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Unified Diff: third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc

Issue 2764243002: Move files in wtf/ to platform/wtf/ (Part 9). (Closed)
Patch Set: Rebase. Created 3 years, 9 months ago
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Index: third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
diff --git a/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc b/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
deleted file mode 100644
index 44ecae68f6e8e0280833fd74f83e4efa56b75f44..0000000000000000000000000000000000000000
--- a/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
+++ /dev/null
@@ -1,739 +0,0 @@
-// Copyright 2010 the V8 project authors. All rights reserved.
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are
-// met:
-//
-// * Redistributions of source code must retain the above copyright
-// notice, this list of conditions and the following disclaimer.
-// * Redistributions in binary form must reproduce the above
-// copyright notice, this list of conditions and the following
-// disclaimer in the documentation and/or other materials provided
-// with the distribution.
-// * Neither the name of Google Inc. nor the names of its
-// contributors may be used to endorse or promote products derived
-// from this software without specific prior written permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
-#include "fast-dtoa.h"
-
-#include "cached-powers.h"
-#include "diy-fp.h"
-#include "double.h"
-
-namespace WTF {
-
-namespace double_conversion {
-
- // The minimal and maximal target exponent define the range of w's binary
- // exponent, where 'w' is the result of multiplying the input by a cached power
- // of ten.
- //
- // A different range might be chosen on a different platform, to optimize digit
- // generation, but a smaller range requires more powers of ten to be cached.
- static const int kMinimalTargetExponent = -60;
- static const int kMaximalTargetExponent = -32;
-
-
- // Adjusts the last digit of the generated number, and screens out generated
- // solutions that may be inaccurate. A solution may be inaccurate if it is
- // outside the safe interval, or if we cannot prove that it is closer to the
- // input than a neighboring representation of the same length.
- //
- // Input: * buffer containing the digits of too_high / 10^kappa
- // * the buffer's length
- // * distance_too_high_w == (too_high - w).f() * unit
- // * unsafe_interval == (too_high - too_low).f() * unit
- // * rest = (too_high - buffer * 10^kappa).f() * unit
- // * ten_kappa = 10^kappa * unit
- // * unit = the common multiplier
- // Output: returns true if the buffer is guaranteed to contain the closest
- // representable number to the input.
- // Modifies the generated digits in the buffer to approach (round towards) w.
- static bool RoundWeed(Vector<char> buffer,
- int length,
- uint64_t distance_too_high_w,
- uint64_t unsafe_interval,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit) {
- uint64_t small_distance = distance_too_high_w - unit;
- uint64_t big_distance = distance_too_high_w + unit;
- // Let w_low = too_high - big_distance, and
- // w_high = too_high - small_distance.
- // Note: w_low < w < w_high
- //
- // The real w (* unit) must lie somewhere inside the interval
- // ]w_low; w_high[ (often written as "(w_low; w_high)")
-
- // Basically the buffer currently contains a number in the unsafe interval
- // ]too_low; too_high[ with too_low < w < too_high
- //
- // too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- // ^v 1 unit ^ ^ ^ ^
- // boundary_high --------------------- . . . .
- // ^v 1 unit . . . .
- // - - - - - - - - - - - - - - - - - - - + - - + - - - - - - . .
- // . . ^ . .
- // . big_distance . . .
- // . . . . rest
- // small_distance . . . .
- // v . . . .
- // w_high - - - - - - - - - - - - - - - - - - . . . .
- // ^v 1 unit . . . .
- // w ---------------------------------------- . . . .
- // ^v 1 unit v . . .
- // w_low - - - - - - - - - - - - - - - - - - - - - . . .
- // . . v
- // buffer --------------------------------------------------+-------+--------
- // . .
- // safe_interval .
- // v .
- // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .
- // ^v 1 unit .
- // boundary_low ------------------------- unsafe_interval
- // ^v 1 unit v
- // too_low - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- //
- //
- // Note that the value of buffer could lie anywhere inside the range too_low
- // to too_high.
- //
- // boundary_low, boundary_high and w are approximations of the real boundaries
- // and v (the input number). They are guaranteed to be precise up to one unit.
- // In fact the error is guaranteed to be strictly less than one unit.
