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. 4 5package big 6 7import ( 8 "math/rand" 9 "testing" 10) 11 12type funWW func(x, y, c Word) (z1, z0 Word) 13type argWW struct { 14 x, y, c, z1, z0 Word 15} 16 17var sumWW = []argWW{ 18 {0, 0, 0, 0, 0}, 19 {0, 1, 0, 0, 1}, 20 {0, 0, 1, 0, 1}, 21 {0, 1, 1, 0, 2}, 22 {12345, 67890, 0, 0, 80235}, 23 {12345, 67890, 1, 0, 80236}, 24 {_M, 1, 0, 1, 0}, 25 {_M, 0, 1, 1, 0}, 26 {_M, 1, 1, 1, 1}, 27 {_M, _M, 0, 1, _M - 1}, 28 {_M, _M, 1, 1, _M}, 29} 30 31func testFunWW(t *testing.T, msg string, f funWW, a argWW) { 32 z1, z0 := f(a.x, a.y, a.c) 33 if z1 != a.z1 || z0 != a.z0 { 34 t.Errorf("%s%+v\n\tgot z1:z0 = %#x:%#x; want %#x:%#x", msg, a, z1, z0, a.z1, a.z0) 35 } 36} 37 38func TestFunWW(t *testing.T) { 39 for _, a := range sumWW { 40 arg := a 41 testFunWW(t, "addWW_g", addWW_g, arg) 42 43 arg = argWW{a.y, a.x, a.c, a.z1, a.z0} 44 testFunWW(t, "addWW_g symmetric", addWW_g, arg) 45 46 arg = argWW{a.z0, a.x, a.c, a.z1, a.y} 47 testFunWW(t, "subWW_g", subWW_g, arg) 48 49 arg = argWW{a.z0, a.y, a.c, a.z1, a.x} 50 testFunWW(t, "subWW_g symmetric", subWW_g, arg) 51 } 52} 53 54type funVV func(z, x, y []Word) (c Word) 55type argVV struct { 56 z, x, y nat 57 c Word 58} 59 60var sumVV = []argVV{ 61 {}, 62 {nat{0}, nat{0}, nat{0}, 0}, 63 {nat{1}, nat{1}, nat{0}, 0}, 64 {nat{0}, nat{_M}, nat{1}, 1}, 65 {nat{80235}, nat{12345}, nat{67890}, 0}, 66 {nat{_M - 1}, nat{_M}, nat{_M}, 1}, 67 {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, nat{1, 0, 0, 0}, 1}, 68 {nat{0, 0, 0, _M}, nat{_M, _M, _M, _M - 1}, nat{1, 0, 0, 0}, 0}, 69 {nat{0, 0, 0, 0}, nat{_M, 0, _M, 0}, nat{1, _M, 0, _M}, 1}, 70} 71 72func testFunVV(t *testing.T, msg string, f funVV, a argVV) { 73 z := make(nat, len(a.z)) 74 c := f(z, a.x, a.y) 75 for i, zi := range z { 76 if zi != a.z[i] { 77 t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i]) 78 break 79 } 80 } 81 if c != a.c { 82 t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c) 83 } 84} 85 86func TestFunVV(t *testing.T) { 87 for _, a := range sumVV { 88 arg := a 89 testFunVV(t, "addVV_g", addVV_g, arg) 90 testFunVV(t, "addVV", addVV, arg) 91 92 arg = argVV{a.z, a.y, a.x, a.c} 93 testFunVV(t, "addVV_g symmetric", addVV_g, arg) 94 testFunVV(t, "addVV symmetric", addVV, arg) 95 96 arg = argVV{a.x, a.z, a.y, a.c} 97 testFunVV(t, "subVV_g", subVV_g, arg) 98 testFunVV(t, "subVV", subVV, arg) 99 100 arg = argVV{a.y, a.z, a.x, a.c} 101 testFunVV(t, "subVV_g symmetric", subVV_g, arg) 102 testFunVV(t, "subVV symmetric", subVV, arg) 103 } 104} 105 106// Always the same seed for reproducible results. 