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https://github.com/ClickHouse/ClickHouse.git
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Use double-conversion as submodule
This commit is contained in:
proller
alexey-milovidov
parent
dc6127f672
commit
d8a92e80d6
3
.gitmodules
vendored
3
.gitmodules
vendored
@ -25,3 +25,6 @@
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[submodule "contrib/capnproto"]
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path = contrib/capnproto
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url = https://github.com/capnproto/capnproto.git
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[submodule "contrib/double-conversion"]
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path = contrib/double-conversion
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url = https://github.com/google/double-conversion.git
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@ -3,5 +3,5 @@ set(DIVIDE_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/contrib/libdivide)
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set(CITYHASH_CONTRIB_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/contrib/libcityhash/include)
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set(COMMON_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/libs/libcommon/include ${ClickHouse_BINARY_DIR}/libs/libcommon/include)
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set(DBMS_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/dbms/src ${ClickHouse_BINARY_DIR}/dbms/src)
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set(DOUBLE_CONVERSION_CONTRIB_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/contrib/libdouble-conversion)
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set(DOUBLE_CONVERSION_CONTRIB_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/contrib/double-conversion)
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set(PCG_RANDOM_INCLUDE_DIR ${ClickHouse_SOURCE_DIR}/contrib/libpcg-random/include)
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2
contrib/CMakeLists.txt
vendored
2
contrib/CMakeLists.txt
vendored
@ -17,7 +17,7 @@ if (USE_INTERNAL_RE2_LIBRARY)
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endif ()
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if (USE_INTERNAL_DOUBLE_CONVERSION_LIBRARY)
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add_subdirectory (libdouble-conversion)
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add_subdirectory (double-conversion)
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endif ()
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if (USE_INTERNAL_ZOOKEEPER_LIBRARY)
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1
contrib/double-conversion
vendored
Submodule
1
contrib/double-conversion
vendored
Submodule
@ -0,0 +1 @@
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Subproject commit cf2f0f3d547dc73b4612028a155b80536902ba02
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@ -1,22 +0,0 @@
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add_library (double-conversion
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double-conversion/bignum.cc
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double-conversion/bignum-dtoa.cc
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double-conversion/bignum-dtoa.h
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double-conversion/bignum.h
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double-conversion/cached-powers.cc
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double-conversion/cached-powers.h
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double-conversion/diy-fp.cc
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double-conversion/diy-fp.h
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double-conversion/double-conversion.cc
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double-conversion/double-conversion.h
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double-conversion/fast-dtoa.cc
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double-conversion/fast-dtoa.h
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double-conversion/fixed-dtoa.cc
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double-conversion/fixed-dtoa.h
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double-conversion/ieee.h
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double-conversion/strtod.cc
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double-conversion/strtod.h
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double-conversion/utils.h
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)
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target_include_directories (double-conversion PUBLIC .)
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@ -1,26 +0,0 @@
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Copyright 2006-2011, the V8 project authors. All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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||||
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* Redistributions of source code must retain the above copyright
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||||
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
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||||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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@ -1 +0,0 @@
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https://github.com/google/double-conversion/tree/cf2f0f3d547dc73b4612028a155b80536902ba02
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@ -1,641 +0,0 @@
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// Copyright 2010 the V8 project authors. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * 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.
|
||||
//
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// 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
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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#include <cmath>
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#include <double-conversion/bignum-dtoa.h>
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#include <double-conversion/bignum.h>
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#include <double-conversion/ieee.h>
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namespace double_conversion {
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static int NormalizedExponent(uint64_t significand, int exponent) {
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ASSERT(significand != 0);
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while ((significand & Double::kHiddenBit) == 0) {
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significand = significand << 1;
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exponent = exponent - 1;
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}
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return exponent;
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}
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// Forward declarations:
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// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
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static int EstimatePower(int exponent);
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// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
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// and denominator.
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static void InitialScaledStartValues(uint64_t significand,
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int exponent,
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bool lower_boundary_is_closer,
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int estimated_power,
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bool need_boundary_deltas,
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Bignum* numerator,
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Bignum* denominator,
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Bignum* delta_minus,
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Bignum* delta_plus);
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// Multiplies numerator/denominator so that its values lies in the range 1-10.
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// Returns decimal_point s.t.
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// v = numerator'/denominator' * 10^(decimal_point-1)
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// where numerator' and denominator' are the values of numerator and
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// denominator after the call to this function.
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static void FixupMultiply10(int estimated_power, bool is_even,
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int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus);
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// Generates digits from the left to the right and stops when the generated
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// digits yield the shortest decimal representation of v.
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static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus,
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bool is_even,
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Vector<char> buffer, int* length);
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// Generates 'requested_digits' after the decimal point.
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static void BignumToFixed(int requested_digits, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length);
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// Generates 'count' digits of numerator/denominator.
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// Once 'count' digits have been produced rounds the result depending on the
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// remainder (remainders of exactly .5 round upwards). Might update the
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// decimal_point when rounding up (for example for 0.9999).
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static void GenerateCountedDigits(int count, int* decimal_point,
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Bignum* numerator, Bignum* denominator,
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Vector<char>(buffer), int* length);
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void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
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Vector<char> buffer, int* length, int* decimal_point) {
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ASSERT(v > 0);
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ASSERT(!Double(v).IsSpecial());
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uint64_t significand;
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int exponent;
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bool lower_boundary_is_closer;
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if (mode == BIGNUM_DTOA_SHORTEST_SINGLE) {
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float f = static_cast<float>(v);
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ASSERT(f == v);
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significand = Single(f).Significand();
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exponent = Single(f).Exponent();
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lower_boundary_is_closer = Single(f).LowerBoundaryIsCloser();
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} else {
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significand = Double(v).Significand();
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exponent = Double(v).Exponent();
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lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser();
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}
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bool need_boundary_deltas =
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(mode == BIGNUM_DTOA_SHORTEST || mode == BIGNUM_DTOA_SHORTEST_SINGLE);
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bool is_even = (significand & 1) == 0;
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int normalized_exponent = NormalizedExponent(significand, exponent);
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// estimated_power might be too low by 1.
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int estimated_power = EstimatePower(normalized_exponent);
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// Shortcut for Fixed.
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// The requested digits correspond to the digits after the point. If the
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// number is much too small, then there is no need in trying to get any
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// digits.
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if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
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buffer[0] = '\0';
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*length = 0;
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// Set decimal-point to -requested_digits. This is what Gay does.
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// Note that it should not have any effect anyways since the string is
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// empty.
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*decimal_point = -requested_digits;
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return;
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}
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Bignum numerator;
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Bignum denominator;
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Bignum delta_minus;
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Bignum delta_plus;
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// Make sure the bignum can grow large enough. The smallest double equals
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// 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
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// The maximum double is 1.7976931348623157e308 which needs fewer than
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// 308*4 binary digits.
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ASSERT(Bignum::kMaxSignificantBits >= 324*4);
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InitialScaledStartValues(significand, exponent, lower_boundary_is_closer,
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estimated_power, need_boundary_deltas,
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&numerator, &denominator,
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&delta_minus, &delta_plus);
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// We now have v = (numerator / denominator) * 10^estimated_power.
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FixupMultiply10(estimated_power, is_even, decimal_point,
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&numerator, &denominator,
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&delta_minus, &delta_plus);
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// We now have v = (numerator / denominator) * 10^(decimal_point-1), and
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// 1 <= (numerator + delta_plus) / denominator < 10
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switch (mode) {
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case BIGNUM_DTOA_SHORTEST:
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case BIGNUM_DTOA_SHORTEST_SINGLE:
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GenerateShortestDigits(&numerator, &denominator,
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&delta_minus, &delta_plus,
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is_even, buffer, length);
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break;
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case BIGNUM_DTOA_FIXED:
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BignumToFixed(requested_digits, decimal_point,
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&numerator, &denominator,
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buffer, length);
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break;
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case BIGNUM_DTOA_PRECISION:
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GenerateCountedDigits(requested_digits, decimal_point,
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&numerator, &denominator,
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buffer, length);
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break;
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default:
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UNREACHABLE();
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}
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buffer[*length] = '\0';
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}
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// The procedure starts generating digits from the left to the right and stops
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// when the generated digits yield the shortest decimal representation of v. A
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// decimal representation of v is a number lying closer to v than to any other
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// double, so it converts to v when read.
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//
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// This is true if d, the decimal representation, is between m- and m+, the
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// upper and lower boundaries. d must be strictly between them if !is_even.
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// m- := (numerator - delta_minus) / denominator
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// m+ := (numerator + delta_plus) / denominator
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//
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// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
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// If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
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// will be produced. This should be the standard precondition.
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static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
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Bignum* delta_minus, Bignum* delta_plus,
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bool is_even,
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Vector<char> buffer, int* length) {
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// Small optimization: if delta_minus and delta_plus are the same just reuse
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// one of the two bignums.
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if (Bignum::Equal(*delta_minus, *delta_plus)) {
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delta_plus = delta_minus;
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}
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*length = 0;
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for (;;) {
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uint16_t digit;
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digit = numerator->DivideModuloIntBignum(*denominator);
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ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
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// digit = numerator / denominator (integer division).
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// numerator = numerator % denominator.
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buffer[(*length)++] = static_cast<char>(digit + '0');
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// Can we stop already?
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// If the remainder of the division is less than the distance to the lower
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// boundary we can stop. In this case we simply round down (discarding the
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// remainder).
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// Similarly we test if we can round up (using the upper boundary).
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bool in_delta_room_minus;
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bool in_delta_room_plus;
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if (is_even) {
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in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
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} else {
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in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
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}
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if (is_even) {
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in_delta_room_plus =
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Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
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} else {
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in_delta_room_plus =
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Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
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}
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if (!in_delta_room_minus && !in_delta_room_plus) {
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// Prepare for next iteration.
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numerator->Times10();
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delta_minus->Times10();
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// We optimized delta_plus to be equal to delta_minus (if they share the
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// same value). So don't multiply delta_plus if they point to the same
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// object.
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if (delta_minus != delta_plus) {
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delta_plus->Times10();
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}
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} else if (in_delta_room_minus && in_delta_room_plus) {
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// Let's see if 2*numerator < denominator.
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// If yes, then the next digit would be < 5 and we can round down.
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int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
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if (compare < 0) {
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// Remaining digits are less than .5. -> Round down (== do nothing).
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} else if (compare > 0) {
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// Remaining digits are more than .5 of denominator. -> Round up.
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// Note that the last digit could not be a '9' as otherwise the whole
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// loop would have stopped earlier.
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// We still have an assert here in case the preconditions were not
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// satisfied.
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||||
ASSERT(buffer[(*length) - 1] != '9');
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buffer[(*length) - 1]++;
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} else {
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// Halfway case.
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// TODO(floitsch): need a way to solve half-way cases.
|
||||
// For now let's round towards even (since this is what Gay seems to
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// do).
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||||
if ((buffer[(*length) - 1] - '0') % 2 == 0) {
|
||||
// Round down => Do nothing.
|
||||
} else {
|
||||
ASSERT(buffer[(*length) - 1] != '9');
|
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buffer[(*length) - 1]++;
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||||
}
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||||
}
|
||||
return;
|
||||
} else if (in_delta_room_minus) {
|
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// Round down (== do nothing).
|
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return;
|
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} else { // in_delta_room_plus
|
||||
// Round up.
|
||||
// Note again that the last digit could not be '9' since this would have
|
||||
// stopped the loop earlier.
|
||||
// We still have an ASSERT here, in case the preconditions were not
|
||||
// satisfied.
|
||||
ASSERT(buffer[(*length) -1] != '9');
|
||||
buffer[(*length) - 1]++;
|
||||
return;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Let v = numerator / denominator < 10.
|
||||
// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
|
||||
// from left to right. Once 'count' digits have been produced we decide wether
|
||||
// to round up or down. Remainders of exactly .5 round upwards. Numbers such
|
||||
// as 9.999999 propagate a carry all the way, and change the
|
||||
// exponent (decimal_point), when rounding upwards.
|
||||
static void GenerateCountedDigits(int count, int* decimal_point,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Vector<char> buffer, int* length) {
|
||||
ASSERT(count >= 0);
|
||||
for (int i = 0; i < count - 1; ++i) {
|
||||
uint16_t digit;
|
||||
digit = numerator->DivideModuloIntBignum(*denominator);
|
||||
ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
|
||||
// digit = numerator / denominator (integer division).
|
||||
// numerator = numerator % denominator.
|
||||
buffer[i] = static_cast<char>(digit + '0');
|
||||
// Prepare for next iteration.
|
||||
numerator->Times10();
|
||||
}
|
||||
// Generate the last digit.
|
||||
uint16_t digit;
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digit = numerator->DivideModuloIntBignum(*denominator);
|
||||
if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
|
||||
digit++;
|
||||
}
|
||||
ASSERT(digit <= 10);
|
||||
buffer[count - 1] = static_cast<char>(digit + '0');
|
||||
// Correct bad digits (in case we had a sequence of '9's). Propagate the
|
||||
// carry until we hat a non-'9' or til we reach the first digit.
|
||||
for (int i = count - 1; i > 0; --i) {
|
||||
if (buffer[i] != '0' + 10) break;
|
||||
buffer[i] = '0';
|
||||
buffer[i - 1]++;
|
||||
}
|
||||
if (buffer[0] == '0' + 10) {
|
||||
// Propagate a carry past the top place.
|
||||
buffer[0] = '1';
|
||||
(*decimal_point)++;
|
||||
}
|
||||
*length = count;
|
||||
}
|
||||
|
||||
|
||||
// Generates 'requested_digits' after the decimal point. It might omit
|
||||
// trailing '0's. If the input number is too small then no digits at all are
|
||||
// generated (ex.: 2 fixed digits for 0.00001).
|
||||
//
|
||||
// Input verifies: 1 <= (numerator + delta) / denominator < 10.
|
||||
static void BignumToFixed(int requested_digits, int* decimal_point,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Vector<char>(buffer), int* length) {
|
||||
// Note that we have to look at more than just the requested_digits, since
|
||||
// a number could be rounded up. Example: v=0.5 with requested_digits=0.
|
||||
// Even though the power of v equals 0 we can't just stop here.
|
||||
if (-(*decimal_point) > requested_digits) {
|
||||
// The number is definitively too small.
|
||||
// Ex: 0.001 with requested_digits == 1.
|
||||
// Set decimal-point to -requested_digits. This is what Gay does.
|
||||
// Note that it should not have any effect anyways since the string is
|
||||
// empty.
|
||||
*decimal_point = -requested_digits;
|
||||
*length = 0;
|
||||
return;
|
||||
} else if (-(*decimal_point) == requested_digits) {
|
||||
// We only need to verify if the number rounds down or up.
|
||||
// Ex: 0.04 and 0.06 with requested_digits == 1.
|
||||
ASSERT(*decimal_point == -requested_digits);
|
||||
// Initially the fraction lies in range (1, 10]. Multiply the denominator
|
||||
// by 10 so that we can compare more easily.
|
||||
denominator->Times10();
|
||||
if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
|
||||
// If the fraction is >= 0.5 then we have to include the rounded
|
||||
// digit.
|
||||
buffer[0] = '1';
|
||||
*length = 1;
|
||||
(*decimal_point)++;
|
||||
} else {
|
||||
// Note that we caught most of similar cases earlier.
|
||||
*length = 0;
|
||||
}
|
||||
return;
|
||||
} else {
|
||||
// The requested digits correspond to the digits after the point.
|
||||
// The variable 'needed_digits' includes the digits before the point.
|
||||
int needed_digits = (*decimal_point) + requested_digits;
|
||||
GenerateCountedDigits(needed_digits, decimal_point,
|
||||
numerator, denominator,
|
||||
buffer, length);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Returns an estimation of k such that 10^(k-1) <= v < 10^k where
|
||||
// v = f * 2^exponent and 2^52 <= f < 2^53.
|
||||
// v is hence a normalized double with the given exponent. The output is an
|
||||
// approximation for the exponent of the decimal approimation .digits * 10^k.
|
||||
//
|
||||
// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
|
||||
// Note: this property holds for v's upper boundary m+ too.
|
||||
// 10^k <= m+ < 10^k+1.
|
||||
// (see explanation below).
|
||||
//
|
||||
// Examples:
|
||||
// EstimatePower(0) => 16
|
||||
// EstimatePower(-52) => 0
|
||||
//
|
||||
// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
|
||||
static int EstimatePower(int exponent) {
|
||||
// This function estimates log10 of v where v = f*2^e (with e == exponent).
|
||||
// Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
|
||||
// Note that f is bounded by its container size. Let p = 53 (the double's
|
||||
// significand size). Then 2^(p-1) <= f < 2^p.
|
||||
//
|
||||
// Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
|
||||
// to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
|
||||
// The computed number undershoots by less than 0.631 (when we compute log3
|
||||
// and not log10).
|
||||
//
|
||||
// Optimization: since we only need an approximated result this computation
|
||||
// can be performed on 64 bit integers. On x86/x64 architecture the speedup is
|
||||
// not really measurable, though.
|
||||
//
|
||||
// Since we want to avoid overshooting we decrement by 1e10 so that
|
||||
// floating-point imprecisions don't affect us.
|
||||
//
|
||||
// Explanation for v's boundary m+: the computation takes advantage of
|
||||
// the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
|
||||
// (even for denormals where the delta can be much more important).
|
||||
|
||||
const double k1Log10 = 0.30102999566398114; // 1/lg(10)
|
||||
|
||||
// For doubles len(f) == 53 (don't forget the hidden bit).
|
||||
const int kSignificandSize = Double::kSignificandSize;
|
||||
double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
|
||||
return static_cast<int>(estimate);
|
||||
}
|
||||
|
||||
|
||||
// See comments for InitialScaledStartValues.
