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Posted to commits@impala.apache.org by cs...@apache.org on 2021/04/28 09:10:14 UTC
[impala] 01/02: IMPALA-10654: Fix precision loss in DecimalValue to
double conversion.
This is an automated email from the ASF dual-hosted git repository.
csringhofer pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/impala.git
commit af6adf7618f50444f50bc53e42b676f5a377f386
Author: Amogh Margoor <am...@cloudera.com>
AuthorDate: Fri Apr 9 14:59:43 2021 +0100
IMPALA-10654: Fix precision loss in DecimalValue to double conversion.
Original approach to convert DecimalValue(internal representation
of decimals) to double was not accurate.
It was:
static_cast<double>(value_) / pow(10.0, scale).
However only integers from −2^53 to 2^53 can be represented
accurately by double precision without any loss.
Hence, it would not work for numbers like -0.43149576573887316.
For DecimalValue representing -0.43149576573887316, value_ would be
-43149576573887316 and scale would be 17. As value_ < -2^53,
result would not be accurate. In newer approach we are using third
party library https://github.com/lemire/fast_double_parser, which
handles above scenario in a performant manner.
Testing:
1. Added End to End Tests covering following scenarios:
a. Test to show precision limitation of 16 in the write path
b. DecimalValue's value_ between -2^53 and 2^53.
b. value_ outside above range but abs(value_) < UINT64_MAX
c. abs(value_) > UINT64_MAX -covers DecimalValue<__int128_t>
2. Ran existing backend and end-to-end tests completely
Change-Id: I56f0652cb8f81a491b87d9b108a94c00ae6c99a1
Reviewed-on: http://gerrit.cloudera.org:8080/17303
Reviewed-by: Impala Public Jenkins <im...@cloudera.com>
Tested-by: Impala Public Jenkins <im...@cloudera.com>
---
be/src/runtime/decimal-value.inline.h | 40 +-
be/src/thirdparty/fast_double_parser/LICENSE | 201 ++++
be/src/thirdparty/fast_double_parser/LICENSE.BSL | 25 +
be/src/thirdparty/fast_double_parser/README.md | 3 +
.../fast_double_parser/fast_double_parser.h | 1264 ++++++++++++++++++++
bin/rat_exclude_files.txt | 1 +
.../functional-query/queries/QueryTest/values.test | 34 +
tests/query_test/test_insert_parquet.py | 12 +
8 files changed, 1579 insertions(+), 1 deletion(-)
diff --git a/be/src/runtime/decimal-value.inline.h b/be/src/runtime/decimal-value.inline.h
index 35af6f0..3af1d7a 100644
--- a/be/src/runtime/decimal-value.inline.h
+++ b/be/src/runtime/decimal-value.inline.h
@@ -18,6 +18,7 @@
#pragma once
#include "runtime/decimal-value.h"
+#include "thirdparty/fast_double_parser/fast_double_parser.h"
#include <cmath>
#include <functional>
@@ -723,7 +724,44 @@ inline std::string DecimalValue<T>::ToString(int precision, int scale) const {
template<typename T>
inline double DecimalValue<T>::ToDouble(int scale) const {
- return static_cast<double>(value_) / pow(10.0, scale);
+ // Original approach was to use:
+ // static_cast<double>(value_) / pow(10.0, scale).
+ // However only integers from −2^53 to 2^53 can be represented accurately by
+ // double precision without any loss.
+ // Hence, it would not work for numbers like -0.43149576573887316.
+ // For DecimalValue representing -0.43149576573887316, value_ would be
+ // -43149576573887316 and scale would be 17. As value_ < -2^53, result would
+ // not be accurate. In newer approach we are using
+ // third party library https://github.com/lemire/fast_double_parser,
+ // which handles above scenario in a performant manner.
+
+ bool success = false;
+ bool is_negative = false;
+ T abs_value = value_;
+ if (value_ < 0) {
+ is_negative = true;
+ // for computing absolute value cannot use std::abs
+ // as it's not supported for __int128_t
+ abs_value *= -1;
+ }
+ double result = 0;
+ // compute_float_64 only supports uint64_t currently
+ if (abs_value <= UINT64_MAX) {
+ // compute_float_64 computes value * 10^(power) whereas we want to compute
+ // value/ (10 ^ (scale)). Hence (-scale) will be passed as power to the function.
+ // It expects value to be absolute and for negative value is_negative will be set.
+ result = fast_double_parser::compute_float_64(-scale, abs_value, is_negative,
+ &success);
+ }
+ // Fallback to original approach. This is not always accurate as described above.
+ // Other alternative would be to convert value_ to string and parse it into
+ // double using std:strtod. However std::strtod is atleast 4X slower
+ // than this approach (https://github.com/lemire/fast_double_parser#sample-results)
+ // and that is excluding cost to convert value_ to string.
+ if (!success) {
+ result = static_cast<double>(value_) / pow(10.0, scale);
+ }
+ return result;
}
template<typename T>
diff --git a/be/src/thirdparty/fast_double_parser/LICENSE b/be/src/thirdparty/fast_double_parser/LICENSE
new file mode 100644
index 0000000..3dc249d
--- /dev/null
+++ b/be/src/thirdparty/fast_double_parser/LICENSE
@@ -0,0 +1,201 @@
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diff --git a/be/src/thirdparty/fast_double_parser/LICENSE.BSL b/be/src/thirdparty/fast_double_parser/LICENSE.BSL
new file mode 100644
index 0000000..59024e3
--- /dev/null
+++ b/be/src/thirdparty/fast_double_parser/LICENSE.BSL
@@ -0,0 +1,25 @@
+Copyright (c) Daniel Lemire
+
+Boost Software License - Version 1.0 - August 17th, 2003
+
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diff --git a/be/src/thirdparty/fast_double_parser/README.md b/be/src/thirdparty/fast_double_parser/README.md
new file mode 100644
index 0000000..a39f296
--- /dev/null
+++ b/be/src/thirdparty/fast_double_parser/README.md
@@ -0,0 +1,3 @@
+This library is copied from https://github.com/lemire/fast_double_parser can be used under Apache License 2.0 or the Boost Software License 1.0. It provides fast function to parse strings containing decimal numbers into double-precision (binary64) floating-point values. The internal representation of Decimal values in the library resembles Impala's `DecimalValue`. Library functions will be used to convert `DecimalValue` to `double` accurately and efficiently.
+
+Latest commit id of the library: e4f6319bfa9cbc829f7f99ae88c1d2fb205c15e8
\ No newline at end of file
diff --git a/be/src/thirdparty/fast_double_parser/fast_double_parser.h b/be/src/thirdparty/fast_double_parser/fast_double_parser.h
new file mode 100644
index 0000000..1d14a6e
--- /dev/null
+++ b/be/src/thirdparty/fast_double_parser/fast_double_parser.h
@@ -0,0 +1,1264 @@
+
+#ifndef FAST_DOUBLE_PARSER_H
+#define FAST_DOUBLE_PARSER_H
+
+#include <cfloat>
+#include <cinttypes>
+#include <cmath>
+#include <cstdint>
+#include <cstdio>
+#include <cstdlib>
+#include <cstring>
+#include <locale.h>
+#if (defined(sun) || defined(__sun))
+#define FAST_DOUBLE_PARSER_SOLARIS
+#endif
+
+#if defined(__CYGWIN__) || defined(__MINGW32__) || defined(__MINGW64__)
+#define FAST_DOUBLE_PARSER_CYGWIN
+#endif
+
+/**
+ * Determining whether we should import xlocale.h or not is
+ * a bit of a nightmare.
+ */
+#if defined(FAST_DOUBLE_PARSER_SOLARIS) || defined(FAST_DOUBLE_PARSER_CYGWIN)
+// Anything at all that is related to cygwin, msys, solaris and so forth will
+// always use this fallback because we cannot rely on it behaving as normal
+// gcc.
+#include <locale>
+#include <sstream>
+// workaround for CYGWIN
+static inline double cygwin_strtod_l(const char* start, char** end) {
+ double d;
+ std::stringstream ss;
+ ss.imbue(std::locale::classic());
+ ss << start;
+ ss >> d;
+ if(ss.fail()) { *end = nullptr; }
+ if(ss.eof()) { ss.clear(); }
+ auto nread = ss.tellg();
+ *end = const_cast<char*>(start) + nread;
+ return d;
+}
+#else
+
+#ifdef __has_include
+// This is the easy case: we have __has_include and can check whether
+// xlocale is available. If so, we load it up.
+#if __has_include(<xlocale.h>)
+#include <xlocale.h>
+#endif // __has_include
+#else // We do not have __has_include
+
+#ifdef __GLIBC__
+#include <features.h>
+#if !((__GLIBC__ > 2) || ((__GLIBC__ == 2) && (__GLIBC_MINOR__ > 25)))
+#include <xlocale.h> // old glibc
+#endif
+#else // not glibc
+#if !(defined(_WIN32) || (__FreeBSD_version < 1000010))
+#include <xlocale.h>
+#endif
+#endif
+#endif // __has_include
+
+
+#endif // defined(FAST_DOUBLE_PARSER_SOLARIS) || defined(FAST_DOUBLE_PARSER_CYGWIN)
+
+
+
+#ifdef _MSC_VER
+#include <intrin.h>
+#define WARN_UNUSED
+#else
+#define WARN_UNUSED __attribute__((warn_unused_result))
+#endif
+
+namespace fast_double_parser {
+
+/**
+ * The smallest non-zero float (binary64) is 2^−1074.
+ * We take as input numbers of the form w x 10^q where w < 2^64.
+ * We have that w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076.
+ * However, we have that
+ * (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
+ * Thus it is possible for a number of the form w * 10^-342 where
+ * w is a 64-bit value to be a non-zero floating-point number.
+ *********
+ * If we are solely interested in the *normal* numbers then the
+ * smallest value is 2^-1022. We can generate a value larger
+ * than 2^-1022 with expressions of the form w * 10^-326.
+ * Thus we need to pick FASTFLOAT_SMALLEST_POWER >= -326.
+ *********
+ * Any number of form w * 10^309 where w>= 1 is going to be
+ * infinite in binary64 so we never need to worry about powers
+ * of 5 greater than 308.
