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Posted to commits@couchdb.apache.org by rn...@apache.org on 2013/12/24 00:31:16 UTC
[07/12] Replace ejson with jiffy
http://git-wip-us.apache.org/repos/asf/couchdb/blob/2e6092e4/src/jiffy/c_src/double-conversion/fast-dtoa.cc
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diff --git a/src/jiffy/c_src/double-conversion/fast-dtoa.cc b/src/jiffy/c_src/double-conversion/fast-dtoa.cc
new file mode 100644
index 0000000..b2f7b8d
--- /dev/null
+++ b/src/jiffy/c_src/double-conversion/fast-dtoa.cc
@@ -0,0 +1,666 @@
+// Copyright 2012 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 "ieee.h"
+
+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;
+}
+
+// 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.
+//
+// Returns power == 10^(exponent_plus_one-1) such that
+// power <= number < power * 10.
+// If number_bits == 0 then 0^(0-1) is returned.
+// The number of bits must be <= 32.
+// Precondition: number < (1 << (number_bits + 1)).
+
+// Inspired by the method for finding an integer log base 10 from here:
+// http://graphics.stanford.edu/~seander/bithacks.html#IntegerLog10
+static unsigned int const kSmallPowersOfTen[] =
+ {0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
+ 1000000000};
+
+static void BiggestPowerTen(uint32_t number,
+ int number_bits,
+ uint32_t* power,
+ int* exponent_plus_one) {
+ ASSERT(number < (1u << (number_bits + 1)));
+ // 1233/4096 is approximately 1/lg(10).
+ int exponent_plus_one_guess = ((number_bits + 1) * 1233 >> 12);
+ // We increment to skip over the first entry in the kPowersOf10 table.
+ // Note: kPowersOf10[i] == 10^(i-1).
+ exponent_plus_one_guess++;
+ // We don't have any guarantees that 2^number_bits <= number.
+ // TODO(floitsch): can we change the 'while' into an 'if'? We definitely see
+ // number < (2^number_bits - 1), but I haven't encountered
+ // number < (2^number_bits - 2) yet.
+ while (number < kSmallPowersOfTen[exponent_plus_one_guess]) {
+ exponent_plus_one_guess--;
+ if (exponent_plus_one_guess <= 0)
+ break;
+ }
+ *power = kSmallPowersOfTen[exponent_plus_one_guess];
+ *exponent_plus_one = exponent_plus_one_guess;
+}
+
+// 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_plus_one;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent_plus_one);
+ *kappa = divisor_exponent_plus_one;
+ *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) {
+ int digit = 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.
+ 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);
+ }
+ }
+}
+
+
+
+// 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_plus_one;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent_plus_one);
+ *kappa = divisor_exponent_plus_one;
+ *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) {
+ int digit = 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.
+ int digit = static_cast<int>(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,
+ FastDtoaMode mode,
+ 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;
+ if (mode == FAST_DTOA_SHORTEST) {
+ Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+ } else {
+ ASSERT(mode == FAST_DTOA_SHORTEST_SINGLE);
+ float single_v = static_cast<float>(v);
+ Single(single_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:
+ case FAST_DTOA_SHORTEST_SINGLE:
+ result = Grisu3(v, mode, 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
http://git-wip-us.apache.org/repos/asf/couchdb/blob/2e6092e4/src/jiffy/c_src/double-conversion/fast-dtoa.h
----------------------------------------------------------------------
diff --git a/src/jiffy/c_src/double-conversion/fast-dtoa.h b/src/jiffy/c_src/double-conversion/fast-dtoa.h
new file mode 100644
index 0000000..5f1e8ee
--- /dev/null
+++ b/src/jiffy/c_src/double-conversion/fast-dtoa.h
@@ -0,0 +1,88 @@
+// 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.
+
+#ifndef DOUBLE_CONVERSION_FAST_DTOA_H_
+#define DOUBLE_CONVERSION_FAST_DTOA_H_
+
+#include "utils.h"
+
+namespace double_conversion {
+
+enum FastDtoaMode {
+ // Computes the shortest representation of the given input. The returned
+ // result will be the most accurate number of this length. Longer
+ // representations might be more accurate.
+ FAST_DTOA_SHORTEST,
+ // Same as FAST_DTOA_SHORTEST but for single-precision floats.
