Update V8 to r4588
We're using WebKit r58033, as used by
http://src.chromium.org/svn/releases/5.0.387.0/DEPS
This requires http://v8.googlecode.com/svn/trunk@4465 but this version has a
crashing bug for ARM. Instead we use http://v8.googlecode.com/svn/trunk@4588,
which is used by http://src.chromium.org/svn/releases/6.0.399.0/DEPS
Note that a trivial bug fix was required in arm/codegen-arm.cc. This is guarded
with ANDROID. See http://code.google.com/p/v8/issues/detail?id=703
Change-Id: I459647a8286c4f8c7405f0c5581ecbf051a6f1e8
diff --git a/src/fast-dtoa.cc b/src/fast-dtoa.cc
new file mode 100644
index 0000000..4c0d15d
--- /dev/null
+++ b/src/fast-dtoa.cc
@@ -0,0 +1,512 @@
+// 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 "v8.h"
+
+#include "fast-dtoa.h"
+
+#include "cached-powers.h"
+#include "diy-fp.h"
+#include "double.h"
+
+namespace v8 {
+namespace internal {
+
+// 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 minimal_target_exponent = -60;
+static const int maximal_target_exponent = -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 ctannot 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.
+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_low[ (often written as "(w_low; w_low)")
+
+ // 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 rounding
+ // the buffer. If we have two potential representations we need to make sure
+ // that the chosen one is closer to w_low and w_high since v can be anywhere
+ // between them.
+ //
+ // 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
+ 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);
+}
+
+
+
+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 than 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: (1 << number_bits) <= number < (1 << (number_bits + 1)).
+static void BiggestPowerTen(uint32_t number,
+ int number_bits,
+ uint32_t* power,
+ int* exponent) {
+ 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 minimal_target_exponent and
+// maximal_target_exponent.
+// 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 that a unit of their last digits.
+// * low.e() == w.e() == high.e()
+// * low < w < high, and taking into account their error: low~ <= high~
+// * minimal_target_exponent <= w.e() <= maximal_target_exponent
+// 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 comma 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.
+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(minimal_target_exponent <= w.e() && w.e() <= maximal_target_exponent);
+ // 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 divider;
+ int divider_exponent;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ ÷r, ÷r_exponent);
+ *kappa = divider_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 divider exponent + 1. And the divider is the biggest power of ten
+ // that is smaller than integrals.
+ while (*kappa > 0) {
+ int digit = integrals / divider;
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ integrals %= divider;
+ (*kappa)--;
+ // Note that kappa now equals the exponent of the divider 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>(divider) << -one.e(), unit);
+ }
+ divider /= 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.
+ // Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
+ // increase its (imaginary) exponent. At the same time we decrease the
+ // divider's (one's) exponent and shift its significand.
+ // Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
+ // fractionals.f *= 10;
+ // fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
+ // one.f >>= 1; one.e++; // value remains unchanged.
+ // and we have again fractionals.e == one.e which allows us to divide
+ // fractionals.f() by one.f()
+ // We simply combine the *= 10 and the >>= 1.
+ while (true) {
+ fractionals *= 5;
+ unit *= 5;
+ unsafe_interval.set_f(unsafe_interval.f() * 5);
+ unsafe_interval.set_e(unsafe_interval.e() + 1); // Will be optimized out.
+ one.set_f(one.f() >> 1);
+ one.set_e(one.e() + 1);
+ // Integer division by one.
+ int digit = static_cast<int>(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);
+ }
+ }
+}
+
+
+// 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.
+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
+ GetCachedPower(w.e() + DiyFp::kSignificandSize, minimal_target_exponent,
+ maximal_target_exponent, &mk, &ten_mk);
+ ASSERT(minimal_target_exponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize &&
+ maximal_target_exponent >= 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;
+}
+
+
+bool FastDtoa(double v,
+ Vector<char> buffer,
+ int* sign,
+ int* length,
+ int* point) {
+ ASSERT(v != 0);
+ ASSERT(!Double(v).IsSpecial());
+
+ if (v < 0) {
+ v = -v;
+ *sign = 1;
+ } else {
+ *sign = 0;
+ }
+ int decimal_exponent;
+ bool result = grisu3(v, buffer, length, &decimal_exponent);
+ *point = *length + decimal_exponent;
+ buffer[*length] = '\0';
+ return result;
+}
+
+} } // namespace v8::internal