449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
937 "230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
938 "5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
939 "203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
942 var composites
= []string{
943 "21284175091214687912771199898307297748211672914763848041968395774954376176754",
944 "6084766654921918907427900243509372380954290099172559290432744450051395395951",
945 "84594350493221918389213352992032324280367711247940675652888030554255915464401",
946 "82793403787388584738507275144194252681",
949 func TestProbablyPrime(t
*testing
.T
) {
954 for i
, s
:= range primes
{
955 p
, _
:= new(Int
).SetString(s
, 10)
956 if !p
.ProbablyPrime(nreps
) {
957 t
.Errorf("#%d prime found to be non-prime (%s)", i
, s
)
961 for i
, s
:= range composites
{
962 c
, _
:= new(Int
).SetString(s
, 10)
963 if c
.ProbablyPrime(nreps
) {
964 t
.Errorf("#%d composite found to be prime (%s)", i
, s
)
972 type intShiftTest
struct {
978 var rshTests
= []intShiftTest
{
994 {"4294967296", 0, "4294967296"},
995 {"4294967296", 1, "2147483648"},
996 {"4294967296", 2, "1073741824"},
997 {"18446744073709551616", 0, "18446744073709551616"},
998 {"18446744073709551616", 1, "9223372036854775808"},
999 {"18446744073709551616", 2, "4611686018427387904"},
1000 {"18446744073709551616", 64, "1"},
1001 {"340282366920938463463374607431768211456", 64, "18446744073709551616"},
1002 {"340282366920938463463374607431768211456", 128, "1"},
1005 func TestRsh(t
*testing
.T
) {
1006 for i
, test
:= range rshTests
{
1007 in
, _
:= new(Int
).SetString(test
.in
, 10)
1008 expected
, _
:= new(Int
).SetString(test
.out
, 10)
1009 out
:= new(Int
).Rsh(in
, test
.shift
)
1011 if !isNormalized(out
) {
1012 t
.Errorf("#%d: %v is not normalized", i
, *out
)
1014 if out
.Cmp(expected
) != 0 {
1015 t
.Errorf("#%d: got %s want %s", i
, out
, expected
)
1020 func TestRshSelf(t
*testing
.T
) {
1021 for i
, test
:= range rshTests
{
1022 z
, _
:= new(Int
).SetString(test
.in
, 10)
1023 expected
, _
:= new(Int
).SetString(test
.out
, 10)
1024 z
.Rsh(z
, test
.shift
)
1026 if !isNormalized(z
) {
1027 t
.Errorf("#%d: %v is not normalized", i
, *z
)
1029 if z
.Cmp(expected
) != 0 {
1030 t
.Errorf("#%d: got %s want %s", i
, z
, expected
)
1035 var lshTests
= []intShiftTest
{
1046 {"4294967296", 0, "4294967296"},
1047 {"4294967296", 1, "8589934592"},
1048 {"4294967296", 2, "17179869184"},
1049 {"18446744073709551616", 0, "18446744073709551616"},
1050 {"9223372036854775808", 1, "18446744073709551616"},
1051 {"4611686018427387904", 2, "18446744073709551616"},
1052 {"1", 64, "18446744073709551616"},
1053 {"18446744073709551616", 64, "340282366920938463463374607431768211456"},
1054 {"1", 128, "340282366920938463463374607431768211456"},
1057 func TestLsh(t
*testing
.T
) {
1058 for i
, test
:= range lshTests
{
1059 in
, _
:= new(Int
).SetString(test
.in
, 10)
1060 expected
, _
:= new(Int
).SetString(test
.out
, 10)
1061 out
:= new(Int
).Lsh(in
, test
.shift
)
1063 if !isNormalized(out
) {
1064 t
.Errorf("#%d: %v is not normalized", i
, *out
)
1066 if out
.Cmp(expected
) != 0 {
1067 t
.Errorf("#%d: got %s want %s", i
, out
, expected
)
1072 func TestLshSelf(t
*testing
.T
) {
1073 for i
, test
:= range lshTests
{
1074 z
, _
:= new(Int
).SetString(test
.in
, 10)
1075 expected
, _
:= new(Int
).SetString(test
.out
, 10)