+ FAST_DTOA_SHORTEST_SINGLE,
+ // Computes a representation where the precision (number of digits) is
+ // given as input. The precision is independent of the decimal point.
+ FAST_DTOA_PRECISION
+};
+
+// FastDtoa will produce at most kFastDtoaMaximalLength digits. This does not
+// include the terminating '\0' character.
+static const int kFastDtoaMaximalLength = 17;
+// Same for single-precision numbers.
+static const int kFastDtoaMaximalSingleLength = 9;
+
+// Provides a decimal representation of v.
+// The result should be interpreted as buffer * 10^(point - length).
+//
+// Precondition:
+// * v must be a strictly positive finite double.
+//
+// Returns true if it succeeds, otherwise the result can not be trusted.
+// There will be *length digits inside the buffer followed by a null terminator.
+// If the function returns true and mode equals
+// - FAST_DTOA_SHORTEST, then
+// the parameter requested_digits is ignored.
+// The result satisfies
+// v == (double) (buffer * 10^(point - length)).
+// The digits in the buffer are the shortest representation possible. E.g.
+// if 0.099999999999 and 0.1 represent the same double then "1" is returned
+// with point = 0.
+// The last digit will be closest to the actual v. That is, even if several
+// digits might correctly yield 'v' when read again, the buffer will contain
+// the one closest to v.
+// - FAST_DTOA_PRECISION, then
+// the buffer contains requested_digits digits.
+// the difference v - (buffer * 10^(point-length)) is closest to zero for
+// all possible representations of requested_digits digits.
+// If there are two values that are equally close, then FastDtoa returns
+// false.
+// For both modes the buffer must be large enough to hold the result.
+bool FastDtoa(double d,
+ FastDtoaMode mode,
+ int requested_digits,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_point);
+
+} // namespace double_conversion
+
+#endif // DOUBLE_CONVERSION_FAST_DTOA_H_
http://git-wip-us.apache.org/repos/asf/couchdb/blob/2e6092e4/src/jiffy/c_src/double-conversion/fixed-dtoa.cc
----------------------------------------------------------------------
diff --git a/src/jiffy/c_src/double-conversion/fixed-dtoa.cc b/src/jiffy/c_src/double-conversion/fixed-dtoa.cc
new file mode 100644
index 0000000..d56b144
--- /dev/null
+++ b/src/jiffy/c_src/double-conversion/fixed-dtoa.cc
@@ -0,0 +1,402 @@
+// 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 <math.h>
+
+#include "fixed-dtoa.h"
+#include "ieee.h"
+
+namespace double_conversion {
+
+// Represents a 128bit type. This class should be replaced by a native type on
+// platforms that support 128bit integers.
+class UInt128 {
+ public:
+ UInt128() : high_bits_(0), low_bits_(0) { }
+ UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
+
+ void Multiply(uint32_t multiplicand) {
+ uint64_t accumulator;
+
+ accumulator = (low_bits_ & kMask32) * multiplicand;
+ uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
+ accumulator >>= 32;
+ accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
+ low_bits_ = (accumulator << 32) + part;
+ accumulator >>= 32;
+ accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
+ part = static_cast<uint32_t>(accumulator & kMask32);
+ accumulator >>= 32;
+ accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
+ high_bits_ = (accumulator << 32) + part;
+ ASSERT((accumulator >> 32) == 0);
+ }
+
+ void Shift(int shift_amount) {
+ ASSERT(-64 <= shift_amount && shift_amount <= 64);
+ if (shift_amount == 0) {
+ return;
+ } else if (shift_amount == -64) {
+ high_bits_ = low_bits_;
+ low_bits_ = 0;
+ } else if (shift_amount == 64) {
+ low_bits_ = high_bits_;
+ high_bits_ = 0;
+ } else if (shift_amount <= 0) {
+ high_bits_ <<= -shift_amount;
+ high_bits_ += low_bits_ >> (64 + shift_amount);
+ low_bits_ <<= -shift_amount;
+ } else {
+ low_bits_ >>= shift_amount;
+ low_bits_ += high_bits_ << (64 - shift_amount);
+ high_bits_ >>= shift_amount;
+ }
+ }
+
+ // Modifies *this to *this MOD (2^power).
+ // Returns *this DIV (2^power).