+ */
+#define FASTFLOAT_SMALLEST_POWER -325
+#define FASTFLOAT_LARGEST_POWER 308
+
+#ifdef _MSC_VER
+#ifndef really_inline
+#define really_inline __forceinline
+#endif // really_inline
+#ifndef unlikely
+#define unlikely(x) x
+#endif // unlikely
+#else // _MSC_VER
+#ifndef unlikely
+#define unlikely(x) __builtin_expect(!!(x), 0)
+#endif // unlikely
+#ifndef really_inline
+#define really_inline __attribute__((always_inline)) inline
+#endif // really_inline
+#endif // _MSC_VER
+
+struct value128 {
+ uint64_t low;
+ uint64_t high;
+};
+
+#ifdef _MSC_VER
+#define FAST_DOUBLE_PARSER_VISUAL_STUDIO 1
+#ifdef __clang__
+// clang under visual studio
+#define FAST_DOUBLE_PARSER_CLANG_VISUAL_STUDIO 1
+#else
+// just regular visual studio (best guess)
+#define FAST_DOUBLE_PARSER_REGULAR_VISUAL_STUDIO 1
+#endif // __clang__
+#endif // _MSC_VER
+
+#if defined(FAST_DOUBLE_PARSER_REGULAR_VISUAL_STUDIO) && \
+ !defined(_M_X64) && !defined(_M_ARM64)// _umul128 for x86, arm
+// this is a slow emulation routine for 32-bit Windows
+//
+static inline uint64_t __emulu(uint32_t x, uint32_t y) {
+ return x * (uint64_t)y;
+}
+static inline uint64_t _umul128(uint64_t ab, uint64_t cd, uint64_t *hi) {
+ uint64_t ad = __emulu((uint32_t)(ab >> 32), (uint32_t)cd);
+ uint64_t bd = __emulu((uint32_t)ab, (uint32_t)cd);
+ uint64_t adbc = ad + __emulu((uint32_t)ab, (uint32_t)(cd >> 32));
+ uint64_t adbc_carry = !!(adbc < ad);
+ uint64_t lo = bd + (adbc << 32);
+ *hi = __emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
+ (adbc_carry << 32) + !!(lo < bd);
+ return lo;
+}
+#endif
+
+// We need a backup on old systems.
+// credit: https://stackoverflow.com/questions/28868367/getting-the-high-part-of-64-bit-integer-multiplication
+really_inline uint64_t Emulate64x64to128(uint64_t& r_hi, const uint64_t x, const uint64_t y) {
+ const uint64_t x0 = (uint32_t)x, x1 = x >> 32;
+ const uint64_t y0 = (uint32_t)y, y1 = y >> 32;
+ const uint64_t p11 = x1 * y1, p01 = x0 * y1;
+ const uint64_t p10 = x1 * y0, p00 = x0 * y0;
+
+ // 64-bit product + two 32-bit values
+ const uint64_t middle = p10 + (p00 >> 32) + (uint32_t)p01;
+
+ // 64-bit product + two 32-bit values
+ r_hi = p11 + (middle >> 32) + (p01 >> 32);
+
+ // Add LOW PART and lower half of MIDDLE PART
+ return (middle << 32) | (uint32_t)p00;
+}
+
+really_inline value128 full_multiplication(uint64_t value1, uint64_t value2) {
+ value128 answer;
+#ifdef FAST_DOUBLE_PARSER_REGULAR_VISUAL_STUDIO
+#ifdef _M_ARM64
+ // ARM64 has native support for 64-bit multiplications, no need to emultate
+ answer.high = __umulh(value1, value2);
+ answer.low = value1 * value2;
+#else
+ answer.low = _umul128(value1, value2, &answer.high); // _umul128 not available on ARM64
+#endif // _M_ARM64
+#else // SIMDJSON_REGULAR_VISUAL_STUDIO
+#ifdef __SIZEOF_INT128__ // this is what we have on most 32-bit systems
+ __uint128_t r = ((__uint128_t)value1) * value2;
+ answer.low = uint64_t(r);
+ answer.high = uint64_t(r >> 64);
+#else
+ // fallback
+ answer.low = Emulate64x64to128(answer.high, value1, value2);
+#endif
+#endif
+ return answer;
+}
+
+
+/* result might be undefined when input_num is zero */
+inline int leading_zeroes(uint64_t input_num) {
+#ifdef _MSC_VER
+ unsigned long leading_zero = 0;
+ // Search the mask data from most significant bit (MSB)
+ // to least significant bit (LSB) for a set bit (1).
+ if (_BitScanReverse64(&leading_zero, input_num))
+ return (int)(63 - leading_zero);
+ else
+ return 64;
+#else
+ return __builtin_clzll(input_num);
+#endif // _MSC_VER
+}
+
+static inline bool is_integer(char c) {
+ return (c >= '0' && c <= '9');
+ // this gets compiled to (uint8_t)(c - '0') <= 9 on all decent compilers
+}
+
+
+/**
+ * When mapping numbers from decimal to binary,
+ * we go from w * 10^q to m * 2^p but we have
+ * 10^q = 5^q * 2^q, so effectively
+ * we are trying to match
+ * w * 2^q * 5^q to m * 2^p. Thus the powers of two
+ * are not a concern since they can be represented
+ * exactly using the binary notation, only the powers of five
+ * affect the binary significand.
+ */
+
+// Attempts to compute i * 10^(power) exactly; and if "negative" is
+// true, negate the result.
+// This function will only work in some cases, when it does not work, success is
+// set to false. This should work *most of the time* (like 99% of the time).
+// We assume that power is in the [FASTFLOAT_SMALLEST_POWER,
+// FASTFLOAT_LARGEST_POWER] interval: the caller is responsible for this check.
+really_inline double compute_float_64(int64_t power, uint64_t i, bool negative,
+ bool *success) {
+
+ // Precomputed powers of ten from 10^0 to 10^22. These
+ // can be represented exactly using the double type.
+ static const double power_of_ten[] = {
+ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
+ 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
+
+ // The mantissas of powers of ten from -308 to 308, extended out to sixty four
+ // bits. The array contains the powers of ten approximated
+ // as a 64-bit mantissa. It goes from 10^FASTFLOAT_SMALLEST_POWER to
+ // 10^FASTFLOAT_LARGEST_POWER (inclusively).
+ // The mantissa is truncated, and
+ // never rounded up. Uses about 5KB.
+ static const uint64_t mantissa_64[] = {
+ 0xa5ced43b7e3e9188, 0xcf42894a5dce35ea,
+ 0x818995ce7aa0e1b2, 0xa1ebfb4219491a1f,
+ 0xca66fa129f9b60a6, 0xfd00b897478238d0,
+ 0x9e20735e8cb16382, 0xc5a890362fddbc62,
+ 0xf712b443bbd52b7b, 0x9a6bb0aa55653b2d,
+ 0xc1069cd4eabe89f8, 0xf148440a256e2c76,
+ 0x96cd2a865764dbca, 0xbc807527ed3e12bc,
+ 0xeba09271e88d976b, 0x93445b8731587ea3,
+ 0xb8157268fdae9e4c, 0xe61acf033d1a45df,
+ 0x8fd0c16206306bab, 0xb3c4f1ba87bc8696,
+ 0xe0b62e2929aba83c, 0x8c71dcd9ba0b4925,
+ 0xaf8e5410288e1b6f, 0xdb71e91432b1a24a,
+ 0x892731ac9faf056e, 0xab70fe17c79ac6ca,
+ 0xd64d3d9db981787d, 0x85f0468293f0eb4e,
+ 0xa76c582338ed2621, 0xd1476e2c07286faa,
+ 0x82cca4db847945ca, 0xa37fce126597973c,
+ 0xcc5fc196fefd7d0c, 0xff77b1fcbebcdc4f,
+ 0x9faacf3df73609b1, 0xc795830d75038c1d,
+ 0xf97ae3d0d2446f25, 0x9becce62836ac577,
+ 0xc2e801fb244576d5, 0xf3a20279ed56d48a,
+ 0x9845418c345644d6, 0xbe5691ef416bd60c,
+ 0xedec366b11c6cb8f, 0x94b3a202eb1c3f39,
+ 0xb9e08a83a5e34f07, 0xe858ad248f5c22c9,
+ 0x91376c36d99995be, 0xb58547448ffffb2d,