107var rnd = rand.New(rand.NewSource(0)) 108 109func rndW() Word { 110 return Word(rnd.Int63()<<1 | rnd.Int63n(2)) 111} 112 113func rndV(n int) []Word { 114 v := make([]Word, n) 115 for i := range v { 116 v[i] = rndW() 117 } 118 return v 119} 120 121func benchmarkFunVV(b *testing.B, f funVV, n int) { 122 x := rndV(n) 123 y := rndV(n) 124 z := make([]Word, n) 125 b.SetBytes(int64(n * _W)) 126 b.ResetTimer() 127 for i := 0; i < b.N; i++ { 128 f(z, x, y) 129 } 130} 131 132func BenchmarkAddVV_1(b *testing.B) { benchmarkFunVV(b, addVV, 1) } 133func BenchmarkAddVV_2(b *testing.B) { benchmarkFunVV(b, addVV, 2) } 134func BenchmarkAddVV_3(b *testing.B) { benchmarkFunVV(b, addVV, 3) } 135func BenchmarkAddVV_4(b *testing.B) { benchmarkFunVV(b, addVV, 4) } 136func BenchmarkAddVV_5(b *testing.B) { benchmarkFunVV(b, addVV, 5) } 137func BenchmarkAddVV_1e1(b *testing.B) { benchmarkFunVV(b, addVV, 1e1) } 138func BenchmarkAddVV_1e2(b *testing.B) { benchmarkFunVV(b, addVV, 1e2) } 139func BenchmarkAddVV_1e3(b *testing.B) { benchmarkFunVV(b, addVV, 1e3) } 140func BenchmarkAddVV_1e4(b *testing.B) { benchmarkFunVV(b, addVV, 1e4) } 141func BenchmarkAddVV_1e5(b *testing.B) { benchmarkFunVV(b, addVV, 1e5) } 142 143type funVW func(z, x []Word, y Word) (c Word) 144type argVW struct { 145 z, x nat 146 y Word 147 c Word 148} 149 150var sumVW = []argVW{ 151 {}, 152 {nil, nil, 2, 2}, 153 {nat{0}, nat{0}, 0, 0}, 154 {nat{1}, nat{0}, 1, 0}, 155 {nat{1}, nat{1}, 0, 0}, 156 {nat{0}, nat{_M}, 1, 1}, 157 {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, 1, 1}, 158} 159 160var prodVW = []argVW{ 161 {}, 162 {nat{0}, nat{0}, 0, 0}, 163 {nat{0}, nat{_M}, 0, 0}, 164 {nat{0}, nat{0}, _M, 0}, 165 {nat{1}, nat{1}, 1, 0}, 166 {nat{22793}, nat{991}, 23, 0}, 167 {nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0}, 168 {nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0}, 169 {nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0}, 170 {nat{_M << 1 & _M}, nat{_M}, 1 << 1, _M >> (_W - 1)}, 171 {nat{_M << 7 & _M}, nat{_M}, 1 << 7, _M >> (_W - 7)}, 172 {nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, _M >> (_W - 7)}, 173} 174 175var lshVW = []argVW{ 176 {}, 177 {nat{0}, nat{0}, 0, 0}, 178 {nat{0}, nat{0}, 1, 0}, 179 {nat{0}, nat{0}, 20, 0}, 180 181 {nat{_M}, nat{_M}, 0, 0}, 182 {nat{_M << 1 & _M}, nat{_M}, 1, 1}, 183 {nat{_M << 20 & _M}, nat{_M}, 20, _M >> (_W - 20)}, 184 185 {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0}, 186 {nat{_M << 1 & _M, _M, _M}, nat{_M, _M, _M}, 1, 1}, 187 {nat{_M << 20 & _M, _M, _M}, nat{_M, _M, _M}, 20, _M >> (_W - 20)}, 188} 189 190var rshVW = []argVW{ 191 {}, 192 {nat{0}, nat{0}, 0, 0}, 193 {nat{0}, nat{0}, 1, 0}, 194 {nat{0}, nat{0}, 20, 0}, 195 196 {nat{_M}, nat{_M}, 0, 0}, 197 {nat{_M >> 1}, nat{_M}, 1, _M << (_W - 1) & _M}, 198 {nat{_M >> 20}, nat{_M}, 20, _M << (_W - 20) & _M}, 199 200 {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0}, 201 {nat{_M, _M, _M >> 1}, nat{_M, _M, _M}, 1, _M << (_W - 1) & _M}, 202 {nat{_M, _M, _M >> 