+ int DivModPowerOf2(int power) {
+ if (power >= 64) {
+ int result = static_cast<int>(high_bits_ >> (power - 64));
+ high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
+ return result;
+ } else {
+ uint64_t part_low = low_bits_ >> power;
+ uint64_t part_high = high_bits_ << (64 - power);
+ int result = static_cast<int>(part_low + part_high);
+ high_bits_ = 0;
+ low_bits_ -= part_low << power;
+ return result;
+ }
+ }
+
+ bool IsZero() const {
+ return high_bits_ == 0 && low_bits_ == 0;
+ }
+
+ int BitAt(int position) {
+ if (position >= 64) {
+ return static_cast<int>(high_bits_ >> (position - 64)) & 1;
+ } else {
+ return static_cast<int>(low_bits_ >> position) & 1;
+ }
+ }
+
+ private:
+ static const uint64_t kMask32 = 0xFFFFFFFF;
+ // Value == (high_bits_ << 64) + low_bits_
+ uint64_t high_bits_;
+ uint64_t low_bits_;
+};
+
+
+static const int kDoubleSignificandSize = 53; // Includes the hidden bit.
+
+
+static void FillDigits32FixedLength(uint32_t number, int requested_length,
+ Vector<char> buffer, int* length) {
+ for (int i = requested_length - 1; i >= 0; --i) {
+ buffer[(*length) + i] = '0' + number % 10;
+ number /= 10;
+ }
+ *length += requested_length;
+}
+
+
+static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
+ int number_length = 0;
+ // We fill the digits in reverse order and exchange them afterwards.
+ while (number != 0) {
+ int digit = number % 10;
+ number /= 10;
+ buffer[(*length) + number_length] = '0' + digit;
+ number_length++;
+ }
+ // Exchange the digits.
+ int i = *length;
+ int j = *length + number_length - 1;
+ while (i < j) {
+ char tmp = buffer[i];
+ buffer[i] = buffer[j];
+ buffer[j] = tmp;
+ i++;
+ j--;
+ }
+ *length += number_length;
+}
+
+
+static void FillDigits64FixedLength(uint64_t number, int requested_length,
+ Vector<char> buffer, int* length) {
+ const uint32_t kTen7 = 10000000;
+ // For efficiency cut the number into 3 uint32_t parts, and print those.
+ uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+ number /= kTen7;
+ uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+ uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+
+ FillDigits32FixedLength(part0, 3, buffer, length);
+ FillDigits32FixedLength(part1, 7, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+}
+
+
+static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
+ const uint32_t kTen7 = 10000000;
+ // For efficiency cut the number into 3 uint32_t parts, and print those.
+ uint32_t part2 = static_cast<uint32_t>(number % kTen7);
+ number /= kTen7;
+ uint32_t part1 = static_cast<uint32_t>(number % kTen7);
+ uint32_t part0 = static_cast<uint32_t>(number / kTen7);
+
+ if (part0 != 0) {
+ FillDigits32(part0, buffer, length);
+ FillDigits32FixedLength(part1, 7, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+ } else if (part1 != 0) {
+ FillDigits32(part1, buffer, length);
+ FillDigits32FixedLength(part2, 7, buffer, length);
+ } else {
+ FillDigits32(part2, buffer, length);
+ }
+}
+
+
+static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
+ // An empty buffer represents 0.
+ if (*length == 0) {
+ buffer[0] = '1';
+ *decimal_point = 1;
+ *length = 1;
+ return;
+ }
+ // Round the last digit until we either have a digit that was not '9' or until
+ // we reached the first digit.
+ buffer[(*length) - 1]++;
+ for (int i = (*length) - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) {
+ return;
+ }
+ buffer[i] = '0';
+ buffer[i - 1]++;
+ }
+ // If the first digit is now '0' + 10, we would need to set it to '0' and add
+ // a '1' in front. However we reach the first digit only if all following
+ // digits had been '9' before rounding up. Now all trailing digits are '0' and
+ // we simply switch the first digit to '1' and update the decimal-point
+ // (indicating that the point is now one digit to the right).
+ if (buffer[0] == '0' + 10) {
+ buffer[0] = '1';
+ (*decimal_point)++;
+ }
+}
+
+
+// The given fractionals number represents a fixed-point number with binary
+// point at bit (-exponent).
+// Preconditions:
+// -128 <= exponent <= 0.
