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[/] [openrisc/] [trunk/] [gnu-dev/] [or1k-gcc/] [libgo/] [go/] [math/] [big/] [nat_test.go] - Blame information for rev 747

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Line No. Rev Author Line
1 747 jeremybenn 
// 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.
4 
 
5 
package big
6 
 
7 
import (
8 
        "io"
9 
        "strings"
10 
        "testing"
11 
)
12 
 
13 
var cmpTests = []struct {
14 
        x, y nat
15 
        r    int
16 
}{
17 
        {nil, nil, 0},
18 
        {nil, nat(nil), 0},
19 
        {nat(nil), nil, 0},
20 
        {nat(nil), nat(nil), 0},
21 
        {nat{0}, nat{0}, 0},
22 
        {nat{0}, nat{1}, -1},
23 
        {nat{1}, nat{0}, 1},
24 
        {nat{1}, nat{1}, 0},
25 
        {nat{0, _M}, nat{1}, 1},
26 
        {nat{1}, nat{0, _M}, -1},
27 
        {nat{1, _M}, nat{0, _M}, 1},
28 
        {nat{0, _M}, nat{1, _M}, -1},
29 
        {nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
30 
        {nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
31 
}
32 
 
33 
func TestCmp(t *testing.T) {
34 
        for i, a := range cmpTests {
35 
                r := a.x.cmp(a.y)
36 
                if r != a.r {
37 
                        t.Errorf("#%d got r = %v; want %v", i, r, a.r)
38 
                }
39 
        }
40 
}
41 
 
42 
type funNN func(z, x, y nat) nat
43 
type argNN struct {
44 
        z, x, y nat
45 
}
46 
 
47 
var sumNN = []argNN{
48 
        {},
49 
        {nat{1}, nil, nat{1}},
50 
        {nat{1111111110}, nat{123456789}, nat{987654321}},
51 
        {nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
52 
        {nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
53 
        {nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
54 
}
55 
 
56 
var prodNN = []argNN{
57 
        {},
58 
        {nil, nil, nil},
59 
        {nil, nat{991}, nil},
60 
        {nat{991}, nat{991}, nat{1}},
61 
        {nat{991 * 991}, nat{991}, nat{991}},
62 
        {nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
63 
        {nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
64 
        {nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
65 
}
66 
 
67 
func TestSet(t *testing.T) {
68 
        for _, a := range sumNN {
69 
                z := nat(nil).set(a.z)
70 
                if z.cmp(a.z) != 0 {
71 
                        t.Errorf("got z = %v; want %v", z, a.z)
72 
                }
73 
        }
74 
}
75 
 
76 
func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
77 
        z := f(nil, a.x, a.y)
78 
        if z.cmp(a.z) != 0 {
79 
                t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
80 
        }
81 
}
82 
 
83 
func TestFunNN(t *testing.T) {
84 
        for _, a := range sumNN {
85 
                arg := a
86 
                testFunNN(t, "add", nat.add, arg)
87 
 
88 
                arg = argNN{a.z, a.y, a.x}
89 
                testFunNN(t, "add symmetric", nat.add, arg)
90 
 
91 
                arg = argNN{a.x, a.z, a.y}
92 
                testFunNN(t, "sub", nat.sub, arg)
93 
 
94 
                arg = argNN{a.y, a.z, a.x}
95 
                testFunNN(t, "sub symmetric", nat.sub, arg)
96 
        }
97 
 
98 
        for _, a := range prodNN {
99 
                arg := a
100 
                testFunNN(t, "mul", nat.mul, arg)
101 
 
102 
                arg = argNN{a.z, a.y, a.x}
103 
                testFunNN(t, "mul symmetric", nat.mul, arg)
104 
        }
105 
}
106 
 