20}, nat{_M, _M, _M}, 20, _M << (_W - 20) & _M}, 203} 204 205func testFunVW(t *testing.T, msg string, f funVW, a argVW) { 206 z := make(nat, len(a.z)) 207 c := f(z, a.x, a.y) 208 for i, zi := range z { 209 if zi != a.z[i] { 210 t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i]) 211 break 212 } 213 } 214 if c != a.c { 215 t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c) 216 } 217} 218 219func makeFunVW(f func(z, x []Word, s uint) (c Word)) funVW { 220 return func(z, x []Word, s Word) (c Word) { 221 return f(z, x, uint(s)) 222 } 223} 224 225func TestFunVW(t *testing.T) { 226 for _, a := range sumVW { 227 arg := a 228 testFunVW(t, "addVW_g", addVW_g, arg) 229 testFunVW(t, "addVW", addVW, arg) 230 231 arg = argVW{a.x, a.z, a.y, a.c} 232 testFunVW(t, "subVW_g", subVW_g, arg) 233 testFunVW(t, "subVW", subVW, arg) 234 } 235 236 shlVW_g := makeFunVW(shlVU_g) 237 shlVW := makeFunVW(shlVU) 238 for _, a := range lshVW { 239 arg := a 240 testFunVW(t, "shlVU_g", shlVW_g, arg) 241 testFunVW(t, "shlVU", shlVW, arg) 242 } 243 244 shrVW_g := makeFunVW(shrVU_g) 245 shrVW := makeFunVW(shrVU) 246 for _, a := range rshVW { 247 arg := a 248 testFunVW(t, "shrVU_g", shrVW_g, arg) 249 testFunVW(t, "shrVU", shrVW, arg) 250 } 251} 252 253func benchmarkFunVW(b *testing.B, f funVW, n int) { 254 x := rndV(n) 255 y := rndW() 256 z := make([]Word, n) 257 b.SetBytes(int64(n * _W)) 258 b.ResetTimer() 259 for i := 0; i < b.N; i++ { 260 f(z, x, y) 261 } 262} 263 264func BenchmarkAddVW_1(b *testing.B) { benchmarkFunVW(b, addVW, 1) } 265func BenchmarkAddVW_2(b *testing.B) { benchmarkFunVW(b, addVW, 2) } 266func BenchmarkAddVW_3(b *testing.B) { benchmarkFunVW(b, addVW, 3) } 267func BenchmarkAddVW_4(b *testing.B) { benchmarkFunVW(b, addVW, 4) } 268func BenchmarkAddVW_5(b *testing.B) { benchmarkFunVW(b, addVW, 5) } 269func BenchmarkAddVW_1e1(b *testing.B) { benchmarkFunVW(b, addVW, 1e1) } 270func BenchmarkAddVW_1e2(b *testing.B) { benchmarkFunVW(b, addVW, 1e2) } 271func BenchmarkAddVW_1e3(b *testing.B) { benchmarkFunVW(b, addVW, 1e3) } 272func BenchmarkAddVW_1e4(b *testing.B) { benchmarkFunVW(b, addVW, 1e4) } 273func BenchmarkAddVW_1e5(b *testing.B) { benchmarkFunVW(b, addVW, 1e5) } 274 275type funVWW func(z, x []Word, y, r Word) (c Word) 276type argVWW struct { 277 z, x nat 278 y, r Word 279 c Word 280} 281 282var prodVWW = []argVWW{ 283 {}, 284 {nat{0}, nat{0}, 0, 0, 0}, 285 {nat{991}, nat{0}, 0, 991, 0}, 286 {nat{0}, nat{_M}, 0, 0, 0}, 287 {nat{991}, nat{_M}, 0, 991, 0}, 288 {nat{0}, nat{0}, _M, 0, 0}, 289 {nat{991}, nat{0}, _M, 991, 0}, 290 {nat{1}, nat{1}, 1, 0, 0}, 291 {nat{992}, nat{1}, 1, 991, 0}, 292 {nat{22793}, nat{991}, 23, 0, 0}, 293 {nat{22800}, nat{991}, 23, 7, 0}, 294 {nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0, 0}, 295 {nat{7, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 