1076 z
.Lsh(z
, test
.shift
)
1078 if !isNormalized(z
) {
1079 t
.Errorf("#%d: %v is not normalized", i
, *z
)
1081 if z
.Cmp(expected
) != 0 {
1082 t
.Errorf("#%d: got %s want %s", i
, z
, expected
)
1087 func TestLshRsh(t
*testing
.T
) {
1088 for i
, test
:= range rshTests
{
1089 in
, _
:= new(Int
).SetString(test
.in
, 10)
1090 out
:= new(Int
).Lsh(in
, test
.shift
)
1091 out
= out
.Rsh(out
, test
.shift
)
1093 if !isNormalized(out
) {
1094 t
.Errorf("#%d: %v is not normalized", i
, *out
)
1096 if in
.Cmp(out
) != 0 {
1097 t
.Errorf("#%d: got %s want %s", i
, out
, in
)
1100 for i
, test
:= range lshTests
{
1101 in
, _
:= new(Int
).SetString(test
.in
, 10)
1102 out
:= new(Int
).Lsh(in
, test
.shift
)
1103 out
.Rsh(out
, test
.shift
)
1105 if !isNormalized(out
) {
1106 t
.Errorf("#%d: %v is not normalized", i
, *out
)
1108 if in
.Cmp(out
) != 0 {
1109 t
.Errorf("#%d: got %s want %s", i
, out
, in
)
1114 var int64Tests
= []int64{
1122 9223372036854775807,
1123 -9223372036854775807,
1124 -9223372036854775808,
1127 func TestInt64(t
*testing
.T
) {
1128 for i
, testVal
:= range int64Tests
{
1129 in
:= NewInt(testVal
)
1133 t
.Errorf("#%d got %d want %d", i
, out
, testVal
)
1138 var uint64Tests
= []uint64{
1145 9223372036854775807,
1146 9223372036854775808,
1147 18446744073709551615, // 1<<64 - 1
1150 func TestUint64(t
*testing
.T
) {
1152 for i
, testVal
:= range uint64Tests
{
1153 in
.SetUint64(testVal
)
1157 t
.Errorf("#%d got %d want %d", i
, out
, testVal
)
1160 str
:= fmt
.Sprint(testVal
)
1161 strOut
:= in
.String()
1163 t
.Errorf("#%d.String got %s want %s", i
, strOut
, str
)
1168 var bitwiseTests
= []struct {
1170 and
, or
, xor
, andNot
string
1172 {"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
1173 {"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
1174 {"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
1175 {"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
1176 {"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"},
1177 {"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
1178 {"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
1179 {"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
1180 {"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
1181 {"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
1182 {"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
1183 {"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
1184 {"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
1186 "0x1000009dc6e3d9822cba04129bcbe3401",
1187 "0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1188 "0x1000001186210100001000009048c2001",
1189 "0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1190 "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1191 "0x8c40c2d8822caa04120b8321400",
1194 "0x1000009dc6e3d9822cba04129bcbe3401",
1195 "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1196 "0x8c40c2d8822caa04120b8321401",
1197 "-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
1198 "-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
1199 "0x1000001186210100001000009048c2000",
1202 "-0x1000009dc6e3d9822cba04129bcbe3401",
1203 "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
1204 "-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
1205 "-0x1000001186210100001000009048c2001",
1206 "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