107 
var mulRangesN = []struct {
108 
        a, b uint64
109 
        prod string
110 
}{
111 
        {0, 0, "0"},
112 
        {1, 1, "1"},
113 
        {1, 2, "2"},
114 
        {1, 3, "6"},
115 
        {10, 10, "10"},
116 
        {0, 100, "0"},
117 
        {0, 1e9, "0"},
118 
        {1, 0, "1"},                    // empty range
119 
        {100, 1, "1"},                  // empty range
120 
        {1, 10, "3628800"},             // 10!
121 
        {1, 20, "2432902008176640000"}, // 20!
122 
        {1, 100,
123 
                "933262154439441526816992388562667004907159682643816214685929" +
124 
                        "638952175999932299156089414639761565182862536979208272237582" +
125 
                        "51185210916864000000000000000000000000", // 100!
126 
        },
127 
}
128 
 
129 
func TestMulRangeN(t *testing.T) {
130 
        for i, r := range mulRangesN {
131 
                prod := nat(nil).mulRange(r.a, r.b).decimalString()
132 
                if prod != r.prod {
133 
                        t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
134 
                }
135 
        }
136 
}
137 
 
138 
var mulArg, mulTmp nat
139 
 
140 
func init() {
141 
        const n = 1000
142 
        mulArg = make(nat, n)
143 
        for i := 0; i < n; i++ {
144 
                mulArg[i] = _M
145 
        }
146 
}
147 
 
148 
func benchmarkMulLoad() {
149 
        for j := 1; j <= 10; j++ {
150 
                x := mulArg[0 : j*100]
151 
                mulTmp.mul(x, x)
152 
        }
153 
}
154 
 
155 
func BenchmarkMul(b *testing.B) {
156 
        for i := 0; i < b.N; i++ {
157 
                benchmarkMulLoad()
158 
        }
159 
}
160 
 
161 
func toString(x nat, charset string) string {
162 
        base := len(charset)
163 
 
164 
        // special cases
165 
        switch {
166 
        case base < 2:
167 
                panic("illegal base")
168 
        case len(x) == 0:
169 
                return string(charset[0])
170 
        }
171 
 
172 
        // allocate buffer for conversion
173 
        i := x.bitLen()/log2(Word(base)) + 1 // +1: round up
174 
        s := make([]byte, i)
175 
 
176 
        // don't destroy x
177 
        q := nat(nil).set(x)
178 
 
179 
        // convert
180 
        for len(q) > 0 {
181 
                i--
182 
                var r Word
183 
                q, r = q.divW(q, Word(base))
184 
                s[i] = charset[r]
185 
        }
186 
 
187 
        return string(s[i:])
188 
}
189 
 
190 
var strTests = []struct {
191 
        x nat    // nat value to be converted
192 
        c string // conversion charset
193 
        s string // expected result
194 
}{
195 
        {nil, "01", "0"},
196 
        {nat{1}, "01", "1"},
197 
        {nat{0xc5}, "01", "11000101"},
198 
        {nat{03271}, lowercaseDigits[0:8], "3271"},
199 
        {nat{10}, lowercaseDigits[0:10], "10"},
200 
        {nat{1234567890}, uppercaseDigits[0:10], "1234567890"},
201 
        {nat{0xdeadbeef}, lowercaseDigits[0:16], "deadbeef"},
202 
        {nat{0xdeadbeef}, uppercaseDigits[0:16], "DEADBEEF"},
203 
        {nat{0x229be7}, lowercaseDigits[0:17], "1a2b3c"},
204 
        {nat{0x309663e6}, uppercaseDigits[0:32], "O9COV6"},
205 
}
206 
 
207 
func TestString(t *testing.T) {
208 
        for _, a := range strTests {
209 
                s := a.x.string(a.c)
210 
                if s != a.s {
211 
                        t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
212 
                }
213 
 
214 
                x, b, err := nat(nil).scan(strings.NewReader(a.s), len(a.c))
215 
                if x.cmp(a.x) != 0 {
216 
                        t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
217 
                }
218 
                if b != len(a.c) {
219 
                        t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, len(a.c))
220 
                }
221 
                if err != nil {
222 
                        t.Errorf("scan%+v\n\tgot error = %s", a, err)
223 
                }
224 
        }
225 
}
226 
 
227 
var natScanTests = []struct {
228 
        s    string // string to be scanned
229 
        base int    // input base
230 
        x    nat    // expected nat
231 
        b    int    // expected base
232 
        ok   bool   // expected success
233 
        next rune   // next character (or 0, if at EOF)
234 
}{
235 
        // error: illegal base
236 
        {base: -1},
237 
        {base: 1},
238 
        {base: 37},
239 
 