7, 0}, 296 {nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0, 0}, 297 {nat{991, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 991, 0}, 298 {nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0, 0}, 299 {nat{991, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 991, 0}, 300 {nat{_M << 1 & _M}, nat{_M}, 1 << 1, 0, _M >> (_W - 1)}, 301 {nat{_M<<1&_M + 1}, nat{_M}, 1 << 1, 1, _M >> (_W - 1)}, 302 {nat{_M << 7 & _M}, nat{_M}, 1 << 7, 0, _M >> (_W - 7)}, 303 {nat{_M<<7&_M + 1<<6}, nat{_M}, 1 << 7, 1 << 6, _M >> (_W - 7)}, 304 {nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 0, _M >> (_W - 7)}, 305 {nat{_M<<7&_M + 1<<6, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 1 << 6, _M >> (_W - 7)}, 306} 307 308func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) { 309 z := make(nat, len(a.z)) 310 c := f(z, a.x, a.y, a.r) 311 for i, zi := range z { 312 if zi != a.z[i] { 313 t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i]) 314 break 315 } 316 } 317 if c != a.c { 318 t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c) 319 } 320} 321 322// TODO(gri) mulAddVWW and divWVW are symmetric operations but 323// their signature is not symmetric. Try to unify. 324 325type funWVW func(z []Word, xn Word, x []Word, y Word) (r Word) 326type argWVW struct { 327 z nat 328 xn Word 329 x nat 330 y Word 331 r Word 332} 333 334func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) { 335 z := make(nat, len(a.z)) 336 r := f(z, a.xn, a.x, a.y) 337 for i, zi := range z { 338 if zi != a.z[i] { 339 t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i]) 340 break 341 } 342 } 343 if r != a.r { 344 t.Errorf("%s%+v\n\tgot r = %#x; want %#x", msg, a, r, a.r) 345 } 346} 347 348func TestFunVWW(t *testing.T) { 349 for _, a := range prodVWW { 350 arg := a 351 testFunVWW(t, "mulAddVWW_g", mulAddVWW_g, arg) 352 testFunVWW(t, "mulAddVWW", mulAddVWW, arg) 353 354 if a.y != 0 && a.r < a.y { 355 arg := argWVW{a.x, a.c, a.z, a.y, a.r} 356 testFunWVW(t, "divWVW_g", divWVW_g, arg) 357 testFunWVW(t, "divWVW", divWVW, arg) 358 } 359 } 360} 361 362var mulWWTests = []struct { 363 x, y Word 364 q, r Word 365}{ 366 {_M, _M, _M - 1, 1}, 367 // 32 bit only: {0xc47dfa8c, 50911, 0x98a4, 0x998587f4}, 368} 369 370func TestMulWW(t *testing.T) { 371 for i, test := range mulWWTests { 372 q, r := mulWW_g(test.x, test.y) 373 if q != test.q || r != test.r { 374 t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r) 375 } 376 } 377} 378 379var mulAddWWWTests = []struct { 380 x, y, c Word 381 q, r Word 382}{ 383 // TODO(agl): These will only work on 64-bit platforms. 