|
||||
static void InitialScaledStartValuesPositiveExponent(
|
||||
uint64_t significand, int exponent,
|
||||
int estimated_power, bool need_boundary_deltas,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Bignum* delta_minus, Bignum* delta_plus) {
|
||||
// A positive exponent implies a positive power.
|
||||
ASSERT(estimated_power >= 0);
|
||||
// Since the estimated_power is positive we simply multiply the denominator
|
||||
// by 10^estimated_power.
|
||||
|
||||
// numerator = v.
|
||||
numerator->AssignUInt64(significand);
|
||||
numerator->ShiftLeft(exponent);
|
||||
// denominator = 10^estimated_power.
|
||||
denominator->AssignPowerUInt16(10, estimated_power);
|
||||
|
||||
if (need_boundary_deltas) {
|
||||
// Introduce a common denominator so that the deltas to the boundaries are
|
||||
// integers.
|
||||
denominator->ShiftLeft(1);
|
||||
numerator->ShiftLeft(1);
|
||||
// Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
|
||||
// denominator (of 2) delta_plus equals 2^e.
|
||||
delta_plus->AssignUInt16(1);
|
||||
delta_plus->ShiftLeft(exponent);
|
||||
// Same for delta_minus. The adjustments if f == 2^p-1 are done later.
|
||||
delta_minus->AssignUInt16(1);
|
||||
delta_minus->ShiftLeft(exponent);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// See comments for InitialScaledStartValues
|
||||
static void InitialScaledStartValuesNegativeExponentPositivePower(
|
||||
uint64_t significand, int exponent,
|
||||
int estimated_power, bool need_boundary_deltas,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Bignum* delta_minus, Bignum* delta_plus) {
|
||||
// v = f * 2^e with e < 0, and with estimated_power >= 0.
|
||||
// This means that e is close to 0 (have a look at how estimated_power is
|
||||
// computed).
|
||||
|
||||
// numerator = significand
|
||||
// since v = significand * 2^exponent this is equivalent to
|
||||
// numerator = v * / 2^-exponent
|
||||
numerator->AssignUInt64(significand);
|
||||
// denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
|
||||
denominator->AssignPowerUInt16(10, estimated_power);
|
||||
denominator->ShiftLeft(-exponent);
|
||||
|
||||
if (need_boundary_deltas) {
|
||||
// Introduce a common denominator so that the deltas to the boundaries are
|
||||
// integers.
|
||||
denominator->ShiftLeft(1);
|
||||
numerator->ShiftLeft(1);
|
||||
// Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
|
||||
// denominator (of 2) delta_plus equals 2^e.
|
||||
// Given that the denominator already includes v's exponent the distance
|
||||
// to the boundaries is simply 1.
|
||||
delta_plus->AssignUInt16(1);
|
||||
// Same for delta_minus. The adjustments if f == 2^p-1 are done later.
|
||||
delta_minus->AssignUInt16(1);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// See comments for InitialScaledStartValues
|
||||
static void InitialScaledStartValuesNegativeExponentNegativePower(
|
||||
uint64_t significand, int exponent,
|
||||
int estimated_power, bool need_boundary_deltas,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Bignum* delta_minus, Bignum* delta_plus) {
|
||||
// Instead of multiplying the denominator with 10^estimated_power we
|
||||
// multiply all values (numerator and deltas) by 10^-estimated_power.
|
||||
|
||||
// Use numerator as temporary container for power_ten.
|
||||
Bignum* power_ten = numerator;
|
||||
power_ten->AssignPowerUInt16(10, -estimated_power);
|
||||
|
||||
if (need_boundary_deltas) {
|
||||
// Since power_ten == numerator we must make a copy of 10^estimated_power
|
||||
// before we complete the computation of the numerator.
|
||||
// delta_plus = delta_minus = 10^estimated_power
|
||||
delta_plus->AssignBignum(*power_ten);
|
||||
delta_minus->AssignBignum(*power_ten);
|
||||
}
|
||||
|
||||
// numerator = significand * 2 * 10^-estimated_power
|
||||
// since v = significand * 2^exponent this is equivalent to
|
||||
// numerator = v * 10^-estimated_power * 2 * 2^-exponent.
|
||||
// Remember: numerator has been abused as power_ten. So no need to assign it
|
||||
// to itself.
|
||||
ASSERT(numerator == power_ten);
|
||||
numerator->MultiplyByUInt64(significand);
|
||||
|
||||
// denominator = 2 * 2^-exponent with exponent < 0.
|
||||
denominator->AssignUInt16(1);
|
||||
denominator->ShiftLeft(-exponent);
|
||||
|
||||
if (need_boundary_deltas) {
|
||||
// Introduce a common denominator so that the deltas to the boundaries are
|
||||
// integers.
|
||||
numerator->ShiftLeft(1);
|
||||
denominator->ShiftLeft(1);
|
||||
// With this shift the boundaries have their correct value, since
|
||||
// delta_plus = 10^-estimated_power, and
|
||||
// delta_minus = 10^-estimated_power.
|
||||
// These assignments have been done earlier.
|
||||
// The adjustments if f == 2^p-1 (lower boundary is closer) are done later.
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Let v = significand * 2^exponent.
|
||||
// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
|
||||
// and denominator. The functions GenerateShortestDigits and
|
||||
// GenerateCountedDigits will then convert this ratio to its decimal
|
||||
// representation d, with the required accuracy.
|
||||
// Then d * 10^estimated_power is the representation of v.
|
||||
// (Note: the fraction and the estimated_power might get adjusted before
|
||||
// generating the decimal representation.)
|
||||
//
|
||||
// The initial start values consist of:
|
||||
// - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
|
||||
// - a scaled (common) denominator.
|
||||
// optionally (used by GenerateShortestDigits to decide if it has the shortest
|
||||
// decimal converting back to v):
|
||||
// - v - m-: the distance to the lower boundary.
|
||||
// - m+ - v: the distance to the upper boundary.
|
||||
//
|
||||
// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
|
||||
//
|
||||
// Let ep == estimated_power, then the returned values will satisfy:
|
||||
// v / 10^ep = numerator / denominator.
|
||||
// v's boundarys m- and m+:
|
||||
// m- / 10^ep == v / 10^ep - delta_minus / denominator
|
||||
// m+ / 10^ep == v / 10^ep + delta_plus / denominator
|
||||
// Or in other words:
|
||||
// m- == v - delta_minus * 10^ep / denominator;
|
||||
// m+ == v + delta_plus * 10^ep / denominator;
|
||||
//
|
||||
// Since 10^(k-1) <= v < 10^k (with k == estimated_power)
|
||||
// or 10^k <= v < 10^(k+1)
|
||||
// we then have 0.1 <= numerator/denominator < 1
|
||||
// or 1 <= numerator/denominator < 10
|
||||
//
|
||||
// It is then easy to kickstart the digit-generation routine.
|
||||
//
|
||||
// The boundary-deltas are only filled if the mode equals BIGNUM_DTOA_SHORTEST
|
||||
// or BIGNUM_DTOA_SHORTEST_SINGLE.
|
||||
|
||||
static void InitialScaledStartValues(uint64_t significand,
|
||||
int exponent,
|
||||
bool lower_boundary_is_closer,
|
||||
int estimated_power,
|
||||
bool need_boundary_deltas,
|
||||
Bignum* numerator,
|
||||
Bignum* denominator,
|
||||
Bignum* delta_minus,
|
||||
Bignum* delta_plus) {
|
||||
if (exponent >= 0) {
|
||||
InitialScaledStartValuesPositiveExponent(
|
||||
significand, exponent, estimated_power, need_boundary_deltas,
|
||||
numerator, denominator, delta_minus, delta_plus);
|
||||
} else if (estimated_power >= 0) {
|
||||
InitialScaledStartValuesNegativeExponentPositivePower(
|
||||
significand, exponent, estimated_power, need_boundary_deltas,
|
||||
numerator, denominator, delta_minus, delta_plus);
|
||||
} else {
|
||||
InitialScaledStartValuesNegativeExponentNegativePower(
|
||||
significand, exponent, estimated_power, need_boundary_deltas,
|
||||
numerator, denominator, delta_minus, delta_plus);
|
||||
}
|
||||
|
||||
if (need_boundary_deltas && lower_boundary_is_closer) {
|
||||
// The lower boundary is closer at half the distance of "normal" numbers.
|
||||
// Increase the common denominator and adapt all but the delta_minus.
|
||||
denominator->ShiftLeft(1); // *2
|
||||
numerator->ShiftLeft(1); // *2
|
||||
delta_plus->ShiftLeft(1); // *2
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// This routine multiplies numerator/denominator so that its values lies in the
|
||||
// range 1-10. That is after a call to this function we have:
|
||||
// 1 <= (numerator + delta_plus) /denominator < 10.
|
||||
// Let numerator the input before modification and numerator' the argument
|
||||
// after modification, then the output-parameter decimal_point is such that
|
||||
// numerator / denominator * 10^estimated_power ==
|
||||
// numerator' / denominator' * 10^(decimal_point - 1)
|
||||
// In some cases estimated_power was too low, and this is already the case. We
|
||||
// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
|
||||
// estimated_power) but do not touch the numerator or denominator.
|
||||
// Otherwise the routine multiplies the numerator and the deltas by 10.
|
||||
static void FixupMultiply10(int estimated_power, bool is_even,
|
||||
int* decimal_point,
|
||||
Bignum* numerator, Bignum* denominator,
|
||||
Bignum* delta_minus, Bignum* delta_plus) {
|
||||
bool in_range;
|
||||
if (is_even) {
|
||||
// For IEEE doubles half-way cases (in decimal system numbers ending with 5)
|
||||
// are rounded to the closest floating-point number with even significand.
|
||||
in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
|
||||
} else {
|
||||
in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
|
||||
}
|
||||
if (in_range) {
|
||||
// Since numerator + delta_plus >= denominator we already have
|
||||
// 1 <= numerator/denominator < 10. Simply update the estimated_power.
|
||||
*decimal_point = estimated_power + 1;
|
||||
} else {
|
||||
*decimal_point = estimated_power;
|
||||
numerator->Times10();
|
||||
if (Bignum::Equal(*delta_minus, *delta_plus)) {
|
||||
delta_minus->Times10();
|
||||
delta_plus->AssignBignum(*delta_minus);
|
||||
} else {
|
||||
delta_minus->Times10();
|
||||
delta_plus->Times10();
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace double_conversion
|
||||
@ -1,84 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_BIGNUM_DTOA_H_
|
||||
#define DOUBLE_CONVERSION_BIGNUM_DTOA_H_
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
enum BignumDtoaMode {
|
||||
// Return the shortest correct representation.
|
||||
// For example the output of 0.299999999999999988897 is (the less accurate but
|
||||
// correct) 0.3.
|
||||
BIGNUM_DTOA_SHORTEST,
|
||||
// Same as BIGNUM_DTOA_SHORTEST but for single-precision floats.
|
||||
BIGNUM_DTOA_SHORTEST_SINGLE,
|
||||
// Return a fixed number of digits after the decimal point.
|
||||
// For instance fixed(0.1, 4) becomes 0.1000
|
||||
// If the input number is big, the output will be big.
|
||||
BIGNUM_DTOA_FIXED,
|
||||
// Return a fixed number of digits, no matter what the exponent is.
|
||||
BIGNUM_DTOA_PRECISION
|
||||
};
|
||||
|
||||
// Converts the given double 'v' to ascii.
|
||||
// The result should be interpreted as buffer * 10^(point-length).
|
||||
// The buffer will be null-terminated.
|
||||
//
|
||||
// The input v must be > 0 and different from NaN, and Infinity.
|
||||
//
|
||||
// The output depends on the given mode:
|
||||
// - SHORTEST: produce the least amount of digits for which the internal
|
||||
// identity requirement is still satisfied. If the digits are printed
|
||||
// (together with the correct exponent) then reading this number will give
|
||||
// 'v' again. The buffer will choose the representation that is closest to
|
||||
// 'v'. If there are two at the same distance, than the number is round up.
|
||||
// In this mode the 'requested_digits' parameter is ignored.
|
||||
// - FIXED: produces digits necessary to print a given number with
|
||||
// 'requested_digits' digits after the decimal point. The produced digits
|
||||
// might be too short in which case the caller has to fill the gaps with '0's.
|
||||
// Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
|
||||
// Halfway cases are rounded up. The call toFixed(0.15, 2) thus returns
|
||||
// buffer="2", point=0.
|
||||
// Note: the length of the returned buffer has no meaning wrt the significance
|
||||
// of its digits. That is, just because it contains '0's does not mean that
|
||||
// any other digit would not satisfy the internal identity requirement.
|
||||
// - PRECISION: produces 'requested_digits' where the first digit is not '0'.
|
||||
// Even though the length of produced digits usually equals
|
||||
// 'requested_digits', the function is allowed to return fewer digits, in
|
||||
// which case the caller has to fill the missing digits with '0's.
|
||||
// Halfway cases are again rounded up.
|
||||
// 'BignumDtoa' expects the given buffer to be big enough to hold all digits
|
||||
// and a terminating null-character.
|
||||
void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
|
||||
Vector<char> buffer, int* length, int* point);
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_BIGNUM_DTOA_H_
|
||||
@ -1,767 +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 <double-conversion/bignum.h>
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
Bignum::Bignum()
|
||||
: bigits_buffer_(), bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) {
|
||||
for (int i = 0; i < kBigitCapacity; ++i) {
|
||||
bigits_[i] = 0;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
template<typename S>
|
||||
static int BitSize(S value) {
|
||||
(void) value; // Mark variable as used.
|
||||
return 8 * sizeof(value);
|
||||
}
|
||||
|
||||
// Guaranteed to lie in one Bigit.
|
||||
void Bignum::AssignUInt16(uint16_t value) {
|
||||
ASSERT(kBigitSize >= BitSize(value));
|
||||
Zero();
|
||||
if (value == 0) return;
|
||||
|
||||
EnsureCapacity(1);
|
||||
bigits_[0] = value;
|
||||
used_digits_ = 1;
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AssignUInt64(uint64_t value) {
|
||||
const int kUInt64Size = 64;
|
||||
|
||||
Zero();
|
||||
if (value == 0) return;
|
||||
|
||||
int needed_bigits = kUInt64Size / kBigitSize + 1;
|
||||
EnsureCapacity(needed_bigits);
|
||||
for (int i = 0; i < needed_bigits; ++i) {
|
||||
bigits_[i] = value & kBigitMask;
|
||||
value = value >> kBigitSize;
|
||||
}
|
||||
used_digits_ = needed_bigits;
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AssignBignum(const Bignum& other) {
|
||||
exponent_ = other.exponent_;
|
||||
for (int i = 0; i < other.used_digits_; ++i) {
|
||||
bigits_[i] = other.bigits_[i];
|
||||
}
|
||||
// Clear the excess digits (if there were any).
|
||||
for (int i = other.used_digits_; i < used_digits_; ++i) {
|
||||
bigits_[i] = 0;
|
||||
}
|
||||
used_digits_ = other.used_digits_;
|
||||
}
|
||||
|
||||
|
||||
static uint64_t ReadUInt64(Vector<const char> buffer,
|
||||
int from,
|
||||
int digits_to_read) {
|
||||
uint64_t result = 0;
|
||||
for (int i = from; i < from + digits_to_read; ++i) {
|
||||
int digit = buffer[i] - '0';
|
||||
ASSERT(0 <= digit && digit <= 9);
|
||||
result = result * 10 + digit;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AssignDecimalString(Vector<const char> value) {
|
||||
// 2^64 = 18446744073709551616 > 10^19
|
||||
const int kMaxUint64DecimalDigits = 19;
|
||||
Zero();
|
||||
int length = value.length();
|
||||
unsigned int pos = 0;
|
||||
// Let's just say that each digit needs 4 bits.
|
||||
while (length >= kMaxUint64DecimalDigits) {
|
||||
uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
|
||||
pos += kMaxUint64DecimalDigits;
|
||||
length -= kMaxUint64DecimalDigits;
|
||||
MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
|
||||
AddUInt64(digits);
|
||||
}
|
||||
uint64_t digits = ReadUInt64(value, pos, length);
|
||||
MultiplyByPowerOfTen(length);
|
||||
AddUInt64(digits);
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
static int HexCharValue(char c) {
|
||||
if ('0' <= c && c <= '9') return c - '0';
|
||||
if ('a' <= c && c <= 'f') return 10 + c - 'a';
|
||||
ASSERT('A' <= c && c <= 'F');
|
||||
return 10 + c - 'A';
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AssignHexString(Vector<const char> value) {
|
||||
Zero();
|
||||
int length = value.length();
|
||||
|
||||
int needed_bigits = length * 4 / kBigitSize + 1;
|
||||
EnsureCapacity(needed_bigits);
|
||||
int string_index = length - 1;
|
||||
for (int i = 0; i < needed_bigits - 1; ++i) {
|
||||
// These bigits are guaranteed to be "full".
|
||||
Chunk current_bigit = 0;
|
||||
for (int j = 0; j < kBigitSize / 4; j++) {
|
||||
current_bigit += HexCharValue(value[string_index--]) << (j * 4);
|
||||
}
|
||||
bigits_[i] = current_bigit;
|
||||
}
|
||||
used_digits_ = needed_bigits - 1;
|
||||
|
||||
Chunk most_significant_bigit = 0; // Could be = 0;
|
||||
for (int j = 0; j <= string_index; ++j) {
|
||||
most_significant_bigit <<= 4;
|
||||
most_significant_bigit += HexCharValue(value[j]);
|
||||
}
|
||||
if (most_significant_bigit != 0) {
|
||||
bigits_[used_digits_] = most_significant_bigit;
|
||||
used_digits_++;
|
||||
}
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AddUInt64(uint64_t operand) {
|
||||
if (operand == 0) return;
|
||||
Bignum other;
|
||||
other.AssignUInt64(operand);
|
||||
AddBignum(other);
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AddBignum(const Bignum& other) {
|
||||
ASSERT(IsClamped());
|
||||
ASSERT(other.IsClamped());
|
||||
|
||||
// If this has a greater exponent than other append zero-bigits to this.
