cpython/Python/dtoa.c at main · https-github-com-nzysoft/cpython · GitHub

History

2813 lines (2544 loc) · 77.6 KB

Raw

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611

612

613

614

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

722

723

724

725

726

727

728

729

730

731

732

733

734

735

736

737

738

739

740

741

742

743

744

745

746

747

748

749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

769

770

771

772

773

774

775

776

777

778

779

780

781

782

783

784

785

786

787

788

789

790

791

792

793

794

795

796

797

798

799

800

801

802

803

804

805

806

807

808

809

810

811

812

813

814

815

816

817

818

819

820

821

822

823

824

825

826

827

828

829

830

831

832

833

834

835

836

837

838

839

840

841

842

843

844

845

846

847

848

849

850

851

852

853

854

855

856

857

858

859

860

861

862

863

864

865

866

867

868

869

870

871

872

873

874

875

876

877

878

879

880

881

882

883

884

885

886

887

888

889

890

891

892

893

894

895

896

897

898

899

900

901

902

903

904

905

906

907

908

909

910

911

912

913

914

915

916

917

918

919

920

921

922

923

924

925

926

927

928

929

930

931

932

933

934

935

936

937

938

939

940

941

942

943

944

945

946

947

948

949

950

951

952

953

954

955

956

957

958

959

960

961

962

963

964

965

966

967

968

969

970

971

972

973

974

975

976

977

978

979

980

981

982

983

984

985

986

987

988

989

990

991

992

993

994

995

996

997

998

999

1000

/****************************************************************

* The author of this software is David M. Gay.

* Permission to use, copy, modify, and distribute this software for any

* purpose without fee is hereby granted, provided that this entire notice

* is included in all copies of any software which is or includes a copy

* or modification of this software and in all copies of the supporting

* documentation for such software.

* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY

* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

***************************************************************/

/****************************************************************

* This is dtoa.c by David M. Gay, downloaded from

* http://www.netlib.org/fp/dtoa.c on April 15, 2009 and modified for

* inclusion into the Python core by Mark E. T. Dickinson and Eric V. Smith.

* Please remember to check http://www.netlib.org/fp regularly (and especially

* before any Python release) for bugfixes and updates.

* The major modifications from Gay's original code are as follows:

* 0. The original code has been specialized to Python's needs by removing

* many of the #ifdef'd sections. In particular, code to support VAX and

* IBM floating-point formats, hex NaNs, hex floats, locale-aware

* treatment of the decimal point, and setting of the inexact flag have

* been removed.

* 1. We use PyMem_Malloc and PyMem_Free in place of malloc and free.

* 2. The public functions strtod, dtoa and freedtoa all now have

* a _Py_dg_ prefix.

* 3. Instead of assuming that PyMem_Malloc always succeeds, we thread

* PyMem_Malloc failures through the code. The functions

* Balloc, multadd, s2b, i2b, mult, pow5mult, lshift, diff, d2b

* of return type *Bigint all return NULL to indicate a malloc failure.

* Similarly, rv_alloc and nrv_alloc (return type char *) return NULL on

* failure. bigcomp now has return type int (it used to be void) and

* returns -1 on failure and 0 otherwise. _Py_dg_dtoa returns NULL

* on failure. _Py_dg_strtod indicates failure due to malloc failure

* by returning -1.0, setting errno=ENOMEM and *se to s00.

* 4. The static variable dtoa_result has been removed. Callers of

* _Py_dg_dtoa are expected to call _Py_dg_freedtoa to free

* the memory allocated by _Py_dg_dtoa.

* 5. The code has been reformatted to better fit with Python's

* C style guide (PEP 7).

* 6. A bug in the memory allocation has been fixed: to avoid FREEing memory

* that hasn't been MALLOC'ed, private_mem should only be used when k <=

* Kmax.

* 7. _Py_dg_strtod has been modified so that it doesn't accept strings with

* leading whitespace.

* 8. A corner case where _Py_dg_dtoa didn't strip trailing zeros has been

* fixed. (bugs.python.org/issue40780)

***************************************************************/

/* Please send bug reports for the original dtoa.c code to David M. Gay (dmg

* at acm dot org, with " at " changed at "@" and " dot " changed to ".").