240 
        // error: no mantissa
241 
        {},
242 
        {s: "?"},
243 
        {base: 10},
244 
        {base: 36},
245 
        {s: "?", base: 10},
246 
        {s: "0x"},
247 
        {s: "345", base: 2},
248 
 
249 
        // no errors
250 
        {"0", 0, nil, 10, true, 0},
251 
        {"0", 10, nil, 10, true, 0},
252 
        {"0", 36, nil, 36, true, 0},
253 
        {"1", 0, nat{1}, 10, true, 0},
254 
        {"1", 10, nat{1}, 10, true, 0},
255 
        {"0 ", 0, nil, 10, true, ' '},
256 
        {"08", 0, nil, 10, true, '8'},
257 
        {"018", 0, nat{1}, 8, true, '8'},
258 
        {"0b1", 0, nat{1}, 2, true, 0},
259 
        {"0b11000101", 0, nat{0xc5}, 2, true, 0},
260 
        {"03271", 0, nat{03271}, 8, true, 0},
261 
        {"10ab", 0, nat{10}, 10, true, 'a'},
262 
        {"1234567890", 0, nat{1234567890}, 10, true, 0},
263 
        {"xyz", 36, nat{(33*36+34)*36 + 35}, 36, true, 0},
264 
        {"xyz?", 36, nat{(33*36+34)*36 + 35}, 36, true, '?'},
265 
        {"0x", 16, nil, 16, true, 'x'},
266 
        {"0xdeadbeef", 0, nat{0xdeadbeef}, 16, true, 0},
267 
        {"0XDEADBEEF", 0, nat{0xdeadbeef}, 16, true, 0},
268 
}
269 
 
270 
func TestScanBase(t *testing.T) {
271 
        for _, a := range natScanTests {
272 
                r := strings.NewReader(a.s)
273 
                x, b, err := nat(nil).scan(r, a.base)
274 
                if err == nil && !a.ok {
275 
                        t.Errorf("scan%+v\n\texpected error", a)
276 
                }
277 
                if err != nil {
278 
                        if a.ok {
279 
                                t.Errorf("scan%+v\n\tgot error = %s", a, err)
280 
                        }
281 
                        continue
282 
                }
283 
                if x.cmp(a.x) != 0 {
284 
                        t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
285 
                }
286 
                if b != a.b {
287 
                        t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.base)
288 
                }
289 
                next, _, err := r.ReadRune()
290 
                if err == io.EOF {
291 
                        next = 0
292 
                        err = nil
293 
                }
294 
                if err == nil && next != a.next {
295 
                        t.Errorf("scan%+v\n\tgot next = %q; want %q", a, next, a.next)
296 
                }
297 
        }
298 
}
299 
 
300 
var pi = "3" +
301 
        "14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651" +
302 
        "32823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461" +
303 
        "28475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920" +
304 
        "96282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179" +
305 
        "31051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798" +
306 
        "60943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901" +
307 
        "22495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837" +
308 
        "29780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083" +
309 
        "81420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909" +
310 
        "21642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
311 
        "55748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035" +
312 
        "63707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104" +
313 
        "75216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992" +
314 
        "45863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818" +
315 
        "34797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548" +
316 
        "16136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179" +
317 
        "04946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886" +
318 
        "26945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645" +
319 
        "99581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745" +
320 
        "53050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
321 
        "68683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244" +
322 
        "13654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767" +
323 
        "88952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288" +
324 
        "79710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821" +
325 
        "68299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610" +
326 
        "21359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435" +
327 
        "06430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675" +
328 
        "14269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672" +
329 
        "21825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539" +
330 
        "05796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007" +
331 
        "23055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816" +
332 
        "90915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398" +
333 
        "31501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064" +
334 
        "20467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325" +
335 
        "97463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100" +
336 
        "44929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915" +
337 
        "44110104468232527162010526522721116603966655730925471105578537634668206531098965269186205647693125705863566201" +
338 
        "85581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318" +
339 
        "58676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797" +
340 
        "27082668306343285878569830523580893306575740679545716377525420211495576158140025012622859413021647155097925923" +
341 
        "09907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111" +
342 
        "79042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043" +
343 
        "06332175182979866223717215916077166925474873898665494945011465406284336639379003976926567214638530673609657120" +
344 
        "91807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862" +
345 
        "94726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939" +
346 
        "78054193414473774418426312986080998886874132604721569516239658645730216315981931951673538129741677294786724229" +
347 
        "24654366800980676928238280689964004824354037014163149658979409243237896907069779422362508221688957383798623001" +
348 
        "59377647165122893578601588161755782973523344604281512627203734314653197777416031990665541876397929334419521541" +
349 
        "34189948544473456738316249934191318148092777710386387734317720754565453220777092120190516609628049092636019759" +
350 
        "88281613323166636528619326686336062735676303544776280350450777235547105859548702790814356240145171806246436267" +
351 
        "94561275318134078330336254232783944975382437205835311477119926063813346776879695970309833913077109870408591337"
352 
 