+ 0xe2e69915b3fff9f9, 0x8dd01fad907ffc3b,
+ 0xb1442798f49ffb4a, 0xdd95317f31c7fa1d,
+ 0x8a7d3eef7f1cfc52, 0xad1c8eab5ee43b66,
+ 0xd863b256369d4a40, 0x873e4f75e2224e68,
+ 0xa90de3535aaae202, 0xd3515c2831559a83,
+ 0x8412d9991ed58091, 0xa5178fff668ae0b6,
+ 0xce5d73ff402d98e3, 0x80fa687f881c7f8e,
+ 0xa139029f6a239f72, 0xc987434744ac874e,
+ 0xfbe9141915d7a922, 0x9d71ac8fada6c9b5,
+ 0xc4ce17b399107c22, 0xf6019da07f549b2b,
+ 0x99c102844f94e0fb, 0xc0314325637a1939,
+ 0xf03d93eebc589f88, 0x96267c7535b763b5,
+ 0xbbb01b9283253ca2, 0xea9c227723ee8bcb,
+ 0x92a1958a7675175f, 0xb749faed14125d36,
+ 0xe51c79a85916f484, 0x8f31cc0937ae58d2,
+ 0xb2fe3f0b8599ef07, 0xdfbdcece67006ac9,
+ 0x8bd6a141006042bd, 0xaecc49914078536d,
+ 0xda7f5bf590966848, 0x888f99797a5e012d,
+ 0xaab37fd7d8f58178, 0xd5605fcdcf32e1d6,
+ 0x855c3be0a17fcd26, 0xa6b34ad8c9dfc06f,
+ 0xd0601d8efc57b08b, 0x823c12795db6ce57,
+ 0xa2cb1717b52481ed, 0xcb7ddcdda26da268,
+ 0xfe5d54150b090b02, 0x9efa548d26e5a6e1,
+ 0xc6b8e9b0709f109a, 0xf867241c8cc6d4c0,
+ 0x9b407691d7fc44f8, 0xc21094364dfb5636,
+ 0xf294b943e17a2bc4, 0x979cf3ca6cec5b5a,
+ 0xbd8430bd08277231, 0xece53cec4a314ebd,
+ 0x940f4613ae5ed136, 0xb913179899f68584,
+ 0xe757dd7ec07426e5, 0x9096ea6f3848984f,
+ 0xb4bca50b065abe63, 0xe1ebce4dc7f16dfb,
+ 0x8d3360f09cf6e4bd, 0xb080392cc4349dec,
+ 0xdca04777f541c567, 0x89e42caaf9491b60,
+ 0xac5d37d5b79b6239, 0xd77485cb25823ac7,
+ 0x86a8d39ef77164bc, 0xa8530886b54dbdeb,
+ 0xd267caa862a12d66, 0x8380dea93da4bc60,
+ 0xa46116538d0deb78, 0xcd795be870516656,
+ 0x806bd9714632dff6, 0xa086cfcd97bf97f3,
+ 0xc8a883c0fdaf7df0, 0xfad2a4b13d1b5d6c,
+ 0x9cc3a6eec6311a63, 0xc3f490aa77bd60fc,
+ 0xf4f1b4d515acb93b, 0x991711052d8bf3c5,
+ 0xbf5cd54678eef0b6, 0xef340a98172aace4,
+ 0x9580869f0e7aac0e, 0xbae0a846d2195712,
+ 0xe998d258869facd7, 0x91ff83775423cc06,
+ 0xb67f6455292cbf08, 0xe41f3d6a7377eeca,
+ 0x8e938662882af53e, 0xb23867fb2a35b28d,
+ 0xdec681f9f4c31f31, 0x8b3c113c38f9f37e,
+ 0xae0b158b4738705e, 0xd98ddaee19068c76,
+ 0x87f8a8d4cfa417c9, 0xa9f6d30a038d1dbc,
+ 0xd47487cc8470652b, 0x84c8d4dfd2c63f3b,
+ 0xa5fb0a17c777cf09, 0xcf79cc9db955c2cc,
+ 0x81ac1fe293d599bf, 0xa21727db38cb002f,
+ 0xca9cf1d206fdc03b, 0xfd442e4688bd304a,
+ 0x9e4a9cec15763e2e, 0xc5dd44271ad3cdba,
+ 0xf7549530e188c128, 0x9a94dd3e8cf578b9,
+ 0xc13a148e3032d6e7, 0xf18899b1bc3f8ca1,
+ 0x96f5600f15a7b7e5, 0xbcb2b812db11a5de,
+ 0xebdf661791d60f56, 0x936b9fcebb25c995,
+ 0xb84687c269ef3bfb, 0xe65829b3046b0afa,
+ 0x8ff71a0fe2c2e6dc, 0xb3f4e093db73a093,
+ 0xe0f218b8d25088b8, 0x8c974f7383725573,
+ 0xafbd2350644eeacf, 0xdbac6c247d62a583,
+ 0x894bc396ce5da772, 0xab9eb47c81f5114f,
+ 0xd686619ba27255a2, 0x8613fd0145877585,
+ 0xa798fc4196e952e7, 0xd17f3b51fca3a7a0,
+ 0x82ef85133de648c4, 0xa3ab66580d5fdaf5,
+ 0xcc963fee10b7d1b3, 0xffbbcfe994e5c61f,
+ 0x9fd561f1fd0f9bd3, 0xc7caba6e7c5382c8,
+ 0xf9bd690a1b68637b, 0x9c1661a651213e2d,
+ 0xc31bfa0fe5698db8, 0xf3e2f893dec3f126,
+ 0x986ddb5c6b3a76b7, 0xbe89523386091465,
+ 0xee2ba6c0678b597f, 0x94db483840b717ef,
+ 0xba121a4650e4ddeb, 0xe896a0d7e51e1566,
+ 0x915e2486ef32cd60, 0xb5b5ada8aaff80b8,
+ 0xe3231912d5bf60e6, 0x8df5efabc5979c8f,
+ 0xb1736b96b6fd83b3, 0xddd0467c64bce4a0,
+ 0x8aa22c0dbef60ee4, 0xad4ab7112eb3929d,
+ 0xd89d64d57a607744, 0x87625f056c7c4a8b,
+ 0xa93af6c6c79b5d2d, 0xd389b47879823479,
+ 0x843610cb4bf160cb, 0xa54394fe1eedb8fe,
+ 0xce947a3da6a9273e, 0x811ccc668829b887,
+ 0xa163ff802a3426a8, 0xc9bcff6034c13052,
+ 0xfc2c3f3841f17c67, 0x9d9ba7832936edc0,
+ 0xc5029163f384a931, 0xf64335bcf065d37d,
+ 0x99ea0196163fa42e, 0xc06481fb9bcf8d39,
+ 0xf07da27a82c37088, 0x964e858c91ba2655,
+ 0xbbe226efb628afea, 0xeadab0aba3b2dbe5,
+ 0x92c8ae6b464fc96f, 0xb77ada0617e3bbcb,
+ 0xe55990879ddcaabd, 0x8f57fa54c2a9eab6,
+ 0xb32df8e9f3546564, 0xdff9772470297ebd,
+ 0x8bfbea76c619ef36, 0xaefae51477a06b03,
+ 0xdab99e59958885c4, 0x88b402f7fd75539b,
+ 0xaae103b5fcd2a881, 0xd59944a37c0752a2,
+ 0x857fcae62d8493a5, 0xa6dfbd9fb8e5b88e,
+ 0xd097ad07a71f26b2, 0x825ecc24c873782f,
+ 0xa2f67f2dfa90563b, 0xcbb41ef979346bca,
+ 0xfea126b7d78186bc, 0x9f24b832e6b0f436,
+ 0xc6ede63fa05d3143, 0xf8a95fcf88747d94,
+ 0x9b69dbe1b548ce7c, 0xc24452da229b021b,
+ 0xf2d56790ab41c2a2, 0x97c560ba6b0919a5,
+ 0xbdb6b8e905cb600f, 0xed246723473e3813,
+ 0x9436c0760c86e30b, 0xb94470938fa89bce,
+ 0xe7958cb87392c2c2, 0x90bd77f3483bb9b9,
+ 0xb4ecd5f01a4aa828, 0xe2280b6c20dd5232,
+ 0x8d590723948a535f, 0xb0af48ec79ace837,
+ 0xdcdb1b2798182244, 0x8a08f0f8bf0f156b,
+ 0xac8b2d36eed2dac5, 0xd7adf884aa879177,
+ 0x86ccbb52ea94baea, 0xa87fea27a539e9a5,
+ 0xd29fe4b18e88640e, 0x83a3eeeef9153e89,
+ 0xa48ceaaab75a8e2b, 0xcdb02555653131b6,
+ 0x808e17555f3ebf11, 0xa0b19d2ab70e6ed6,
+ 0xc8de047564d20a8b, 0xfb158592be068d2e,
+ 0x9ced737bb6c4183d, 0xc428d05aa4751e4c,
+ 0xf53304714d9265df, 0x993fe2c6d07b7fab,
+ 0xbf8fdb78849a5f96, 0xef73d256a5c0f77c,
+ 0x95a8637627989aad, 0xbb127c53b17ec159,
+ 0xe9d71b689dde71af, 0x9226712162ab070d,
+ 0xb6b00d69bb55c8d1, 0xe45c10c42a2b3b05,
+ 0x8eb98a7a9a5b04e3, 0xb267ed1940f1c61c,
+ 0xdf01e85f912e37a3, 0x8b61313bbabce2c6,
+ 0xae397d8aa96c1b77, 0xd9c7dced53c72255,
+ 0x881cea14545c7575, 0xaa242499697392d2,
+ 0xd4ad2dbfc3d07787, 0x84ec3c97da624ab4,
+ 0xa6274bbdd0fadd61, 0xcfb11ead453994ba,
+ 0x81ceb32c4b43fcf4, 0xa2425ff75e14fc31,
+ 0xcad2f7f5359a3b3e, 0xfd87b5f28300ca0d,
+ 0x9e74d1b791e07e48, 0xc612062576589dda,
+ 0xf79687aed3eec551, 0x9abe14cd44753b52,
+ 0xc16d9a0095928a27, 0xf1c90080baf72cb1,
+ 0x971da05074da7bee, 0xbce5086492111aea,
+ 0xec1e4a7db69561a5, 0x9392ee8e921d5d07,
+ 0xb877aa3236a4b449, 0xe69594bec44de15b,
+ 0x901d7cf73ab0acd9, 0xb424dc35095cd80f,
+ 0xe12e13424bb40e13, 0x8cbccc096f5088cb,
+ 0xafebff0bcb24aafe, 0xdbe6fecebdedd5be,
+ 0x89705f4136b4a597, 0xabcc77118461cefc,
+ 0xd6bf94d5e57a42bc, 0x8637bd05af6c69b5,
+ 0xa7c5ac471b478423, 0xd1b71758e219652b,
+ 0x83126e978d4fdf3b, 0xa3d70a3d70a3d70a,
+ 0xcccccccccccccccc, 0x8000000000000000,
+ 0xa000000000000000, 0xc800000000000000,
+ 0xfa00000000000000, 0x9c40000000000000,
+ 0xc350000000000000, 0xf424000000000000,
+ 0x9896800000000000, 0xbebc200000000000,
+ 0xee6b280000000000, 0x9502f90000000000,
+ 0xba43b74000000000, 0xe8d4a51000000000,
+ 0x9184e72a00000000, 0xb5e620f480000000,
+ 0xe35fa931a0000000, 0x8e1bc9bf04000000,
+ 0xb1a2bc2ec5000000, 0xde0b6b3a76400000,