* Please report bugs for this modified version using the Python issue tracker

* (http://bugs.python.org). */

/* On a machine with IEEE extended-precision registers, it is

* necessary to specify double-precision (53-bit) rounding precision

* before invoking strtod or dtoa. If the machine uses (the equivalent

* of) Intel 80x87 arithmetic, the call

* _control87(PC_53, MCW_PC);

* does this with many compilers. Whether this or another call is

* appropriate depends on the compiler; for this to work, it may be

* necessary to #include "float.h" or another system-dependent header

* file.

/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.

* This strtod returns a nearest machine number to the input decimal

* string (or sets errno to ERANGE). With IEEE arithmetic, ties are

* broken by the IEEE round-even rule. Otherwise ties are broken by

* biased rounding (add half and chop).

* Inspired loosely by William D. Clinger's paper "How to Read Floating

* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].

* Modifications:

* 1. We only require IEEE, IBM, or VAX double-precision

* arithmetic (not IEEE double-extended).

* 2. We get by with floating-point arithmetic in a case that

* Clinger missed -- when we're computing d * 10^n

* for a small integer d and the integer n is not too

* much larger than 22 (the maximum integer k for which

* we can represent 10^k exactly), we may be able to

* compute (d*10^k) * 10^(e-k) with just one roundoff.

* 3. Rather than a bit-at-a-time adjustment of the binary

* result in the hard case, we use floating-point

* arithmetic to determine the adjustment to within

* one bit; only in really hard cases do we need to

* compute a second residual.

* 4. Because of 3., we don't need a large table of powers of 10

* for ten-to-e (just some small tables, e.g. of 10^k

* for 0 <= k <= 22).

/* Linking of Python's #defines to Gay's #defines starts here. */

#include "Python.h"

#include "pycore_dtoa.h" // _PY_SHORT_FLOAT_REPR

#include "pycore_pystate.h" // _PyInterpreterState_GET()

#include <stdlib.h> // exit()

/* if _PY_SHORT_FLOAT_REPR == 0, then don't even try to compile

the following code */

#if _PY_SHORT_FLOAT_REPR == 1

#include "float.h"

#define MALLOC PyMem_Malloc

#define FREE PyMem_Free

/* This code should also work for ARM mixed-endian format on little-endian

machines, where doubles have byte order 45670123 (in increasing address

order, 0 being the least significant byte). */

#ifdef DOUBLE_IS_LITTLE_ENDIAN_IEEE754

# define IEEE_8087

#endif

#if defined(DOUBLE_IS_BIG_ENDIAN_IEEE754) || \

defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754)

# define IEEE_MC68k

#endif

#if defined(IEEE_8087) + defined(IEEE_MC68k) != 1

#error "Exactly one of IEEE_8087 or IEEE_MC68k should be defined."

#endif

/* The code below assumes that the endianness of integers matches the

endianness of the two 32-bit words of a double. Check this. */

#if defined(WORDS_BIGENDIAN) && (defined(DOUBLE_IS_LITTLE_ENDIAN_IEEE754) || \

defined(DOUBLE_IS_ARM_MIXED_ENDIAN_IEEE754))

#error "doubles and ints have incompatible endianness"

#endif

#if !defined(WORDS_BIGENDIAN) && defined(DOUBLE_IS_BIG_ENDIAN_IEEE754)

#error "doubles and ints have incompatible endianness"

#endif

// ULong is defined in pycore_dtoa.h.

typedef int32_t Long;

typedef uint64_t ULLong;

#undef DEBUG

#ifdef Py_DEBUG

#define DEBUG

#endif

/* End Python #define linking */

#ifdef DEBUG

#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}

#endif

typedef union { double d; ULong L[2]; } U;

#ifdef IEEE_8087

#define word0(x) (x)->L[1]

#define word1(x) (x)->L[0]

#else

#define word0(x) (x)->L[0]

#define word1(x) (x)->L[1]