- //
- // Anything that lies outside the unsafe interval is guaranteed not to round
- // to v when read again.
- // Anything that lies inside the safe interval is guaranteed to round to v
- // when read again.
- // If the number inside the buffer lies inside the unsafe interval but not
- // inside the safe interval then we simply do not know and bail out (returning
- // false).
- //
- // Similarly we have to take into account the imprecision of 'w' when finding
- // the closest representation of 'w'. If we have two potential
- // representations, and one is closer to both w_low and w_high, then we know
- // it is closer to the actual value v.
- //
- // By generating the digits of too_high we got the largest (closest to
- // too_high) buffer that is still in the unsafe interval. In the case where
- // w_high < buffer < too_high we try to decrement the buffer.
- // This way the buffer approaches (rounds towards) w.
- // There are 3 conditions that stop the decrementation process:
- // 1) the buffer is already below w_high
- // 2) decrementing the buffer would make it leave the unsafe interval
- // 3) decrementing the buffer would yield a number below w_high and farther
- // away than the current number. In other words:
- // (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
- // Instead of using the buffer directly we use its distance to too_high.
- // Conceptually rest ~= too_high - buffer
- // We need to do the following tests in this order to avoid over- and
- // underflows.
- ASSERT(rest <= unsafe_interval);
- while (rest < small_distance && // Negated condition 1
- unsafe_interval - rest >= ten_kappa && // Negated condition 2
- (rest + ten_kappa < small_distance || // buffer{-1} > w_high
- small_distance - rest >= rest + ten_kappa - small_distance)) {
- buffer[length - 1]--;
- rest += ten_kappa;
- }
-
- // We have approached w+ as much as possible. We now test if approaching w-
- // would require changing the buffer. If yes, then we have two possible
- // representations close to w, but we cannot decide which one is closer.
- if (rest < big_distance &&
- unsafe_interval - rest >= ten_kappa &&
- (rest + ten_kappa < big_distance ||
- big_distance - rest > rest + ten_kappa - big_distance)) {
- return false;
- }
-
- // Weeding test.
- // The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
- // Since too_low = too_high - unsafe_interval this is equivalent to
- // [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
- // Conceptually we have: rest ~= too_high - buffer
- return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
- }
-
-
- // Rounds the buffer upwards if the result is closer to v by possibly adding
- // 1 to the buffer. If the precision of the calculation is not sufficient to
- // round correctly, return false.
- // The rounding might shift the whole buffer in which case the kappa is
- // adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
- //
- // If 2*rest > ten_kappa then the buffer needs to be round up.
- // rest can have an error of +/- 1 unit. This function accounts for the
- // imprecision and returns false, if the rounding direction cannot be
- // unambiguously determined.
- //
- // Precondition: rest < ten_kappa.
- static bool RoundWeedCounted(Vector<char> buffer,
- int length,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit,
- int* kappa) {
- ASSERT(rest < ten_kappa);
- // The following tests are done in a specific order to avoid overflows. They
- // will work correctly with any uint64 values of rest < ten_kappa and unit.
- //
- // If the unit is too big, then we don't know which way to round. For example
- // a unit of 50 means that the real number lies within rest +/- 50. If
- // 10^kappa == 40 then there is no way to tell which way to round.
- if (unit >= ten_kappa) return false;
- // Even if unit is just half the size of 10^kappa we are already completely
- // lost. (And after the previous test we know that the expression will not
- // over/underflow.)
- if (ten_kappa - unit <= unit) return false;
- // If 2 * (rest + unit) <= 10^kappa we can safely round down.
- if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
- return true;
- }
- // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
- if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
- // Increment the last digit recursively until we find a non '9' digit.
- buffer[length - 1]++;
- for (int i = length - 1; i > 0; --i) {
- if (buffer[i] != '0' + 10) break;
- buffer[i] = '0';
- buffer[i - 1]++;
- }
- // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
- // exception of the first digit all digits are now '0'. Simply switch the
- // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
- // the power (the kappa) is increased.