+// 0 <= fractionals * 2^exponent < 1
+// The buffer holds the result.
+// The function will round its result. During the rounding-process digits not
+// generated by this function might be updated, and the decimal-point variable
+// might be updated. If this function generates the digits 99 and the buffer
+// already contained "199" (thus yielding a buffer of "19999") then a
+// rounding-up will change the contents of the buffer to "20000".
+static void FillFractionals(uint64_t fractionals, int exponent,
+ int fractional_count, Vector<char> buffer,
+ int* length, int* decimal_point) {
+ ASSERT(-128 <= exponent && exponent <= 0);
+ // 'fractionals' is a fixed-point number, with binary point at bit
+ // (-exponent). Inside the function the non-converted remainder of fractionals
+ // is a fixed-point number, with binary point at bit 'point'.
+ if (-exponent <= 64) {
+ // One 64 bit number is sufficient.
+ ASSERT(fractionals >> 56 == 0);
+ int point = -exponent;
+ for (int i = 0; i < fractional_count; ++i) {
+ if (fractionals == 0) break;
+ // Instead of multiplying by 10 we multiply by 5 and adjust the point
+ // location. This way the fractionals variable will not overflow.
+ // Invariant at the beginning of the loop: fractionals < 2^point.
+ // Initially we have: point <= 64 and fractionals < 2^56
+ // After each iteration the point is decremented by one.
+ // Note that 5^3 = 125 < 128 = 2^7.
+ // Therefore three iterations of this loop will not overflow fractionals
+ // (even without the subtraction at the end of the loop body). At this
+ // time point will satisfy point <= 61 and therefore fractionals < 2^point
+ // and any further multiplication of fractionals by 5 will not overflow.
+ fractionals *= 5;
+ point--;
+ int digit = static_cast<int>(fractionals >> point);
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ fractionals -= static_cast<uint64_t>(digit) << point;
+ }
+ // If the first bit after the point is set we have to round up.
+ if (((fractionals >> (point - 1)) & 1) == 1) {
+ RoundUp(buffer, length, decimal_point);
+ }
+ } else { // We need 128 bits.
+ ASSERT(64 < -exponent && -exponent <= 128);
+ UInt128 fractionals128 = UInt128(fractionals, 0);
+ fractionals128.Shift(-exponent - 64);
+ int point = 128;
+ for (int i = 0; i < fractional_count; ++i) {
+ if (fractionals128.IsZero()) break;
+ // As before: instead of multiplying by 10 we multiply by 5 and adjust the
+ // point location.
+ // This multiplication will not overflow for the same reasons as before.
+ fractionals128.Multiply(5);
+ point--;
+ int digit = fractionals128.DivModPowerOf2(point);
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ }
+ if (fractionals128.BitAt(point - 1) == 1) {
+ RoundUp(buffer, length, decimal_point);
+ }
+ }
+}
+
+
+// Removes leading and trailing zeros.
+// If leading zeros are removed then the decimal point position is adjusted.
+static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
+ while (*length > 0 && buffer[(*length) - 1] == '0') {
+ (*length)--;
+ }
+ int first_non_zero = 0;
+ while (first_non_zero < *length && buffer[first_non_zero] == '0') {
+ first_non_zero++;
+ }
+ if (first_non_zero != 0) {
+ for (int i = first_non_zero; i < *length; ++i) {
+ buffer[i - first_non_zero] = buffer[i];
+ }
+ *length -= first_non_zero;
+ *decimal_point -= first_non_zero;
+ }
+}
+
+
+bool FastFixedDtoa(double v,
+ int fractional_count,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_point) {
+ const uint32_t kMaxUInt32 = 0xFFFFFFFF;
+ uint64_t significand = Double(v).Significand();
+ int exponent = Double(v).Exponent();
+ // v = significand * 2^exponent (with significand a 53bit integer).
+ // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
+ // don't know how to compute the representation. 2^73 ~= 9.5*10^21.
+ // If necessary this limit could probably be increased, but we don't need
+ // more.
+ if (exponent > 20) return false;
+ if (fractional_count > 20) return false;
+ *length = 0;
+ // At most kDoubleSignificandSize bits of the significand are non-zero.
+ // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
+ // bits: 0..11*..0xxx..53*..xx
+ if (exponent + kDoubleSignificandSize > 64) {
+ // The exponent must be > 11.