#endif

#define dval(x) (x)->d

#ifndef STRTOD_DIGLIM

#define STRTOD_DIGLIM 40

#endif

/* maximum permitted exponent value for strtod; exponents larger than

MAX_ABS_EXP in absolute value get truncated to +-MAX_ABS_EXP. MAX_ABS_EXP

should fit into an int. */

#ifndef MAX_ABS_EXP

#define MAX_ABS_EXP 1100000000U

#endif

/* Bound on length of pieces of input strings in _Py_dg_strtod; specifically,

this is used to bound the total number of digits ignoring leading zeros and

the number of digits that follow the decimal point. Ideally, MAX_DIGITS

should satisfy MAX_DIGITS + 400 < MAX_ABS_EXP; that ensures that the

exponent clipping in _Py_dg_strtod can't affect the value of the output. */

#ifndef MAX_DIGITS

#define MAX_DIGITS 1000000000U

#endif

/* Guard against trying to use the above values on unusual platforms with ints

* of width less than 32 bits. */

#if MAX_ABS_EXP > INT_MAX

#error "MAX_ABS_EXP should fit in an int"

#endif

#if MAX_DIGITS > INT_MAX

#error "MAX_DIGITS should fit in an int"

#endif

/* The following definition of Storeinc is appropriate for MIPS processors.

* An alternative that might be better on some machines is

* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)

#if defined(IEEE_8087)

#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \

((unsigned short *)a)[0] = (unsigned short)c, a++)

#else

#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \

((unsigned short *)a)[1] = (unsigned short)c, a++)

#endif

/* #define P DBL_MANT_DIG */

/* Ten_pmax = floor(P*log(2)/log(5)) */

/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */

/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */

/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */

#define Exp_shift 20

#define Exp_shift1 20

#define Exp_msk1 0x100000

#define Exp_msk11 0x100000

#define Exp_mask 0x7ff00000

#define P 53

#define Nbits 53

#define Bias 1023

#define Emax 1023

#define Emin (-1022)

#define Etiny (-1074) /* smallest denormal is 2**Etiny */

#define Exp_1 0x3ff00000

#define Exp_11 0x3ff00000

#define Ebits 11

#define Frac_mask 0xfffff

#define Frac_mask1 0xfffff

#define Ten_pmax 22

#define Bletch 0x10

#define Bndry_mask 0xfffff

#define Bndry_mask1 0xfffff

#define Sign_bit 0x80000000

#define Log2P 1

#define Tiny0 0

#define Tiny1 1

#define Quick_max 14

#define Int_max 14

#ifndef Flt_Rounds

#ifdef FLT_ROUNDS

#define Flt_Rounds FLT_ROUNDS

#else

#define Flt_Rounds 1

#endif

#endif /*Flt_Rounds*/

#define Rounding Flt_Rounds

#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))

#define Big1 0xffffffff

/* Bits of the representation of positive infinity. */

#define POSINF_WORD0 0x7ff00000

#define POSINF_WORD1 0

/* struct BCinfo is used to pass information from _Py_dg_strtod to bigcomp */

typedef struct BCinfo BCinfo;

struct

BCinfo {

int e0, nd, nd0, scale;

};

#define FFFFFFFF 0xffffffffUL

/* struct Bigint is used to represent arbitrary-precision integers. These

integers are stored in sign-magnitude format, with the magnitude stored as

an array of base 2**32 digits. Bigints are always normalized: if x is a

Bigint then x->wds >= 1, and either x->wds == 1 or x[wds-1] is nonzero.

The Bigint fields are as follows:

- next is a header used by Balloc and Bfree to keep track of lists

of freed Bigints; it's also used for the linked list of

powers of 5 of the form 5**2**i used by pow5mult.

- k indicates which pool this Bigint was allocated from

- maxwds is the maximum number of words space was allocated for

(usually maxwds == 2**k)

- sign is 1 for negative Bigints, 0 for positive. The sign is unused

(ignored on inputs, set to 0 on outputs) in almost all operations

involving Bigints: a notable exception is the diff function, which

ignores signs on inputs but sets the sign of the output correctly.

- wds is the actual number of significant words

- x contains the vector of words (digits) for this Bigint, from least

significant (x[0]) to most significant (x[wds-1]).