353 
// Test case for BenchmarkScanPi.
354 
func TestScanPi(t *testing.T) {
355 
        var x nat
356 
        z, _, err := x.scan(strings.NewReader(pi), 10)
357 
        if err != nil {
358 
                t.Errorf("scanning pi: %s", err)
359 
        }
360 
        if s := z.decimalString(); s != pi {
361 
                t.Errorf("scanning pi: got %s", s)
362 
        }
363 
}
364 
 
365 
func BenchmarkScanPi(b *testing.B) {
366 
        for i := 0; i < b.N; i++ {
367 
                var x nat
368 
                x.scan(strings.NewReader(pi), 10)
369 
        }
370 
}
371 
 
372 
func BenchmarkScan10Base2(b *testing.B)     { ScanHelper(b, 2, 10, 10) }
373 
func BenchmarkScan100Base2(b *testing.B)    { ScanHelper(b, 2, 10, 100) }
374 
func BenchmarkScan1000Base2(b *testing.B)   { ScanHelper(b, 2, 10, 1000) }
375 
func BenchmarkScan10000Base2(b *testing.B)  { ScanHelper(b, 2, 10, 10000) }
376 
func BenchmarkScan100000Base2(b *testing.B) { ScanHelper(b, 2, 10, 100000) }
377 
 
378 
func BenchmarkScan10Base8(b *testing.B)     { ScanHelper(b, 8, 10, 10) }
379 
func BenchmarkScan100Base8(b *testing.B)    { ScanHelper(b, 8, 10, 100) }
380 
func BenchmarkScan1000Base8(b *testing.B)   { ScanHelper(b, 8, 10, 1000) }
381 
func BenchmarkScan10000Base8(b *testing.B)  { ScanHelper(b, 8, 10, 10000) }
382 
func BenchmarkScan100000Base8(b *testing.B) { ScanHelper(b, 8, 10, 100000) }
383 
 
384 
func BenchmarkScan10Base10(b *testing.B)     { ScanHelper(b, 10, 10, 10) }
385 
func BenchmarkScan100Base10(b *testing.B)    { ScanHelper(b, 10, 10, 100) }
386 
func BenchmarkScan1000Base10(b *testing.B)   { ScanHelper(b, 10, 10, 1000) }
387 
func BenchmarkScan10000Base10(b *testing.B)  { ScanHelper(b, 10, 10, 10000) }
388 
func BenchmarkScan100000Base10(b *testing.B) { ScanHelper(b, 10, 10, 100000) }
389 
 
390 
func BenchmarkScan10Base16(b *testing.B)     { ScanHelper(b, 16, 10, 10) }
391 
func BenchmarkScan100Base16(b *testing.B)    { ScanHelper(b, 16, 10, 100) }
392 
func BenchmarkScan1000Base16(b *testing.B)   { ScanHelper(b, 16, 10, 1000) }
393 
func BenchmarkScan10000Base16(b *testing.B)  { ScanHelper(b, 16, 10, 10000) }
394 
func BenchmarkScan100000Base16(b *testing.B) { ScanHelper(b, 16, 10, 100000) }
395 
 