+ //
+ // We know that v = significand * 2^exponent.
+ // And the exponent > 11.
+ // We simplify the task by dividing v by 10^17.
+ // The quotient delivers the first digits, and the remainder fits into a 64
+ // bit number.
+ // Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
+ const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17
+ uint64_t divisor = kFive17;
+ int divisor_power = 17;
+ uint64_t dividend = significand;
+ uint32_t quotient;
+ uint64_t remainder;
+ // Let v = f * 2^e with f == significand and e == exponent.
+ // Then need q (quotient) and r (remainder) as follows:
+ // v = q * 10^17 + r
+ // f * 2^e = q * 10^17 + r
+ // f * 2^e = q * 5^17 * 2^17 + r
+ // If e > 17 then
+ // f * 2^(e-17) = q * 5^17 + r/2^17
+ // else
+ // f = q * 5^17 * 2^(17-e) + r/2^e
+ if (exponent > divisor_power) {
+ // We only allow exponents of up to 20 and therefore (17 - e) <= 3
+ dividend <<= exponent - divisor_power;
+ quotient = static_cast<uint32_t>(dividend / divisor);
+ remainder = (dividend % divisor) << divisor_power;
+ } else {
+ divisor <<= divisor_power - exponent;
+ quotient = static_cast<uint32_t>(dividend / divisor);
+ remainder = (dividend % divisor) << exponent;
+ }
+ FillDigits32(quotient, buffer, length);
+ FillDigits64FixedLength(remainder, divisor_power, buffer, length);
+ *decimal_point = *length;
+ } else if (exponent >= 0) {
+ // 0 <= exponent <= 11
+ significand <<= exponent;
+ FillDigits64(significand, buffer, length);
+ *decimal_point = *length;
+ } else if (exponent > -kDoubleSignificandSize) {
+ // We have to cut the number.
+ uint64_t integrals = significand >> -exponent;
+ uint64_t fractionals = significand - (integrals << -exponent);
+ if (integrals > kMaxUInt32) {
+ FillDigits64(integrals, buffer, length);
+ } else {
+ FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
+ }
+ *decimal_point = *length;
+ FillFractionals(fractionals, exponent, fractional_count,
+ buffer, length, decimal_point);
+ } else if (exponent < -128) {
+ // This configuration (with at most 20 digits) means that all digits must be
+ // 0.
+ ASSERT(fractional_count <= 20);
+ buffer[0] = '\0';
+ *length = 0;
+ *decimal_point = -fractional_count;
+ } else {
+ *decimal_point = 0;
+ FillFractionals(significand, exponent, fractional_count,
+ buffer, length, decimal_point);
+ }
+ TrimZeros(buffer, length, decimal_point);
+ buffer[*length] = '\0';
+ if ((*length) == 0) {
+ // The string is empty and the decimal_point thus has no importance. Mimick
+ // Gay's dtoa and and set it to -fractional_count.
+ *decimal_point = -fractional_count;
+ }
+ return true;
+}
+
+} // namespace double_conversion
http://git-wip-us.apache.org/repos/asf/couchdb/blob/2e6092e4/src/jiffy/c_src/double-conversion/fixed-dtoa.h
----------------------------------------------------------------------
diff --git a/src/jiffy/c_src/double-conversion/fixed-dtoa.h b/src/jiffy/c_src/double-conversion/fixed-dtoa.h
new file mode 100644
index 0000000..3bdd08e
--- /dev/null
+++ b/src/jiffy/c_src/double-conversion/fixed-dtoa.h
@@ -0,0 +1,56 @@
+// 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.
+
+#ifndef DOUBLE_CONVERSION_FIXED_DTOA_H_
+#define DOUBLE_CONVERSION_FIXED_DTOA_H_
+
+#include "utils.h"
+
+namespace double_conversion {
+
+// Produces digits necessary to print a given number with
+// 'fractional_count' digits after the decimal point.
+// The buffer must be big enough to hold the result plus one terminating null
+// character.
+//
+// The produced digits might be too short in which case the caller has to fill
+// the gaps with '0's.
+// Example: FastFixedDtoa(0.001, 5, ...) is allowed to return buffer = "1", and
+// decimal_point = -2.
+// Halfway cases are rounded towards +/-Infinity (away from 0). The call
+// FastFixedDtoa(0.15, 2, ...) thus returns buffer = "2", decimal_point = 0.