// struct Bigint is defined in pycore_dtoa.h.

typedef struct Bigint Bigint;

#ifndef Py_USING_MEMORY_DEBUGGER

/* Memory management: memory is allocated from, and returned to, Kmax+1 pools

of memory, where pool k (0 <= k <= Kmax) is for Bigints b with b->maxwds ==

1 << k. These pools are maintained as linked lists, with freelist[k]

pointing to the head of the list for pool k.

On allocation, if there's no free slot in the appropriate pool, MALLOC is

called to get more memory. This memory is not returned to the system until

Python quits. There's also a private memory pool that's allocated from

in preference to using MALLOC.

For Bigints with more than (1 << Kmax) digits (which implies at least 1233

decimal digits), memory is directly allocated using MALLOC, and freed using

FREE.

XXX: it would be easy to bypass this memory-management system and

translate each call to Balloc into a call to PyMem_Malloc, and each

Bfree to PyMem_Free. Investigate whether this has any significant

performance on impact. */

#define freelist interp->dtoa.freelist

#define private_mem interp->dtoa.preallocated

#define pmem_next interp->dtoa.preallocated_next

/* Allocate space for a Bigint with up to 1<<k digits */

static Bigint *

Balloc(int k)

{

int x;

Bigint *rv;

unsigned int len;

PyInterpreterState *interp = _PyInterpreterState_GET();

if (k <= Bigint_Kmax && (rv = freelist[k]))

freelist[k] = rv->next;

else {

x = 1 << k;

len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)

/sizeof(double);

if (k <= Bigint_Kmax &&

pmem_next - private_mem + len <= (Py_ssize_t)Bigint_PREALLOC_SIZE

) {

rv = (Bigint*)pmem_next;

pmem_next += len;

}

else {

rv = (Bigint*)MALLOC(len*sizeof(double));

if (rv == NULL)

return NULL;

}

rv->k = k;

rv->maxwds = x;

}

rv->sign = rv->wds = 0;

return rv;

}

/* Free a Bigint allocated with Balloc */

static void

Bfree(Bigint *v)

{

if (v) {

if (v->k > Bigint_Kmax)

FREE((void*)v);

else {

PyInterpreterState *interp = _PyInterpreterState_GET();

v->next = freelist[v->k];

freelist[v->k] = v;

}

#undef pmem_next

#undef private_mem

#undef freelist

#else

/* Alternative versions of Balloc and Bfree that use PyMem_Malloc and

PyMem_Free directly in place of the custom memory allocation scheme above.

These are provided for the benefit of memory debugging tools like

Valgrind. */

/* Allocate space for a Bigint with up to 1<<k digits */

static Bigint *

Balloc(int k)

{

int x;

Bigint *rv;

unsigned int len;

x = 1 << k;

len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)

/sizeof(double);

rv = (Bigint*)MALLOC(len*sizeof(double));

if (rv == NULL)

return NULL;

rv->k = k;

rv->maxwds = x;

rv->sign = rv->wds = 0;

return rv;

}

/* Free a Bigint allocated with Balloc */

static void

Bfree(Bigint *v)

{

if (v) {

FREE((void*)v);

}

#endif /* Py_USING_MEMORY_DEBUGGER */

#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \

y->wds*sizeof(Long) + 2*sizeof(int))

/* Multiply a Bigint b by m and add a. Either modifies b in place and returns

a pointer to the modified b, or Bfrees b and returns a pointer to a copy.

On failure, return NULL. In this case, b will have been already freed. */

static Bigint *

multadd(Bigint *b, int m, int a) /* multiply by m and add a */

{

int i, wds;

ULong *x;

ULLong carry, y;

Bigint *b1;

wds = b->wds;

x = b->x;

i = 0;

carry = a;

do {

y = *x * (ULLong)m + carry;

carry = y >> 32;

*x++ = (ULong)(y & FFFFFFFF);

}

while(++i < wds);

if (carry) {

if (wds >= b->maxwds) {

b1 = Balloc(b->k+1);

if (b1 == NULL){

Bfree(b);

return NULL;

}

Bcopy(b1, b);

Bfree(b);

b = b1;

}

b->x[wds++] = (ULong)carry;

b->wds = wds;