+ 0x8ac7230489e80000, 0xad78ebc5ac620000,
+ 0xd8d726b7177a8000, 0x878678326eac9000,
+ 0xa968163f0a57b400, 0xd3c21bcecceda100,
+ 0x84595161401484a0, 0xa56fa5b99019a5c8,
+ 0xcecb8f27f4200f3a, 0x813f3978f8940984,
+ 0xa18f07d736b90be5, 0xc9f2c9cd04674ede,
+ 0xfc6f7c4045812296, 0x9dc5ada82b70b59d,
+ 0xc5371912364ce305, 0xf684df56c3e01bc6,
+ 0x9a130b963a6c115c, 0xc097ce7bc90715b3,
+ 0xf0bdc21abb48db20, 0x96769950b50d88f4,
+ 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd,
+ 0x92efd1b8d0cf37be, 0xb7abc627050305ad,
+ 0xe596b7b0c643c719, 0x8f7e32ce7bea5c6f,
+ 0xb35dbf821ae4f38b, 0xe0352f62a19e306e,
+ 0x8c213d9da502de45, 0xaf298d050e4395d6,
+ 0xdaf3f04651d47b4c, 0x88d8762bf324cd0f,
+ 0xab0e93b6efee0053, 0xd5d238a4abe98068,
+ 0x85a36366eb71f041, 0xa70c3c40a64e6c51,
+ 0xd0cf4b50cfe20765, 0x82818f1281ed449f,
+ 0xa321f2d7226895c7, 0xcbea6f8ceb02bb39,
+ 0xfee50b7025c36a08, 0x9f4f2726179a2245,
+ 0xc722f0ef9d80aad6, 0xf8ebad2b84e0d58b,
+ 0x9b934c3b330c8577, 0xc2781f49ffcfa6d5,
+ 0xf316271c7fc3908a, 0x97edd871cfda3a56,
+ 0xbde94e8e43d0c8ec, 0xed63a231d4c4fb27,
+ 0x945e455f24fb1cf8, 0xb975d6b6ee39e436,
+ 0xe7d34c64a9c85d44, 0x90e40fbeea1d3a4a,
+ 0xb51d13aea4a488dd, 0xe264589a4dcdab14,
+ 0x8d7eb76070a08aec, 0xb0de65388cc8ada8,
+ 0xdd15fe86affad912, 0x8a2dbf142dfcc7ab,
+ 0xacb92ed9397bf996, 0xd7e77a8f87daf7fb,
+ 0x86f0ac99b4e8dafd, 0xa8acd7c0222311bc,
+ 0xd2d80db02aabd62b, 0x83c7088e1aab65db,
+ 0xa4b8cab1a1563f52, 0xcde6fd5e09abcf26,
+ 0x80b05e5ac60b6178, 0xa0dc75f1778e39d6,
+ 0xc913936dd571c84c, 0xfb5878494ace3a5f,
+ 0x9d174b2dcec0e47b, 0xc45d1df942711d9a,
+ 0xf5746577930d6500, 0x9968bf6abbe85f20,
+ 0xbfc2ef456ae276e8, 0xefb3ab16c59b14a2,
+ 0x95d04aee3b80ece5, 0xbb445da9ca61281f,
+ 0xea1575143cf97226, 0x924d692ca61be758,
+ 0xb6e0c377cfa2e12e, 0xe498f455c38b997a,
+ 0x8edf98b59a373fec, 0xb2977ee300c50fe7,
+ 0xdf3d5e9bc0f653e1, 0x8b865b215899f46c,
+ 0xae67f1e9aec07187, 0xda01ee641a708de9,
+ 0x884134fe908658b2, 0xaa51823e34a7eede,
+ 0xd4e5e2cdc1d1ea96, 0x850fadc09923329e,
+ 0xa6539930bf6bff45, 0xcfe87f7cef46ff16,
+ 0x81f14fae158c5f6e, 0xa26da3999aef7749,
+ 0xcb090c8001ab551c, 0xfdcb4fa002162a63,
+ 0x9e9f11c4014dda7e, 0xc646d63501a1511d,
+ 0xf7d88bc24209a565, 0x9ae757596946075f,
+ 0xc1a12d2fc3978937, 0xf209787bb47d6b84,
+ 0x9745eb4d50ce6332, 0xbd176620a501fbff,
+ 0xec5d3fa8ce427aff, 0x93ba47c980e98cdf,
+ 0xb8a8d9bbe123f017, 0xe6d3102ad96cec1d,
+ 0x9043ea1ac7e41392, 0xb454e4a179dd1877,
+ 0xe16a1dc9d8545e94, 0x8ce2529e2734bb1d,
+ 0xb01ae745b101e9e4, 0xdc21a1171d42645d,
+ 0x899504ae72497eba, 0xabfa45da0edbde69,
+ 0xd6f8d7509292d603, 0x865b86925b9bc5c2,
+ 0xa7f26836f282b732, 0xd1ef0244af2364ff,
+ 0x8335616aed761f1f, 0xa402b9c5a8d3a6e7,
+ 0xcd036837130890a1, 0x802221226be55a64,
+ 0xa02aa96b06deb0fd, 0xc83553c5c8965d3d,
+ 0xfa42a8b73abbf48c, 0x9c69a97284b578d7,
+ 0xc38413cf25e2d70d, 0xf46518c2ef5b8cd1,
+ 0x98bf2f79d5993802, 0xbeeefb584aff8603,
+ 0xeeaaba2e5dbf6784, 0x952ab45cfa97a0b2,
+ 0xba756174393d88df, 0xe912b9d1478ceb17,
+ 0x91abb422ccb812ee, 0xb616a12b7fe617aa,
+ 0xe39c49765fdf9d94, 0x8e41ade9fbebc27d,
+ 0xb1d219647ae6b31c, 0xde469fbd99a05fe3,
+ 0x8aec23d680043bee, 0xada72ccc20054ae9,
+ 0xd910f7ff28069da4, 0x87aa9aff79042286,
+ 0xa99541bf57452b28, 0xd3fa922f2d1675f2,
+ 0x847c9b5d7c2e09b7, 0xa59bc234db398c25,
+ 0xcf02b2c21207ef2e, 0x8161afb94b44f57d,
+ 0xa1ba1ba79e1632dc, 0xca28a291859bbf93,
+ 0xfcb2cb35e702af78, 0x9defbf01b061adab,
+ 0xc56baec21c7a1916, 0xf6c69a72a3989f5b,
+ 0x9a3c2087a63f6399, 0xc0cb28a98fcf3c7f,
+ 0xf0fdf2d3f3c30b9f, 0x969eb7c47859e743,
+ 0xbc4665b596706114, 0xeb57ff22fc0c7959,
+ 0x9316ff75dd87cbd8, 0xb7dcbf5354e9bece,
+ 0xe5d3ef282a242e81, 0x8fa475791a569d10,
+ 0xb38d92d760ec4455, 0xe070f78d3927556a,
+ 0x8c469ab843b89562, 0xaf58416654a6babb,
+ 0xdb2e51bfe9d0696a, 0x88fcf317f22241e2,
+ 0xab3c2fddeeaad25a, 0xd60b3bd56a5586f1,
+ 0x85c7056562757456, 0xa738c6bebb12d16c,
+ 0xd106f86e69d785c7, 0x82a45b450226b39c,
+ 0xa34d721642b06084, 0xcc20ce9bd35c78a5,
+ 0xff290242c83396ce, 0x9f79a169bd203e41,
+ 0xc75809c42c684dd1, 0xf92e0c3537826145,
+ 0x9bbcc7a142b17ccb, 0xc2abf989935ddbfe,
+ 0xf356f7ebf83552fe, 0x98165af37b2153de,
+ 0xbe1bf1b059e9a8d6, 0xeda2ee1c7064130c,
+ 0x9485d4d1c63e8be7, 0xb9a74a0637ce2ee1,
+ 0xe8111c87c5c1ba99, 0x910ab1d4db9914a0,
+ 0xb54d5e4a127f59c8, 0xe2a0b5dc971f303a,
+ 0x8da471a9de737e24, 0xb10d8e1456105dad,
+ 0xdd50f1996b947518, 0x8a5296ffe33cc92f,
+ 0xace73cbfdc0bfb7b, 0xd8210befd30efa5a,
+ 0x8714a775e3e95c78, 0xa8d9d1535ce3b396,
+ 0xd31045a8341ca07c, 0x83ea2b892091e44d,
+ 0xa4e4b66b68b65d60, 0xce1de40642e3f4b9,
+ 0x80d2ae83e9ce78f3, 0xa1075a24e4421730,
+ 0xc94930ae1d529cfc, 0xfb9b7cd9a4a7443c,
+ 0x9d412e0806e88aa5, 0xc491798a08a2ad4e,
+ 0xf5b5d7ec8acb58a2, 0x9991a6f3d6bf1765,
+ 0xbff610b0cc6edd3f, 0xeff394dcff8a948e,
+ 0x95f83d0a1fb69cd9, 0xbb764c4ca7a4440f,
+ 0xea53df5fd18d5513, 0x92746b9be2f8552c,
+ 0xb7118682dbb66a77, 0xe4d5e82392a40515,
+ 0x8f05b1163ba6832d, 0xb2c71d5bca9023f8,
+ 0xdf78e4b2bd342cf6, 0x8bab8eefb6409c1a,
+ 0xae9672aba3d0c320, 0xda3c0f568cc4f3e8,
+ 0x8865899617fb1871, 0xaa7eebfb9df9de8d,
+ 0xd51ea6fa85785631, 0x8533285c936b35de,
+ 0xa67ff273b8460356, 0xd01fef10a657842c,
+ 0x8213f56a67f6b29b, 0xa298f2c501f45f42,
+ 0xcb3f2f7642717713, 0xfe0efb53d30dd4d7,
+ 0x9ec95d1463e8a506, 0xc67bb4597ce2ce48,
+ 0xf81aa16fdc1b81da, 0x9b10a4e5e9913128,
+ 0xc1d4ce1f63f57d72, 0xf24a01a73cf2dccf,
+ 0x976e41088617ca01, 0xbd49d14aa79dbc82,
+ 0xec9c459d51852ba2, 0x93e1ab8252f33b45,
+ 0xb8da1662e7b00a17, 0xe7109bfba19c0c9d,
+ 0x906a617d450187e2, 0xb484f9dc9641e9da,
+ 0xe1a63853bbd26451, 0x8d07e33455637eb2,
+ 0xb049dc016abc5e5f, 0xdc5c5301c56b75f7,
+ 0x89b9b3e11b6329ba, 0xac2820d9623bf429,
+ 0xd732290fbacaf133, 0x867f59a9d4bed6c0,
+ 0xa81f301449ee8c70, 0xd226fc195c6a2f8c,
+ 0x83585d8fd9c25db7, 0xa42e74f3d032f525,
+ 0xcd3a1230c43fb26f, 0x80444b5e7aa7cf85,
+ 0xa0555e361951c366, 0xc86ab5c39fa63440,
+ 0xfa856334878fc150, 0x9c935e00d4b9d8d2,
+ 0xc3b8358109e84f07, 0xf4a642e14c6262c8,
+ 0x98e7e9cccfbd7dbd, 0xbf21e44003acdd2c,
+ 0xeeea5d5004981478, 0x95527a5202df0ccb,
+ 0xbaa718e68396cffd, 0xe950df20247c83fd,
+ 0x91d28b7416cdd27e, 0xb6472e511c81471d,
+ 0xe3d8f9e563a198e5, 0x8e679c2f5e44ff8f};
+ // A complement to mantissa_64
+ // complete to a 128-bit mantissa.
+ // Uses about 5KB but is rarely accessed.