+// The returned buffer may contain digits that would be truncated from the
+// shortest representation of the input.
+//
+// This method only works for some parameters. If it can't handle the input it
+// returns false. The output is null-terminated when the function succeeds.
+bool FastFixedDtoa(double v, int fractional_count,
+ Vector<char> buffer, int* length, int* decimal_point);
+
+} // namespace double_conversion
+
+#endif // DOUBLE_CONVERSION_FIXED_DTOA_H_
http://git-wip-us.apache.org/repos/asf/couchdb/blob/2e6092e4/src/jiffy/c_src/double-conversion/ieee.h
----------------------------------------------------------------------
diff --git a/src/jiffy/c_src/double-conversion/ieee.h b/src/jiffy/c_src/double-conversion/ieee.h
new file mode 100644
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--- /dev/null
+++ b/src/jiffy/c_src/double-conversion/ieee.h
@@ -0,0 +1,398 @@
+// Copyright 2012 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.
+
+#ifndef DOUBLE_CONVERSION_DOUBLE_H_
+#define DOUBLE_CONVERSION_DOUBLE_H_
+
+#include "diy-fp.h"
+
+namespace double_conversion {
+
+// We assume that doubles and uint64_t have the same endianness.
+static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
+static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
+static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
+static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
+
+// Helper functions for doubles.
+class Double {
+ public:
+ static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000);
+ static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000);
+ static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
+ static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000);
+ static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
+ static const int kSignificandSize = 53;
+
+ Double() : d64_(0) {}
+ explicit Double(double d) : d64_(double_to_uint64(d)) {}
+ explicit Double(uint64_t d64) : d64_(d64) {}
+ explicit Double(DiyFp diy_fp)
+ : d64_(DiyFpToUint64(diy_fp)) {}
+
+ // The value encoded by this Double must be greater or equal to +0.0.
+ // It must not be special (infinity, or NaN).
+ DiyFp AsDiyFp() const {
+ ASSERT(Sign() > 0);
+ ASSERT(!IsSpecial());
+ return DiyFp(Significand(), Exponent());
+ }
+
+ // The value encoded by this Double must be strictly greater than 0.
+ DiyFp AsNormalizedDiyFp() const {
+ ASSERT(value() > 0.0);
+ uint64_t f = Significand();
+ int e = Exponent();
+
+ // The current double could be a denormal.
+ while ((f & kHiddenBit) == 0) {
+ f <<= 1;
+ e--;
+ }
+ // Do the final shifts in one go.
+ f <<= DiyFp::kSignificandSize - kSignificandSize;
+ e -= DiyFp::kSignificandSize - kSignificandSize;
+ return DiyFp(f, e);
+ }
+
+ // Returns the double's bit as uint64.
+ uint64_t AsUint64() const {
+ return d64_;
+ }
+
+ // Returns the next greater double. Returns +infinity on input +infinity.
+ double NextDouble() const {
+ if (d64_ == kInfinity) return Double(kInfinity).value();
+ if (Sign() < 0 && Significand() == 0) {
+ // -0.0
+ return 0.0;
+ }
+ if (Sign() < 0) {
+ return Double(d64_ - 1).value();
+ } else {
+ return Double(d64_ + 1).value();
+ }
+ }
+
+ double PreviousDouble() const {
+ if (d64_ == (kInfinity | kSignMask)) return -Double::Infinity();
+ if (Sign() < 0) {
+ return Double(d64_ + 1).value();
+ } else {
+ if (Significand() == 0) return -0.0;
+ return Double(d64_ - 1).value();
+ }
+ }
+
+ int Exponent() const {
+ if (IsDenormal()) return kDenormalExponent;
+
+ uint64_t d64 = AsUint64();
+ int biased_e =
+ static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
+ return biased_e - kExponentBias;
+ }
+
+ uint64_t Significand() const {
+ uint64_t d64 = AsUint64();
+ uint64_t significand = d64 & kSignificandMask;
+ if (!IsDenormal()) {
+ return significand + kHiddenBit;
+ } else {
+ return significand;
+ }
+ }
+
+ // Returns true if the double is a denormal.
+ bool IsDenormal() const {
+ uint64_t d64 = AsUint64();
+ return (d64 & kExponentMask) == 0;
+ }
+
+ // We consider denormals not to be special.
