2012-03-05 10:04:10 +00:00
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// Copyright 2012 the V8 project authors. All rights reserved.
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2014-04-29 06:42:26 +00:00
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// Use of this source code is governed by a BSD-style license that can be
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// found in the LICENSE file.
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2010-10-07 08:54:10 +00:00
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#include <stdarg.h>
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2013-04-19 13:26:47 +00:00
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#include <cmath>
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2010-10-07 08:54:10 +00:00
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2014-06-20 08:40:11 +00:00
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#include "src/v8.h"
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2014-06-03 08:12:43 +00:00
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#include "src/bignum.h"
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#include "src/cached-powers.h"
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#include "src/double.h"
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2014-06-20 08:40:11 +00:00
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#include "src/globals.h"
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#include "src/strtod.h"
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#include "src/utils.h"
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2010-10-07 08:54:10 +00:00
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namespace v8 {
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namespace internal {
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2010-10-07 12:53:59 +00:00
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// 2^53 = 9007199254740992.
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// Any integer with at most 15 decimal digits will hence fit into a double
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// (which has a 53bit significand) without loss of precision.
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static const int kMaxExactDoubleIntegerDecimalDigits = 15;
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2010-10-21 11:54:32 +00:00
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// 2^64 = 18446744073709551616 > 10^19
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2010-10-07 12:53:59 +00:00
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static const int kMaxUint64DecimalDigits = 19;
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2010-10-21 11:54:32 +00:00
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2010-10-14 13:47:48 +00:00
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// Max double: 1.7976931348623157 x 10^308
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// Min non-zero double: 4.9406564584124654 x 10^-324
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// Any x >= 10^309 is interpreted as +infinity.
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// Any x <= 10^-324 is interpreted as 0.
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// Note that 2.5e-324 (despite being smaller than the min double) will be read
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// as non-zero (equal to the min non-zero double).
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static const int kMaxDecimalPower = 309;
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static const int kMinDecimalPower = -324;
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2010-10-07 12:53:59 +00:00
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2010-10-21 11:54:32 +00:00
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// 2^64 = 18446744073709551616
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static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF);
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2010-10-07 12:53:59 +00:00
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static const double exact_powers_of_ten[] = {
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1.0, // 10^0
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10.0,
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100.0,
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1000.0,
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10000.0,
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100000.0,
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1000000.0,
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10000000.0,
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100000000.0,
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1000000000.0,
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10000000000.0, // 10^10
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100000000000.0,
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1000000000000.0,
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10000000000000.0,
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100000000000000.0,
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1000000000000000.0,
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10000000000000000.0,
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100000000000000000.0,
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1000000000000000000.0,
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10000000000000000000.0,
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100000000000000000000.0, // 10^20
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1000000000000000000000.0,
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// 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
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10000000000000000000000.0
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};
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static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);
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2010-11-08 11:49:47 +00:00
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// Maximum number of significant digits in the decimal representation.
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// In fact the value is 772 (see conversions.cc), but to give us some margin
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// we round up to 780.
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static const int kMaxSignificantDecimalDigits = 780;
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2010-10-07 12:53:59 +00:00
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2010-10-14 13:47:48 +00:00
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static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
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for (int i = 0; i < buffer.length(); i++) {
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if (buffer[i] != '0') {
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2010-10-26 13:30:31 +00:00
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return buffer.SubVector(i, buffer.length());
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2010-10-14 13:47:48 +00:00
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}
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}
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2010-10-26 14:13:21 +00:00
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return Vector<const char>(buffer.start(), 0);
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2010-10-14 13:47:48 +00:00
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}
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static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
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2010-10-07 12:53:59 +00:00
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for (int i = buffer.length() - 1; i >= 0; --i) {
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if (buffer[i] != '0') {
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2010-10-26 13:30:31 +00:00
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return buffer.SubVector(0, i + 1);
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2010-10-07 12:53:59 +00:00
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}
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}
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2010-10-26 14:13:21 +00:00
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return Vector<const char>(buffer.start(), 0);
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2010-10-07 12:53:59 +00:00
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}
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2010-11-08 11:49:47 +00:00
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static void TrimToMaxSignificantDigits(Vector<const char> buffer,
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int exponent,
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char* significant_buffer,
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int* significant_exponent) {
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for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
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significant_buffer[i] = buffer[i];
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}
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// The input buffer has been trimmed. Therefore the last digit must be
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// different from '0'.
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ASSERT(buffer[buffer.length() - 1] != '0');
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// Set the last digit to be non-zero. This is sufficient to guarantee
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// correct rounding.
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significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
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*significant_exponent =
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exponent + (buffer.length() - kMaxSignificantDecimalDigits);
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}
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2013-07-05 09:52:11 +00:00
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2010-10-21 11:54:32 +00:00
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// Reads digits from the buffer and converts them to a uint64.