+ static const uint64_t mantissa_128[] = {
+ 0x419ea3bd35385e2d, 0x52064cac828675b9,
+ 0x7343efebd1940993, 0x1014ebe6c5f90bf8,
+ 0xd41a26e077774ef6, 0x8920b098955522b4,
+ 0x55b46e5f5d5535b0, 0xeb2189f734aa831d,
+ 0xa5e9ec7501d523e4, 0x47b233c92125366e,
+ 0x999ec0bb696e840a, 0xc00670ea43ca250d,
+ 0x380406926a5e5728, 0xc605083704f5ecf2,
+ 0xf7864a44c633682e, 0x7ab3ee6afbe0211d,
+ 0x5960ea05bad82964, 0x6fb92487298e33bd,
+ 0xa5d3b6d479f8e056, 0x8f48a4899877186c,
+ 0x331acdabfe94de87, 0x9ff0c08b7f1d0b14,
+ 0x7ecf0ae5ee44dd9, 0xc9e82cd9f69d6150,
+ 0xbe311c083a225cd2, 0x6dbd630a48aaf406,
+ 0x92cbbccdad5b108, 0x25bbf56008c58ea5,
+ 0xaf2af2b80af6f24e, 0x1af5af660db4aee1,
+ 0x50d98d9fc890ed4d, 0xe50ff107bab528a0,
+ 0x1e53ed49a96272c8, 0x25e8e89c13bb0f7a,
+ 0x77b191618c54e9ac, 0xd59df5b9ef6a2417,
+ 0x4b0573286b44ad1d, 0x4ee367f9430aec32,
+ 0x229c41f793cda73f, 0x6b43527578c1110f,
+ 0x830a13896b78aaa9, 0x23cc986bc656d553,
+ 0x2cbfbe86b7ec8aa8, 0x7bf7d71432f3d6a9,
+ 0xdaf5ccd93fb0cc53, 0xd1b3400f8f9cff68,
+ 0x23100809b9c21fa1, 0xabd40a0c2832a78a,
+ 0x16c90c8f323f516c, 0xae3da7d97f6792e3,
+ 0x99cd11cfdf41779c, 0x40405643d711d583,
+ 0x482835ea666b2572, 0xda3243650005eecf,
+ 0x90bed43e40076a82, 0x5a7744a6e804a291,
+ 0x711515d0a205cb36, 0xd5a5b44ca873e03,
+ 0xe858790afe9486c2, 0x626e974dbe39a872,
+ 0xfb0a3d212dc8128f, 0x7ce66634bc9d0b99,
+ 0x1c1fffc1ebc44e80, 0xa327ffb266b56220,
+ 0x4bf1ff9f0062baa8, 0x6f773fc3603db4a9,
+ 0xcb550fb4384d21d3, 0x7e2a53a146606a48,
+ 0x2eda7444cbfc426d, 0xfa911155fefb5308,
+ 0x793555ab7eba27ca, 0x4bc1558b2f3458de,
+ 0x9eb1aaedfb016f16, 0x465e15a979c1cadc,
+ 0xbfacd89ec191ec9, 0xcef980ec671f667b,
+ 0x82b7e12780e7401a, 0xd1b2ecb8b0908810,
+ 0x861fa7e6dcb4aa15, 0x67a791e093e1d49a,
+ 0xe0c8bb2c5c6d24e0, 0x58fae9f773886e18,
+ 0xaf39a475506a899e, 0x6d8406c952429603,
+ 0xc8e5087ba6d33b83, 0xfb1e4a9a90880a64,
+ 0x5cf2eea09a55067f, 0xf42faa48c0ea481e,
+ 0xf13b94daf124da26, 0x76c53d08d6b70858,
+ 0x54768c4b0c64ca6e, 0xa9942f5dcf7dfd09,
+ 0xd3f93b35435d7c4c, 0xc47bc5014a1a6daf,
+ 0x359ab6419ca1091b, 0xc30163d203c94b62,
+ 0x79e0de63425dcf1d, 0x985915fc12f542e4,
+ 0x3e6f5b7b17b2939d, 0xa705992ceecf9c42,
+ 0x50c6ff782a838353, 0xa4f8bf5635246428,
+ 0x871b7795e136be99, 0x28e2557b59846e3f,
+ 0x331aeada2fe589cf, 0x3ff0d2c85def7621,
+ 0xfed077a756b53a9, 0xd3e8495912c62894,
+ 0x64712dd7abbbd95c, 0xbd8d794d96aacfb3,
+ 0xecf0d7a0fc5583a0, 0xf41686c49db57244,
+ 0x311c2875c522ced5, 0x7d633293366b828b,
+ 0xae5dff9c02033197, 0xd9f57f830283fdfc,
+ 0xd072df63c324fd7b, 0x4247cb9e59f71e6d,
+ 0x52d9be85f074e608, 0x67902e276c921f8b,
+ 0xba1cd8a3db53b6, 0x80e8a40eccd228a4,
+ 0x6122cd128006b2cd, 0x796b805720085f81,
+ 0xcbe3303674053bb0, 0xbedbfc4411068a9c,
+ 0xee92fb5515482d44, 0x751bdd152d4d1c4a,
+ 0xd262d45a78a0635d, 0x86fb897116c87c34,
+ 0xd45d35e6ae3d4da0, 0x8974836059cca109,
+ 0x2bd1a438703fc94b, 0x7b6306a34627ddcf,
+ 0x1a3bc84c17b1d542, 0x20caba5f1d9e4a93,
+ 0x547eb47b7282ee9c, 0xe99e619a4f23aa43,
+ 0x6405fa00e2ec94d4, 0xde83bc408dd3dd04,
+ 0x9624ab50b148d445, 0x3badd624dd9b0957,
+ 0xe54ca5d70a80e5d6, 0x5e9fcf4ccd211f4c,
+ 0x7647c3200069671f, 0x29ecd9f40041e073,
+ 0xf468107100525890, 0x7182148d4066eeb4,
+ 0xc6f14cd848405530, 0xb8ada00e5a506a7c,
+ 0xa6d90811f0e4851c, 0x908f4a166d1da663,
+ 0x9a598e4e043287fe, 0x40eff1e1853f29fd,
+ 0xd12bee59e68ef47c, 0x82bb74f8301958ce,
+ 0xe36a52363c1faf01, 0xdc44e6c3cb279ac1,
+ 0x29ab103a5ef8c0b9, 0x7415d448f6b6f0e7,
+ 0x111b495b3464ad21, 0xcab10dd900beec34,
+ 0x3d5d514f40eea742, 0xcb4a5a3112a5112,
+ 0x47f0e785eaba72ab, 0x59ed216765690f56,
+ 0x306869c13ec3532c, 0x1e414218c73a13fb,
+ 0xe5d1929ef90898fa, 0xdf45f746b74abf39,
+ 0x6b8bba8c328eb783, 0x66ea92f3f326564,
+ 0xc80a537b0efefebd, 0xbd06742ce95f5f36,
+ 0x2c48113823b73704, 0xf75a15862ca504c5,
+ 0x9a984d73dbe722fb, 0xc13e60d0d2e0ebba,
+ 0x318df905079926a8, 0xfdf17746497f7052,
+ 0xfeb6ea8bedefa633, 0xfe64a52ee96b8fc0,
+ 0x3dfdce7aa3c673b0, 0x6bea10ca65c084e,
+ 0x486e494fcff30a62, 0x5a89dba3c3efccfa,
+ 0xf89629465a75e01c, 0xf6bbb397f1135823,
+ 0x746aa07ded582e2c, 0xa8c2a44eb4571cdc,
+ 0x92f34d62616ce413, 0x77b020baf9c81d17,
+ 0xace1474dc1d122e, 0xd819992132456ba,
+ 0x10e1fff697ed6c69, 0xca8d3ffa1ef463c1,
+ 0xbd308ff8a6b17cb2, 0xac7cb3f6d05ddbde,
+ 0x6bcdf07a423aa96b, 0x86c16c98d2c953c6,
+ 0xe871c7bf077ba8b7, 0x11471cd764ad4972,
+ 0xd598e40d3dd89bcf, 0x4aff1d108d4ec2c3,
+ 0xcedf722a585139ba, 0xc2974eb4ee658828,
+ 0x733d226229feea32, 0x806357d5a3f525f,
+ 0xca07c2dcb0cf26f7, 0xfc89b393dd02f0b5,
+ 0xbbac2078d443ace2, 0xd54b944b84aa4c0d,
+ 0xa9e795e65d4df11, 0x4d4617b5ff4a16d5,
+ 0x504bced1bf8e4e45, 0xe45ec2862f71e1d6,
+ 0x5d767327bb4e5a4c, 0x3a6a07f8d510f86f,
+ 0x890489f70a55368b, 0x2b45ac74ccea842e,
+ 0x3b0b8bc90012929d, 0x9ce6ebb40173744,
+ 0xcc420a6a101d0515, 0x9fa946824a12232d,
+ 0x47939822dc96abf9, 0x59787e2b93bc56f7,
+ 0x57eb4edb3c55b65a, 0xede622920b6b23f1,
+ 0xe95fab368e45eced, 0x11dbcb0218ebb414,
+ 0xd652bdc29f26a119, 0x4be76d3346f0495f,
+ 0x6f70a4400c562ddb, 0xcb4ccd500f6bb952,
+ 0x7e2000a41346a7a7, 0x8ed400668c0c28c8,
+ 0x728900802f0f32fa, 0x4f2b40a03ad2ffb9,
+ 0xe2f610c84987bfa8, 0xdd9ca7d2df4d7c9,
+ 0x91503d1c79720dbb, 0x75a44c6397ce912a,
+ 0xc986afbe3ee11aba, 0xfbe85badce996168,
+ 0xfae27299423fb9c3, 0xdccd879fc967d41a,
+ 0x5400e987bbc1c920, 0x290123e9aab23b68,
+ 0xf9a0b6720aaf6521, 0xf808e40e8d5b3e69,
+ 0xb60b1d1230b20e04, 0xb1c6f22b5e6f48c2,
+ 0x1e38aeb6360b1af3, 0x25c6da63c38de1b0,
+ 0x579c487e5a38ad0e, 0x2d835a9df0c6d851,
+ 0xf8e431456cf88e65, 0x1b8e9ecb641b58ff,
+ 0xe272467e3d222f3f, 0x5b0ed81dcc6abb0f,
+ 0x98e947129fc2b4e9, 0x3f2398d747b36224,
+ 0x8eec7f0d19a03aad, 0x1953cf68300424ac,
+ 0x5fa8c3423c052dd7, 0x3792f412cb06794d,
+ 0xe2bbd88bbee40bd0, 0x5b6aceaeae9d0ec4,
+ 0xf245825a5a445275, 0xeed6e2f0f0d56712,
+ 0x55464dd69685606b, 0xaa97e14c3c26b886,
+ 0xd53dd99f4b3066a8, 0xe546a8038efe4029,
+ 0xde98520472bdd033, 0x963e66858f6d4440,
+ 0xdde7001379a44aa8, 0x5560c018580d5d52,
+ 0xaab8f01e6e10b4a6, 0xcab3961304ca70e8,
+ 0x3d607b97c5fd0d22, 0x8cb89a7db77c506a,
+ 0x77f3608e92adb242, 0x55f038b237591ed3,
+ 0x6b6c46dec52f6688, 0x2323ac4b3b3da015,
+ 0xabec975e0a0d081a, 0x96e7bd358c904a21,
+ 0x7e50d64177da2e54, 0xdde50bd1d5d0b9e9,
+ 0x955e4ec64b44e864, 0xbd5af13bef0b113e,
+ 0xecb1ad8aeacdd58e, 0x67de18eda5814af2,
+ 0x80eacf948770ced7, 0xa1258379a94d028d,
+ 0x96ee45813a04330, 0x8bca9d6e188853fc,
+ 0x775ea264cf55347d, 0x95364afe032a819d,
+ 0x3a83ddbd83f52204, 0xc4926a9672793542,
+ 0x75b7053c0f178293, 0x5324c68b12dd6338,
+ 0xd3f6fc16ebca5e03, 0x88f4bb1ca6bcf584,