+ // Hence only Infinity and NaN are special.
+ bool IsSpecial() const {
+ uint64_t d64 = AsUint64();
+ return (d64 & kExponentMask) == kExponentMask;
+ }
+
+ bool IsNan() const {
+ uint64_t d64 = AsUint64();
+ return ((d64 & kExponentMask) == kExponentMask) &&
+ ((d64 & kSignificandMask) != 0);
+ }
+
+ bool IsInfinite() const {
+ uint64_t d64 = AsUint64();
+ return ((d64 & kExponentMask) == kExponentMask) &&
+ ((d64 & kSignificandMask) == 0);
+ }
+
+ int Sign() const {
+ uint64_t d64 = AsUint64();
+ return (d64 & kSignMask) == 0? 1: -1;
+ }
+
+ // Precondition: the value encoded by this Double must be greater or equal
+ // than +0.0.
+ DiyFp UpperBoundary() const {
+ ASSERT(Sign() > 0);
+ return DiyFp(Significand() * 2 + 1, Exponent() - 1);
+ }
+
+ // Computes the two boundaries of this.
+ // The bigger boundary (m_plus) is normalized. The lower boundary has the same
+ // exponent as m_plus.
+ // Precondition: the value encoded by this Double must be greater than 0.
+ void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
+ ASSERT(value() > 0.0);
+ DiyFp v = this->AsDiyFp();
+ DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
+ DiyFp m_minus;
+ if (LowerBoundaryIsCloser()) {
+ m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
+ } else {
+ m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
+ }
+ m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
+ m_minus.set_e(m_plus.e());
+ *out_m_plus = m_plus;
+ *out_m_minus = m_minus;
+ }
+
+ bool LowerBoundaryIsCloser() const {
+ // The boundary is closer if the significand is of the form f == 2^p-1 then
+ // the lower boundary is closer.
+ // Think of v = 1000e10 and v- = 9999e9.
+ // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
+ // at a distance of 1e8.
+ // The only exception is for the smallest normal: the largest denormal is
+ // at the same distance as its successor.
+ // Note: denormals have the same exponent as the smallest normals.
+ bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
+ return physical_significand_is_zero && (Exponent() != kDenormalExponent);
+ }
+
+ double value() const { return uint64_to_double(d64_); }
+
+ // Returns the significand size for a given order of magnitude.
+ // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
+ // This function returns the number of significant binary digits v will have
+ // once it's encoded into a double. In almost all cases this is equal to
+ // kSignificandSize. The only exceptions are denormals. They start with
+ // leading zeroes and their effective significand-size is hence smaller.
+ static int SignificandSizeForOrderOfMagnitude(int order) {
+ if (order >= (kDenormalExponent + kSignificandSize)) {
+ return kSignificandSize;
+ }
+ if (order <= kDenormalExponent) return 0;
+ return order - kDenormalExponent;
+ }
+
+ static double Infinity() {
+ return Double(kInfinity).value();
+ }
+
+ static double NaN() {
+ return Double(kNaN).value();
+ }
+
+ private:
+ static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
+ static const int kDenormalExponent = -kExponentBias + 1;
+ static const int kMaxExponent = 0x7FF - kExponentBias;
+ static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000);
+ static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000);
+
+ const uint64_t d64_;
+
+ static uint64_t DiyFpToUint64(DiyFp diy_fp) {
+ uint64_t significand = diy_fp.f();
+ int exponent = diy_fp.e();
+ while (significand > kHiddenBit + kSignificandMask) {
+ significand >>= 1;
+ exponent++;
+ }
+ if (exponent >= kMaxExponent) {
+ return kInfinity;
+ }
+ if (exponent < kDenormalExponent) {
+ return 0;
+ }
+ while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
+ significand <<= 1;
+ exponent--;
+ }
+ uint64_t biased_exponent;
+ if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
+ biased_exponent = 0;
+ } else {
+ biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
+ }
+ return (significand & kSignificandMask) |
+ (biased_exponent << kPhysicalSignificandSize);
+ }
+};
+
+class Single {
+ public:
+ static const uint32_t kSignMask = 0x80000000;
+ static const uint32_t kExponentMask = 0x7F800000;
+ static const uint32_t kSignificandMask = 0x007FFFFF;
+ static const uint32_t kHiddenBit = 0x00800000;
+ static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit.