- if (buffer[0] == '0' + 10) {
- buffer[0] = '1';
- (*kappa) += 1;
- }
- return true;
- }
- return false;
- }
-
-
- static const uint32_t kTen4 = 10000;
- static const uint32_t kTen5 = 100000;
- static const uint32_t kTen6 = 1000000;
- static const uint32_t kTen7 = 10000000;
- static const uint32_t kTen8 = 100000000;
- static const uint32_t kTen9 = 1000000000;
-
- // Returns the biggest power of ten that is less than or equal to the given
- // number. We furthermore receive the maximum number of bits 'number' has.
- // If number_bits == 0 then 0^-1 is returned
- // The number of bits must be <= 32.
- // Precondition: number < (1 << (number_bits + 1)).
- static void BiggestPowerTen(uint32_t number,
- int number_bits,
- uint32_t* power,
- int* exponent) {
- ASSERT(number < (uint32_t)(1 << (number_bits + 1)));
-
- switch (number_bits) {
- case 32:
- case 31:
- case 30:
- if (kTen9 <= number) {
- *power = kTen9;
- *exponent = 9;
- break;
- } // else fallthrough
- case 29:
- case 28:
- case 27:
- if (kTen8 <= number) {
- *power = kTen8;
- *exponent = 8;
- break;
- } // else fallthrough
- case 26:
- case 25:
- case 24:
- if (kTen7 <= number) {
- *power = kTen7;
- *exponent = 7;
- break;
- } // else fallthrough
- case 23:
- case 22:
- case 21:
- case 20:
- if (kTen6 <= number) {
- *power = kTen6;
- *exponent = 6;
- break;
- } // else fallthrough
- case 19:
- case 18:
- case 17:
- if (kTen5 <= number) {
- *power = kTen5;
- *exponent = 5;
- break;
- } // else fallthrough
- case 16:
- case 15:
- case 14:
- if (kTen4 <= number) {
- *power = kTen4;
- *exponent = 4;
- break;
- } // else fallthrough
- case 13:
- case 12:
- case 11:
- case 10:
- if (1000 <= number) {
- *power = 1000;
- *exponent = 3;
- break;
- } // else fallthrough
- case 9:
- case 8:
- case 7:
- if (100 <= number) {
- *power = 100;
- *exponent = 2;
- break;
- } // else fallthrough
- case 6:
- case 5:
- case 4:
- if (10 <= number) {
- *power = 10;
- *exponent = 1;
- break;
- } // else fallthrough
- case 3:
- case 2:
- case 1:
- if (1 <= number) {
- *power = 1;
- *exponent = 0;
- break;
- } // else fallthrough
- case 0:
- *power = 0;
- *exponent = -1;
- break;
- default:
- // Following assignments are here to silence compiler warnings.
- *power = 0;
- *exponent = 0;
- UNREACHABLE();
- }
- }
-
-
- // Generates the digits of input number w.
- // w is a floating-point number (DiyFp), consisting of a significand and an
- // exponent. Its exponent is bounded by kMinimalTargetExponent and
- // kMaximalTargetExponent.
- // Hence -60 <= w.e() <= -32.
- //
- // Returns false if it fails, in which case the generated digits in the buffer
- // should not be used.
- // Preconditions:
- // * low, w and high are correct up to 1 ulp (unit in the last place). That
- // is, their error must be less than a unit of their last digits.
- // * low.e() == w.e() == high.e()
- // * low < w < high, and taking into account their error: low~ <= high~
- // * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
- // Postconditions: returns false if procedure fails.
- // otherwise:
- // * buffer is not null-terminated, but len contains the number of digits.
- // * buffer contains the shortest possible decimal digit-sequence
- // such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
- // correct values of low and high (without their error).
- // * if more than one decimal representation gives the minimal number of
- // decimal digits then the one closest to W (where W is the correct value
- // of w) is chosen.
- // Remark: this procedure takes into account the imprecision of its input
- // numbers. If the precision is not enough to guarantee all the postconditions
- // then false is returned. This usually happens rarely (~0.5%).
- //
- // Say, for the sake of example, that
- // w.e() == -48, and w.f() == 0x1234567890abcdef
- // w's value can be computed by w.f() * 2^w.e()
- // We can obtain w's integral digits by simply shifting w.f() by -w.e().
- // -> w's integral part is 0x1234
- // w's fractional part is therefore 0x567890abcdef.
- // Printing w's integral part is easy (simply print 0x1234 in decimal).