|
||||
// After this call exponent_ <= other.exponent_.
|
||||
Align(other);
|
||||
|
||||
// There are two possibilities:
|
||||
// aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
|
||||
// bbbbb 00000000
|
||||
// ----------------
|
||||
// ccccccccccc 0000
|
||||
// or
|
||||
// aaaaaaaaaa 0000
|
||||
// bbbbbbbbb 0000000
|
||||
// -----------------
|
||||
// cccccccccccc 0000
|
||||
// In both cases we might need a carry bigit.
|
||||
|
||||
EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_);
|
||||
Chunk carry = 0;
|
||||
int bigit_pos = other.exponent_ - exponent_;
|
||||
ASSERT(bigit_pos >= 0);
|
||||
for (int i = 0; i < other.used_digits_; ++i) {
|
||||
Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
|
||||
bigits_[bigit_pos] = sum & kBigitMask;
|
||||
carry = sum >> kBigitSize;
|
||||
bigit_pos++;
|
||||
}
|
||||
|
||||
while (carry != 0) {
|
||||
Chunk sum = bigits_[bigit_pos] + carry;
|
||||
bigits_[bigit_pos] = sum & kBigitMask;
|
||||
carry = sum >> kBigitSize;
|
||||
bigit_pos++;
|
||||
}
|
||||
used_digits_ = Max(bigit_pos, used_digits_);
|
||||
ASSERT(IsClamped());
|
||||
}
|
||||
|
||||
|
||||
void Bignum::SubtractBignum(const Bignum& other) {
|
||||
ASSERT(IsClamped());
|
||||
ASSERT(other.IsClamped());
|
||||
// We require this to be bigger than other.
|
||||
ASSERT(LessEqual(other, *this));
|
||||
|
||||
Align(other);
|
||||
|
||||
int offset = other.exponent_ - exponent_;
|
||||
Chunk borrow = 0;
|
||||
int i;
|
||||
for (i = 0; i < other.used_digits_; ++i) {
|
||||
ASSERT((borrow == 0) || (borrow == 1));
|
||||
Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow;
|
||||
bigits_[i + offset] = difference & kBigitMask;
|
||||
borrow = difference >> (kChunkSize - 1);
|
||||
}
|
||||
while (borrow != 0) {
|
||||
Chunk difference = bigits_[i + offset] - borrow;
|
||||
bigits_[i + offset] = difference & kBigitMask;
|
||||
borrow = difference >> (kChunkSize - 1);
|
||||
++i;
|
||||
}
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
void Bignum::ShiftLeft(int shift_amount) {
|
||||
if (used_digits_ == 0) return;
|
||||
exponent_ += shift_amount / kBigitSize;
|
||||
int local_shift = shift_amount % kBigitSize;
|
||||
EnsureCapacity(used_digits_ + 1);
|
||||
BigitsShiftLeft(local_shift);
|
||||
}
|
||||
|
||||
|
||||
void Bignum::MultiplyByUInt32(uint32_t factor) {
|
||||
if (factor == 1) return;
|
||||
if (factor == 0) {
|
||||
Zero();
|
||||
return;
|
||||
}
|
||||
if (used_digits_ == 0) return;
|
||||
|
||||
// The product of a bigit with the factor is of size kBigitSize + 32.
|
||||
// Assert that this number + 1 (for the carry) fits into double chunk.
|
||||
ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
|
||||
DoubleChunk carry = 0;
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry;
|
||||
bigits_[i] = static_cast<Chunk>(product & kBigitMask);
|
||||
carry = (product >> kBigitSize);
|
||||
}
|
||||
while (carry != 0) {
|
||||
EnsureCapacity(used_digits_ + 1);
|
||||
bigits_[used_digits_] = carry & kBigitMask;
|
||||
used_digits_++;
|
||||
carry >>= kBigitSize;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void Bignum::MultiplyByUInt64(uint64_t factor) {
|
||||
if (factor == 1) return;
|
||||
if (factor == 0) {
|
||||
Zero();
|
||||
return;
|
||||
}
|
||||
ASSERT(kBigitSize < 32);
|
||||
uint64_t carry = 0;
|
||||
uint64_t low = factor & 0xFFFFFFFF;
|
||||
uint64_t high = factor >> 32;
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
uint64_t product_low = low * bigits_[i];
|
||||
uint64_t product_high = high * bigits_[i];
|
||||
uint64_t tmp = (carry & kBigitMask) + product_low;
|
||||
bigits_[i] = tmp & kBigitMask;
|
||||
carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
|
||||
(product_high << (32 - kBigitSize));
|
||||
}
|
||||
while (carry != 0) {
|
||||
EnsureCapacity(used_digits_ + 1);
|
||||
bigits_[used_digits_] = carry & kBigitMask;
|
||||
used_digits_++;
|
||||
carry >>= kBigitSize;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void Bignum::MultiplyByPowerOfTen(int exponent) {
|
||||
const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d);
|
||||
const uint16_t kFive1 = 5;
|
||||
const uint16_t kFive2 = kFive1 * 5;
|
||||
const uint16_t kFive3 = kFive2 * 5;
|
||||
const uint16_t kFive4 = kFive3 * 5;
|
||||
const uint16_t kFive5 = kFive4 * 5;
|
||||
const uint16_t kFive6 = kFive5 * 5;
|
||||
const uint32_t kFive7 = kFive6 * 5;
|
||||
const uint32_t kFive8 = kFive7 * 5;
|
||||
const uint32_t kFive9 = kFive8 * 5;
|
||||
const uint32_t kFive10 = kFive9 * 5;
|
||||
const uint32_t kFive11 = kFive10 * 5;
|
||||
const uint32_t kFive12 = kFive11 * 5;
|
||||
const uint32_t kFive13 = kFive12 * 5;
|
||||
const uint32_t kFive1_to_12[] =
|
||||
{ kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
|
||||
kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
|
||||
|
||||
ASSERT(exponent >= 0);
|
||||
if (exponent == 0) return;
|
||||
if (used_digits_ == 0) return;
|
||||
|
||||
// We shift by exponent at the end just before returning.
|
||||
int remaining_exponent = exponent;
|
||||
while (remaining_exponent >= 27) {
|
||||
MultiplyByUInt64(kFive27);
|
||||
remaining_exponent -= 27;
|
||||
}
|
||||
while (remaining_exponent >= 13) {
|
||||
MultiplyByUInt32(kFive13);
|
||||
remaining_exponent -= 13;
|
||||
}
|
||||
if (remaining_exponent > 0) {
|
||||
MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
|
||||
}
|
||||
ShiftLeft(exponent);
|
||||
}
|
||||
|
||||
|
||||
void Bignum::Square() {
|
||||
ASSERT(IsClamped());
|
||||
int product_length = 2 * used_digits_;
|
||||
EnsureCapacity(product_length);
|
||||
|
||||
// Comba multiplication: compute each column separately.
|
||||
// Example: r = a2a1a0 * b2b1b0.
|
||||
// r = 1 * a0b0 +
|
||||
// 10 * (a1b0 + a0b1) +
|
||||
// 100 * (a2b0 + a1b1 + a0b2) +
|
||||
// 1000 * (a2b1 + a1b2) +
|
||||
// 10000 * a2b2
|
||||
//
|
||||
// In the worst case we have to accumulate nb-digits products of digit*digit.
|
||||
//
|
||||
// Assert that the additional number of bits in a DoubleChunk are enough to
|
||||
// sum up used_digits of Bigit*Bigit.
|
||||
if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
|
||||
UNIMPLEMENTED();
|
||||
}
|
||||
DoubleChunk accumulator = 0;
|
||||
// First shift the digits so we don't overwrite them.
|
||||
int copy_offset = used_digits_;
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
bigits_[copy_offset + i] = bigits_[i];
|
||||
}
|
||||
// We have two loops to avoid some 'if's in the loop.
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
// Process temporary digit i with power i.
|
||||
// The sum of the two indices must be equal to i.
|
||||
int bigit_index1 = i;
|
||||
int bigit_index2 = 0;
|
||||
// Sum all of the sub-products.
|
||||
while (bigit_index1 >= 0) {
|
||||
Chunk chunk1 = bigits_[copy_offset + bigit_index1];
|
||||
Chunk chunk2 = bigits_[copy_offset + bigit_index2];
|
||||
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
|
||||
bigit_index1--;
|
||||
bigit_index2++;
|
||||
}
|
||||
bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
|
||||
accumulator >>= kBigitSize;
|
||||
}
|
||||
for (int i = used_digits_; i < product_length; ++i) {
|
||||
int bigit_index1 = used_digits_ - 1;
|
||||
int bigit_index2 = i - bigit_index1;
|
||||
// Invariant: sum of both indices is again equal to i.
|
||||
// Inner loop runs 0 times on last iteration, emptying accumulator.
|
||||
while (bigit_index2 < used_digits_) {
|
||||
Chunk chunk1 = bigits_[copy_offset + bigit_index1];
|
||||
Chunk chunk2 = bigits_[copy_offset + bigit_index2];
|
||||
accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
|
||||
bigit_index1--;
|
||||
bigit_index2++;
|
||||
}
|
||||
// The overwritten bigits_[i] will never be read in further loop iterations,
|
||||
// because bigit_index1 and bigit_index2 are always greater
|
||||
// than i - used_digits_.
|
||||
bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask;
|
||||
accumulator >>= kBigitSize;
|
||||
}
|
||||
// Since the result was guaranteed to lie inside the number the
|
||||
// accumulator must be 0 now.
|
||||
ASSERT(accumulator == 0);
|
||||
|
||||
// Don't forget to update the used_digits and the exponent.
|
||||
used_digits_ = product_length;
|
||||
exponent_ *= 2;
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) {
|
||||
ASSERT(base != 0);
|
||||
ASSERT(power_exponent >= 0);
|
||||
if (power_exponent == 0) {
|
||||
AssignUInt16(1);
|
||||
return;
|
||||
}
|
||||
Zero();
|
||||
int shifts = 0;
|
||||
// We expect base to be in range 2-32, and most often to be 10.
|
||||
// It does not make much sense to implement different algorithms for counting
|
||||
// the bits.
|
||||
while ((base & 1) == 0) {
|
||||
base >>= 1;
|
||||
shifts++;
|
||||
}
|
||||
int bit_size = 0;
|
||||
int tmp_base = base;
|
||||
while (tmp_base != 0) {
|
||||
tmp_base >>= 1;
|
||||
bit_size++;
|
||||
}
|
||||
int final_size = bit_size * power_exponent;
|
||||
// 1 extra bigit for the shifting, and one for rounded final_size.
|
||||
EnsureCapacity(final_size / kBigitSize + 2);
|
||||
|
||||
// Left to Right exponentiation.
|
||||
int mask = 1;
|
||||
while (power_exponent >= mask) mask <<= 1;
|
||||
|
||||
// The mask is now pointing to the bit above the most significant 1-bit of
|
||||
// power_exponent.
|
||||
// Get rid of first 1-bit;
|
||||
mask >>= 2;
|
||||
uint64_t this_value = base;
|
||||
|
||||
bool delayed_multiplication = false;
|
||||
const uint64_t max_32bits = 0xFFFFFFFF;
|
||||
while (mask != 0 && this_value <= max_32bits) {
|
||||
this_value = this_value * this_value;
|
||||
// Verify that there is enough space in this_value to perform the
|
||||
// multiplication. The first bit_size bits must be 0.
|
||||
if ((power_exponent & mask) != 0) {
|
||||
ASSERT(bit_size > 0);
|
||||
uint64_t base_bits_mask =
|
||||
~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
|
||||
bool high_bits_zero = (this_value & base_bits_mask) == 0;
|
||||
if (high_bits_zero) {
|
||||
this_value *= base;
|
||||
} else {
|
||||
delayed_multiplication = true;
|
||||
}
|
||||
}
|
||||
mask >>= 1;
|
||||
}
|
||||
AssignUInt64(this_value);
|
||||
if (delayed_multiplication) {
|
||||
MultiplyByUInt32(base);
|
||||
}
|
||||
|
||||
// Now do the same thing as a bignum.
|
||||
while (mask != 0) {
|
||||
Square();
|
||||
if ((power_exponent & mask) != 0) {
|
||||
MultiplyByUInt32(base);
|
||||
}
|
||||
mask >>= 1;
|
||||
}
|
||||
|
||||
// And finally add the saved shifts.
|
||||
ShiftLeft(shifts * power_exponent);
|
||||
}
|
||||
|
||||
|
||||
// Precondition: this/other < 16bit.
|
||||
uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
|
||||
ASSERT(IsClamped());
|
||||
ASSERT(other.IsClamped());
|
||||
ASSERT(other.used_digits_ > 0);
|
||||
|
||||
// Easy case: if we have less digits than the divisor than the result is 0.
|
||||
// Note: this handles the case where this == 0, too.
|
||||
if (BigitLength() < other.BigitLength()) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
Align(other);
|
||||
|
||||
uint16_t result = 0;
|
||||
|
||||
// Start by removing multiples of 'other' until both numbers have the same
|
||||
// number of digits.
|
||||
while (BigitLength() > other.BigitLength()) {
|
||||
// This naive approach is extremely inefficient if `this` divided by other
|
||||
// is big. This function is implemented for doubleToString where
|
||||
// the result should be small (less than 10).
|
||||
ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
|
||||
ASSERT(bigits_[used_digits_ - 1] < 0x10000);
|
||||
// Remove the multiples of the first digit.
|
||||
// Example this = 23 and other equals 9. -> Remove 2 multiples.
|
||||
result += static_cast<uint16_t>(bigits_[used_digits_ - 1]);
|
||||
SubtractTimes(other, bigits_[used_digits_ - 1]);
|
||||
}
|
||||
|
||||
ASSERT(BigitLength() == other.BigitLength());
|
||||
|
||||
// Both bignums are at the same length now.
|
||||
// Since other has more than 0 digits we know that the access to
|
||||
// bigits_[used_digits_ - 1] is safe.
|
||||
Chunk this_bigit = bigits_[used_digits_ - 1];
|
||||
Chunk other_bigit = other.bigits_[other.used_digits_ - 1];
|
||||
|
||||
if (other.used_digits_ == 1) {
|
||||
// Shortcut for easy (and common) case.
|
||||
int quotient = this_bigit / other_bigit;
|
||||
bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
|
||||
ASSERT(quotient < 0x10000);
|
||||
result += static_cast<uint16_t>(quotient);
|
||||
Clamp();
|
||||
return result;
|
||||
}
|
||||
|
||||
int division_estimate = this_bigit / (other_bigit + 1);
|
||||
ASSERT(division_estimate < 0x10000);
|
||||
result += static_cast<uint16_t>(division_estimate);
|
||||
SubtractTimes(other, division_estimate);
|
||||
|
||||
if (other_bigit * (division_estimate + 1) > this_bigit) {
|
||||
// No need to even try to subtract. Even if other's remaining digits were 0
|
||||
// another subtraction would be too much.
|
||||
return result;
|
||||
}
|
||||
|
||||
while (LessEqual(other, *this)) {
|
||||
SubtractBignum(other);
|
||||
result++;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
template<typename S>
|
||||
static int SizeInHexChars(S number) {
|
||||
ASSERT(number > 0);
|
||||
int result = 0;
|
||||
while (number != 0) {
|
||||
number >>= 4;
|
||||
result++;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
static char HexCharOfValue(int value) {
|
||||
ASSERT(0 <= value && value <= 16);
|
||||
if (value < 10) return static_cast<char>(value + '0');
|
||||
return static_cast<char>(value - 10 + 'A');
|
||||
}
|
||||
|
||||
|
||||
bool Bignum::ToHexString(char* buffer, int buffer_size) const {
|
||||
ASSERT(IsClamped());
|
||||
// Each bigit must be printable as separate hex-character.
|
||||
ASSERT(kBigitSize % 4 == 0);
|
||||
const int kHexCharsPerBigit = kBigitSize / 4;
|
||||
|
||||
if (used_digits_ == 0) {
|
||||
if (buffer_size < 2) return false;
|
||||
buffer[0] = '0';
|
||||
buffer[1] = '\0';
|
||||
return true;
|
||||
}
|
||||
// We add 1 for the terminating '\0' character.
|
||||
int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
|
||||
SizeInHexChars(bigits_[used_digits_ - 1]) + 1;
|
||||
if (needed_chars > buffer_size) return false;
|
||||
int string_index = needed_chars - 1;
|
||||
buffer[string_index--] = '\0';
|
||||
for (int i = 0; i < exponent_; ++i) {
|
||||
for (int j = 0; j < kHexCharsPerBigit; ++j) {
|
||||
buffer[string_index--] = '0';
|
||||
}
|
||||
}
|
||||
for (int i = 0; i < used_digits_ - 1; ++i) {
|
||||
Chunk current_bigit = bigits_[i];
|
||||
for (int j = 0; j < kHexCharsPerBigit; ++j) {
|
||||
buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
|
||||
current_bigit >>= 4;
|
||||
}
|
||||
}
|
||||
// And finally the last bigit.
|
||||
Chunk most_significant_bigit = bigits_[used_digits_ - 1];
|
||||
while (most_significant_bigit != 0) {
|
||||
buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
|
||||
most_significant_bigit >>= 4;
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
|
||||
Bignum::Chunk Bignum::BigitAt(int index) const {
|
||||
if (index >= BigitLength()) return 0;
|
||||
if (index < exponent_) return 0;
|
||||
return bigits_[index - exponent_];
|
||||
}
|
||||
|
||||
|
||||
int Bignum::Compare(const Bignum& a, const Bignum& b) {
|
||||
ASSERT(a.IsClamped());
|
||||
ASSERT(b.IsClamped());
|
||||
int bigit_length_a = a.BigitLength();
|
||||
int bigit_length_b = b.BigitLength();
|
||||
if (bigit_length_a < bigit_length_b) return -1;
|
||||
if (bigit_length_a > bigit_length_b) return +1;
|
||||
for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) {
|
||||
Chunk bigit_a = a.BigitAt(i);
|
||||
Chunk bigit_b = b.BigitAt(i);
|
||||
if (bigit_a < bigit_b) return -1;
|
||||
if (bigit_a > bigit_b) return +1;
|
||||
// Otherwise they are equal up to this digit. Try the next digit.