384 // {15064310297182388543, 0xe7df04d2d35d5d80, 13537600649892366549, 13644450054494335067, 10832252001440893781}, 385 // {15064310297182388543, 0xdab2f18048baa68d, 13644450054494335067, 12869334219691522700, 14233854684711418382}, 386 {_M, _M, 0, _M - 1, 1}, 387 {_M, _M, _M, _M, 0}, 388} 389 390func TestMulAddWWW(t *testing.T) { 391 for i, test := range mulAddWWWTests { 392 q, r := mulAddWWW_g(test.x, test.y, test.c) 393 if q != test.q || r != test.r { 394 t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r) 395 } 396 } 397} 398 399func benchmarkAddMulVVW(b *testing.B, n int) { 400 x := rndV(n) 401 y := rndW() 402 z := make([]Word, n) 403 b.SetBytes(int64(n * _W)) 404 b.ResetTimer() 405 for i := 0; i < b.N; i++ { 406 addMulVVW(z, x, y) 407 } 408} 409 410func BenchmarkAddMulVVW_1(b *testing.B) { benchmarkAddMulVVW(b, 1) } 411func BenchmarkAddMulVVW_2(b *testing.B) { benchmarkAddMulVVW(b, 2) } 412func BenchmarkAddMulVVW_3(b *testing.B) { benchmarkAddMulVVW(b, 3) } 413func BenchmarkAddMulVVW_4(b *testing.B) { benchmarkAddMulVVW(b, 4) } 414func BenchmarkAddMulVVW_5(b *testing.B) { benchmarkAddMulVVW(b, 5) } 415func BenchmarkAddMulVVW_1e1(b *testing.B) { benchmarkAddMulVVW(b, 1e1) } 416func BenchmarkAddMulVVW_1e2(b *testing.B) { benchmarkAddMulVVW(b, 1e2) } 417func BenchmarkAddMulVVW_1e3(b *testing.B) { benchmarkAddMulVVW(b, 1e3) } 418func BenchmarkAddMulVVW_1e4(b *testing.B) { benchmarkAddMulVVW(b, 1e4) } 419func BenchmarkAddMulVVW_1e5(b *testing.B) { benchmarkAddMulVVW(b, 1e5) } 420 421func testWordBitLen(t *testing.T, fname string, f func(Word) int) { 422 for i := 0; i <= _W; i++ { 423 x := Word(1) << uint(i-1) // i == 0 => x == 0 424 n := f(x) 425 if n != i { 426 t.Errorf("got %d; want %d for %s(%#x)", n, i, fname, x) 427 } 428 } 429} 430 431func TestWordBitLen(t *testing.T) { 432 testWordBitLen(t, "bitLen", bitLen) 433 testWordBitLen(t, "bitLen_g", bitLen_g) 434} 435 436// runs b.N iterations of bitLen called on a Word containing (1 << nbits)-1. 437func benchmarkBitLenN(b *testing.B, nbits uint) { 438 testword := Word((uint64(1) << nbits) - 1) 439 for i := 0; i < b.N; i++ { 440 bitLen(testword) 441 } 442} 443 444// Individual bitLen tests. Numbers chosen to examine both sides 445// of powers-of-two boundaries. 446func BenchmarkBitLen0(b *testing.B) { benchmarkBitLenN(b, 0) } 447func BenchmarkBitLen1(b *testing.B) { benchmarkBitLenN(b, 1) } 448func BenchmarkBitLen2(b *testing.B) { benchmarkBitLenN(b, 2) } 449func BenchmarkBitLen3(b *testing.B) { benchmarkBitLenN(b, 3) } 450func BenchmarkBitLen4(b *testing.B) { benchmarkBitLenN(b, 4) } 451func BenchmarkBitLen5(b *testing.B) { benchmarkBitLenN(b, 5) } 452func BenchmarkBitLen8(b *testing.B) { benchmarkBitLenN(b, 8) } 453func BenchmarkBitLen9(b *testing.B) { benchmarkBitLenN(b, 9) } 454func BenchmarkBitLen16(b *testing.B) { benchmarkBitLenN(b, 16) } 455func BenchmarkBitLen17(b *testing.B) { benchmarkBitLenN(b, 17) } 456func BenchmarkBitLen31(b *testing.B) { benchmarkBitLenN(b, 31) } 457