- // In order to print its fraction we repeatedly multiply the fraction by 10 and
- // get each digit. Example the first digit after the point would be computed by
- // (0x567890abcdef * 10) >> 48. -> 3
- // The whole thing becomes slightly more complicated because we want to stop
- // once we have enough digits. That is, once the digits inside the buffer
- // represent 'w' we can stop. Everything inside the interval low - high
- // represents w. However we have to pay attention to low, high and w's
- // imprecision.
- static bool DigitGen(DiyFp low,
- DiyFp w,
- DiyFp high,
- Vector<char> buffer,
- int* length,
- int* kappa) {
- ASSERT(low.e() == w.e() && w.e() == high.e());
- ASSERT(low.f() + 1 <= high.f() - 1);
- ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
- // low, w and high are imprecise, but by less than one ulp (unit in the last
- // place).
- // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
- // the new numbers are outside of the interval we want the final
- // representation to lie in.
- // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
- // numbers that are certain to lie in the interval. We will use this fact
- // later on.
- // We will now start by generating the digits within the uncertain
- // interval. Later we will weed out representations that lie outside the safe
- // interval and thus _might_ lie outside the correct interval.
- uint64_t unit = 1;
- DiyFp too_low = DiyFp(low.f() - unit, low.e());
- DiyFp too_high = DiyFp(high.f() + unit, high.e());
- // too_low and too_high are guaranteed to lie outside the interval we want the
- // generated number in.
- DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
- // We now cut the input number into two parts: the integral digits and the
- // fractionals. We will not write any decimal separator though, but adapt
- // kappa instead.
- // Reminder: we are currently computing the digits (stored inside the buffer)
- // such that: too_low < buffer * 10^kappa < too_high
- // We use too_high for the digit_generation and stop as soon as possible.
- // If we stop early we effectively round down.
- DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
- // Division by one is a shift.
- uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
- // Modulo by one is an and.
- uint64_t fractionals = too_high.f() & (one.f() - 1);
- uint32_t divisor;
- int divisor_exponent;
- BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- &divisor, &divisor_exponent);
- *kappa = divisor_exponent + 1;
- *length = 0;
- // Loop invariant: buffer = too_high / 10^kappa (integer division)
- // The invariant holds for the first iteration: kappa has been initialized
- // with the divisor exponent + 1. And the divisor is the biggest power of ten
- // that is smaller than integrals.
- while (*kappa > 0) {
- char digit = static_cast<char>(integrals / divisor);
- buffer[*length] = '0' + digit;
- (*length)++;
- integrals %= divisor;
- (*kappa)--;
- // Note that kappa now equals the exponent of the divisor and that the
- // invariant thus holds again.
- uint64_t rest =
- (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
- // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
- // Reminder: unsafe_interval.e() == one.e()
- if (rest < unsafe_interval.f()) {
- // Rounding down (by not emitting the remaining digits) yields a number
- // that lies within the unsafe interval.
- return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
- unsafe_interval.f(), rest,
- static_cast<uint64_t>(divisor) << -one.e(), unit);
- }
- divisor /= 10;
- }
-
- // The integrals have been generated. We are at the point of the decimal
- // separator. In the following loop we simply multiply the remaining digits by
- // 10 and divide by one. We just need to pay attention to multiply associated
- // data (like the interval or 'unit'), too.
- // Note that the multiplication by 10 does not overflow, because w.e >= -60
- // and thus one.e >= -60.
- ASSERT(one.e() >= -60);
- ASSERT(fractionals < one.f());
- ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
- while (true) {
- fractionals *= 10;
- unit *= 10;
- unsafe_interval.set_f(unsafe_interval.f() * 10);
- // Integer division by one.
- char digit = static_cast<char>(fractionals >> -one.e());
- buffer[*length] = '0' + digit;
- (*length)++;
- fractionals &= one.f() - 1; // Modulo by one.
- (*kappa)--;
- if (fractionals < unsafe_interval.f()) {
- return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
- unsafe_interval.f(), fractionals, one.f(), unit);
- }
- }
- }
-
-
-
- // Generates (at most) requested_digits digits of input number w.
- // w is a floating-point number (DiyFp), consisting of a significand and an
- // exponent. Its exponent is bounded by kMinimalTargetExponent and
- // kMaximalTargetExponent.