}

return b;

}

/* convert a string s containing nd decimal digits (possibly containing a

decimal separator at position nd0, which is ignored) to a Bigint. This

function carries on where the parsing code in _Py_dg_strtod leaves off: on

entry, y9 contains the result of converting the first 9 digits. Returns

NULL on failure. */

static Bigint *

s2b(const char *s, int nd0, int nd, ULong y9)

{

Bigint *b;

int i, k;

Long x, y;

x = (nd + 8) / 9;

for(k = 0, y = 1; x > y; y <<= 1, k++) ;

b = Balloc(k);

if (b == NULL)

return NULL;

b->x[0] = y9;

b->wds = 1;

if (nd <= 9)

return b;

s += 9;

for (i = 9; i < nd0; i++) {

b = multadd(b, 10, *s++ - '0');

if (b == NULL)

return NULL;

}

s++;

for(; i < nd; i++) {

b = multadd(b, 10, *s++ - '0');

if (b == NULL)

return NULL;

}

return b;

}

/* count leading 0 bits in the 32-bit integer x. */

static int

hi0bits(ULong x)

{

int k = 0;

if (!(x & 0xffff0000)) {

k = 16;

x <<= 16;

}

if (!(x & 0xff000000)) {

k += 8;

x <<= 8;

}

if (!(x & 0xf0000000)) {

k += 4;

x <<= 4;

}

if (!(x & 0xc0000000)) {

k += 2;

x <<= 2;

}

if (!(x & 0x80000000)) {

k++;

if (!(x & 0x40000000))

return 32;

}

return k;

}

/* count trailing 0 bits in the 32-bit integer y, and shift y right by that

number of bits. */

static int

lo0bits(ULong *y)

{

int k;

ULong x = *y;

if (x & 7) {

if (x & 1)

return 0;

if (x & 2) {

*y = x >> 1;

return 1;

}

*y = x >> 2;

return 2;

}

k = 0;

if (!(x & 0xffff)) {

k = 16;

x >>= 16;

}

if (!(x & 0xff)) {

k += 8;

x >>= 8;

}

if (!(x & 0xf)) {

k += 4;

x >>= 4;

}

if (!(x & 0x3)) {

k += 2;

x >>= 2;

}

if (!(x & 1)) {

k++;

x >>= 1;

if (!x)

return 32;

}

*y = x;

return k;

}

/* convert a small nonnegative integer to a Bigint */

static Bigint *

i2b(int i)

{

Bigint *b;

b = Balloc(1);

if (b == NULL)

return NULL;

b->x[0] = i;

b->wds = 1;

return b;

}

/* multiply two Bigints. Returns a new Bigint, or NULL on failure. Ignores

the signs of a and b. */

static Bigint *

mult(Bigint *a, Bigint *b)

{

Bigint *c;

int k, wa, wb, wc;

ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;

ULong y;

ULLong carry, z;

if ((!a->x[0] && a->wds == 1) || (!b->x[0] && b->wds == 1)) {

c = Balloc(0);

if (c == NULL)

return NULL;

c->wds = 1;

c->x[0] = 0;

return c;

}

if (a->wds < b->wds) {

c = a;

a = b;

b = c;

}

k = a->k;

wa = a->wds;

wb = b->wds;

wc = wa + wb;

if (wc > a->maxwds)

k++;

c = Balloc(k);

if (c == NULL)

return NULL;

for(x = c->x, xa = x + wc; x < xa; x++)

*x = 0;

xa = a->x;

xae = xa + wa;

xb = b->x;

xbe = xb + wb;

xc0 = c->x;

for(; xb < xbe; xc0++) {

if ((y = *xb++)) {

x = xa;

xc = xc0;

carry = 0;

do {

z = *x++ * (ULLong)y + *xc + carry;

carry = z >> 32;

*xc++ = (ULong)(z & FFFFFFFF);

}

while(x < xae);

*xc = (ULong)carry;

}

for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;

c->wds = wc;

return c;