396 
func ScanHelper(b *testing.B, base int, x, y Word) {
397 
        b.StopTimer()
398 
        var z nat
399 
        z = z.expWW(x, y)
400 
 
401 
        var s string
402 
        s = z.string(lowercaseDigits[0:base])
403 
        if t := toString(z, lowercaseDigits[0:base]); t != s {
404 
                b.Fatalf("scanning: got %s; want %s", s, t)
405 
        }
406 
        b.StartTimer()
407 
 
408 
        for i := 0; i < b.N; i++ {
409 
                z.scan(strings.NewReader(s), base)
410 
        }
411 
}
412 
 
413 
func BenchmarkString10Base2(b *testing.B)     { StringHelper(b, 2, 10, 10) }
414 
func BenchmarkString100Base2(b *testing.B)    { StringHelper(b, 2, 10, 100) }
415 
func BenchmarkString1000Base2(b *testing.B)   { StringHelper(b, 2, 10, 1000) }
416 
func BenchmarkString10000Base2(b *testing.B)  { StringHelper(b, 2, 10, 10000) }
417 
func BenchmarkString100000Base2(b *testing.B) { StringHelper(b, 2, 10, 100000) }
418 
 
419 
func BenchmarkString10Base8(b *testing.B)     { StringHelper(b, 8, 10, 10) }
420 
func BenchmarkString100Base8(b *testing.B)    { StringHelper(b, 8, 10, 100) }
421 
func BenchmarkString1000Base8(b *testing.B)   { StringHelper(b, 8, 10, 1000) }
422 
func BenchmarkString10000Base8(b *testing.B)  { StringHelper(b, 8, 10, 10000) }
423 
func BenchmarkString100000Base8(b *testing.B) { StringHelper(b, 8, 10, 100000) }
424 
 
425 
func BenchmarkString10Base10(b *testing.B)     { StringHelper(b, 10, 10, 10) }
426 
func BenchmarkString100Base10(b *testing.B)    { StringHelper(b, 10, 10, 100) }
427 
func BenchmarkString1000Base10(b *testing.B)   { StringHelper(b, 10, 10, 1000) }
428 
func BenchmarkString10000Base10(b *testing.B)  { StringHelper(b, 10, 10, 10000) }
429 
func BenchmarkString100000Base10(b *testing.B) { StringHelper(b, 10, 10, 100000) }
430 
 
431 
func BenchmarkString10Base16(b *testing.B)     { StringHelper(b, 16, 10, 10) }
432 
func BenchmarkString100Base16(b *testing.B)    { StringHelper(b, 16, 10, 100) }
433 
func BenchmarkString1000Base16(b *testing.B)   { StringHelper(b, 16, 10, 1000) }
434 
func BenchmarkString10000Base16(b *testing.B)  { StringHelper(b, 16, 10, 10000) }
435 
func BenchmarkString100000Base16(b *testing.B) { StringHelper(b, 16, 10, 100000) }
436 
 
437 
func StringHelper(b *testing.B, base int, x, y Word) {
438 
        b.StopTimer()
439 
        var z nat
440 
        z = z.expWW(x, y)
441 
        z.string(lowercaseDigits[0:base]) // warm divisor cache
442 
        b.StartTimer()
443 
 
444 
        for i := 0; i < b.N; i++ {
445 
                _ = z.string(lowercaseDigits[0:base])
446 
        }
447 
}
448 
 