- // Hence -60 <= w.e() <= -32.
- //
- // Returns false if it fails, in which case the generated digits in the buffer
- // should not be used.
- // Preconditions:
- // * w is correct up to 1 ulp (unit in the last place). That
- // is, its error must be strictly less than a unit of its last digit.
- // * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
- //
- // Postconditions: returns false if procedure fails.
- // otherwise:
- // * buffer is not null-terminated, but length contains the number of
- // digits.
- // * the representation in buffer is the most precise representation of
- // requested_digits digits.
- // * buffer contains at most requested_digits digits of w. If there are less
- // than requested_digits digits then some trailing '0's have been removed.
- // * kappa is such that
- // w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
- //
- // Remark: This procedure takes into account the imprecision of its input
- // numbers. If the precision is not enough to guarantee all the postconditions
- // then false is returned. This usually happens rarely, but the failure-rate
- // increases with higher requested_digits.
- static bool DigitGenCounted(DiyFp w,
- int requested_digits,
- Vector<char> buffer,
- int* length,
- int* kappa) {
- ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
- ASSERT(kMinimalTargetExponent >= -60);
- ASSERT(kMaximalTargetExponent <= -32);
- // w is assumed to have an error less than 1 unit. Whenever w is scaled we
- // also scale its error.
- uint64_t w_error = 1;
- // We cut the input number into two parts: the integral digits and the
- // fractional digits. We don't emit any decimal separator, but adapt kappa
- // instead. Example: instead of writing "1.2" we put "12" into the buffer and
- // increase kappa by 1.
- DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
- // Division by one is a shift.
- uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
- // Modulo by one is an and.
- uint64_t fractionals = w.f() & (one.f() - 1);
- uint32_t divisor;
- int divisor_exponent;
- BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- &divisor, &divisor_exponent);
- *kappa = divisor_exponent + 1;
- *length = 0;
-
- // Loop invariant: buffer = w / 10^kappa (integer division)
- // The invariant holds for the first iteration: kappa has been initialized
- // with the divisor exponent + 1. And the divisor is the biggest power of ten
- // that is smaller than 'integrals'.
- while (*kappa > 0) {
- char digit = static_cast<char>(integrals / divisor);
- buffer[*length] = '0' + digit;
- (*length)++;
- requested_digits--;
- integrals %= divisor;
- (*kappa)--;
- // Note that kappa now equals the exponent of the divisor and that the
- // invariant thus holds again.
- if (requested_digits == 0) break;
- divisor /= 10;
- }
-
- if (requested_digits == 0) {
- uint64_t rest =
- (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
- return RoundWeedCounted(buffer, *length, rest,
- static_cast<uint64_t>(divisor) << -one.e(), w_error,
- kappa);
- }
-
- // The integrals have been generated. We are at the point of the decimal
- // separator. In the following loop we simply multiply the remaining digits by
- // 10 and divide by one. We just need to pay attention to multiply associated
- // data (the 'unit'), too.
- // Note that the multiplication by 10 does not overflow, because w.e >= -60
- // and thus one.e >= -60.
- ASSERT(one.e() >= -60);
- ASSERT(fractionals < one.f());
- ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
- while (requested_digits > 0 && fractionals > w_error) {
- fractionals *= 10;
- w_error *= 10;
- // Integer division by one.
- char digit = static_cast<char>(fractionals >> -one.e());
- buffer[*length] = '0' + digit;
- (*length)++;
- requested_digits--;
- fractionals &= one.f() - 1; // Modulo by one.
- (*kappa)--;
- }
- if (requested_digits != 0) return false;
- return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
- kappa);
- }
-
-
- // Provides a decimal representation of v.
- // Returns true if it succeeds, otherwise the result cannot be trusted.
- // There will be *length digits inside the buffer (not null-terminated).
- // If the function returns true then
- // v == (double) (buffer * 10^decimal_exponent).
- // The digits in the buffer are the shortest representation possible: no
- // 0.09999999999999999 instead of 0.1. The shorter representation will even be
- // chosen even if the longer one would be closer to v.
- // The last digit will be closest to the actual v. That is, even if several
- // digits might correctly yield 'v' when read again, the closest will be
- // computed.