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
|
||||
ASSERT(a.IsClamped());
|
||||
ASSERT(b.IsClamped());
|
||||
ASSERT(c.IsClamped());
|
||||
if (a.BigitLength() < b.BigitLength()) {
|
||||
return PlusCompare(b, a, c);
|
||||
}
|
||||
if (a.BigitLength() + 1 < c.BigitLength()) return -1;
|
||||
if (a.BigitLength() > c.BigitLength()) return +1;
|
||||
// The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
|
||||
// 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
|
||||
// of 'a'.
|
||||
if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) {
|
||||
return -1;
|
||||
}
|
||||
|
||||
Chunk borrow = 0;
|
||||
// Starting at min_exponent all digits are == 0. So no need to compare them.
|
||||
int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_);
|
||||
for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
|
||||
Chunk chunk_a = a.BigitAt(i);
|
||||
Chunk chunk_b = b.BigitAt(i);
|
||||
Chunk chunk_c = c.BigitAt(i);
|
||||
Chunk sum = chunk_a + chunk_b;
|
||||
if (sum > chunk_c + borrow) {
|
||||
return +1;
|
||||
} else {
|
||||
borrow = chunk_c + borrow - sum;
|
||||
if (borrow > 1) return -1;
|
||||
borrow <<= kBigitSize;
|
||||
}
|
||||
}
|
||||
if (borrow == 0) return 0;
|
||||
return -1;
|
||||
}
|
||||
|
||||
|
||||
void Bignum::Clamp() {
|
||||
while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
|
||||
used_digits_--;
|
||||
}
|
||||
if (used_digits_ == 0) {
|
||||
// Zero.
|
||||
exponent_ = 0;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
bool Bignum::IsClamped() const {
|
||||
return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
|
||||
}
|
||||
|
||||
|
||||
void Bignum::Zero() {
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
bigits_[i] = 0;
|
||||
}
|
||||
used_digits_ = 0;
|
||||
exponent_ = 0;
|
||||
}
|
||||
|
||||
|
||||
void Bignum::Align(const Bignum& other) {
|
||||
if (exponent_ > other.exponent_) {
|
||||
// If "X" represents a "hidden" digit (by the exponent) then we are in the
|
||||
// following case (a == this, b == other):
|
||||
// a: aaaaaaXXXX or a: aaaaaXXX
|
||||
// b: bbbbbbX b: bbbbbbbbXX
|
||||
// We replace some of the hidden digits (X) of a with 0 digits.
|
||||
// a: aaaaaa000X or a: aaaaa0XX
|
||||
int zero_digits = exponent_ - other.exponent_;
|
||||
EnsureCapacity(used_digits_ + zero_digits);
|
||||
for (int i = used_digits_ - 1; i >= 0; --i) {
|
||||
bigits_[i + zero_digits] = bigits_[i];
|
||||
}
|
||||
for (int i = 0; i < zero_digits; ++i) {
|
||||
bigits_[i] = 0;
|
||||
}
|
||||
used_digits_ += zero_digits;
|
||||
exponent_ -= zero_digits;
|
||||
ASSERT(used_digits_ >= 0);
|
||||
ASSERT(exponent_ >= 0);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void Bignum::BigitsShiftLeft(int shift_amount) {
|
||||
ASSERT(shift_amount < kBigitSize);
|
||||
ASSERT(shift_amount >= 0);
|
||||
Chunk carry = 0;
|
||||
for (int i = 0; i < used_digits_; ++i) {
|
||||
Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount);
|
||||
bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
|
||||
carry = new_carry;
|
||||
}
|
||||
if (carry != 0) {
|
||||
bigits_[used_digits_] = carry;
|
||||
used_digits_++;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
void Bignum::SubtractTimes(const Bignum& other, int factor) {
|
||||
ASSERT(exponent_ <= other.exponent_);
|
||||
if (factor < 3) {
|
||||
for (int i = 0; i < factor; ++i) {
|
||||
SubtractBignum(other);
|
||||
}
|
||||
return;
|
||||
}
|
||||
Chunk borrow = 0;
|
||||
int exponent_diff = other.exponent_ - exponent_;
|
||||
for (int i = 0; i < other.used_digits_; ++i) {
|
||||
DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i];
|
||||
DoubleChunk remove = borrow + product;
|
||||
Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask);
|
||||
bigits_[i + exponent_diff] = difference & kBigitMask;
|
||||
borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
|
||||
(remove >> kBigitSize));
|
||||
}
|
||||
for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
|
||||
if (borrow == 0) return;
|
||||
Chunk difference = bigits_[i] - borrow;
|
||||
bigits_[i] = difference & kBigitMask;
|
||||
borrow = difference >> (kChunkSize - 1);
|
||||
}
|
||||
Clamp();
|
||||
}
|
||||
|
||||
|
||||
} // namespace double_conversion
|
||||
@ -1,144 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_BIGNUM_H_
|
||||
#define DOUBLE_CONVERSION_BIGNUM_H_
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
class Bignum {
|
||||
public:
|
||||
// 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
|
||||
// This bignum can encode much bigger numbers, since it contains an
|
||||
// exponent.
|
||||
static const int kMaxSignificantBits = 3584;
|
||||
|
||||
Bignum();
|
||||
void AssignUInt16(uint16_t value);
|
||||
void AssignUInt64(uint64_t value);
|
||||
void AssignBignum(const Bignum& other);
|
||||
|
||||
void AssignDecimalString(Vector<const char> value);
|
||||
void AssignHexString(Vector<const char> value);
|
||||
|
||||
void AssignPowerUInt16(uint16_t base, int exponent);
|
||||
|
||||
void AddUInt64(uint64_t operand);
|
||||
void AddBignum(const Bignum& other);
|
||||
// Precondition: this >= other.
|
||||
void SubtractBignum(const Bignum& other);
|
||||
|
||||
void Square();
|
||||
void ShiftLeft(int shift_amount);
|
||||
void MultiplyByUInt32(uint32_t factor);
|
||||
void MultiplyByUInt64(uint64_t factor);
|
||||
void MultiplyByPowerOfTen(int exponent);
|
||||
void Times10() { return MultiplyByUInt32(10); }
|
||||
// Pseudocode:
|
||||
// int result = this / other;
|
||||
// this = this % other;
|
||||
// In the worst case this function is in O(this/other).
|
||||
uint16_t DivideModuloIntBignum(const Bignum& other);
|
||||
|
||||
bool ToHexString(char* buffer, int buffer_size) const;
|
||||
|
||||
// Returns
|
||||
// -1 if a < b,
|
||||
// 0 if a == b, and
|
||||
// +1 if a > b.
|
||||
static int Compare(const Bignum& a, const Bignum& b);
|
||||
static bool Equal(const Bignum& a, const Bignum& b) {
|
||||
return Compare(a, b) == 0;
|
||||
}
|
||||
static bool LessEqual(const Bignum& a, const Bignum& b) {
|
||||
return Compare(a, b) <= 0;
|
||||
}
|
||||
static bool Less(const Bignum& a, const Bignum& b) {
|
||||
return Compare(a, b) < 0;
|
||||
}
|
||||
// Returns Compare(a + b, c);
|
||||
static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c);
|
||||
// Returns a + b == c
|
||||
static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
|
||||
return PlusCompare(a, b, c) == 0;
|
||||
}
|
||||
// Returns a + b <= c
|
||||
static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) {
|
||||
return PlusCompare(a, b, c) <= 0;
|
||||
}
|
||||
// Returns a + b < c
|
||||
static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) {
|
||||
return PlusCompare(a, b, c) < 0;
|
||||
}
|
||||
private:
|
||||
typedef uint32_t Chunk;
|
||||
typedef uint64_t DoubleChunk;
|
||||
|
||||
static const int kChunkSize = sizeof(Chunk) * 8;
|
||||
static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8;
|
||||
// With bigit size of 28 we loose some bits, but a double still fits easily
|
||||
// into two chunks, and more importantly we can use the Comba multiplication.
|
||||
static const int kBigitSize = 28;
|
||||
static const Chunk kBigitMask = (1 << kBigitSize) - 1;
|
||||
// Every instance allocates kBigitLength chunks on the stack. Bignums cannot
|
||||
// grow. There are no checks if the stack-allocated space is sufficient.
|
||||
static const int kBigitCapacity = kMaxSignificantBits / kBigitSize;
|
||||
|
||||
void EnsureCapacity(int size) {
|
||||
if (size > kBigitCapacity) {
|
||||
UNREACHABLE();
|
||||
}
|
||||
}
|
||||
void Align(const Bignum& other);
|
||||
void Clamp();
|
||||
bool IsClamped() const;
|
||||
void Zero();
|
||||
// Requires this to have enough capacity (no tests done).
|
||||
// Updates used_digits_ if necessary.
|
||||
// shift_amount must be < kBigitSize.
|
||||
void BigitsShiftLeft(int shift_amount);
|
||||
// BigitLength includes the "hidden" digits encoded in the exponent.
|
||||
int BigitLength() const { return used_digits_ + exponent_; }
|
||||
Chunk BigitAt(int index) const;
|
||||
void SubtractTimes(const Bignum& other, int factor);
|
||||
|
||||
Chunk bigits_buffer_[kBigitCapacity];
|
||||
// A vector backed by bigits_buffer_. This way accesses to the array are
|
||||
// checked for out-of-bounds errors.
|
||||
Vector<Chunk> bigits_;
|
||||
int used_digits_;
|
||||
// The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
|
||||
int exponent_;
|
||||
|
||||
DC_DISALLOW_COPY_AND_ASSIGN(Bignum);
|
||||
};
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_BIGNUM_H_
|
||||
@ -1,175 +0,0 @@
|
||||
// Copyright 2006-2008 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 <climits>
|
||||
#include <cmath>
|
||||
#include <cstdarg>
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
#include <double-conversion/cached-powers.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
struct CachedPower {
|
||||
uint64_t significand;
|
||||
int16_t binary_exponent;
|
||||
int16_t decimal_exponent;
|
||||
};
|
||||
|
||||
static const CachedPower kCachedPowers[] = {
|
||||
{UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348},
|
||||
{UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340},
|
||||
{UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332},
|
||||
{UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324},
|
||||
{UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316},
|
||||
{UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308},
|
||||
{UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300},
|
||||
{UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292},
|
||||
{UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284},
|
||||
{UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276},
|
||||
{UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268},
|
||||
{UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260},
|
||||
{UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252},
|
||||
{UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244},
|
||||
{UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236},
|
||||
{UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228},
|
||||
{UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220},
|
||||
{UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212},
|
||||
{UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204},
|
||||
{UINT64_2PART_C(0xef340a98, 172aace5), -715, -196},
|
||||
{UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188},
|
||||
{UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180},
|
||||
{UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172},
|
||||
{UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164},
|
||||
{UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156},
|
||||
{UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148},
|
||||
{UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140},
|
||||
{UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132},
|
||||
{UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124},
|
||||
{UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116},
|
||||
{UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108},
|
||||
{UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100},
|
||||
{UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92},
|
||||
{UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84},
|
||||
{UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76},
|
||||
{UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68},
|
||||
{UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60},
|
||||
{UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52},
|
||||
{UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44},
|
||||
{UINT64_2PART_C(0xaa242499, 697392d3), -183, -36},
|
||||
{UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28},
|
||||
{UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20},
|
||||
{UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12},
|
||||
{UINT64_2PART_C(0xd1b71758, e219652c), -77, -4},
|
||||
{UINT64_2PART_C(0x9c400000, 00000000), -50, 4},
|
||||
{UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12},
|
||||
{UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20},
|
||||
{UINT64_2PART_C(0x813f3978, f8940984), 30, 28},
|
||||
{UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36},
|
||||
{UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44},
|
||||
{UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52},
|
||||
{UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60},
|
||||
{UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68},
|
||||
{UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76},
|
||||
{UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84},
|
||||
{UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92},
|
||||
{UINT64_2PART_C(0x924d692c, a61be758), 269, 100},
|
||||
{UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108},
|
||||
{UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116},
|
||||
{UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124},
|
||||
{UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132},
|
||||
{UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140},
|
||||
{UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148},
|
||||
{UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156},
|
||||
{UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164},
|
||||
{UINT64_2PART_C(0xa59bc234, db398c25), 508, 172},
|
||||
{UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180},
|
||||
{UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188},
|
||||
{UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196},
|
||||
{UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204},
|
||||
{UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212},
|
||||
{UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220},
|
||||
{UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228},
|
||||
{UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236},
|
||||
{UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244},
|
||||
{UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252},
|
||||
{UINT64_2PART_C(0xd01fef10, a657842c), 800, 260},
|
||||
{UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268},
|
||||
{UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276},
|
||||
{UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284},
|
||||
{UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292},
|
||||
{UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300},
|
||||
{UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308},
|
||||
{UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316},
|
||||
{UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324},
|
||||
{UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332},
|
||||
{UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340},
|
||||
};
|
||||
|
||||
static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent.
|
||||
static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
|
||||
// Difference between the decimal exponents in the table above.
|
||||
const int PowersOfTenCache::kDecimalExponentDistance = 8;
|
||||
const int PowersOfTenCache::kMinDecimalExponent = -348;
|
||||
const int PowersOfTenCache::kMaxDecimalExponent = 340;
|
||||
|
||||
void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
|
||||
int min_exponent,
|
||||
int max_exponent,
|
||||
DiyFp* power,
|
||||
int* decimal_exponent) {
|
||||
int kQ = DiyFp::kSignificandSize;
|
||||
double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10);
|
||||
int foo = kCachedPowersOffset;
|
||||
int index =
|
||||
(foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
|
||||
ASSERT(0 <= index && index < static_cast<int>(ARRAY_SIZE(kCachedPowers)));
|
||||
CachedPower cached_power = kCachedPowers[index];
|
||||
ASSERT(min_exponent <= cached_power.binary_exponent);
|
||||
(void) max_exponent; // Mark variable as used.
|
||||
ASSERT(cached_power.binary_exponent <= max_exponent);
|
||||
*decimal_exponent = cached_power.decimal_exponent;
|
||||
*power = DiyFp(cached_power.significand, cached_power.binary_exponent);
|
||||
}
|
||||
|
||||
|
||||
void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
|
||||
DiyFp* power,
|
||||
int* found_exponent) {
|
||||
ASSERT(kMinDecimalExponent <= requested_exponent);
|
||||
ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
|
||||
int index =
|
||||
(requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
|
||||
CachedPower cached_power = kCachedPowers[index];
|
||||
*power = DiyFp(cached_power.significand, cached_power.binary_exponent);
|
||||
*found_exponent = cached_power.decimal_exponent;
|
||||
ASSERT(*found_exponent <= requested_exponent);
|
||||
ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
|
||||
}
|
||||
|
||||
} // namespace double_conversion
|
||||
@ -1,64 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_CACHED_POWERS_H_
|
||||
#define DOUBLE_CONVERSION_CACHED_POWERS_H_
|
||||
|
||||
#include <double-conversion/diy-fp.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
class PowersOfTenCache {
|
||||
public:
|
||||
|
||||
// Not all powers of ten are cached. The decimal exponent of two neighboring
|
||||
// cached numbers will differ by kDecimalExponentDistance.
|
||||
static const int kDecimalExponentDistance;
|
||||
|
||||
static const int kMinDecimalExponent;
|
||||
static const int kMaxDecimalExponent;
|
||||
|
||||
// Returns a cached power-of-ten with a binary exponent in the range
|
||||
// [min_exponent; max_exponent] (boundaries included).
|
||||
static void GetCachedPowerForBinaryExponentRange(int min_exponent,
|
||||
int max_exponent,
|
||||
DiyFp* power,
|
||||
int* decimal_exponent);
|
||||
|
||||
// Returns a cached power of ten x ~= 10^k such that
|
||||
// k <= decimal_exponent < k + kCachedPowersDecimalDistance.
|
||||
// The given decimal_exponent must satisfy
|
||||
// kMinDecimalExponent <= requested_exponent, and
|
||||
// requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance.
|
||||
static void GetCachedPowerForDecimalExponent(int requested_exponent,
|
||||
DiyFp* power,
|
||||
int* found_exponent);
|
||||
};
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_CACHED_POWERS_H_
|
||||
@ -1,57 +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 <double-conversion/diy-fp.h>
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
void DiyFp::Multiply(const DiyFp& other) {
|
||||
// Simply "emulates" a 128 bit multiplication.
|
||||
// However: the resulting number only contains 64 bits. The least
|
||||
// significant 64 bits are only used for rounding the most significant 64
|
||||
// bits.