+ static const int kSignificandSize = 24;
+
+ Single() : d32_(0) {}
+ explicit Single(float f) : d32_(float_to_uint32(f)) {}
+ explicit Single(uint32_t d32) : d32_(d32) {}
+
+ // The value encoded by this Single must be greater or equal to +0.0.
+ // It must not be special (infinity, or NaN).
+ DiyFp AsDiyFp() const {
+ ASSERT(Sign() > 0);
+ ASSERT(!IsSpecial());
+ return DiyFp(Significand(), Exponent());
+ }
+
+ // Returns the single's bit as uint64.
+ uint32_t AsUint32() const {
+ return d32_;
+ }
+
+ int Exponent() const {
+ if (IsDenormal()) return kDenormalExponent;
+
+ uint32_t d32 = AsUint32();
+ int biased_e =
+ static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
+ return biased_e - kExponentBias;
+ }
+
+ uint32_t Significand() const {
+ uint32_t d32 = AsUint32();
+ uint32_t significand = d32 & kSignificandMask;
+ if (!IsDenormal()) {
+ return significand + kHiddenBit;
+ } else {
+ return significand;
+ }
+ }
+
+ // Returns true if the single is a denormal.
+ bool IsDenormal() const {
+ uint32_t d32 = AsUint32();
+ return (d32 & kExponentMask) == 0;
+ }
+
+ // We consider denormals not to be special.
+ // Hence only Infinity and NaN are special.
+ bool IsSpecial() const {
+ uint32_t d32 = AsUint32();
+ return (d32 & kExponentMask) == kExponentMask;
+ }
+
+ bool IsNan() const {
+ uint32_t d32 = AsUint32();
+ return ((d32 & kExponentMask) == kExponentMask) &&
+ ((d32 & kSignificandMask) != 0);
+ }
+
+ bool IsInfinite() const {
+ uint32_t d32 = AsUint32();
+ return ((d32 & kExponentMask) == kExponentMask) &&
+ ((d32 & kSignificandMask) == 0);
+ }
+
+ int Sign() const {
+ uint32_t d32 = AsUint32();
+ return (d32 & kSignMask) == 0? 1: -1;
+ }
+
+ // Computes the two boundaries of this.
+ // The bigger boundary (m_plus) is normalized. The lower boundary has the same
+ // exponent as m_plus.
+ // Precondition: the value encoded by this Single must be greater than 0.
+ void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
+ ASSERT(value() > 0.0);
+ DiyFp v = this->AsDiyFp();
+ DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
+ DiyFp m_minus;
+ if (LowerBoundaryIsCloser()) {
+ m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
+ } else {
+ m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
+ }
+ m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
+ m_minus.set_e(m_plus.e());
+ *out_m_plus = m_plus;
+ *out_m_minus = m_minus;
+ }
+
+ // Precondition: the value encoded by this Single must be greater or equal
+ // than +0.0.
+ DiyFp UpperBoundary() const {
+ ASSERT(Sign() > 0);
+ return DiyFp(Significand() * 2 + 1, Exponent() - 1);
+ }
+
+ bool LowerBoundaryIsCloser() const {
+ // The boundary is closer if the significand is of the form f == 2^p-1 then
+ // the lower boundary is closer.
+ // Think of v = 1000e10 and v- = 9999e9.
+ // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
+ // at a distance of 1e8.
+ // The only exception is for the smallest normal: the largest denormal is
+ // at the same distance as its successor.
+ // Note: denormals have the same exponent as the smallest normals.
+ bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
+ return physical_significand_is_zero && (Exponent() != kDenormalExponent);
+ }
+
+ float value() const { return uint32_to_float(d32_); }
+
+ static float Infinity() {
+ return Single(kInfinity).value();
+ }
+
+ static float NaN() {
+ return Single(kNaN).value();
+ }
+
+ private:
+ static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
+ static const int kDenormalExponent = -kExponentBias + 1;
+ static const int kMaxExponent = 0xFF - kExponentBias;
+ static const uint32_t kInfinity = 0x7F800000;
+ static const uint32_t kNaN = 0x7FC00000;
+
+ const uint32_t d32_;
+};
+
+} // namespace double_conversion
+
+#endif // DOUBLE_CONVERSION_DOUBLE_H_