- static bool Grisu3(double v,
- Vector<char> buffer,
- int* length,
- int* decimal_exponent) {
- DiyFp w = Double(v).AsNormalizedDiyFp();
- // boundary_minus and boundary_plus are the boundaries between v and its
- // closest floating-point neighbors. Any number strictly between
- // boundary_minus and boundary_plus will round to v when convert to a double.
- // Grisu3 will never output representations that lie exactly on a boundary.
- DiyFp boundary_minus, boundary_plus;
- Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
- ASSERT(boundary_plus.e() == w.e());
- DiyFp ten_mk; // Cached power of ten: 10^-k
- int mk; // -k
- int ten_mk_minimal_binary_exponent =
- kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- int ten_mk_maximal_binary_exponent =
- kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
- ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize) &&
- (kMaximalTargetExponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize));
- // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
- // 64 bit significand and ten_mk is thus only precise up to 64 bits.
-
- // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
- // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
- // off by a small amount.
- // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
- // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
- // (f-1) * 2^e < w*10^k < (f+1) * 2^e
- DiyFp scaled_w = DiyFp::Times(w, ten_mk);
- ASSERT(scaled_w.e() ==
- boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
- // In theory it would be possible to avoid some recomputations by computing
- // the difference between w and boundary_minus/plus (a power of 2) and to
- // compute scaled_boundary_minus/plus by subtracting/adding from
- // scaled_w. However the code becomes much less readable and the speed
- // enhancements are not terriffic.
- DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
- DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
-
- // DigitGen will generate the digits of scaled_w. Therefore we have
- // v == (double) (scaled_w * 10^-mk).
- // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
- // integer than it will be updated. For instance if scaled_w == 1.23 then
- // the buffer will be filled with "123" und the decimal_exponent will be
- // decreased by 2.
- int kappa;
- bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
- buffer, length, &kappa);
- *decimal_exponent = -mk + kappa;
- return result;
- }
-
-
- // The "counted" version of grisu3 (see above) only generates requested_digits
- // number of digits. This version does not generate the shortest representation,
- // and with enough requested digits 0.1 will at some point print as 0.9999999...
- // Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
- // therefore the rounding strategy for halfway cases is irrelevant.
- static bool Grisu3Counted(double v,
- int requested_digits,
- Vector<char> buffer,
- int* length,
- int* decimal_exponent) {
- DiyFp w = Double(v).AsNormalizedDiyFp();
- DiyFp ten_mk; // Cached power of ten: 10^-k
- int mk; // -k
- int ten_mk_minimal_binary_exponent =
- kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- int ten_mk_maximal_binary_exponent =
- kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
- ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize) &&
- (kMaximalTargetExponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize));
- // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
- // 64 bit significand and ten_mk is thus only precise up to 64 bits.
-
- // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
- // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
- // off by a small amount.
- // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
- // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
- // (f-1) * 2^e < w*10^k < (f+1) * 2^e
- DiyFp scaled_w = DiyFp::Times(w, ten_mk);
-
- // We now have (double) (scaled_w * 10^-mk).
- // DigitGen will generate the first requested_digits digits of scaled_w and
- // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
- // will not always be exactly the same since DigitGenCounted only produces a
- // limited number of digits.)
- int kappa;
- bool result = DigitGenCounted(scaled_w, requested_digits,
- buffer, length, &kappa);
- *decimal_exponent = -mk + kappa;
- return result;
- }
-
-
- bool FastDtoa(double v,
- FastDtoaMode mode,
- int requested_digits,
- Vector<char> buffer,
- int* length,
- int* decimal_point) {
- ASSERT(v > 0);
- ASSERT(!Double(v).IsSpecial());
-
- bool result = false;
- int decimal_exponent = 0;
- switch (mode) {
- case FAST_DTOA_SHORTEST:
- result = Grisu3(v, buffer, length, &decimal_exponent);
- break;
- case FAST_DTOA_PRECISION:
- result = Grisu3Counted(v, requested_digits,
- buffer, length, &decimal_exponent);
- break;
- default:
- UNREACHABLE();
- }
- if (result) {
- *decimal_point = *length + decimal_exponent;
- buffer[*length] = '\0';
- }
- return result;
- }
-
-} // namespace double_conversion
-
-} // namespace WTF
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