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// Reads in as many digits as fit into a uint64.
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// When the string starts with "1844674407370955161" no further digit is read.
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// Since 2^64 = 18446744073709551616 it would still be possible read another
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// digit if it was less or equal than 6, but this would complicate the code.
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static uint64_t ReadUint64(Vector<const char> buffer,
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int* number_of_read_digits) {
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2010-10-07 12:53:59 +00:00
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uint64_t result = 0;
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2010-10-21 11:54:32 +00:00
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int i = 0;
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while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
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int digit = buffer[i++] - '0';
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2010-10-07 12:53:59 +00:00
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ASSERT(0 <= digit && digit <= 9);
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result = 10 * result + digit;
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}
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2010-10-21 11:54:32 +00:00
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*number_of_read_digits = i;
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2010-10-07 12:53:59 +00:00
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return result;
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}
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2010-10-21 11:54:32 +00:00
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// Reads a DiyFp from the buffer.
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// The returned DiyFp is not necessarily normalized.
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// If remaining_decimals is zero then the returned DiyFp is accurate.
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// Otherwise it has been rounded and has error of at most 1/2 ulp.
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static void ReadDiyFp(Vector<const char> buffer,
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DiyFp* result,
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int* remaining_decimals) {
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int read_digits;
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uint64_t significand = ReadUint64(buffer, &read_digits);
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if (buffer.length() == read_digits) {
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*result = DiyFp(significand, 0);
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*remaining_decimals = 0;
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} else {
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// Round the significand.
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if (buffer[read_digits] >= '5') {
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significand++;
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}
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// Compute the binary exponent.
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int exponent = 0;
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*result = DiyFp(significand, exponent);
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*remaining_decimals = buffer.length() - read_digits;
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}
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}
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2010-10-18 15:19:39 +00:00
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static bool DoubleStrtod(Vector<const char> trimmed,
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int exponent,
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double* result) {
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2014-05-23 16:37:27 +00:00
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#if (V8_TARGET_ARCH_IA32 || V8_TARGET_ARCH_X87 || defined(USE_SIMULATOR)) && \
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!defined(_MSC_VER)
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2010-10-18 15:19:39 +00:00
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// On x86 the floating-point stack can be 64 or 80 bits wide. If it is
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// 80 bits wide (as is the case on Linux) then double-rounding occurs and the
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// result is not accurate.
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2012-03-05 10:04:10 +00:00
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// We know that Windows32 with MSVC, unlike with MinGW32, uses 64 bits and is
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// therefore accurate.
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// Note that the ARM and MIPS simulators are compiled for 32bits. They
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// therefore exhibit the same problem.
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2010-10-18 15:19:39 +00:00
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return false;
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#endif
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2010-10-07 12:53:59 +00:00
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if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
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2010-10-21 11:54:32 +00:00
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int read_digits;
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2010-10-07 12:53:59 +00:00
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// The trimmed input fits into a double.
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// If the 10^exponent (resp. 10^-exponent) fits into a double too then we
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// can compute the result-double simply by multiplying (resp. dividing) the
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// two numbers.
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// This is possible because IEEE guarantees that floating-point operations
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// return the best possible approximation.
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if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
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// 10^-exponent fits into a double.
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2010-10-21 11:54:32 +00:00
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*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
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ASSERT(read_digits == trimmed.length());
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2010-10-18 15:19:39 +00:00
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*result /= exact_powers_of_ten[-exponent];
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return true;
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2010-10-07 12:53:59 +00:00
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}
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if (0 <= exponent && exponent < kExactPowersOfTenSize) {
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// 10^exponent fits into a double.
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2010-10-21 11:54:32 +00:00
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*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
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ASSERT(read_digits == trimmed.length());
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2010-10-18 15:19:39 +00:00
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*result *= exact_powers_of_ten[exponent];
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return true;
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2010-10-07 12:53:59 +00:00
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}
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int remaining_digits =
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kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
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if ((0 <= exponent) &&
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(exponent - remaining_digits < kExactPowersOfTenSize)) {
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// The trimmed string was short and we can multiply it with
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// 10^remaining_digits. As a result the remaining exponent now fits
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// into a double too.
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2010-10-21 11:54:32 +00:00
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*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
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ASSERT(read_digits == trimmed.length());
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2010-10-18 15:19:39 +00:00
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*result *= exact_powers_of_ten[remaining_digits];
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*result *= exact_powers_of_ten[exponent - remaining_digits];
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return true;
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2010-10-07 12:53:59 +00:00
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}
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}
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2010-10-18 15:19:39 +00:00
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return false;
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}
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2010-10-21 11:54:32 +00:00
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// Returns 10^exponent as an exact DiyFp.