|
||||
const uint64_t kM32 = 0xFFFFFFFFU;
|
||||
uint64_t a = f_ >> 32;
|
||||
uint64_t b = f_ & kM32;
|
||||
uint64_t c = other.f_ >> 32;
|
||||
uint64_t d = other.f_ & kM32;
|
||||
uint64_t ac = a * c;
|
||||
uint64_t bc = b * c;
|
||||
uint64_t ad = a * d;
|
||||
uint64_t bd = b * d;
|
||||
uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
|
||||
// By adding 1U << 31 to tmp we round the final result.
|
||||
// Halfway cases will be round up.
|
||||
tmp += 1U << 31;
|
||||
uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
|
||||
e_ += other.e_ + 64;
|
||||
f_ = result_f;
|
||||
}
|
||||
|
||||
} // namespace double_conversion
|
||||
@ -1,118 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_DIY_FP_H_
|
||||
#define DOUBLE_CONVERSION_DIY_FP_H_
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
// This "Do It Yourself Floating Point" class implements a floating-point number
|
||||
// with a uint64 significand and an int exponent. Normalized DiyFp numbers will
|
||||
// have the most significant bit of the significand set.
|
||||
// Multiplication and Subtraction do not normalize their results.
|
||||
// DiyFp are not designed to contain special doubles (NaN and Infinity).
|
||||
class DiyFp {
|
||||
public:
|
||||
static const int kSignificandSize = 64;
|
||||
|
||||
DiyFp() : f_(0), e_(0) {}
|
||||
DiyFp(uint64_t significand, int exponent) : f_(significand), e_(exponent) {}
|
||||
|
||||
// this = this - other.
|
||||
// The exponents of both numbers must be the same and the significand of this
|
||||
// must be bigger than the significand of other.
|
||||
// The result will not be normalized.
|
||||
void Subtract(const DiyFp& other) {
|
||||
ASSERT(e_ == other.e_);
|
||||
ASSERT(f_ >= other.f_);
|
||||
f_ -= other.f_;
|
||||
}
|
||||
|
||||
// Returns a - b.
|
||||
// The exponents of both numbers must be the same and this must be bigger
|
||||
// than other. The result will not be normalized.
|
||||
static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
|
||||
DiyFp result = a;
|
||||
result.Subtract(b);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
// this = this * other.
|
||||
void Multiply(const DiyFp& other);
|
||||
|
||||
// returns a * b;
|
||||
static DiyFp Times(const DiyFp& a, const DiyFp& b) {
|
||||
DiyFp result = a;
|
||||
result.Multiply(b);
|
||||
return result;
|
||||
}
|
||||
|
||||
void Normalize() {
|
||||
ASSERT(f_ != 0);
|
||||
uint64_t significand = f_;
|
||||
int exponent = e_;
|
||||
|
||||
// This method is mainly called for normalizing boundaries. In general
|
||||
// boundaries need to be shifted by 10 bits. We thus optimize for this case.
|
||||
const uint64_t k10MSBits = UINT64_2PART_C(0xFFC00000, 00000000);
|
||||
while ((significand & k10MSBits) == 0) {
|
||||
significand <<= 10;
|
||||
exponent -= 10;
|
||||
}
|
||||
while ((significand & kUint64MSB) == 0) {
|
||||
significand <<= 1;
|
||||
exponent--;
|
||||
}
|
||||
f_ = significand;
|
||||
e_ = exponent;
|
||||
}
|
||||
|
||||
static DiyFp Normalize(const DiyFp& a) {
|
||||
DiyFp result = a;
|
||||
result.Normalize();
|
||||
return result;
|
||||
}
|
||||
|
||||
uint64_t f() const { return f_; }
|
||||
int e() const { return e_; }
|
||||
|
||||
void set_f(uint64_t new_value) { f_ = new_value; }
|
||||
void set_e(int new_value) { e_ = new_value; }
|
||||
|
||||
private:
|
||||
static const uint64_t kUint64MSB = UINT64_2PART_C(0x80000000, 00000000);
|
||||
|
||||
uint64_t f_;
|
||||
int e_;
|
||||
};
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_DIY_FP_H_
|
||||
File diff suppressed because it is too large
Load Diff
@ -1,546 +0,0 @@
|
||||
// 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_CONVERSION_H_
|
||||
#define DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
class DoubleToStringConverter {
|
||||
public:
|
||||
// When calling ToFixed with a double > 10^kMaxFixedDigitsBeforePoint
|
||||
// or a requested_digits parameter > kMaxFixedDigitsAfterPoint then the
|
||||
// function returns false.
|
||||
static const int kMaxFixedDigitsBeforePoint = 60;
|
||||
static const int kMaxFixedDigitsAfterPoint = 60;
|
||||
|
||||
// When calling ToExponential with a requested_digits
|
||||
// parameter > kMaxExponentialDigits then the function returns false.
|
||||
static const int kMaxExponentialDigits = 120;
|
||||
|
||||
// When calling ToPrecision with a requested_digits
|
||||
// parameter < kMinPrecisionDigits or requested_digits > kMaxPrecisionDigits
|
||||
// then the function returns false.
|
||||
static const int kMinPrecisionDigits = 1;
|
||||
static const int kMaxPrecisionDigits = 120;
|
||||
|
||||
enum Flags {
|
||||
NO_FLAGS = 0,
|
||||
EMIT_POSITIVE_EXPONENT_SIGN = 1,
|
||||
EMIT_TRAILING_DECIMAL_POINT = 2,
|
||||
EMIT_TRAILING_ZERO_AFTER_POINT = 4,
|
||||
UNIQUE_ZERO = 8
|
||||
};
|
||||
|
||||
// Flags should be a bit-or combination of the possible Flags-enum.
|
||||
// - NO_FLAGS: no special flags.
|
||||
// - EMIT_POSITIVE_EXPONENT_SIGN: when the number is converted into exponent
|
||||
// form, emits a '+' for positive exponents. Example: 1.2e+2.
|
||||
// - EMIT_TRAILING_DECIMAL_POINT: when the input number is an integer and is
|
||||
// converted into decimal format then a trailing decimal point is appended.
|
||||
// Example: 2345.0 is converted to "2345.".
|
||||
// - EMIT_TRAILING_ZERO_AFTER_POINT: in addition to a trailing decimal point
|
||||
// emits a trailing '0'-character. This flag requires the
|
||||
// EXMIT_TRAILING_DECIMAL_POINT flag.
|
||||
// Example: 2345.0 is converted to "2345.0".
|
||||
// - UNIQUE_ZERO: "-0.0" is converted to "0.0".
|
||||
//
|
||||
// Infinity symbol and nan_symbol provide the string representation for these
|
||||
// special values. If the string is NULL and the special value is encountered
|
||||
// then the conversion functions return false.
|
||||
//
|
||||
// The exponent_character is used in exponential representations. It is
|
||||
// usually 'e' or 'E'.
|
||||
//
|
||||
// When converting to the shortest representation the converter will
|
||||
// represent input numbers in decimal format if they are in the interval
|
||||
// [10^decimal_in_shortest_low; 10^decimal_in_shortest_high[
|
||||
// (lower boundary included, greater boundary excluded).
|
||||
// Example: with decimal_in_shortest_low = -6 and
|
||||
// decimal_in_shortest_high = 21:
|
||||
// ToShortest(0.000001) -> "0.000001"
|
||||
// ToShortest(0.0000001) -> "1e-7"
|
||||
// ToShortest(111111111111111111111.0) -> "111111111111111110000"
|
||||
// ToShortest(100000000000000000000.0) -> "100000000000000000000"
|
||||
// ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
|
||||
//
|
||||
// When converting to precision mode the converter may add
|
||||
// max_leading_padding_zeroes before returning the number in exponential
|
||||
// format.
|
||||
// Example with max_leading_padding_zeroes_in_precision_mode = 6.
|
||||
// ToPrecision(0.0000012345, 2) -> "0.0000012"
|
||||
// ToPrecision(0.00000012345, 2) -> "1.2e-7"
|
||||
// Similarily the converter may add up to
|
||||
// max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
|
||||
// returning an exponential representation. A zero added by the
|
||||
// EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
|
||||
// Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
|
||||
// ToPrecision(230.0, 2) -> "230"
|
||||
// ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
|
||||
// ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
|
||||
DoubleToStringConverter(int flags,
|
||||
const char* infinity_symbol,
|
||||
const char* nan_symbol,
|
||||
char exponent_character,
|
||||
int decimal_in_shortest_low,
|
||||
int decimal_in_shortest_high,
|
||||
int max_leading_padding_zeroes_in_precision_mode,
|
||||
int max_trailing_padding_zeroes_in_precision_mode)
|
||||
: flags_(flags),
|
||||
infinity_symbol_(infinity_symbol),
|
||||
nan_symbol_(nan_symbol),
|
||||
exponent_character_(exponent_character),
|
||||
decimal_in_shortest_low_(decimal_in_shortest_low),
|
||||
decimal_in_shortest_high_(decimal_in_shortest_high),
|
||||
max_leading_padding_zeroes_in_precision_mode_(
|
||||
max_leading_padding_zeroes_in_precision_mode),
|
||||
max_trailing_padding_zeroes_in_precision_mode_(
|
||||
max_trailing_padding_zeroes_in_precision_mode) {
|
||||
// When 'trailing zero after the point' is set, then 'trailing point'
|
||||
// must be set too.
|
||||
ASSERT(((flags & EMIT_TRAILING_DECIMAL_POINT) != 0) ||
|
||||
!((flags & EMIT_TRAILING_ZERO_AFTER_POINT) != 0));
|
||||
}
|
||||
|
||||
// Returns a converter following the EcmaScript specification.
|
||||
static const DoubleToStringConverter& EcmaScriptConverter();
|
||||
|
||||
// Computes the shortest string of digits that correctly represent the input
|
||||
// number. Depending on decimal_in_shortest_low and decimal_in_shortest_high
|
||||
// (see constructor) it then either returns a decimal representation, or an
|
||||
// exponential representation.
|
||||
// Example with decimal_in_shortest_low = -6,
|
||||
// decimal_in_shortest_high = 21,
|
||||
// EMIT_POSITIVE_EXPONENT_SIGN activated, and
|
||||
// EMIT_TRAILING_DECIMAL_POINT deactived:
|
||||
// ToShortest(0.000001) -> "0.000001"
|
||||
// ToShortest(0.0000001) -> "1e-7"
|
||||
// ToShortest(111111111111111111111.0) -> "111111111111111110000"
|
||||
// ToShortest(100000000000000000000.0) -> "100000000000000000000"
|
||||
// ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21"
|
||||
//
|
||||
// Note: the conversion may round the output if the returned string
|
||||
// is accurate enough to uniquely identify the input-number.
|
||||
// For example the most precise representation of the double 9e59 equals
|
||||
// "899999999999999918767229449717619953810131273674690656206848", but
|
||||
// the converter will return the shorter (but still correct) "9e59".
|
||||
//
|
||||
// Returns true if the conversion succeeds. The conversion always succeeds
|
||||
// except when the input value is special and no infinity_symbol or
|
||||
// nan_symbol has been given to the constructor.
|
||||
bool ToShortest(double value, StringBuilder* result_builder) const {
|
||||
return ToShortestIeeeNumber(value, result_builder, SHORTEST);
|
||||
}
|
||||
|
||||
// Same as ToShortest, but for single-precision floats.
|
||||
bool ToShortestSingle(float value, StringBuilder* result_builder) const {
|
||||
return ToShortestIeeeNumber(value, result_builder, SHORTEST_SINGLE);
|
||||
}
|
||||
|
||||
|
||||
// Computes a decimal representation with a fixed number of digits after the
|
||||
// decimal point. The last emitted digit is rounded.
|
||||
//
|
||||
// Examples:
|
||||
// ToFixed(3.12, 1) -> "3.1"
|
||||
// ToFixed(3.1415, 3) -> "3.142"
|
||||
// ToFixed(1234.56789, 4) -> "1234.5679"
|
||||
// ToFixed(1.23, 5) -> "1.23000"
|
||||
// ToFixed(0.1, 4) -> "0.1000"
|
||||
// ToFixed(1e30, 2) -> "1000000000000000019884624838656.00"
|
||||
// ToFixed(0.1, 30) -> "0.100000000000000005551115123126"
|
||||
// ToFixed(0.1, 17) -> "0.10000000000000001"
|
||||
//
|
||||
// If requested_digits equals 0, then the tail of the result depends on
|
||||
// the EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT.
|
||||
// Examples, for requested_digits == 0,
|
||||
// let EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT be
|
||||
// - false and false: then 123.45 -> 123
|
||||
// 0.678 -> 1
|
||||
// - true and false: then 123.45 -> 123.
|
||||
// 0.678 -> 1.
|
||||
// - true and true: then 123.45 -> 123.0
|
||||
// 0.678 -> 1.0
|
||||
//
|
||||
// Returns true if the conversion succeeds. The conversion always succeeds
|
||||
// except for the following cases:
|
||||
// - the input value is special and no infinity_symbol or nan_symbol has
|
||||
// been provided to the constructor,
|
||||
// - 'value' > 10^kMaxFixedDigitsBeforePoint, or
|
||||
// - 'requested_digits' > kMaxFixedDigitsAfterPoint.
|
||||
// The last two conditions imply that the result will never contain more than
|
||||
// 1 + kMaxFixedDigitsBeforePoint + 1 + kMaxFixedDigitsAfterPoint characters
|
||||
// (one additional character for the sign, and one for the decimal point).
|
||||
bool ToFixed(double value,
|
||||
int requested_digits,
|
||||
StringBuilder* result_builder) const;
|
||||
|
||||
// Computes a representation in exponential format with requested_digits
|
||||
// after the decimal point. The last emitted digit is rounded.
|
||||
// If requested_digits equals -1, then the shortest exponential representation
|
||||
// is computed.
|
||||
//
|
||||
// Examples with EMIT_POSITIVE_EXPONENT_SIGN deactivated, and
|
||||
// exponent_character set to 'e'.
|
||||
// ToExponential(3.12, 1) -> "3.1e0"
|
||||
// ToExponential(5.0, 3) -> "5.000e0"
|
||||
// ToExponential(0.001, 2) -> "1.00e-3"
|
||||
// ToExponential(3.1415, -1) -> "3.1415e0"
|
||||
// ToExponential(3.1415, 4) -> "3.1415e0"
|
||||
// ToExponential(3.1415, 3) -> "3.142e0"
|
||||
// ToExponential(123456789000000, 3) -> "1.235e14"
|
||||
// ToExponential(1000000000000000019884624838656.0, -1) -> "1e30"
|
||||
// ToExponential(1000000000000000019884624838656.0, 32) ->
|
||||
// "1.00000000000000001988462483865600e30"
|
||||
// ToExponential(1234, 0) -> "1e3"
|
||||
//
|
||||
// Returns true if the conversion succeeds. The conversion always succeeds
|
||||
// except for the following cases:
|
||||
// - the input value is special and no infinity_symbol or nan_symbol has
|
||||
// been provided to the constructor,
|
||||
// - 'requested_digits' > kMaxExponentialDigits.
|
||||
// The last condition implies that the result will never contain more than
|
||||
// kMaxExponentialDigits + 8 characters (the sign, the digit before the
|
||||
// decimal point, the decimal point, the exponent character, the
|
||||
// exponent's sign, and at most 3 exponent digits).
|
||||
bool ToExponential(double value,
|
||||
int requested_digits,
|
||||
StringBuilder* result_builder) const;
|
||||
|
||||
// Computes 'precision' leading digits of the given 'value' and returns them
|
||||
// either in exponential or decimal format, depending on
|
||||
// max_{leading|trailing}_padding_zeroes_in_precision_mode (given to the
|
||||
// constructor).
|
||||
// The last computed digit is rounded.
|
||||
//
|
||||
// Example with max_leading_padding_zeroes_in_precision_mode = 6.
|
||||
// ToPrecision(0.0000012345, 2) -> "0.0000012"
|
||||
// ToPrecision(0.00000012345, 2) -> "1.2e-7"
|
||||
// Similarily the converter may add up to
|
||||
// max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid
|
||||
// returning an exponential representation. A zero added by the
|
||||
// EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit.
|
||||
// Examples for max_trailing_padding_zeroes_in_precision_mode = 1:
|
||||
// ToPrecision(230.0, 2) -> "230"
|
||||
// ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT.
|
||||
// ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT.
|
||||
// Examples for max_trailing_padding_zeroes_in_precision_mode = 3, and no
|
||||
// EMIT_TRAILING_ZERO_AFTER_POINT:
|
||||
// ToPrecision(123450.0, 6) -> "123450"
|
||||
// ToPrecision(123450.0, 5) -> "123450"
|
||||
// ToPrecision(123450.0, 4) -> "123500"
|
||||
// ToPrecision(123450.0, 3) -> "123000"
|
||||
// ToPrecision(123450.0, 2) -> "1.2e5"
|
||||
//
|
||||
// Returns true if the conversion succeeds. The conversion always succeeds
|
||||
// except for the following cases:
|
||||
// - the input value is special and no infinity_symbol or nan_symbol has
|
||||
// been provided to the constructor,
|
||||
// - precision < kMinPericisionDigits
|
||||
// - precision > kMaxPrecisionDigits
|
||||
// The last condition implies that the result will never contain more than
|
||||
// kMaxPrecisionDigits + 7 characters (the sign, the decimal point, the
|
||||
// exponent character, the exponent's sign, and at most 3 exponent digits).
|
||||
bool ToPrecision(double value,
|
||||
int precision,
|
||||
StringBuilder* result_builder) const;
|
||||
|
||||
enum DtoaMode {
|
||||
// Produce the shortest correct representation.
|
||||
// For example the output of 0.299999999999999988897 is (the less accurate
|
||||
// but correct) 0.3.