1207 "0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
1211 type bitFun
func(z
, x
, y
*Int
) *Int
1213 func testBitFun(t
*testing
.T
, msg
string, f bitFun
, x
, y
*Int
, exp
string) {
1214 expected
:= new(Int
)
1215 expected
.SetString(exp
, 0)
1217 out
:= f(new(Int
), x
, y
)
1218 if out
.Cmp(expected
) != 0 {
1219 t
.Errorf("%s: got %s want %s", msg
, out
, expected
)
1223 func testBitFunSelf(t
*testing
.T
, msg
string, f bitFun
, x
, y
*Int
, exp
string) {
1226 expected
:= new(Int
)
1227 expected
.SetString(exp
, 0)
1229 self
= f(self
, self
, y
)
1230 if self
.Cmp(expected
) != 0 {
1231 t
.Errorf("%s: got %s want %s", msg
, self
, expected
)
1235 func altBit(x
*Int
, i
int) uint {
1236 z
:= new(Int
).Rsh(x
, uint(i
))
1237 z
= z
.And(z
, NewInt(1))
1238 if z
.Cmp(new(Int
)) != 0 {
1244 func altSetBit(z
*Int
, x
*Int
, i
int, b
uint) *Int
{
1246 m
:= one
.Lsh(one
, uint(i
))
1251 return z
.AndNot(x
, m
)
1253 panic("set bit is not 0 or 1")
1256 func testBitset(t
*testing
.T
, x
*Int
) {
1258 z
:= new(Int
).Set(x
)
1259 z1
:= new(Int
).Set(x
)
1260 for i
:= 0; i
< n
+10; i
++ {
1262 old1
:= altBit(z1
, i
)
1264 t
.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1
, i
, old
, old1
)
1266 z
:= new(Int
).SetBit(z
, i
, 1)
1267 z1
:= altSetBit(new(Int
), z1
, i
, 1)
1269 t
.Errorf("bitset: bit %d of %s got 0 want 1", i
, x
)
1272 t
.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z
, z1
)
1275 altSetBit(z1
, z1
, i
, 0)
1277 t
.Errorf("bitset: bit %d of %s got 1 want 0", i
, x
)
1280 t
.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z
, z1
)
1282 altSetBit(z1
, z1
, i
, old
)
1285 t
.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z
, z1
)
1289 t
.Errorf("bitset: got %s want %s", z
, x
)
1293 var bitsetTests
= []struct {
1304 {"0x2000000000000000000000000000", 108, 0},
1305 {"0x2000000000000000000000000000", 109, 1},
1306 {"0x2000000000000000000000000000", 110, 0},
1307 {"-0x2000000000000000000000000001", 108, 1},
1308 {"-0x2000000000000000000000000001", 109, 0},
1309 {"-0x2000000000000000000000000001", 110, 1},
1312 func TestBitSet(t
*testing
.T
) {
1313 for _
, test
:= range bitwiseTests
{
1315 x
.SetString(test
.x
, 0)
1318 x
.SetString(test
.y
, 0)
1321 for i
, test
:= range bitsetTests
{
1323 x
.SetString(test
.x
, 0)
1326 t
.Errorf("#%d got %v want %v", i
, b
, test
.b
)
1330 z
.SetBit(NewInt(0), 2, 1)
1331 if z
.Cmp(NewInt(4)) != 0 {
1332 t
.Errorf("destination leaked into result; got %s want 4", z
)
1336 func BenchmarkBitset(b
*testing
.B
) {
1341 for i
:= b
.N
- 1; i
>= 0; i
-- {
1342 z
.SetBit(z
, i
&512, 1)
1346 func BenchmarkBitsetNeg(b
*testing
.B
) {
1351 for i
:= b
.N
- 1; i
>= 0; i
-- {
1352 z
.SetBit(z
, i
&512, 0)
1356 func BenchmarkBitsetOrig(b
*testing
.B
) {
1358 altSetBit(z
, z
, 512, 1)
1361 for i
:= b
.N
- 1; i
>= 0; i
-- {
1362 altSetBit(z
, z
, i
&512, 1)
1366 func BenchmarkBitsetNegOrig(b
*testing
.B
) {
1368 altSetBit(z
, z
, 512, 0)
1371 for i
:= b
.N
- 1; i
>= 0; i
-- {
1372 altSetBit(z
, z
, i
&512, 0)
1376 func TestBitwise(t
*testing
.T
) {
1379 for _
, test
:= range bitwiseTests
{
1380 x
.SetString(test
.x
, 0)
1381 y
.SetString(test
.y
, 0)
1383 testBitFun(t
, "and", (*Int
).And
, x
, y
, test
.and
)
1384 testBitFunSelf(t
, "and", (*Int
).And
, x
, y
, test
.and
)
1385 testBitFun(t
, "andNot", (*Int
).AndNot
, x
, y
, test
.andNot
)
1386 testBitFunSelf(t