+ 0x2b31e9e3d06c32e5, 0x3aff322e62439fcf,
+ 0x9befeb9fad487c2, 0x4c2ebe687989a9b3,
+ 0xf9d37014bf60a10, 0x538484c19ef38c94,
+ 0x2865a5f206b06fb9, 0xf93f87b7442e45d3,
+ 0xf78f69a51539d748, 0xb573440e5a884d1b,
+ 0x31680a88f8953030, 0xfdc20d2b36ba7c3d,
+ 0x3d32907604691b4c, 0xa63f9a49c2c1b10f,
+ 0xfcf80dc33721d53, 0xd3c36113404ea4a8,
+ 0x645a1cac083126e9, 0x3d70a3d70a3d70a3,
+ 0xcccccccccccccccc, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x0,
+ 0x0, 0x4000000000000000,
+ 0x5000000000000000, 0xa400000000000000,
+ 0x4d00000000000000, 0xf020000000000000,
+ 0x6c28000000000000, 0xc732000000000000,
+ 0x3c7f400000000000, 0x4b9f100000000000,
+ 0x1e86d40000000000, 0x1314448000000000,
+ 0x17d955a000000000, 0x5dcfab0800000000,
+ 0x5aa1cae500000000, 0xf14a3d9e40000000,
+ 0x6d9ccd05d0000000, 0xe4820023a2000000,
+ 0xdda2802c8a800000, 0xd50b2037ad200000,
+ 0x4526f422cc340000, 0x9670b12b7f410000,
+ 0x3c0cdd765f114000, 0xa5880a69fb6ac800,
+ 0x8eea0d047a457a00, 0x72a4904598d6d880,
+ 0x47a6da2b7f864750, 0x999090b65f67d924,
+ 0xfff4b4e3f741cf6d, 0xbff8f10e7a8921a4,
+ 0xaff72d52192b6a0d, 0x9bf4f8a69f764490,
+ 0x2f236d04753d5b4, 0x1d762422c946590,
+ 0x424d3ad2b7b97ef5, 0xd2e0898765a7deb2,
+ 0x63cc55f49f88eb2f, 0x3cbf6b71c76b25fb,
+ 0x8bef464e3945ef7a, 0x97758bf0e3cbb5ac,
+ 0x3d52eeed1cbea317, 0x4ca7aaa863ee4bdd,
+ 0x8fe8caa93e74ef6a, 0xb3e2fd538e122b44,
+ 0x60dbbca87196b616, 0xbc8955e946fe31cd,
+ 0x6babab6398bdbe41, 0xc696963c7eed2dd1,
+ 0xfc1e1de5cf543ca2, 0x3b25a55f43294bcb,
+ 0x49ef0eb713f39ebe, 0x6e3569326c784337,
+ 0x49c2c37f07965404, 0xdc33745ec97be906,
+ 0x69a028bb3ded71a3, 0xc40832ea0d68ce0c,
+ 0xf50a3fa490c30190, 0x792667c6da79e0fa,
+ 0x577001b891185938, 0xed4c0226b55e6f86,
+ 0x544f8158315b05b4, 0x696361ae3db1c721,
+ 0x3bc3a19cd1e38e9, 0x4ab48a04065c723,
+ 0x62eb0d64283f9c76, 0x3ba5d0bd324f8394,
+ 0xca8f44ec7ee36479, 0x7e998b13cf4e1ecb,
+ 0x9e3fedd8c321a67e, 0xc5cfe94ef3ea101e,
+ 0xbba1f1d158724a12, 0x2a8a6e45ae8edc97,
+ 0xf52d09d71a3293bd, 0x593c2626705f9c56,
+ 0x6f8b2fb00c77836c, 0xb6dfb9c0f956447,
+ 0x4724bd4189bd5eac, 0x58edec91ec2cb657,
+ 0x2f2967b66737e3ed, 0xbd79e0d20082ee74,
+ 0xecd8590680a3aa11, 0xe80e6f4820cc9495,
+ 0x3109058d147fdcdd, 0xbd4b46f0599fd415,
+ 0x6c9e18ac7007c91a, 0x3e2cf6bc604ddb0,
+ 0x84db8346b786151c, 0xe612641865679a63,
+ 0x4fcb7e8f3f60c07e, 0xe3be5e330f38f09d,
+ 0x5cadf5bfd3072cc5, 0x73d9732fc7c8f7f6,
+ 0x2867e7fddcdd9afa, 0xb281e1fd541501b8,
+ 0x1f225a7ca91a4226, 0x3375788de9b06958,
+ 0x52d6b1641c83ae, 0xc0678c5dbd23a49a,
+ 0xf840b7ba963646e0, 0xb650e5a93bc3d898,
+ 0xa3e51f138ab4cebe, 0xc66f336c36b10137,
+ 0xb80b0047445d4184, 0xa60dc059157491e5,
+ 0x87c89837ad68db2f, 0x29babe4598c311fb,
+ 0xf4296dd6fef3d67a, 0x1899e4a65f58660c,
+ 0x5ec05dcff72e7f8f, 0x76707543f4fa1f73,
+ 0x6a06494a791c53a8, 0x487db9d17636892,
+ 0x45a9d2845d3c42b6, 0xb8a2392ba45a9b2,
+ 0x8e6cac7768d7141e, 0x3207d795430cd926,
+ 0x7f44e6bd49e807b8, 0x5f16206c9c6209a6,
+ 0x36dba887c37a8c0f, 0xc2494954da2c9789,
+ 0xf2db9baa10b7bd6c, 0x6f92829494e5acc7,
+ 0xcb772339ba1f17f9, 0xff2a760414536efb,
+ 0xfef5138519684aba, 0x7eb258665fc25d69,
+ 0xef2f773ffbd97a61, 0xaafb550ffacfd8fa,
+ 0x95ba2a53f983cf38, 0xdd945a747bf26183,
+ 0x94f971119aeef9e4, 0x7a37cd5601aab85d,
+ 0xac62e055c10ab33a, 0x577b986b314d6009,
+ 0xed5a7e85fda0b80b, 0x14588f13be847307,
+ 0x596eb2d8ae258fc8, 0x6fca5f8ed9aef3bb,
+ 0x25de7bb9480d5854, 0xaf561aa79a10ae6a,
+ 0x1b2ba1518094da04, 0x90fb44d2f05d0842,
+ 0x353a1607ac744a53, 0x42889b8997915ce8,
+ 0x69956135febada11, 0x43fab9837e699095,
+ 0x94f967e45e03f4bb, 0x1d1be0eebac278f5,
+ 0x6462d92a69731732, 0x7d7b8f7503cfdcfe,
+ 0x5cda735244c3d43e, 0x3a0888136afa64a7,
+ 0x88aaa1845b8fdd0, 0x8aad549e57273d45,
+ 0x36ac54e2f678864b, 0x84576a1bb416a7dd,
+ 0x656d44a2a11c51d5, 0x9f644ae5a4b1b325,
+ 0x873d5d9f0dde1fee, 0xa90cb506d155a7ea,
+ 0x9a7f12442d588f2, 0xc11ed6d538aeb2f,
+ 0x8f1668c8a86da5fa, 0xf96e017d694487bc,
+ 0x37c981dcc395a9ac, 0x85bbe253f47b1417,
+ 0x93956d7478ccec8e, 0x387ac8d1970027b2,
+ 0x6997b05fcc0319e, 0x441fece3bdf81f03,
+ 0xd527e81cad7626c3, 0x8a71e223d8d3b074,
+ 0xf6872d5667844e49, 0xb428f8ac016561db,
+ 0xe13336d701beba52, 0xecc0024661173473,
+ 0x27f002d7f95d0190, 0x31ec038df7b441f4,
+ 0x7e67047175a15271, 0xf0062c6e984d386,
+ 0x52c07b78a3e60868, 0xa7709a56ccdf8a82,
+ 0x88a66076400bb691, 0x6acff893d00ea435,
+ 0x583f6b8c4124d43, 0xc3727a337a8b704a,
+ 0x744f18c0592e4c5c, 0x1162def06f79df73,
+ 0x8addcb5645ac2ba8, 0x6d953e2bd7173692,
+ 0xc8fa8db6ccdd0437, 0x1d9c9892400a22a2,
+ 0x2503beb6d00cab4b, 0x2e44ae64840fd61d,
+ 0x5ceaecfed289e5d2, 0x7425a83e872c5f47,
+ 0xd12f124e28f77719, 0x82bd6b70d99aaa6f,
+ 0x636cc64d1001550b, 0x3c47f7e05401aa4e,
+ 0x65acfaec34810a71, 0x7f1839a741a14d0d,
+ 0x1ede48111209a050, 0x934aed0aab460432,
+ 0xf81da84d5617853f, 0x36251260ab9d668e,
+ 0xc1d72b7c6b426019, 0xb24cf65b8612f81f,
+ 0xdee033f26797b627, 0x169840ef017da3b1,
+ 0x8e1f289560ee864e, 0xf1a6f2bab92a27e2,
+ 0xae10af696774b1db, 0xacca6da1e0a8ef29,
+ 0x17fd090a58d32af3, 0xddfc4b4cef07f5b0,
+ 0x4abdaf101564f98e, 0x9d6d1ad41abe37f1,
+ 0x84c86189216dc5ed, 0x32fd3cf5b4e49bb4,
+ 0x3fbc8c33221dc2a1, 0xfabaf3feaa5334a,
+ 0x29cb4d87f2a7400e, 0x743e20e9ef511012,
+ 0x914da9246b255416, 0x1ad089b6c2f7548e,
+ 0xa184ac2473b529b1, 0xc9e5d72d90a2741e,
+ 0x7e2fa67c7a658892, 0xddbb901b98feeab7,
+ 0x552a74227f3ea565, 0xd53a88958f87275f,
+ 0x8a892abaf368f137, 0x2d2b7569b0432d85,
+ 0x9c3b29620e29fc73, 0x8349f3ba91b47b8f,
+ 0x241c70a936219a73, 0xed238cd383aa0110,
+ 0xf4363804324a40aa, 0xb143c6053edcd0d5,
+ 0xdd94b7868e94050a, 0xca7cf2b4191c8326,
+ 0xfd1c2f611f63a3f0, 0xbc633b39673c8cec,
+ 0xd5be0503e085d813, 0x4b2d8644d8a74e18,
+ 0xddf8e7d60ed1219e, 0xcabb90e5c942b503,
+ 0x3d6a751f3b936243, 0xcc512670a783ad4,
+ 0x27fb2b80668b24c5, 0xb1f9f660802dedf6,
+ 0x5e7873f8a0396973, 0xdb0b487b6423e1e8,
+ 0x91ce1a9a3d2cda62, 0x7641a140cc7810fb,
+ 0xa9e904c87fcb0a9d, 0x546345fa9fbdcd44,
+ 0xa97c177947ad4095, 0x49ed8eabcccc485d,
+ 0x5c68f256bfff5a74, 0x73832eec6fff3111,
+ 0xc831fd53c5ff7eab, 0xba3e7ca8b77f5e55,
+ 0x28ce1bd2e55f35eb, 0x7980d163cf5b81b3,
+ 0xd7e105bcc332621f, 0x8dd9472bf3fefaa7,
+ 0xb14f98f6f0feb951, 0x6ed1bf9a569f33d3,
+ 0xa862f80ec4700c8, 0xcd27bb612758c0fa,
+ 0x8038d51cb897789c, 0xe0470a63e6bd56c3,
+ 0x1858ccfce06cac74, 0xf37801e0c43ebc8,
+ 0xd30560258f54e6ba, 0x47c6b82ef32a2069,
+ 0x4cdc331d57fa5441, 0xe0133fe4adf8e952,
+ 0x58180fddd97723a6, 0x570f09eaa7ea7648,};
+
+ // we start with a fast path
+ // It was described in
+ // Clinger WD. How to read floating point numbers accurately.