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// The given exponent must be in the range [1; kDecimalExponentDistance[.
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static DiyFp AdjustmentPowerOfTen(int exponent) {
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ASSERT(0 < exponent);
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ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
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// Simply hardcode the remaining powers for the given decimal exponent
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// distance.
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ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
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switch (exponent) {
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case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60);
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case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57);
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case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54);
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case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50);
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case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47);
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case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44);
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case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40);
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default:
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UNREACHABLE();
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return DiyFp(0, 0);
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}
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}
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// If the function returns true then the result is the correct double.
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// Otherwise it is either the correct double or the double that is just below
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// the correct double.
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static bool DiyFpStrtod(Vector<const char> buffer,
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int exponent,
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double* result) {
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DiyFp input;
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int remaining_decimals;
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ReadDiyFp(buffer, &input, &remaining_decimals);
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// Since we may have dropped some digits the input is not accurate.
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// If remaining_decimals is different than 0 than the error is at most
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// .5 ulp (unit in the last place).
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// We don't want to deal with fractions and therefore keep a common
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// denominator.
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const int kDenominatorLog = 3;
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const int kDenominator = 1 << kDenominatorLog;
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// Move the remaining decimals into the exponent.
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exponent += remaining_decimals;
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int error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
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int old_e = input.e();
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input.Normalize();
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error <<= old_e - input.e();
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ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
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if (exponent < PowersOfTenCache::kMinDecimalExponent) {
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*result = 0.0;
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return true;
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}
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DiyFp cached_power;
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int cached_decimal_exponent;
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PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
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&cached_power,
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&cached_decimal_exponent);
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if (cached_decimal_exponent != exponent) {
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int adjustment_exponent = exponent - cached_decimal_exponent;
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DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
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input.Multiply(adjustment_power);
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if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
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// The product of input with the adjustment power fits into a 64 bit
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// integer.
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ASSERT(DiyFp::kSignificandSize == 64);
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} else {
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// The adjustment power is exact. There is hence only an error of 0.5.
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error += kDenominator / 2;
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}
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}
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input.Multiply(cached_power);
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// The error introduced by a multiplication of a*b equals
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// error_a + error_b + error_a*error_b/2^64 + 0.5
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// Substituting a with 'input' and b with 'cached_power' we have
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// error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
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// error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
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int error_b = kDenominator / 2;
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int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
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int fixed_error = kDenominator / 2;
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error += error_b + error_ab + fixed_error;
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old_e = input.e();
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input.Normalize();
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error <<= old_e - input.e();
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// See if the double's significand changes if we add/subtract the error.
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int order_of_magnitude = DiyFp::kSignificandSize + input.e();
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int effective_significand_size =
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Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
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int precision_digits_count =
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DiyFp::kSignificandSize - effective_significand_size;
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if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
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// This can only happen for very small denormals. In this case the
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|
|
|
// half-way multiplied by the denominator exceeds the range of an uint64.
|
|
|
|
// Simply shift everything to the right.
|
|
|
|
int shift_amount = (precision_digits_count + kDenominatorLog) -
|
|
|
|
DiyFp::kSignificandSize + 1;
|
|
|
|
input.set_f(input.f() >> shift_amount);
|
|
|
|
input.set_e(input.e() + shift_amount);
|
|
|
|
// We add 1 for the lost precision of error, and kDenominator for
|
|
|
|
// the lost precision of input.f().
|
|
|
|
error = (error >> shift_amount) + 1 + kDenominator;
|
|
|
|
precision_digits_count -= shift_amount;
|
|
|
|
}
|
|
|
|
// We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
|
|
|
|
ASSERT(DiyFp::kSignificandSize == 64);
|
|
|
|
ASSERT(precision_digits_count < 64);
|
|
|
|
uint64_t one64 = 1;
|
|
|
|
uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
|
|
|
|
uint64_t precision_bits = input.f() & precision_bits_mask;
|
|
|
|
uint64_t half_way = one64 << (precision_digits_count - 1);
|
|
|
|
precision_bits *= kDenominator;
|
|
|
|
half_way *= kDenominator;
|
|
|
|
DiyFp rounded_input(input.f() >> precision_digits_count,
|
|
|
|
input.e() + precision_digits_count);
|
|
|
|
if (precision_bits >= half_way + error) {
|
|
|
|
rounded_input.set_f(rounded_input.f() + 1);
|
|
|
|
}
|
|
|
|
// If the last_bits are too close to the half-way case than we are too
|
|
|
|
// inaccurate and round down. In this case we return false so that we can
|
|
|
|
// fall back to a more precise algorithm.
|
|
|
|
|
|
|
|
*result = Double(rounded_input).value();
|
|
|
|
if (half_way - error < precision_bits && precision_bits < half_way + error) {
|
|
|
|
// Too imprecise. The caller will have to fall back to a slower version.