}

#ifndef Py_USING_MEMORY_DEBUGGER

/* multiply the Bigint b by 5**k. Returns a pointer to the result, or NULL on

failure; if the returned pointer is distinct from b then the original

Bigint b will have been Bfree'd. Ignores the sign of b. */

static Bigint *

pow5mult(Bigint *b, int k)

{

Bigint *b1, *p5, *p51;

int i;

static const int p05[3] = { 5, 25, 125 };

if ((i = k & 3)) {

b = multadd(b, p05[i-1], 0);

if (b == NULL)

return NULL;

}

if (!(k >>= 2))

return b;

PyInterpreterState *interp = _PyInterpreterState_GET();

p5 = interp->dtoa.p5s;

if (!p5) {

/* first time */

p5 = i2b(625);

if (p5 == NULL) {

Bfree(b);

return NULL;

}

interp->dtoa.p5s = p5;

p5->next = 0;

}

for(;;) {

if (k & 1) {

b1 = mult(b, p5);

Bfree(b);

b = b1;

if (b == NULL)

return NULL;

}

if (!(k >>= 1))

break;

p51 = p5->next;

if (!p51) {

p51 = mult(p5,p5);

if (p51 == NULL) {

Bfree(b);

return NULL;

}

p51->next = 0;

p5->next = p51;

}

p5 = p51;

}

return b;

}

#else

/* Version of pow5mult that doesn't cache powers of 5. Provided for

the benefit of memory debugging tools like Valgrind. */

static Bigint *

pow5mult(Bigint *b, int k)

{

Bigint *b1, *p5, *p51;

int i;

static const int p05[3] = { 5, 25, 125 };

if ((i = k & 3)) {

b = multadd(b, p05[i-1], 0);

if (b == NULL)

return NULL;

}

if (!(k >>= 2))

return b;

p5 = i2b(625);

if (p5 == NULL) {

Bfree(b);

return NULL;

}

for(;;) {

if (k & 1) {

b1 = mult(b, p5);

Bfree(b);

b = b1;

if (b == NULL) {

Bfree(p5);

return NULL;

}

if (!(k >>= 1))

break;

p51 = mult(p5, p5);

Bfree(p5);

p5 = p51;

if (p5 == NULL) {

Bfree(b);

return NULL;

}

Bfree(p5);

return b;

}

#endif /* Py_USING_MEMORY_DEBUGGER */

/* shift a Bigint b left by k bits. Return a pointer to the shifted result,

or NULL on failure. If the returned pointer is distinct from b then the

original b will have been Bfree'd. Ignores the sign of b. */

static Bigint *

lshift(Bigint *b, int k)

{

int i, k1, n, n1;

Bigint *b1;

ULong *x, *x1, *xe, z;

if (!k || (!b->x[0] && b->wds == 1))

return b;

n = k >> 5;

k1 = b->k;

n1 = n + b->wds + 1;

for(i = b->maxwds; n1 > i; i <<= 1)

k1++;

b1 = Balloc(k1);

if (b1 == NULL) {

Bfree(b);

return NULL;

}

x1 = b1->x;

for(i = 0; i < n; i++)

*x1++ = 0;

x = b->x;

xe = x + b->wds;

if (k &= 0x1f) {

k1 = 32 - k;

z = 0;

do {

*x1++ = *x << k | z;

z = *x++ >> k1;

}

while(x < xe);

if ((*x1 = z))

++n1;

}

else do

*x1++ = *x++;

while(x < xe);

b1->wds = n1 - 1;

Bfree(b);

return b1;

}

/* Do a three-way compare of a and b, returning -1 if a < b, 0 if a == b and

1 if a > b. Ignores signs of a and b. */

static int

cmp(Bigint *a, Bigint *b)

{

ULong *xa, *xa0, *xb, *xb0;

int i, j;

i = a->wds;

j = b->wds;

#ifdef DEBUG

if (i > 1 && !a->x[i-1])

Bug("cmp called with a->x[a->wds-1] == 0");

if (j > 1 && !b->x[j-1])

Bug("cmp called with b->x[b->wds-1] == 0");

#endif

if (i -= j)

return i;

xa0 = a->x;

xa = xa0 + j;

xb0 = b->x;

xb = xb0 + j;

for(;;) {

if (*--xa != *--xb)

return *xa < *xb ? -1 : 1;

if (xa <= xa0)

break;