+ // ACM SIGPLAN Notices. 1990
+#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
+ // we do not trust the divisor
+ if (0 <= power && power <= 22 && i <= 9007199254740991) {
+#else
+ if (-22 <= power && power <= 22 && i <= 9007199254740991) {
+#endif
+ // convert the integer into a double. This is lossless since
+ // 0 <= i <= 2^53 - 1.
+ double d = double(i);
+ //
+ // The general idea is as follows.
+ // If 0 <= s < 2^53 and if 10^0 <= p <= 10^22 then
+ // 1) Both s and p can be represented exactly as 64-bit floating-point
+ // values
+ // (binary64).
+ // 2) Because s and p can be represented exactly as floating-point values,
+ // then s * p
+ // and s / p will produce correctly rounded values.
+ //
+ if (power < 0) {
+ d = d / power_of_ten[-power];
+ } else {
+ d = d * power_of_ten[power];
+ }
+ if (negative) {
+ d = -d;
+ }
+ *success = true;
+ return d;
+ }
+ // When 22 < power && power < 22 + 16, we could
+ // hope for another, secondary fast path. It wa
+ // described by David M. Gay in "Correctly rounded
+ // binary-decimal and decimal-binary conversions." (1990)
+ // If you need to compute i * 10^(22 + x) for x < 16,
+ // first compute i * 10^x, if you know that result is exact
+ // (e.g., when i * 10^x < 2^53),
+ // then you can still proceed and do (i * 10^x) * 10^22.
+ // Is this worth your time?
+ // You need 22 < power *and* power < 22 + 16 *and* (i * 10^(x-22) < 2^53)
+ // for this second fast path to work.
+ // If you you have 22 < power *and* power < 22 + 16, and then you
+ // optimistically compute "i * 10^(x-22)", there is still a chance that you
+ // have wasted your time if i * 10^(x-22) >= 2^53. It makes the use cases of
+ // this optimization maybe less common than we would like. Source:
+ // http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
+ // also used in RapidJSON: https://rapidjson.org/strtod_8h_source.html
+
+
+
+ // The fast path has now failed, so we are failing back on the slower path.
+
+ // In the slow path, we need to adjust i so that it is > 1<<63 which is always
+ // possible, except if i == 0, so we handle i == 0 separately.
+ if(i == 0) {
+ return negative ? -0.0 : 0.0;
+ }
+
+
+ // We are going to need to do some 64-bit arithmetic to get a more precise product.
+ // We use a table lookup approach.
+ // It is safe because
+ // power >= FASTFLOAT_SMALLEST_POWER
+ // and power <= FASTFLOAT_LARGEST_POWER
+ // We recover the mantissa of the power, it has a leading 1. It is always
+ // rounded down.
+ uint64_t factor_mantissa = mantissa_64[power - FASTFLOAT_SMALLEST_POWER];
+
+
+ // The exponent is 1024 + 63 + power
+ // + floor(log(5**power)/log(2)).
+ // The 1024 comes from the ieee64 standard.
+ // The 63 comes from the fact that we use a 64-bit word.
+ //
+ // Computing floor(log(5**power)/log(2)) could be
+ // slow. Instead we use a fast function.
+ //
+ // For power in (-400,350), we have that
+ // (((152170 + 65536) * power ) >> 16);
+ // is equal to
+ // floor(log(5**power)/log(2)) + power when power >= 0
+ // and it is equal to
+ // ceil(log(5**-power)/log(2)) + power when power < 0
+ //
+ //
+ // The 65536 is (1<<16) and corresponds to
+ // (65536 * power) >> 16 ---> power
+ //
+ // ((152170 * power ) >> 16) is equal to
+ // floor(log(5**power)/log(2))
+ //
+ // Note that this is not magic: 152170/(1<<16) is
+ // approximatively equal to log(5)/log(2).
+ // The 1<<16 value is a power of two; we could use a
+ // larger power of 2 if we wanted to.
+ //
+ int64_t exponent = (((152170 + 65536) * power) >> 16) + 1024 + 63;
+ // We want the most significant bit of i to be 1. Shift if needed.
+ int lz = leading_zeroes(i);
+ i <<= lz;
+ // We want the most significant 64 bits of the product. We know
+ // this will be non-zero because the most significant bit of i is
+ // 1.
+ value128 product = full_multiplication(i, factor_mantissa);
+ uint64_t lower = product.low;
+ uint64_t upper = product.high;
+ // We know that upper has at most one leading zero because
+ // both i and factor_mantissa have a leading one. This means
+ // that the result is at least as large as ((1<<63)*(1<<63))/(1<<64).
+
+ // As long as the first 9 bits of "upper" are not "1", then we
+ // know that we have an exact computed value for the leading
+ // 55 bits because any imprecision would play out as a +1, in
+ // the worst case.
+ // Having 55 bits is necessary because
+ // we need 53 bits for the mantissa but we have to have one rounding bit and
+ // we can waste a bit if the most significant bit of the product is zero.
+ // We expect this next branch to be rarely taken (say 1% of the time).
+ // When (upper & 0x1FF) == 0x1FF, it can be common for
+ // lower + i < lower to be true (proba. much higher than 1%).
+ if (unlikely((upper & 0x1FF) == 0x1FF) && (lower + i < lower)) {
+ uint64_t factor_mantissa_low =
+ mantissa_128[power - FASTFLOAT_SMALLEST_POWER];
+ // next, we compute the 64-bit x 128-bit multiplication, getting a 192-bit
+ // result (three 64-bit values)
+ product = full_multiplication(i, factor_mantissa_low);
+ uint64_t product_low = product.low;
+ uint64_t product_middle2 = product.high;
+ uint64_t product_middle1 = lower;
+ uint64_t product_high = upper;
+ uint64_t product_middle = product_middle1 + product_middle2;
+ if (product_middle < product_middle1) {
+ product_high++; // overflow carry
+ }
+ // we want to check whether mantissa *i + i would affect our result
+ // This does happen, e.g. with 7.3177701707893310e+15
+ if (((product_middle + 1 == 0) && ((product_high & 0x1FF) == 0x1FF) &&
+ (product_low + i < product_low))) { // let us be prudent and bail out.
+ *success = false;
+ return 0;
+ }
+ upper = product_high;
+ lower = product_middle;
+ }
+ // The final mantissa should be 53 bits with a leading 1.
+ // We shift it so that it occupies 54 bits with a leading 1.
+ ///////
+ uint64_t upperbit = upper >> 63;
+ uint64_t mantissa = upper >> (upperbit + 9);
+ lz += int(1 ^ upperbit);
+ // Here we have mantissa < (1<<54).
+
+ // We have to round to even. The "to even" part
+ // is only a problem when we are right in between two floats
+ // which we guard against.
+ // If we have lots of trailing zeros, we may fall right between two
+ // floating-point values.
+ if (unlikely((lower == 0) && ((upper & 0x1FF) == 0) &&
+ ((mantissa & 3) == 1))) {
+ // if mantissa & 1 == 1 we might need to round up.
+ //
+ // Scenarios:
+ // 1. We are not in the middle. Then we should round up.
+ //
+ // 2. We are right in the middle. Whether we round up depends
+ // on the last significant bit: if it is "one" then we round
+ // up (round to even) otherwise, we do not.
+ //
+ // So if the last significant bit is 1, we can safely round up.
+ // Hence we only need to bail out if (mantissa & 3) == 1.
+ // Otherwise we may need more accuracy or analysis to determine whether
+ // we are exactly between two floating-point numbers.
+ // It can be triggered with 1e23.
+ // Note: because the factor_mantissa and factor_mantissa_low are
+ // almost always rounded down (except for small positive powers),
+ // almost always should round up.