|
|
|
|
// However the returned number is guaranteed to be either the correct
|
|
|
|
// double, or the next-lower double.
|
|
|
|
return false;
|
|
|
|
} else {
|
|
|
|
return true;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
2010-11-08 11:49:47 +00:00
|
|
|
// Returns the correct double for the buffer*10^exponent.
|
|
|
|
// The variable guess should be a close guess that is either the correct double
|
|
|
|
// or its lower neighbor (the nearest double less than the correct one).
|
|
|
|
// Preconditions:
|
|
|
|
// buffer.length() + exponent <= kMaxDecimalPower + 1
|
|
|
|
// buffer.length() + exponent > kMinDecimalPower
|
|
|
|
// buffer.length() <= kMaxDecimalSignificantDigits
|
|
|
|
static double BignumStrtod(Vector<const char> buffer,
|
|
|
|
int exponent,
|
|
|
|
double guess) {
|
|
|
|
if (guess == V8_INFINITY) {
|
|
|
|
return guess;
|
|
|
|
}
|
|
|
|
|
|
|
|
DiyFp upper_boundary = Double(guess).UpperBoundary();
|
|
|
|
|
|
|
|
ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
|
|
|
|
ASSERT(buffer.length() + exponent > kMinDecimalPower);
|
|
|
|
ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
|
|
|
|
// Make sure that the Bignum will be able to hold all our numbers.
|
|
|
|
// Our Bignum implementation has a separate field for exponents. Shifts will
|
|
|
|
// consume at most one bigit (< 64 bits).
|
|
|
|
// ln(10) == 3.3219...
|
|
|
|
ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
|
|
|
|
Bignum input;
|
|
|
|
Bignum boundary;
|
|
|
|
input.AssignDecimalString(buffer);
|
|
|
|
boundary.AssignUInt64(upper_boundary.f());
|
|
|
|
if (exponent >= 0) {
|
|
|
|
input.MultiplyByPowerOfTen(exponent);
|
|
|
|
} else {
|
|
|
|
boundary.MultiplyByPowerOfTen(-exponent);
|
|
|
|
}
|
|
|
|
if (upper_boundary.e() > 0) {
|
|
|
|
boundary.ShiftLeft(upper_boundary.e());
|
|
|
|
} else {
|
|
|
|
input.ShiftLeft(-upper_boundary.e());
|
|
|
|
}
|
|
|
|
int comparison = Bignum::Compare(input, boundary);
|
|
|
|
if (comparison < 0) {
|
|
|
|
return guess;
|
|
|
|
} else if (comparison > 0) {
|
|
|
|
return Double(guess).NextDouble();
|
|
|
|
} else if ((Double(guess).Significand() & 1) == 0) {
|
|
|
|
// Round towards even.
|
|
|
|
return guess;
|
|
|
|
} else {
|
|
|
|
return Double(guess).NextDouble();
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
2010-10-18 15:19:39 +00:00
|
|
|
double Strtod(Vector<const char> buffer, int exponent) {
|
|
|
|
Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
|
|
|
|
Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
|
|
|
|
exponent += left_trimmed.length() - trimmed.length();
|
|
|
|
if (trimmed.length() == 0) return 0.0;
|
2010-11-08 11:49:47 +00:00
|
|
|
if (trimmed.length() > kMaxSignificantDecimalDigits) {
|
|
|
|
char significant_buffer[kMaxSignificantDecimalDigits];
|
|
|
|
int significant_exponent;
|
|
|
|
TrimToMaxSignificantDigits(trimmed, exponent,
|
|
|
|
significant_buffer, &significant_exponent);
|
2010-11-11 16:32:32 +00:00
|
|
|
return Strtod(Vector<const char>(significant_buffer,
|
|
|
|
kMaxSignificantDecimalDigits),
|
|
|
|
significant_exponent);
|
2010-11-08 11:49:47 +00:00
|
|
|
}
|
2010-10-18 15:19:39 +00:00
|
|
|
if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY;
|
|
|
|
if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0;
|
2010-10-21 11:54:32 +00:00
|
|
|
|
2010-11-08 11:49:47 +00:00
|
|
|
double guess;
|
|
|
|
if (DoubleStrtod(trimmed, exponent, &guess) ||
|
|
|
|
DiyFpStrtod(trimmed, exponent, &guess)) {
|
|
|
|
return guess;
|
2010-10-18 15:19:39 +00:00
|
|
|
}
|
2010-11-08 11:49:47 +00:00
|
|
|
return BignumStrtod(trimmed, exponent, guess);
|
2010-10-07 12:53:59 +00:00
|
|
|
}
|
|
|
|
|
2010-10-07 08:54:10 +00:00
|
|
|
} } // namespace v8::internal
|