|
||||
SHORTEST,
|
||||
// Same as SHORTEST, but for single-precision floats.
|
||||
SHORTEST_SINGLE,
|
||||
// Produce a fixed number of digits after the decimal point.
|
||||
// For instance fixed(0.1, 4) becomes 0.1000
|
||||
// If the input number is big, the output will be big.
|
||||
FIXED,
|
||||
// Fixed number of digits (independent of the decimal point).
|
||||
PRECISION
|
||||
};
|
||||
|
||||
// The maximal number of digits that are needed to emit a double in base 10.
|
||||
// A higher precision can be achieved by using more digits, but the shortest
|
||||
// accurate representation of any double will never use more digits than
|
||||
// kBase10MaximalLength.
|
||||
// Note that DoubleToAscii null-terminates its input. So the given buffer
|
||||
// should be at least kBase10MaximalLength + 1 characters long.
|
||||
static const int kBase10MaximalLength = 17;
|
||||
|
||||
// Converts the given double 'v' to ascii. 'v' must not be NaN, +Infinity, or
|
||||
// -Infinity. In SHORTEST_SINGLE-mode this restriction also applies to 'v'
|
||||
// after it has been casted to a single-precision float. That is, in this
|
||||
// mode static_cast<float>(v) must not be NaN, +Infinity or -Infinity.
|
||||
//
|
||||
// The result should be interpreted as buffer * 10^(point-length).
|
||||
//
|
||||
// The output depends on the given mode:
|
||||
// - SHORTEST: produce the least amount of digits for which the internal
|
||||
// identity requirement is still satisfied. If the digits are printed
|
||||
// (together with the correct exponent) then reading this number will give
|
||||
// 'v' again. The buffer will choose the representation that is closest to
|
||||
// 'v'. If there are two at the same distance, than the one farther away
|
||||
// from 0 is chosen (halfway cases - ending with 5 - are rounded up).
|
||||
// In this mode the 'requested_digits' parameter is ignored.
|
||||
// - SHORTEST_SINGLE: same as SHORTEST but with single-precision.
|
||||
// - FIXED: produces digits necessary to print a given number with
|
||||
// 'requested_digits' digits after the decimal point. The produced digits
|
||||
// might be too short in which case the caller has to fill the remainder
|
||||
// with '0's.
|
||||
// Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2.
|
||||
// Halfway cases are rounded towards +/-Infinity (away from 0). The call
|
||||
// toFixed(0.15, 2) thus returns buffer="2", point=0.
|
||||
// The returned buffer may contain digits that would be truncated from the
|
||||
// shortest representation of the input.
|
||||
// - PRECISION: produces 'requested_digits' where the first digit is not '0'.
|
||||
// Even though the length of produced digits usually equals
|
||||
// 'requested_digits', the function is allowed to return fewer digits, in
|
||||
// which case the caller has to fill the missing digits with '0's.
|
||||
// Halfway cases are again rounded away from 0.
|
||||
// DoubleToAscii expects the given buffer to be big enough to hold all
|
||||
// digits and a terminating null-character. In SHORTEST-mode it expects a
|
||||
// buffer of at least kBase10MaximalLength + 1. In all other modes the
|
||||
// requested_digits parameter and the padding-zeroes limit the size of the
|
||||
// output. Don't forget the decimal point, the exponent character and the
|
||||
// terminating null-character when computing the maximal output size.
|
||||
// The given length is only used in debug mode to ensure the buffer is big
|
||||
// enough.
|
||||
static void DoubleToAscii(double v,
|
||||
DtoaMode mode,
|
||||
int requested_digits,
|
||||
char* buffer,
|
||||
int buffer_length,
|
||||
bool* sign,
|
||||
int* length,
|
||||
int* point);
|
||||
|
||||
private:
|
||||
// Implementation for ToShortest and ToShortestSingle.
|
||||
bool ToShortestIeeeNumber(double value,
|
||||
StringBuilder* result_builder,
|
||||
DtoaMode mode) const;
|
||||
|
||||
// If the value is a special value (NaN or Infinity) constructs the
|
||||
// corresponding string using the configured infinity/nan-symbol.
|
||||
// If either of them is NULL or the value is not special then the
|
||||
// function returns false.
|
||||
bool HandleSpecialValues(double value, StringBuilder* result_builder) const;
|
||||
// Constructs an exponential representation (i.e. 1.234e56).
|
||||
// The given exponent assumes a decimal point after the first decimal digit.
|
||||
void CreateExponentialRepresentation(const char* decimal_digits,
|
||||
int length,
|
||||
int exponent,
|
||||
StringBuilder* result_builder) const;
|
||||
// Creates a decimal representation (i.e 1234.5678).
|
||||
void CreateDecimalRepresentation(const char* decimal_digits,
|
||||
int length,
|
||||
int decimal_point,
|
||||
int digits_after_point,
|
||||
StringBuilder* result_builder) const;
|
||||
|
||||
const int flags_;
|
||||
const char* const infinity_symbol_;
|
||||
const char* const nan_symbol_;
|
||||
const char exponent_character_;
|
||||
const int decimal_in_shortest_low_;
|
||||
const int decimal_in_shortest_high_;
|
||||
const int max_leading_padding_zeroes_in_precision_mode_;
|
||||
const int max_trailing_padding_zeroes_in_precision_mode_;
|
||||
|
||||
DC_DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter);
|
||||
};
|
||||
|
||||
|
||||
class StringToDoubleConverter {
|
||||
public:
|
||||
// Enumeration for allowing octals and ignoring junk when converting
|
||||
// strings to numbers.
|
||||
enum Flags {
|
||||
NO_FLAGS = 0,
|
||||
ALLOW_HEX = 1,
|
||||
ALLOW_OCTALS = 2,
|
||||
ALLOW_TRAILING_JUNK = 4,
|
||||
ALLOW_LEADING_SPACES = 8,
|
||||
ALLOW_TRAILING_SPACES = 16,
|
||||
ALLOW_SPACES_AFTER_SIGN = 32,
|
||||
ALLOW_CASE_INSENSIBILITY = 64,
|
||||
};
|
||||
|
||||
// Flags should be a bit-or combination of the possible Flags-enum.
|
||||
// - NO_FLAGS: no special flags.
|
||||
// - ALLOW_HEX: recognizes the prefix "0x". Hex numbers may only be integers.
|
||||
// Ex: StringToDouble("0x1234") -> 4660.0
|
||||
// In StringToDouble("0x1234.56") the characters ".56" are trailing
|
||||
// junk. The result of the call is hence dependent on
|
||||
// the ALLOW_TRAILING_JUNK flag and/or the junk value.
|
||||
// With this flag "0x" is a junk-string. Even with ALLOW_TRAILING_JUNK,
|
||||
// the string will not be parsed as "0" followed by junk.
|
||||
//
|
||||
// - ALLOW_OCTALS: recognizes the prefix "0" for octals:
|
||||
// If a sequence of octal digits starts with '0', then the number is
|
||||
// read as octal integer. Octal numbers may only be integers.
|
||||
// Ex: StringToDouble("01234") -> 668.0
|
||||
// StringToDouble("012349") -> 12349.0 // Not a sequence of octal
|
||||
// // digits.
|
||||
// In StringToDouble("01234.56") the characters ".56" are trailing
|
||||
// junk. The result of the call is hence dependent on
|
||||
// the ALLOW_TRAILING_JUNK flag and/or the junk value.
|
||||
// In StringToDouble("01234e56") the characters "e56" are trailing
|
||||
// junk, too.
|
||||
// - ALLOW_TRAILING_JUNK: ignore trailing characters that are not part of
|
||||
// a double literal.
|
||||
// - ALLOW_LEADING_SPACES: skip over leading whitespace, including spaces,
|
||||
// new-lines, and tabs.
|
||||
// - ALLOW_TRAILING_SPACES: ignore trailing whitespace.
|
||||
// - ALLOW_SPACES_AFTER_SIGN: ignore whitespace after the sign.
|
||||
// Ex: StringToDouble("- 123.2") -> -123.2.
|
||||
// StringToDouble("+ 123.2") -> 123.2
|
||||
// - ALLOW_CASE_INSENSIBILITY: ignore case of characters for special values:
|
||||
// infinity and nan.
|
||||
//
|
||||
// empty_string_value is returned when an empty string is given as input.
|
||||
// If ALLOW_LEADING_SPACES or ALLOW_TRAILING_SPACES are set, then a string
|
||||
// containing only spaces is converted to the 'empty_string_value', too.
|
||||
//
|
||||
// junk_string_value is returned when
|
||||
// a) ALLOW_TRAILING_JUNK is not set, and a junk character (a character not
|
||||
// part of a double-literal) is found.
|
||||
// b) ALLOW_TRAILING_JUNK is set, but the string does not start with a
|
||||
// double literal.
|
||||
//
|
||||
// infinity_symbol and nan_symbol are strings that are used to detect
|
||||
// inputs that represent infinity and NaN. They can be null, in which case
|
||||
// they are ignored.
|
||||
// The conversion routine first reads any possible signs. Then it compares the
|
||||
// following character of the input-string with the first character of
|
||||
// the infinity, and nan-symbol. If either matches, the function assumes, that
|
||||
// a match has been found, and expects the following input characters to match
|
||||
// the remaining characters of the special-value symbol.
|
||||
// This means that the following restrictions apply to special-value symbols:
|
||||
// - they must not start with signs ('+', or '-'),
|
||||
// - they must not have the same first character.
|
||||
// - they must not start with digits.
|
||||
//
|
||||
// Examples:
|
||||
// flags = ALLOW_HEX | ALLOW_TRAILING_JUNK,
|
||||
// empty_string_value = 0.0,
|
||||
// junk_string_value = NaN,
|
||||
// infinity_symbol = "infinity",
|
||||
// nan_symbol = "nan":
|
||||
// StringToDouble("0x1234") -> 4660.0.
|
||||
// StringToDouble("0x1234K") -> 4660.0.
|
||||
// StringToDouble("") -> 0.0 // empty_string_value.
|
||||
// StringToDouble(" ") -> NaN // junk_string_value.
|
||||
// StringToDouble(" 1") -> NaN // junk_string_value.
|
||||
// StringToDouble("0x") -> NaN // junk_string_value.
|
||||
// StringToDouble("-123.45") -> -123.45.
|
||||
// StringToDouble("--123.45") -> NaN // junk_string_value.
|
||||
// StringToDouble("123e45") -> 123e45.
|
||||
// StringToDouble("123E45") -> 123e45.
|
||||
// StringToDouble("123e+45") -> 123e45.
|
||||
// StringToDouble("123E-45") -> 123e-45.
|
||||
// StringToDouble("123e") -> 123.0 // trailing junk ignored.
|
||||
// StringToDouble("123e-") -> 123.0 // trailing junk ignored.
|
||||
// StringToDouble("+NaN") -> NaN // NaN string literal.
|
||||
// StringToDouble("-infinity") -> -inf. // infinity literal.
|
||||
// StringToDouble("Infinity") -> NaN // junk_string_value.
|
||||
//
|
||||
// flags = ALLOW_OCTAL | ALLOW_LEADING_SPACES,
|
||||
// empty_string_value = 0.0,
|
||||
// junk_string_value = NaN,
|
||||
// infinity_symbol = NULL,
|
||||
// nan_symbol = NULL:
|
||||
// StringToDouble("0x1234") -> NaN // junk_string_value.
|
||||
// StringToDouble("01234") -> 668.0.
|
||||
// StringToDouble("") -> 0.0 // empty_string_value.
|
||||
// StringToDouble(" ") -> 0.0 // empty_string_value.
|
||||
// StringToDouble(" 1") -> 1.0
|
||||
// StringToDouble("0x") -> NaN // junk_string_value.
|
||||
// StringToDouble("0123e45") -> NaN // junk_string_value.
|
||||
// StringToDouble("01239E45") -> 1239e45.
|
||||
// StringToDouble("-infinity") -> NaN // junk_string_value.
|
||||
// StringToDouble("NaN") -> NaN // junk_string_value.
|
||||
StringToDoubleConverter(int flags,
|
||||
double empty_string_value,
|
||||
double junk_string_value,
|
||||
const char* infinity_symbol,
|
||||
const char* nan_symbol)
|
||||
: flags_(flags),
|
||||
empty_string_value_(empty_string_value),
|
||||
junk_string_value_(junk_string_value),
|
||||
infinity_symbol_(infinity_symbol),
|
||||
nan_symbol_(nan_symbol) {
|
||||
}
|
||||
|
||||
// Performs the conversion.
|
||||
// The output parameter 'processed_characters_count' is set to the number
|
||||
// of characters that have been processed to read the number.
|
||||
// Spaces than are processed with ALLOW_{LEADING|TRAILING}_SPACES are included
|
||||
// in the 'processed_characters_count'. Trailing junk is never included.
|
||||
double StringToDouble(const char* buffer,
|
||||
int length,
|
||||
int* processed_characters_count) const;
|
||||
|
||||
// Same as StringToDouble above but for 16 bit characters.
|
||||
double StringToDouble(const uc16* buffer,
|
||||
int length,
|
||||
int* processed_characters_count) const;
|
||||
|
||||
// Same as StringToDouble but reads a float.
|
||||
// Note that this is not equivalent to static_cast<float>(StringToDouble(...))
|
||||
// due to potential double-rounding.
|
||||
float StringToFloat(const char* buffer,
|
||||
int length,
|
||||
int* processed_characters_count) const;
|
||||
|
||||
// Same as StringToFloat above but for 16 bit characters.
|
||||
float StringToFloat(const uc16* buffer,
|
||||
int length,
|
||||
int* processed_characters_count) const;
|
||||
|
||||
private:
|
||||
const int flags_;
|
||||
const double empty_string_value_;
|
||||
const double junk_string_value_;
|
||||
const char* const infinity_symbol_;
|
||||
const char* const nan_symbol_;
|
||||
|
||||
template <class Iterator>
|
||||
double StringToIeee(Iterator start_pointer,
|
||||
int length,
|
||||
bool read_as_double,
|
||||
int* processed_characters_count) const;
|
||||
|
||||
DC_DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter);
|
||||
};
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_
|
||||
@ -1,665 +0,0 @@
|
||||
// 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 <double-conversion/fast-dtoa.h>
|
||||
|
||||
#include <double-conversion/cached-powers.h>
|
||||
#include <double-conversion/diy-fp.h>
|
||||
#include <double-conversion/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.
|
||||
if (number < kSmallPowersOfTen[exponent_plus_one_guess]) {
|
||||
exponent_plus_one_guess--;
|
||||
}
|
||||
*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;
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('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());
|
||||
for (;;) {
|
||||
fractionals *= 10;
|
||||
unit *= 10;
|
||||
unsafe_interval.set_f(unsafe_interval.f() * 10);
|
||||
// Integer division by one.
|
||||
int digit = static_cast<int>(fractionals >> -one.e());
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('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;
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('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());
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('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
|
||||
@ -1,88 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_FAST_DTOA_H_
|
||||
#define DOUBLE_CONVERSION_FAST_DTOA_H_
|
||||
|
||||
#include <double-conversion/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_
|
||||
@ -1,405 +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 <cmath>
|
||||
|
||||
#include <double-conversion/fixed-dtoa.h>
|
||||
#include <double-conversion/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) const {
|
||||
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] = static_cast<char>('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,
|
||||
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);
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('0' + digit);
|
||||
(*length)++;
|
||||
fractionals -= static_cast<uint64_t>(digit) << point;
|
||||
}
|
||||
// If the first bit after the point is set we have to round up.
|
||||
ASSERT(fractionals == 0 || point - 1 >= 0);
|
||||
if ((fractionals != 0) && ((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);
|
||||
ASSERT(digit <= 9);
|
||||
buffer[*length] = static_cast<char>('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, 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
|
||||
@ -1,56 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_FIXED_DTOA_H_
|
||||
#define DOUBLE_CONVERSION_FIXED_DTOA_H_
|
||||
|
||||
#include <double-conversion/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_
|
||||
@ -1,402 +0,0 @@
|
||||
// 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 <double-conversion/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 -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);
|
||||
}
|
||||
|
||||
DC_DISALLOW_COPY_AND_ASSIGN(Double);
|
||||
};
|
||||
|
||||
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_;
|
||||
|
||||
DC_DISALLOW_COPY_AND_ASSIGN(Single);
|
||||
};
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_DOUBLE_H_
|
||||
@ -1,555 +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 <climits>
|
||||
#include <cstdarg>
|
||||
|
||||
#include <double-conversion/bignum.h>
|
||||
#include <double-conversion/cached-powers.h>
|
||||
#include <double-conversion/ieee.h>
|
||||
#include <double-conversion/strtod.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
// 2^53 = 9007199254740992.
|
||||
// Any integer with at most 15 decimal digits will hence fit into a double
|
||||
// (which has a 53bit significand) without loss of precision.
|
||||
static const int kMaxExactDoubleIntegerDecimalDigits = 15;
|
||||
// 2^64 = 18446744073709551616 > 10^19
|
||||
static const int kMaxUint64DecimalDigits = 19;
|
||||
|
||||
// Max double: 1.7976931348623157 x 10^308
|
||||
// Min non-zero double: 4.9406564584124654 x 10^-324
|
||||
// Any x >= 10^309 is interpreted as +infinity.
|
||||
// Any x <= 10^-324 is interpreted as 0.
|
||||
// Note that 2.5e-324 (despite being smaller than the min double) will be read
|
||||
// as non-zero (equal to the min non-zero double).