+ *success = false;
+ return 0;
+ }
+ mantissa += mantissa & 1;
+ mantissa >>= 1;
+ // Here we have mantissa < (1<<53), unless there was an overflow
+ if (mantissa >= (1ULL << 53)) {
+ //////////
+ // This will happen when parsing values such as 7.2057594037927933e+16
+ ////////
+ mantissa = (1ULL << 52);
+ lz--; // undo previous addition
+ }
+ mantissa &= ~(1ULL << 52);
+ uint64_t real_exponent = exponent - lz;
+ // we have to check that real_exponent is in range, otherwise we bail out
+ if (unlikely((real_exponent < 1) || (real_exponent > 2046))) {
+ *success = false;
+ return 0;
+ }
+ mantissa |= real_exponent << 52;
+ mantissa |= (((uint64_t)negative) << 63);
+ double d;
+ memcpy(&d, &mantissa, sizeof(d));
+ *success = true;
+ return d;
+}
+// Return the null pointer on error
+static const char * parse_float_strtod(const char *ptr, double *outDouble) {
+ char *endptr;
+#if defined(FAST_DOUBLE_PARSER_SOLARIS) || defined(FAST_DOUBLE_PARSER_CYGWIN)
+ // workround for cygwin, solaris
+ *outDouble = cygwin_strtod_l(ptr, &endptr);
+#elif defined(_WIN32)
+ static _locale_t c_locale = _create_locale(LC_ALL, "C");
+ *outDouble = _strtod_l(ptr, &endptr, c_locale);
+#else
+ static locale_t c_locale = newlocale(LC_ALL_MASK, "C", NULL);
+ *outDouble = strtod_l(ptr, &endptr, c_locale);
+#endif
+ // Some libraries will set errno = ERANGE when the value is subnormal,
+ // yet we may want to be able to parse subnormal values.
+ // However, we do not want to tolerate NAN or infinite values.
+ // There isno realistic application where you might need values so large than
+ // they can't fit in binary64. The maximal value is about 1.7976931348623157
+ // × 10^308 It is an unimaginable large number. There will never be any piece
+ // of engineering involving as many as 10^308 parts. It is estimated that
+ // there are about 10^80 atoms in the universe. The estimate for the total
+ // number of electrons is similar. Using a double-precision floating-point
+ // value, we can represent easily the number of atoms in the universe. We
+ // could also represent the number of ways you can pick any three individual
+ // atoms at random in the universe.
+ if (!std::isfinite(*outDouble)) {
+ return nullptr;
+ }
+ return endptr;
+}
+
+// parse the number at p
+// return the null pointer on error
+WARN_UNUSED
+really_inline const char * parse_number(const char *p, double *outDouble) {
+ const char *pinit = p;
+ bool found_minus = (*p == '-');
+ bool negative = false;
+ if (found_minus) {
+ ++p;
+ negative = true;
+ if (!is_integer(*p)) { // a negative sign must be followed by an integer
+ return nullptr;
+ }
+ }
+ const char *const start_digits = p;
+
+ uint64_t i; // an unsigned int avoids signed overflows (which are bad)
+ if (*p == '0') { // 0 cannot be followed by an integer
+ ++p;
+ if (is_integer(*p)) {
+ return nullptr;
+ }
+ i = 0;
+ } else {
+ if (!(is_integer(*p))) { // must start with an integer
+ return nullptr;
+ }
+ unsigned char digit = *p - '0';
+ i = digit;
+ p++;
+ // the is_made_of_eight_digits_fast routine is unlikely to help here because
+ // we rarely see large integer parts like 123456789
+ while (is_integer(*p)) {
+ digit = *p - '0';
+ // a multiplication by 10 is cheaper than an arbitrary integer
+ // multiplication
+ i = 10 * i + digit; // might overflow, we will handle the overflow later
+ ++p;
+ }
+ }
+ int64_t exponent = 0;
+ const char *first_after_period = NULL;
+ if (*p == '.') {
+ ++p;
+ first_after_period = p;
+ if (is_integer(*p)) {
+ unsigned char digit = *p - '0';
+ ++p;
+ i = i * 10 + digit; // might overflow + multiplication by 10 is likely
+ // cheaper than arbitrary mult.
+ // we will handle the overflow later
+ } else {
+ return nullptr;
+ }
+ while (is_integer(*p)) {
+ unsigned char digit = *p - '0';
+ ++p;
+ i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
+ // because we have parse_highprecision_float later.
+ }
+ exponent = first_after_period - p;
+ }
+ int digit_count =
+ int(p - start_digits - 1); // used later to guard against overflows
+ if (('e' == *p) || ('E' == *p)) {
+ ++p;
+ bool neg_exp = false;
+ if ('-' == *p) {
+ neg_exp = true;
+ ++p;
+ } else if ('+' == *p) {
+ ++p;
+ }
+ if (!is_integer(*p)) {
+ return nullptr;
+ }
+ unsigned char digit = *p - '0';
+ int64_t exp_number = digit;
+ p++;
+ if (is_integer(*p)) {
+ digit = *p - '0';
+ exp_number = 10 * exp_number + digit;
+ ++p;
+ }
+ if (is_integer(*p)) {
+ digit = *p - '0';
+ exp_number = 10 * exp_number + digit;
+ ++p;
+ }
+ while (is_integer(*p)) {
+ digit = *p - '0';
+ if (exp_number < 0x100000000) { // we need to check for overflows
+ exp_number = 10 * exp_number + digit;
+ }
+ ++p;
+ }
+ exponent += (neg_exp ? -exp_number : exp_number);
+ }
+ // If we frequently had to deal with long strings of digits,
+ // we could extend our code by using a 128-bit integer instead
+ // of a 64-bit integer. However, this is uncommon.
+ if (unlikely((digit_count >= 19))) { // this is uncommon
+ // It is possible that the integer had an overflow.
+ // We have to handle the case where we have 0.0000somenumber.
+ const char *start = start_digits;
+ while (*start == '0' || (*start == '.')) {
+ start++;
+ }
+ // we over-decrement by one when there is a decimal separator
+ digit_count -= int(start - start_digits);
+ if (digit_count >= 19) {
+ // Chances are good that we had an overflow!
+ // We start anew.
+ // This will happen in the following examples:
+ // 10000000000000000000000000000000000000000000e+308
+ // 3.1415926535897932384626433832795028841971693993751
+ //
+ return parse_float_strtod(pinit, outDouble);
+ }
+ }
+ if (unlikely(exponent < FASTFLOAT_SMALLEST_POWER) ||
+ (exponent > FASTFLOAT_LARGEST_POWER)) {
+ // this is almost never going to get called!!!
+ // exponent could be as low as 325
+ return parse_float_strtod(pinit, outDouble);
+ }
+ // from this point forward, exponent >= FASTFLOAT_SMALLEST_POWER and
+ // exponent <= FASTFLOAT_LARGEST_POWER
+ bool success = true;
+ *outDouble = compute_float_64(exponent, i, negative, &success);
+ if (!success) {
+ // we are almost never going to get here.
+ return parse_float_strtod(pinit, outDouble);
+ }
+ return p;
+}
+
+} // namespace fast_double_parser
+
+#endif
diff --git a/bin/rat_exclude_files.txt b/bin/rat_exclude_files.txt
index 6d42276..8976ea4 100644
--- a/bin/rat_exclude_files.txt
+++ b/bin/rat_exclude_files.txt
@@ -33,6 +33,7 @@ be/src/gutil/*
be/src/thirdparty/datasketches/*
be/src/thirdparty/murmurhash/*
be/src/thirdparty/mpfit/*
+be/src/thirdparty/fast_double_parser/*
be/src/kudu/gutil
www/highlight/*
www/DataTables*/*
diff --git a/testdata/workloads/functional-query/queries/QueryTest/values.test b/testdata/workloads/functional-query/queries/QueryTest/values.test
index 8630059..7e3e0ec 100644
--- a/testdata/workloads/functional-query/queries/QueryTest/values.test
+++ b/testdata/workloads/functional-query/queries/QueryTest/values.test
@@ -99,3 +99,37 @@ select dbl1 * dbl2 * `dec` from i_2749;
1.1650176
1.4835771
====
+---- QUERY
+# IMPALA-10350: Test the double precision during inserts.
+# For write path to text files, the default precision of 16
+# is a limitation yet to be fixed so test would not see exact values retained.
+drop table if exists i_10350;
+create table i_10350(dbl1 double, dbl2 double);
+# insert one negative value < -2^53 * 10^(-17)
+# and another negative value > -2^53 * 10^(-17)
+# and corresponding positive values.
+insert into table i_10350 values
+ (-0.43149576573887316, -0.231495765738873),
+ (0.43149576573887316, 0.231495765738873);
+select * from i_10350;
+---- RESULTS
+-0.4314957657388732,-0.231495765738873
+0.4314957657388732,0.231495765738873
+---- TYPES
+DOUBLE,DOUBLE
+====
+---- QUERY
+# IMPALA-10654: Test accurate conversion from DecimalValue to double.
+# Test below creates DecimalValue for 0.43149576573887316, 0.231495765738873,
+# -0.43149576573887316, -0.231495765738873 and 0.43149576573887315568
+# which has `value_` > 2^53, < 2^53, < -2^53, > -2^53 and > 2^64 correspondingly.
+select cast(1 - 0.56850423426112684 as double),
+ cast(1 - 0.768504234261127 as double),
+ cast(0.56850423426112684 -1 as double),
+ cast(0.768504234261127 -1 as double),
+ cast(1 - 0.56850423426112684432 as double)
+---- RESULTS
+0.43149576573887316,0.231495765738873,-0.43149576573887316,-0.231495765738873,0.43149576573887316
+---- TYPES
+DOUBLE,DOUBLE,DOUBLE,DOUBLE,DOUBLE
+====
\ No newline at end of file
diff --git a/tests/query_test/test_insert_parquet.py b/tests/query_test/test_insert_parquet.py
index 72885d5..5faf31b 100644
--- a/tests/query_test/test_insert_parquet.py
+++ b/tests/query_test/test_insert_parquet.py
@@ -533,6 +533,18 @@ class TestHdfsParquetTableWriter(ImpalaTestSuite):
self._ctas_and_check_int64_timestamps(vector, unique_database, tmpdir, "micros")
self._ctas_and_check_int64_timestamps(vector, unique_database, tmpdir, "nanos")
+ def test_double_precision(self, vector, unique_database):
+ # IMPALA-10654: Test inserting double into Parquet table retains the precision.
+ src_tbl = "{0}.{1}".format(unique_database, "i10654_parquet")
+ create_tbl_stmt = """create table {0} (dbl1 double)
+ stored as parquet""".format(src_tbl)
+ self.execute_query_expect_success(self.client, create_tbl_stmt)
+ insert_tbl_stmt = """insert into table {0}
+ values (-0.43149576573887316)""".format(src_tbl)
+ self.execute_query_expect_success(self.client, insert_tbl_stmt)
+ select_stmt = """select * from {0}""".format(src_tbl)
+ result = self.run_stmt_in_hive(select_stmt)
+ assert result.split('\n')[1] == '-0.43149576573887316'
@SkipIfIsilon.hive
@SkipIfLocal.hive