}

return 0;

}

/* Take the difference of Bigints a and b, returning a new Bigint. Returns

NULL on failure. The signs of a and b are ignored, but the sign of the

result is set appropriately. */

static Bigint *

diff(Bigint *a, Bigint *b)

{

Bigint *c;

int i, wa, wb;

ULong *xa, *xae, *xb, *xbe, *xc;

ULLong borrow, y;

i = cmp(a,b);

if (!i) {

c = Balloc(0);

if (c == NULL)

return NULL;

c->wds = 1;

c->x[0] = 0;

return c;

}

if (i < 0) {

c = a;

a = b;

b = c;

i = 1;

}

else

i = 0;

c = Balloc(a->k);

if (c == NULL)

return NULL;

c->sign = i;

wa = a->wds;

xa = a->x;

xae = xa + wa;

wb = b->wds;

xb = b->x;

xbe = xb + wb;

xc = c->x;

borrow = 0;

do {

y = (ULLong)*xa++ - *xb++ - borrow;

borrow = y >> 32 & (ULong)1;

*xc++ = (ULong)(y & FFFFFFFF);

}

while(xb < xbe);

while(xa < xae) {

y = *xa++ - borrow;

borrow = y >> 32 & (ULong)1;

*xc++ = (ULong)(y & FFFFFFFF);

}

while(!*--xc)

wa--;

c->wds = wa;

return c;

}

/* Given a positive normal double x, return the difference between x and the

next double up. Doesn't give correct results for subnormals. */

static double

ulp(U *x)

{

Long L;

U u;

L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;

word0(&u) = L;

word1(&u) = 0;

return dval(&u);

}

/* Convert a Bigint to a double plus an exponent */

static double

b2d(Bigint *a, int *e)

{

ULong *xa, *xa0, w, y, z;

int k;

U d;

xa0 = a->x;

xa = xa0 + a->wds;

y = *--xa;

#ifdef DEBUG

if (!y) Bug("zero y in b2d");

#endif

k = hi0bits(y);

*e = 32 - k;

if (k < Ebits) {

word0(&d) = Exp_1 | y >> (Ebits - k);

w = xa > xa0 ? *--xa : 0;

word1(&d) = y << ((32-Ebits) + k) | w >> (Ebits - k);

goto ret_d;

}

z = xa > xa0 ? *--xa : 0;

if (k -= Ebits) {

word0(&d) = Exp_1 | y << k | z >> (32 - k);

y = xa > xa0 ? *--xa : 0;

word1(&d) = z << k | y >> (32 - k);

}

else {

word0(&d) = Exp_1 | y;

word1(&d) = z;

}

ret_d:

return dval(&d);

}

/* Convert a scaled double to a Bigint plus an exponent. Similar to d2b,

except that it accepts the scale parameter used in _Py_dg_strtod (which

should be either 0 or 2*P), and the normalization for the return value is

different (see below). On input, d should be finite and nonnegative, and d

/ 2**scale should be exactly representable as an IEEE 754 double.

Returns a Bigint b and an integer e such that

dval(d) / 2**scale = b * 2**e.

Unlike d2b, b is not necessarily odd: b and e are normalized so

that either 2**(P-1) <= b < 2**P and e >= Etiny, or b < 2**P

and e == Etiny. This applies equally to an input of 0.0: in that

case the return values are b = 0 and e = Etiny.

The above normalization ensures that for all possible inputs d,

2**e gives ulp(d/2**scale).

Returns NULL on failure.

static Bigint *

sd2b(U *d, int scale, int *e)

{

Bigint *b;

b = Balloc(1);

if (b == NULL)

return NULL;

/* First construct b and e assuming that scale == 0. */

b->wds = 2;

b->x[0] = word1(d);

b->x[1] = word0(d) & Frac_mask;

View remainder of file in raw view

cpython/Python/dtoa.c at main · https-github-com-nzysoft/cpython · GitHub

Uh oh!

Expand file tree

Breadcrumbs

dtoa.c

Latest commit

History

Breadcrumbs

dtoa.c

File metadata and controls