449 
func BenchmarkLeafSize0(b *testing.B)  { LeafSizeHelper(b, 10, 0) } // test without splitting
450 
func BenchmarkLeafSize1(b *testing.B)  { LeafSizeHelper(b, 10, 1) }
451 
func BenchmarkLeafSize2(b *testing.B)  { LeafSizeHelper(b, 10, 2) }
452 
func BenchmarkLeafSize3(b *testing.B)  { LeafSizeHelper(b, 10, 3) }
453 
func BenchmarkLeafSize4(b *testing.B)  { LeafSizeHelper(b, 10, 4) }
454 
func BenchmarkLeafSize5(b *testing.B)  { LeafSizeHelper(b, 10, 5) }
455 
func BenchmarkLeafSize6(b *testing.B)  { LeafSizeHelper(b, 10, 6) }
456 
func BenchmarkLeafSize7(b *testing.B)  { LeafSizeHelper(b, 10, 7) }
457 
func BenchmarkLeafSize8(b *testing.B)  { LeafSizeHelper(b, 10, 8) }
458 
func BenchmarkLeafSize9(b *testing.B)  { LeafSizeHelper(b, 10, 9) }
459 
func BenchmarkLeafSize10(b *testing.B) { LeafSizeHelper(b, 10, 10) }
460 
func BenchmarkLeafSize11(b *testing.B) { LeafSizeHelper(b, 10, 11) }
461 
func BenchmarkLeafSize12(b *testing.B) { LeafSizeHelper(b, 10, 12) }
462 
func BenchmarkLeafSize13(b *testing.B) { LeafSizeHelper(b, 10, 13) }
463 
func BenchmarkLeafSize14(b *testing.B) { LeafSizeHelper(b, 10, 14) }
464 
func BenchmarkLeafSize15(b *testing.B) { LeafSizeHelper(b, 10, 15) }
465 
func BenchmarkLeafSize16(b *testing.B) { LeafSizeHelper(b, 10, 16) }
466 
func BenchmarkLeafSize32(b *testing.B) { LeafSizeHelper(b, 10, 32) } // try some large lengths
467 
func BenchmarkLeafSize64(b *testing.B) { LeafSizeHelper(b, 10, 64) }
468 
 
469 
func LeafSizeHelper(b *testing.B, base Word, size int) {
470 
        b.StopTimer()
471 
        originalLeafSize := leafSize
472 
        resetTable(cacheBase10[:])
473 
        leafSize = size
474 
        b.StartTimer()
475 
 
476 
        for d := 1; d <= 10000; d *= 10 {
477 
                b.StopTimer()
478 
                var z nat
479 
                z = z.expWW(base, Word(d))            // build target number
480 
                _ = z.string(lowercaseDigits[0:base]) // warm divisor cache
481 
                b.StartTimer()
482 
 
483 
                for i := 0; i < b.N; i++ {
484 
                        _ = z.string(lowercaseDigits[0:base])
485 
                }
486 
        }
487 
 
488 
        b.StopTimer()
489 
        resetTable(cacheBase10[:])
490 
        leafSize = originalLeafSize
491 
        b.StartTimer()
492 
}
493 
 
494 
func resetTable(table []divisor) {
495 
        if table != nil && table[0].bbb != nil {
496 
                for i := 0; i < len(table); i++ {
497 
                        table[i].bbb = nil
498 
                        table[i].nbits = 0
499 
                        table[i].ndigits = 0
500 
                }
501 
        }
502 
}
503 
 
504 
func TestStringPowers(t *testing.T) {
505 
        var b, p Word
506 
        for b = 2; b <= 16; b++ {
507 
                for p = 0; p <= 512; p++ {
508 
                        x := nat(nil).expWW(b, p)
509 
                        xs := x.string(lowercaseDigits[0:b])
510 
                        xs2 := toString(x, lowercaseDigits[0:b])
511 
                        if xs != xs2 {
512 
                                t.Errorf("failed at %d ** %d in base %d: %s != %s", b, p, b, xs, xs2)
513 
                        }
514 
                }
515 
        }
516 
}
517 
 
518 
func TestLeadingZeros(t *testing.T) {
519 
        var x Word = _B >> 1
520 
        for i := 0; i <= _W; i++ {
521 
                if int(leadingZeros(x)) != i {
522 
                        t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
523 
                }
524 
                x >>= 1
525 
        }
526 
}
527 
 
528 
type shiftTest struct {
529 
        in    nat
530 
        shift uint
531 
        out   nat
532 
}
533 
 
534 
var leftShiftTests = []shiftTest{
535 
        {nil, 0, nil},
536 
        {nil, 1, nil},
537 
        {natOne, 0, natOne},
538 
        {natOne, 1, natTwo},
539 
        {nat{1 << (_W - 1)}, 1, nat{0}},
540 
        {nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
541 
}
542 
 