, "andNot", (*Int
).AndNot
, x
, y
, test
.andNot
)
1387 testBitFun(t
, "or", (*Int
).Or
, x
, y
, test
.or
)
1388 testBitFunSelf(t
, "or", (*Int
).Or
, x
, y
, test
.or
)
1389 testBitFun(t
, "xor", (*Int
).Xor
, x
, y
, test
.xor
)
1390 testBitFunSelf(t
, "xor", (*Int
).Xor
, x
, y
, test
.xor
)
1394 var notTests
= []struct {
1402 {"-81910", "81909"},
1404 "298472983472983471903246121093472394872319615612417471234712061",
1405 "-298472983472983471903246121093472394872319615612417471234712062",
1409 func TestNot(t
*testing
.T
) {
1412 expected
:= new(Int
)
1413 for i
, test
:= range notTests
{
1414 in
.SetString(test
.in
, 10)
1415 expected
.SetString(test
.out
, 10)
1417 if out
.Cmp(expected
) != 0 {
1418 t
.Errorf("#%d: got %s want %s", i
, out
, expected
)
1421 if out
.Cmp(in
) != 0 {
1422 t
.Errorf("#%d: got %s want %s", i
, out
, in
)
1427 var modInverseTests
= []struct {
1433 {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
1436 func TestModInverse(t
*testing
.T
) {
1437 var element
, prime Int
1439 for i
, test
:= range modInverseTests
{
1440 (&element
).SetString(test
.element
, 10)
1441 (&prime
).SetString(test
.prime
, 10)
1442 inverse
:= new(Int
).ModInverse(&element
, &prime
)
1443 inverse
.Mul(inverse
, &element
)
1444 inverse
.Mod(inverse
, &prime
)
1445 if inverse
.Cmp(one
) != 0 {
1446 t
.Errorf("#%d: failed (e·e^(-1)=%s)", i
, inverse
)
1451 var encodingTests
= []string{
1452 "-539345864568634858364538753846587364875430589374589",
1463 "298472983472983471903246121093472394872319615612417471234712061",
1466 func TestIntGobEncoding(t
*testing
.T
) {
1467 var medium bytes
.Buffer
1468 enc
:= gob
.NewEncoder(&medium
)
1469 dec
:= gob
.NewDecoder(&medium
)
1470 for _
, test
:= range encodingTests
{
1471 medium
.Reset() // empty buffer for each test case (in case of failures)
1473 tx
.SetString(test
, 10)
1474 if err
:= enc
.Encode(&tx
); err
!= nil {
1475 t
.Errorf("encoding of %s failed: %s", &tx
, err
)
1478 if err
:= dec
.Decode(&rx
); err
!= nil {
1479 t
.Errorf("decoding of %s failed: %s", &tx
, err
)
1481 if rx
.Cmp(&tx
) != 0 {
1482 t
.Errorf("transmission of %s failed: got %s want %s", &tx
, &rx
, &tx
)
1487 // Sending a nil Int pointer (inside a slice) on a round trip through gob should yield a zero.
1488 // TODO: top-level nils.
1489 func TestGobEncodingNilIntInSlice(t
*testing
.T
) {
1490 buf
:= new(bytes
.Buffer
)
1491 enc
:= gob
.NewEncoder(buf
)
1492 dec
:= gob
.NewDecoder(buf
)
1494 var in
= make([]*Int
, 1)
1495 err
:= enc
.Encode(&in
)
1497 t
.Errorf("gob encode failed: %q", err
)
1500 err
= dec
.Decode(&out
)
1502 t
.Fatalf("gob decode failed: %q", err
)
1505 t
.Fatalf("wrong len; want 1 got %d", len(out
))
1508 if out
[0].Cmp(&zero
) != 0 {
1509 t
.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out
)
1513 func TestIntJSONEncoding(t
*testing
.T
) {
1514 for _
, test
:= range encodingTests
{
1516 tx
.SetString(test
, 10)
1517 b
, err
:= json
.Marshal(&tx
)
1519 t
.Errorf("marshaling of %s failed: %s", &tx
, err
)
1522 if err
:= json
.Unmarshal(b
, &rx
); err
!= nil {
1523 t
.Errorf("unmarshaling of %s failed: %s", &tx
, err
)
1525 if rx
.Cmp(&tx
) != 0 {
1526 t
.Errorf("JSON encoding of %s failed: got %s want %s", &tx
, &rx
, &tx
)
1531 func TestIssue2607(t
*testing
.T
) {
1532 // This code sequence used to hang.
1534 n
.Rand(rand
.New(rand
.NewSource(9)), n
)