|
||||
static const int kMaxDecimalPower = 309;
|
||||
static const int kMinDecimalPower = -324;
|
||||
|
||||
// 2^64 = 18446744073709551616
|
||||
static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
|
||||
|
||||
|
||||
static const double exact_powers_of_ten[] = {
|
||||
1.0, // 10^0
|
||||
10.0,
|
||||
100.0,
|
||||
1000.0,
|
||||
10000.0,
|
||||
100000.0,
|
||||
1000000.0,
|
||||
10000000.0,
|
||||
100000000.0,
|
||||
1000000000.0,
|
||||
10000000000.0, // 10^10
|
||||
100000000000.0,
|
||||
1000000000000.0,
|
||||
10000000000000.0,
|
||||
100000000000000.0,
|
||||
1000000000000000.0,
|
||||
10000000000000000.0,
|
||||
100000000000000000.0,
|
||||
1000000000000000000.0,
|
||||
10000000000000000000.0,
|
||||
100000000000000000000.0, // 10^20
|
||||
1000000000000000000000.0,
|
||||
// 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22
|
||||
10000000000000000000000.0
|
||||
};
|
||||
static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten);
|
||||
|
||||
// Maximum number of significant digits in the decimal representation.
|
||||
// In fact the value is 772 (see conversions.cc), but to give us some margin
|
||||
// we round up to 780.
|
||||
static const int kMaxSignificantDecimalDigits = 780;
|
||||
|
||||
static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) {
|
||||
for (int i = 0; i < buffer.length(); i++) {
|
||||
if (buffer[i] != '0') {
|
||||
return buffer.SubVector(i, buffer.length());
|
||||
}
|
||||
}
|
||||
return Vector<const char>(buffer.start(), 0);
|
||||
}
|
||||
|
||||
|
||||
static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
|
||||
for (int i = buffer.length() - 1; i >= 0; --i) {
|
||||
if (buffer[i] != '0') {
|
||||
return buffer.SubVector(0, i + 1);
|
||||
}
|
||||
}
|
||||
return Vector<const char>(buffer.start(), 0);
|
||||
}
|
||||
|
||||
|
||||
static void CutToMaxSignificantDigits(Vector<const char> buffer,
|
||||
int exponent,
|
||||
char* significant_buffer,
|
||||
int* significant_exponent) {
|
||||
for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) {
|
||||
significant_buffer[i] = buffer[i];
|
||||
}
|
||||
// The input buffer has been trimmed. Therefore the last digit must be
|
||||
// different from '0'.
|
||||
ASSERT(buffer[buffer.length() - 1] != '0');
|
||||
// Set the last digit to be non-zero. This is sufficient to guarantee
|
||||
// correct rounding.
|
||||
significant_buffer[kMaxSignificantDecimalDigits - 1] = '1';
|
||||
*significant_exponent =
|
||||
exponent + (buffer.length() - kMaxSignificantDecimalDigits);
|
||||
}
|
||||
|
||||
|
||||
// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits.
|
||||
// If possible the input-buffer is reused, but if the buffer needs to be
|
||||
// modified (due to cutting), then the input needs to be copied into the
|
||||
// buffer_copy_space.
|
||||
static void TrimAndCut(Vector<const char> buffer, int exponent,
|
||||
char* buffer_copy_space, int space_size,
|
||||
Vector<const char>* trimmed, int* updated_exponent) {
|
||||
Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
|
||||
Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed);
|
||||
exponent += left_trimmed.length() - right_trimmed.length();
|
||||
if (right_trimmed.length() > kMaxSignificantDecimalDigits) {
|
||||
(void) space_size; // Mark variable as used.
|
||||
ASSERT(space_size >= kMaxSignificantDecimalDigits);
|
||||
CutToMaxSignificantDigits(right_trimmed, exponent,
|
||||
buffer_copy_space, updated_exponent);
|
||||
*trimmed = Vector<const char>(buffer_copy_space,
|
||||
kMaxSignificantDecimalDigits);
|
||||
} else {
|
||||
*trimmed = right_trimmed;
|
||||
*updated_exponent = exponent;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Reads digits from the buffer and converts them to a uint64.
|
||||
// Reads in as many digits as fit into a uint64.
|
||||
// When the string starts with "1844674407370955161" no further digit is read.
|
||||
// Since 2^64 = 18446744073709551616 it would still be possible read another
|
||||
// digit if it was less or equal than 6, but this would complicate the code.
|
||||
static uint64_t ReadUint64(Vector<const char> buffer,
|
||||
int* number_of_read_digits) {
|
||||
uint64_t result = 0;
|
||||
int i = 0;
|
||||
while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
|
||||
int digit = buffer[i++] - '0';
|
||||
ASSERT(0 <= digit && digit <= 9);
|
||||
result = 10 * result + digit;
|
||||
}
|
||||
*number_of_read_digits = i;
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
// Reads a DiyFp from the buffer.
|
||||
// The returned DiyFp is not necessarily normalized.
|
||||
// If remaining_decimals is zero then the returned DiyFp is accurate.
|
||||
// Otherwise it has been rounded and has error of at most 1/2 ulp.
|
||||
static void ReadDiyFp(Vector<const char> buffer,
|
||||
DiyFp* result,
|
||||
int* remaining_decimals) {
|
||||
int read_digits;
|
||||
uint64_t significand = ReadUint64(buffer, &read_digits);
|
||||
if (buffer.length() == read_digits) {
|
||||
*result = DiyFp(significand, 0);
|
||||
*remaining_decimals = 0;
|
||||
} else {
|
||||
// Round the significand.
|
||||
if (buffer[read_digits] >= '5') {
|
||||
significand++;
|
||||
}
|
||||
// Compute the binary exponent.
|
||||
int exponent = 0;
|
||||
*result = DiyFp(significand, exponent);
|
||||
*remaining_decimals = buffer.length() - read_digits;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
static bool DoubleStrtod(Vector<const char> trimmed,
|
||||
int exponent,
|
||||
double* result) {
|
||||
#if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS)
|
||||
// On x86 the floating-point stack can be 64 or 80 bits wide. If it is
|
||||
// 80 bits wide (as is the case on Linux) then double-rounding occurs and the
|
||||
// result is not accurate.
|
||||
// We know that Windows32 uses 64 bits and is therefore accurate.
|
||||
// Note that the ARM simulator is compiled for 32bits. It therefore exhibits
|
||||
// the same problem.
|
||||
return false;
|
||||
#endif
|
||||
if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
|
||||
int read_digits;
|
||||
// The trimmed input fits into a double.
|
||||
// If the 10^exponent (resp. 10^-exponent) fits into a double too then we
|
||||
// can compute the result-double simply by multiplying (resp. dividing) the
|
||||
// two numbers.
|
||||
// This is possible because IEEE guarantees that floating-point operations
|
||||
// return the best possible approximation.
|
||||
if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
|
||||
// 10^-exponent fits into a double.
|
||||
*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
|
||||
ASSERT(read_digits == trimmed.length());
|
||||
*result /= exact_powers_of_ten[-exponent];
|
||||
return true;
|
||||
}
|
||||
if (0 <= exponent && exponent < kExactPowersOfTenSize) {
|
||||
// 10^exponent fits into a double.
|
||||
*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
|
||||
ASSERT(read_digits == trimmed.length());
|
||||
*result *= exact_powers_of_ten[exponent];
|
||||
return true;
|
||||
}
|
||||
int remaining_digits =
|
||||
kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
|
||||
if ((0 <= exponent) &&
|
||||
(exponent - remaining_digits < kExactPowersOfTenSize)) {
|
||||
// The trimmed string was short and we can multiply it with
|
||||
// 10^remaining_digits. As a result the remaining exponent now fits
|
||||
// into a double too.
|
||||
*result = static_cast<double>(ReadUint64(trimmed, &read_digits));
|
||||
ASSERT(read_digits == trimmed.length());
|
||||
*result *= exact_powers_of_ten[remaining_digits];
|
||||
*result *= exact_powers_of_ten[exponent - remaining_digits];
|
||||
return true;
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
|
||||
// Returns 10^exponent as an exact DiyFp.
|
||||
// The given exponent must be in the range [1; kDecimalExponentDistance[.
|
||||
static DiyFp AdjustmentPowerOfTen(int exponent) {
|
||||
ASSERT(0 < exponent);
|
||||
ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
|
||||
// Simply hardcode the remaining powers for the given decimal exponent
|
||||
// distance.
|
||||
ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
|
||||
switch (exponent) {
|
||||
case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
|
||||
case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
|
||||
case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
|
||||
case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
|
||||
case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
|
||||
case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
|
||||
case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
|
||||
default:
|
||||
UNREACHABLE();
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// If the function returns true then the result is the correct double.
|
||||
// Otherwise it is either the correct double or the double that is just below
|
||||
// the correct double.
|
||||
static bool DiyFpStrtod(Vector<const char> buffer,
|
||||
int exponent,
|
||||
double* result) {
|
||||
DiyFp input;
|
||||
int remaining_decimals;
|
||||
ReadDiyFp(buffer, &input, &remaining_decimals);
|
||||
// Since we may have dropped some digits the input is not accurate.
|
||||
// If remaining_decimals is different than 0 than the error is at most
|
||||
// .5 ulp (unit in the last place).
|
||||
// We don't want to deal with fractions and therefore keep a common
|
||||
// denominator.
|
||||
const int kDenominatorLog = 3;
|
||||
const int kDenominator = 1 << kDenominatorLog;
|
||||
// Move the remaining decimals into the exponent.
|
||||
exponent += remaining_decimals;
|
||||
uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
|
||||
|
||||
int old_e = input.e();
|
||||
input.Normalize();
|
||||
error <<= old_e - input.e();
|
||||
|
||||
ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
|
||||
if (exponent < PowersOfTenCache::kMinDecimalExponent) {
|
||||
*result = 0.0;
|
||||
return true;
|
||||
}
|
||||
DiyFp cached_power;
|
||||
int cached_decimal_exponent;
|
||||
PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
|
||||
&cached_power,
|
||||
&cached_decimal_exponent);
|
||||
|
||||
if (cached_decimal_exponent != exponent) {
|
||||
int adjustment_exponent = exponent - cached_decimal_exponent;
|
||||
DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
|
||||
input.Multiply(adjustment_power);
|
||||
if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
|
||||
// The product of input with the adjustment power fits into a 64 bit
|
||||
// integer.
|
||||
ASSERT(DiyFp::kSignificandSize == 64);
|
||||
} else {
|
||||
// The adjustment power is exact. There is hence only an error of 0.5.
|
||||
error += kDenominator / 2;
|
||||
}
|
||||
}
|
||||
|
||||
input.Multiply(cached_power);
|
||||
// The error introduced by a multiplication of a*b equals
|
||||
// error_a + error_b + error_a*error_b/2^64 + 0.5
|
||||
// Substituting a with 'input' and b with 'cached_power' we have
|
||||
// error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
|
||||
// error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
|
||||
int error_b = kDenominator / 2;
|
||||
int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
|
||||
int fixed_error = kDenominator / 2;
|
||||
error += error_b + error_ab + fixed_error;
|
||||
|
||||
old_e = input.e();
|
||||
input.Normalize();
|
||||
error <<= old_e - input.e();
|
||||
|
||||
// See if the double's significand changes if we add/subtract the error.
|
||||
int order_of_magnitude = DiyFp::kSignificandSize + input.e();
|
||||
int effective_significand_size =
|
||||
Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
|
||||
int precision_digits_count =
|
||||
DiyFp::kSignificandSize - effective_significand_size;
|
||||
if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
|
||||
// This can only happen for very small denormals. In this case the
|
||||
// half-way multiplied by the denominator exceeds the range of an uint64.
|
||||
// Simply shift everything to the right.
|
||||
int shift_amount = (precision_digits_count + kDenominatorLog) -
|
||||
DiyFp::kSignificandSize + 1;
|
||||
input.set_f(input.f() >> shift_amount);
|
||||
input.set_e(input.e() + shift_amount);
|
||||
// We add 1 for the lost precision of error, and kDenominator for
|
||||
// the lost precision of input.f().
|
||||
error = (error >> shift_amount) + 1 + kDenominator;
|
||||
precision_digits_count -= shift_amount;
|
||||
}
|
||||
// We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
|
||||
ASSERT(DiyFp::kSignificandSize == 64);
|
||||
ASSERT(precision_digits_count < 64);
|
||||
uint64_t one64 = 1;
|
||||
uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
|
||||
uint64_t precision_bits = input.f() & precision_bits_mask;
|
||||
uint64_t half_way = one64 << (precision_digits_count - 1);
|
||||
precision_bits *= kDenominator;
|
||||
half_way *= kDenominator;
|
||||
DiyFp rounded_input(input.f() >> precision_digits_count,
|
||||
input.e() + precision_digits_count);
|
||||
if (precision_bits >= half_way + error) {
|
||||
rounded_input.set_f(rounded_input.f() + 1);
|
||||
}
|
||||
// If the last_bits are too close to the half-way case than we are too
|
||||
// inaccurate and round down. In this case we return false so that we can
|
||||
// fall back to a more precise algorithm.
|
||||
|
||||
*result = Double(rounded_input).value();
|
||||
if (half_way - error < precision_bits && precision_bits < half_way + error) {
|
||||
// Too imprecise. The caller will have to fall back to a slower version.
|
||||
// However the returned number is guaranteed to be either the correct
|
||||
// double, or the next-lower double.
|
||||
return false;
|
||||
} else {
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Returns
|
||||
// - -1 if buffer*10^exponent < diy_fp.
|
||||
// - 0 if buffer*10^exponent == diy_fp.
|
||||
// - +1 if buffer*10^exponent > diy_fp.
|
||||
// Preconditions:
|
||||
// buffer.length() + exponent <= kMaxDecimalPower + 1
|
||||
// buffer.length() + exponent > kMinDecimalPower
|
||||
// buffer.length() <= kMaxDecimalSignificantDigits
|
||||
static int CompareBufferWithDiyFp(Vector<const char> buffer,
|
||||
int exponent,
|
||||
DiyFp diy_fp) {
|
||||
ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
|
||||
ASSERT(buffer.length() + exponent > kMinDecimalPower);
|
||||
ASSERT(buffer.length() <= kMaxSignificantDecimalDigits);
|
||||
// Make sure that the Bignum will be able to hold all our numbers.
|
||||
// Our Bignum implementation has a separate field for exponents. Shifts will
|
||||
// consume at most one bigit (< 64 bits).
|
||||
// ln(10) == 3.3219...
|
||||
ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
|
||||
Bignum buffer_bignum;
|
||||
Bignum diy_fp_bignum;
|
||||
buffer_bignum.AssignDecimalString(buffer);
|
||||
diy_fp_bignum.AssignUInt64(diy_fp.f());
|
||||
if (exponent >= 0) {
|
||||
buffer_bignum.MultiplyByPowerOfTen(exponent);
|
||||
} else {
|
||||
diy_fp_bignum.MultiplyByPowerOfTen(-exponent);
|
||||
}
|
||||
if (diy_fp.e() > 0) {
|
||||
diy_fp_bignum.ShiftLeft(diy_fp.e());
|
||||
} else {
|
||||
buffer_bignum.ShiftLeft(-diy_fp.e());
|
||||
}
|
||||
return Bignum::Compare(buffer_bignum, diy_fp_bignum);
|
||||
}
|
||||
|
||||
|
||||
// Returns true if the guess is the correct double.
|
||||
// Returns false, when guess is either correct or the next-lower double.
|
||||
static bool ComputeGuess(Vector<const char> trimmed, int exponent,
|
||||
double* guess) {
|
||||
if (trimmed.length() == 0) {
|
||||
*guess = 0.0;
|
||||
return true;
|
||||
}
|
||||
if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
|
||||
*guess = Double::Infinity();
|
||||
return true;
|
||||
}
|
||||
if (exponent + trimmed.length() <= kMinDecimalPower) {
|
||||
*guess = 0.0;
|
||||
return true;
|
||||
}
|
||||
|
||||
if (DoubleStrtod(trimmed, exponent, guess) ||
|
||||
DiyFpStrtod(trimmed, exponent, guess)) {
|
||||
return true;
|
||||
}
|
||||
if (*guess == Double::Infinity()) {
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
double Strtod(Vector<const char> buffer, int exponent) {
|
||||
char copy_buffer[kMaxSignificantDecimalDigits];
|
||||
Vector<const char> trimmed;
|
||||
int updated_exponent;
|
||||
TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
|
||||
&trimmed, &updated_exponent);
|
||||
exponent = updated_exponent;
|
||||
|
||||
double guess;
|
||||
bool is_correct = ComputeGuess(trimmed, exponent, &guess);
|
||||
if (is_correct) return guess;
|
||||
|
||||
DiyFp upper_boundary = Double(guess).UpperBoundary();
|
||||
int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
|
||||
if (comparison < 0) {
|
||||
return guess;
|
||||
} else if (comparison > 0) {
|
||||
return Double(guess).NextDouble();
|
||||
} else if ((Double(guess).Significand() & 1) == 0) {
|
||||
// Round towards even.
|
||||
return guess;
|
||||
} else {
|
||||
return Double(guess).NextDouble();
|
||||
}
|
||||
}
|
||||
|
||||
float Strtof(Vector<const char> buffer, int exponent) {
|
||||
char copy_buffer[kMaxSignificantDecimalDigits];
|
||||
Vector<const char> trimmed;
|
||||
int updated_exponent;
|
||||
TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits,
|
||||
&trimmed, &updated_exponent);
|
||||
exponent = updated_exponent;
|
||||
|
||||
double double_guess;
|
||||
bool is_correct = ComputeGuess(trimmed, exponent, &double_guess);
|
||||
|
||||
float float_guess = static_cast<float>(double_guess);
|
||||
if (float_guess == double_guess) {
|
||||
// This shortcut triggers for integer values.