543 
func TestShiftLeft(t *testing.T) {
544 
        for i, test := range leftShiftTests {
545 
                var z nat
546 
                z = z.shl(test.in, test.shift)
547 
                for j, d := range test.out {
548 
                        if j >= len(z) || z[j] != d {
549 
                                t.Errorf("#%d: got: %v want: %v", i, z, test.out)
550 
                                break
551 
                        }
552 
                }
553 
        }
554 
}
555 
 
556 
var rightShiftTests = []shiftTest{
557 
        {nil, 0, nil},
558 
        {nil, 1, nil},
559 
        {natOne, 0, natOne},
560 
        {natOne, 1, nil},
561 
        {natTwo, 1, natOne},
562 
        {nat{0, 1}, 1, nat{1 << (_W - 1)}},
563 
        {nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
564 
}
565 
 
566 
func TestShiftRight(t *testing.T) {
567 
        for i, test := range rightShiftTests {
568 
                var z nat
569 
                z = z.shr(test.in, test.shift)
570 
                for j, d := range test.out {
571 
                        if j >= len(z) || z[j] != d {
572 
                                t.Errorf("#%d: got: %v want: %v", i, z, test.out)
573 
                                break
574 
                        }
575 
                }
576 
        }
577 
}
578 
 
579 
type modWTest struct {
580 
        in       string
581 
        dividend string
582 
        out      string
583 
}
584 
 
585 
var modWTests32 = []modWTest{
586 
        {"23492635982634928349238759823742", "252341", "220170"},
587 
}
588 
 
589 
var modWTests64 = []modWTest{
590 
        {"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
591 
}
592 
 
593 
func runModWTests(t *testing.T, tests []modWTest) {
594 
        for i, test := range tests {
595 
                in, _ := new(Int).SetString(test.in, 10)
596 
                d, _ := new(Int).SetString(test.dividend, 10)
597 
                out, _ := new(Int).SetString(test.out, 10)
598 
 
599 
                r := in.abs.modW(d.abs[0])
600 
                if r != out.abs[0] {
601 
                        t.Errorf("#%d failed: got %s want %s", i, r, out)
602 
                }
603 
        }
604 
}
605 
 
606 
func TestModW(t *testing.T) {
607 
        if _W >= 32 {
608 
                runModWTests(t, modWTests32)
609 
        }
610 
        if _W >= 64 {
611 
                runModWTests(t, modWTests64)
612 
        }
613 
}
614 
 
615 
func TestTrailingZeroBits(t *testing.T) {
616 
        var x Word
617 
        x--
618 
        for i := 0; i < _W; i++ {
619 
                if trailingZeroBits(x) != i {
620 
                        t.Errorf("Failed at step %d: x: %x got: %d", i, x, trailingZeroBits(x))
621 
                }
622 
                x <<= 1
623 
        }
624 
}
625 
 
626 
var expNNTests = []struct {
627 
        x, y, m string
628 
        out     string
629 
}{
630 
        {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
631 
        {"0x8000000000000000", "2", "6719", "4944"},
632 
        {"0x8000000000000000", "3", "6719", "5447"},
633 
        {"0x8000000000000000", "1000", "6719", "1603"},
634 
        {"0x8000000000000000", "1000000", "6719", "3199"},
635 
        {
636 
                "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
637 
                "298472983472983471903246121093472394872319615612417471234712061",
638 
                "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
639 
                "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
640 
        },
641 
}
642 
 
643 
func TestExpNN(t *testing.T) {
644 
        for i, test := range expNNTests {
645 
                x, _, _ := nat(nil).scan(strings.NewReader(test.x), 0)
646 
                y, _, _ := nat(nil).scan(strings.NewReader(test.y), 0)
647 
                out, _, _ := nat(nil).scan(strings.NewReader(test.out), 0)
648 
 
649 
                var m nat
650 
 
651 
                if len(test.m) > 0 {
652 
                        m, _, _ = nat(nil).scan(strings.NewReader(test.m), 0)
653 
                }
654 
 
655 
                z := nat(nil).expNN(x, y, m)
656 
                if z.cmp(out) != 0 {
657 
                        t.Errorf("#%d got %v want %v", i, z, out)
658 
                }
659 
        }
660 
}

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