|
||||
return float_guess;
|
||||
}
|
||||
|
||||
// We must catch double-rounding. Say the double has been rounded up, and is
|
||||
// now a boundary of a float, and rounds up again. This is why we have to
|
||||
// look at previous too.
|
||||
// Example (in decimal numbers):
|
||||
// input: 12349
|
||||
// high-precision (4 digits): 1235
|
||||
// low-precision (3 digits):
|
||||
// when read from input: 123
|
||||
// when rounded from high precision: 124.
|
||||
// To do this we simply look at the neigbors of the correct result and see
|
||||
// if they would round to the same float. If the guess is not correct we have
|
||||
// to look at four values (since two different doubles could be the correct
|
||||
// double).
|
||||
|
||||
double double_next = Double(double_guess).NextDouble();
|
||||
double double_previous = Double(double_guess).PreviousDouble();
|
||||
|
||||
float f1 = static_cast<float>(double_previous);
|
||||
float f2 = float_guess;
|
||||
float f3 = static_cast<float>(double_next);
|
||||
float f4;
|
||||
if (is_correct) {
|
||||
f4 = f3;
|
||||
} else {
|
||||
double double_next2 = Double(double_next).NextDouble();
|
||||
f4 = static_cast<float>(double_next2);
|
||||
}
|
||||
(void) f2; // Mark variable as used.
|
||||
ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4);
|
||||
|
||||
// If the guess doesn't lie near a single-precision boundary we can simply
|
||||
// return its float-value.
|
||||
if (f1 == f4) {
|
||||
return float_guess;
|
||||
}
|
||||
|
||||
ASSERT((f1 != f2 && f2 == f3 && f3 == f4) ||
|
||||
(f1 == f2 && f2 != f3 && f3 == f4) ||
|
||||
(f1 == f2 && f2 == f3 && f3 != f4));
|
||||
|
||||
// guess and next are the two possible canditates (in the same way that
|
||||
// double_guess was the lower candidate for a double-precision guess).
|
||||
float guess = f1;
|
||||
float next = f4;
|
||||
DiyFp upper_boundary;
|
||||
if (guess == 0.0f) {
|
||||
float min_float = 1e-45f;
|
||||
upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp();
|
||||
} else {
|
||||
upper_boundary = Single(guess).UpperBoundary();
|
||||
}
|
||||
int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary);
|
||||
if (comparison < 0) {
|
||||
return guess;
|
||||
} else if (comparison > 0) {
|
||||
return next;
|
||||
} else if ((Single(guess).Significand() & 1) == 0) {
|
||||
// Round towards even.
|
||||
return guess;
|
||||
} else {
|
||||
return next;
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace double_conversion
|
||||
@ -1,45 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_STRTOD_H_
|
||||
#define DOUBLE_CONVERSION_STRTOD_H_
|
||||
|
||||
#include <double-conversion/utils.h>
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
// The buffer must only contain digits in the range [0-9]. It must not
|
||||
// contain a dot or a sign. It must not start with '0', and must not be empty.
|
||||
double Strtod(Vector<const char> buffer, int exponent);
|
||||
|
||||
// The buffer must only contain digits in the range [0-9]. It must not
|
||||
// contain a dot or a sign. It must not start with '0', and must not be empty.
|
||||
float Strtof(Vector<const char> buffer, int exponent);
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_STRTOD_H_
|
||||
@ -1,342 +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.
|
||||
|
||||
#ifndef DOUBLE_CONVERSION_UTILS_H_
|
||||
#define DOUBLE_CONVERSION_UTILS_H_
|
||||
|
||||
#include <cstdlib>
|
||||
#include <cstring>
|
||||
|
||||
#include <cassert>
|
||||
#ifndef ASSERT
|
||||
#define ASSERT(condition) \
|
||||
assert(condition);
|
||||
#endif
|
||||
#ifndef UNIMPLEMENTED
|
||||
#define UNIMPLEMENTED() (abort())
|
||||
#endif
|
||||
#ifndef DOUBLE_CONVERSION_NO_RETURN
|
||||
#ifdef _MSC_VER
|
||||
#define DOUBLE_CONVERSION_NO_RETURN __declspec(noreturn)
|
||||
#else
|
||||
#define DOUBLE_CONVERSION_NO_RETURN __attribute__((noreturn))
|
||||
#endif
|
||||
#endif
|
||||
#ifndef UNREACHABLE
|
||||
#ifdef _MSC_VER
|
||||
void DOUBLE_CONVERSION_NO_RETURN abort_noreturn();
|
||||
inline void abort_noreturn() { abort(); }
|
||||
#define UNREACHABLE() (abort_noreturn())
|
||||
#else
|
||||
#define UNREACHABLE() (abort())
|
||||
#endif
|
||||
#endif
|
||||
|
||||
|
||||
// Double operations detection based on target architecture.
|
||||
// Linux uses a 80bit wide floating point stack on x86. This induces double
|
||||
// rounding, which in turn leads to wrong results.
|
||||
// An easy way to test if the floating-point operations are correct is to
|
||||
// evaluate: 89255.0/1e22. If the floating-point stack is 64 bits wide then
|
||||
// the result is equal to 89255e-22.
|
||||
// The best way to test this, is to create a division-function and to compare
|
||||
// the output of the division with the expected result. (Inlining must be
|
||||
// disabled.)
|
||||
// On Linux,x86 89255e-22 != Div_double(89255.0/1e22)
|
||||
#if defined(_M_X64) || defined(__x86_64__) || \
|
||||
defined(__ARMEL__) || defined(__avr32__) || \
|
||||
defined(__hppa__) || defined(__ia64__) || \
|
||||
defined(__mips__) || \
|
||||
defined(__powerpc__) || defined(__ppc__) || defined(__ppc64__) || \
|
||||
defined(_POWER) || defined(_ARCH_PPC) || defined(_ARCH_PPC64) || \
|
||||
defined(__sparc__) || defined(__sparc) || defined(__s390__) || \
|
||||
defined(__SH4__) || defined(__alpha__) || \
|
||||
defined(_MIPS_ARCH_MIPS32R2) || \
|
||||
defined(__AARCH64EL__) || defined(__aarch64__) || \
|
||||
defined(__riscv)
|
||||
#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1
|
||||
#elif defined(__mc68000__)
|
||||
#undef DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS
|
||||
#elif defined(_M_IX86) || defined(__i386__) || defined(__i386)
|
||||
#if defined(_WIN32)
|
||||
// Windows uses a 64bit wide floating point stack.
|
||||
#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1
|
||||
#else
|
||||
#undef DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS
|
||||
#endif // _WIN32
|
||||
#else
|
||||
#error Target architecture was not detected as supported by Double-Conversion.
|
||||
#endif
|
||||
|
||||
#if defined(__GNUC__)
|
||||
#define DOUBLE_CONVERSION_UNUSED __attribute__((unused))
|
||||
#else
|
||||
#define DOUBLE_CONVERSION_UNUSED
|
||||
#endif
|
||||
|
||||
#if defined(_WIN32) && !defined(__MINGW32__)
|
||||
|
||||
typedef signed char int8_t;
|
||||
typedef unsigned char uint8_t;
|
||||
typedef short int16_t; // NOLINT
|
||||
typedef unsigned short uint16_t; // NOLINT
|
||||
typedef int int32_t;
|
||||
typedef unsigned int uint32_t;
|
||||
typedef __int64 int64_t;
|
||||
typedef unsigned __int64 uint64_t;
|
||||
// intptr_t and friends are defined in crtdefs.h through stdio.h.
|
||||
|
||||
#else
|
||||
|
||||
#include <stdint.h>
|
||||
|
||||
#endif
|
||||
|
||||
typedef uint16_t uc16;
|
||||
|
||||
// The following macro works on both 32 and 64-bit platforms.
|
||||
// Usage: instead of writing 0x1234567890123456
|
||||
// write UINT64_2PART_C(0x12345678,90123456);
|
||||
#define UINT64_2PART_C(a, b) (((static_cast<uint64_t>(a) << 32) + 0x##b##u))
|
||||
|
||||
|
||||
// The expression ARRAY_SIZE(a) is a compile-time constant of type
|
||||
// size_t which represents the number of elements of the given
|
||||
// array. You should only use ARRAY_SIZE on statically allocated
|
||||
// arrays.
|
||||
#ifndef ARRAY_SIZE
|
||||
#define ARRAY_SIZE(a) \
|
||||
((sizeof(a) / sizeof(*(a))) / \
|
||||
static_cast<size_t>(!(sizeof(a) % sizeof(*(a)))))
|
||||
#endif
|
||||
|
||||
// A macro to disallow the evil copy constructor and operator= functions
|
||||
// This should be used in the private: declarations for a class
|
||||
#ifndef DC_DISALLOW_COPY_AND_ASSIGN
|
||||
#define DC_DISALLOW_COPY_AND_ASSIGN(TypeName) \
|
||||
TypeName(const TypeName&); \
|
||||
void operator=(const TypeName&)
|
||||
#endif
|
||||
|
||||
// A macro to disallow all the implicit constructors, namely the
|
||||
// default constructor, copy constructor and operator= functions.
|
||||
//
|
||||
// This should be used in the private: declarations for a class
|
||||
// that wants to prevent anyone from instantiating it. This is
|
||||
// especially useful for classes containing only static methods.
|
||||
#ifndef DC_DISALLOW_IMPLICIT_CONSTRUCTORS
|
||||
#define DC_DISALLOW_IMPLICIT_CONSTRUCTORS(TypeName) \
|
||||
TypeName(); \
|
||||
DC_DISALLOW_COPY_AND_ASSIGN(TypeName)
|
||||
#endif
|
||||
|
||||
namespace double_conversion {
|
||||
|
||||
static const int kCharSize = sizeof(char);
|
||||
|
||||
// Returns the maximum of the two parameters.
|
||||
template <typename T>
|
||||
static T Max(T a, T b) {
|
||||
return a < b ? b : a;
|
||||
}
|
||||
|
||||
|
||||
// Returns the minimum of the two parameters.
|
||||
template <typename T>
|
||||
static T Min(T a, T b) {
|
||||
return a < b ? a : b;
|
||||
}
|
||||
|
||||
|
||||
inline int StrLength(const char* string) {
|
||||
size_t length = strlen(string);
|
||||
ASSERT(length == static_cast<size_t>(static_cast<int>(length)));
|
||||
return static_cast<int>(length);
|
||||
}
|
||||
|
||||
// This is a simplified version of V8's Vector class.
|
||||
template <typename T>
|
||||
class Vector {
|
||||
public:
|
||||
Vector() : start_(NULL), length_(0) {}
|
||||
Vector(T* data, int len) : start_(data), length_(len) {
|
||||
ASSERT(len == 0 || (len > 0 && data != NULL));
|
||||
}
|
||||
|
||||
// Returns a vector using the same backing storage as this one,
|
||||
// spanning from and including 'from', to but not including 'to'.
|
||||
Vector<T> SubVector(int from, int to) {
|
||||
ASSERT(to <= length_);
|
||||
ASSERT(from < to);
|
||||
ASSERT(0 <= from);
|
||||
return Vector<T>(start() + from, to - from);
|
||||
}
|
||||
|
||||
// Returns the length of the vector.
|
||||
int length() const { return length_; }
|
||||
|
||||
// Returns whether or not the vector is empty.
|
||||
bool is_empty() const { return length_ == 0; }
|
||||
|
||||
// Returns the pointer to the start of the data in the vector.
|
||||
T* start() const { return start_; }
|
||||
|
||||
// Access individual vector elements - checks bounds in debug mode.
|
||||
T& operator[](int index) const {
|
||||
ASSERT(0 <= index && index < length_);
|
||||
return start_[index];
|
||||
}
|
||||
|
||||
T& first() { return start_[0]; }
|
||||
|
||||
T& last() { return start_[length_ - 1]; }
|
||||
|
||||
private:
|
||||
T* start_;
|
||||
int length_;
|
||||
};
|
||||
|
||||
|
||||
// Helper class for building result strings in a character buffer. The
|
||||
// purpose of the class is to use safe operations that checks the
|
||||
// buffer bounds on all operations in debug mode.
|
||||
class StringBuilder {
|
||||
public:
|
||||
StringBuilder(char* buffer, int buffer_size)
|
||||
: buffer_(buffer, buffer_size), position_(0) { }
|
||||
|
||||
~StringBuilder() { if (!is_finalized()) Finalize(); }
|
||||
|
||||
int size() const { return buffer_.length(); }
|
||||
|
||||
// Get the current position in the builder.
|
||||
int position() const {
|
||||
ASSERT(!is_finalized());
|
||||
return position_;
|
||||
}
|
||||
|
||||
// Reset the position.
|
||||
void Reset() { position_ = 0; }
|
||||
|
||||
// Add a single character to the builder. It is not allowed to add
|
||||
// 0-characters; use the Finalize() method to terminate the string
|
||||
// instead.
|
||||
void AddCharacter(char c) {
|
||||
ASSERT(c != '\0');
|
||||
ASSERT(!is_finalized() && position_ < buffer_.length());
|
||||
buffer_[position_++] = c;
|
||||
}
|
||||
|
||||
// Add an entire string to the builder. Uses strlen() internally to
|
||||
// compute the length of the input string.
|
||||
void AddString(const char* s) {
|
||||
AddSubstring(s, StrLength(s));
|
||||
}
|
||||
|
||||
// Add the first 'n' characters of the given string 's' to the
|
||||
// builder. The input string must have enough characters.
|
||||
void AddSubstring(const char* s, int n) {
|
||||
ASSERT(!is_finalized() && position_ + n < buffer_.length());
|
||||
ASSERT(static_cast<size_t>(n) <= strlen(s));
|
||||
memmove(&buffer_[position_], s, n * kCharSize);
|
||||
position_ += n;
|
||||
}
|
||||
|
||||
|
||||
// Add character padding to the builder. If count is non-positive,
|
||||
// nothing is added to the builder.
|
||||
void AddPadding(char c, int count) {
|
||||
for (int i = 0; i < count; i++) {
|
||||
AddCharacter(c);
|
||||
}
|
||||
}
|
||||
|
||||
// Finalize the string by 0-terminating it and returning the buffer.
|
||||
char* Finalize() {
|
||||
ASSERT(!is_finalized() && position_ < buffer_.length());
|
||||
buffer_[position_] = '\0';
|
||||
// Make sure nobody managed to add a 0-character to the
|
||||
// buffer while building the string.
|
||||
ASSERT(strlen(buffer_.start()) == static_cast<size_t>(position_));
|
||||
position_ = -1;
|
||||
ASSERT(is_finalized());
|
||||
return buffer_.start();
|
||||
}
|
||||
|
||||
private:
|
||||
Vector<char> buffer_;
|
||||
int position_;
|
||||
|
||||
bool is_finalized() const { return position_ < 0; }
|
||||
|
||||
DC_DISALLOW_IMPLICIT_CONSTRUCTORS(StringBuilder);
|
||||
};
|
||||
|
||||
// The type-based aliasing rule allows the compiler to assume that pointers of
|
||||
// different types (for some definition of different) never alias each other.
|
||||
// Thus the following code does not work:
|
||||
//
|
||||
// float f = foo();
|
||||
// int fbits = *(int*)(&f);
|
||||
//
|
||||
// The compiler 'knows' that the int pointer can't refer to f since the types
|
||||
// don't match, so the compiler may cache f in a register, leaving random data
|
||||
// in fbits. Using C++ style casts makes no difference, however a pointer to
|
||||
// char data is assumed to alias any other pointer. This is the 'memcpy
|
||||
// exception'.
|
||||
//
|
||||
// Bit_cast uses the memcpy exception to move the bits from a variable of one
|
||||
// type of a variable of another type. Of course the end result is likely to
|
||||
// be implementation dependent. Most compilers (gcc-4.2 and MSVC 2005)
|
||||
// will completely optimize BitCast away.
|
||||
//
|
||||
// There is an additional use for BitCast.
|
||||
// Recent gccs will warn when they see casts that may result in breakage due to
|
||||
// the type-based aliasing rule. If you have checked that there is no breakage
|
||||
// you can use BitCast to cast one pointer type to another. This confuses gcc
|
||||
// enough that it can no longer see that you have cast one pointer type to
|
||||
// another thus avoiding the warning.
|
||||
template <class Dest, class Source>
|
||||
inline Dest BitCast(const Source& source) {
|
||||
// Compile time assertion: sizeof(Dest) == sizeof(Source)
|
||||
// A compile error here means your Dest and Source have different sizes.
|
||||
DOUBLE_CONVERSION_UNUSED
|
||||
typedef char VerifySizesAreEqual[sizeof(Dest) == sizeof(Source) ? 1 : -1];
|
||||
|
||||
Dest dest;
|
||||
memmove(&dest, &source, sizeof(dest));
|
||||
return dest;
|
||||
}
|
||||
|
||||
template <class Dest, class Source>
|
||||
inline Dest BitCast(Source* source) {
|
||||
return BitCast<Dest>(reinterpret_cast<uintptr_t>(source));
|
||||
}
|
||||
|
||||
} // namespace double_conversion
|
||||
|
||||
#endif // DOUBLE_CONVERSION_UTILS_H_
|
||||
@ -10,7 +10,7 @@ inc="-I. \
|
||||
-I./build/contrib/libre2 \
|
||||
-I./contrib/libfarmhash \
|
||||
-I./contrib/libmetrohash/src \
|
||||
-I./contrib/libdouble-conversion \
|
||||
-I./contrib/double-conversion \
|
||||
-I./contrib/libcityhash/include \
|
||||
-I./contrib/zookeeper/src/c/include \
|
||||
-I./contrib/zookeeper/src/c/generated \
|
||||
|
||||
Loading…
Reference in New Issue
Block a user