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Diffstat (limited to 'include/rapidjson/internal/diyfp.h')
| -rw-r--r-- | include/rapidjson/internal/diyfp.h | 271 |
1 files changed, 271 insertions, 0 deletions
diff --git a/include/rapidjson/internal/diyfp.h b/include/rapidjson/internal/diyfp.h new file mode 100644 index 0000000..b6c2cf5 --- /dev/null +++ b/include/rapidjson/internal/diyfp.h @@ -0,0 +1,271 @@ +// Tencent is pleased to support the open source community by making RapidJSON available. +// +// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. +// +// Licensed under the MIT License (the "License"); you may not use this file except +// in compliance with the License. You may obtain a copy of the License at +// +// http://opensource.org/licenses/MIT +// +// Unless required by applicable law or agreed to in writing, software distributed +// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR +// CONDITIONS OF ANY KIND, either express or implied. See the License for the +// specific language governing permissions and limitations under the License. + +// This is a C++ header-only implementation of Grisu2 algorithm from the publication: +// Loitsch, Florian. "Printing floating-point numbers quickly and accurately with +// integers." ACM Sigplan Notices 45.6 (2010): 233-243. + +#ifndef RAPIDJSON_DIYFP_H_ +#define RAPIDJSON_DIYFP_H_ + +#include "../rapidjson.h" +#include <limits> + +#if defined(_MSC_VER) && defined(_M_AMD64) && !defined(__INTEL_COMPILER) +#include <intrin.h> +#pragma intrinsic(_BitScanReverse64) +#pragma intrinsic(_umul128) +#endif + +RAPIDJSON_NAMESPACE_BEGIN +namespace internal { + +#ifdef __GNUC__ +RAPIDJSON_DIAG_PUSH +RAPIDJSON_DIAG_OFF(effc++) +#endif + +#ifdef __clang__ +RAPIDJSON_DIAG_PUSH +RAPIDJSON_DIAG_OFF(padded) +#endif + +struct DiyFp { + DiyFp() : f(), e() {} + + DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {} + + explicit DiyFp(double d) { + union { + double d; + uint64_t u64; + } u = { d }; + + int biased_e = static_cast<int>((u.u64 & kDpExponentMask) >> kDpSignificandSize); + uint64_t significand = (u.u64 & kDpSignificandMask); + if (biased_e != 0) { + f = significand + kDpHiddenBit; + e = biased_e - kDpExponentBias; + } + else { + f = significand; + e = kDpMinExponent + 1; + } + } + + DiyFp operator-(const DiyFp& rhs) const { + return DiyFp(f - rhs.f, e); + } + + DiyFp operator*(const DiyFp& rhs) const { +#if defined(_MSC_VER) && defined(_M_AMD64) + uint64_t h; + uint64_t l = _umul128(f, rhs.f, &h); + if (l & (uint64_t(1) << 63)) // rounding + h++; + return DiyFp(h, e + rhs.e + 64); +#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__) + __extension__ typedef unsigned __int128 uint128; + uint128 p = static_cast<uint128>(f) * static_cast<uint128>(rhs.f); + uint64_t h = static_cast<uint64_t>(p >> 64); + uint64_t l = static_cast<uint64_t>(p); + if (l & (uint64_t(1) << 63)) // rounding + h++; + return DiyFp(h, e + rhs.e + 64); +#else + const uint64_t M32 = 0xFFFFFFFF; + const uint64_t a = f >> 32; + const uint64_t b = f & M32; + const uint64_t c = rhs.f >> 32; + const uint64_t d = rhs.f & M32; + const uint64_t ac = a * c; + const uint64_t bc = b * c; + const uint64_t ad = a * d; + const uint64_t bd = b * d; + uint64_t tmp = (bd >> 32) + (ad & M32) + (bc & M32); + tmp += 1U << 31; /// mult_round + return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64); +#endif + } + + DiyFp Normalize() const { + RAPIDJSON_ASSERT(f != 0); // https://stackoverflow.com/a/26809183/291737 +#if defined(_MSC_VER) && defined(_M_AMD64) + unsigned long index; + _BitScanReverse64(&index, f); + return DiyFp(f << (63 - index), e - (63 - index)); +#elif defined(__GNUC__) && __GNUC__ >= 4 + int s = __builtin_clzll(f); + return DiyFp(f << s, e - s); +#else + DiyFp res = *this; + while (!(res.f & (static_cast<uint64_t>(1) << 63))) { + res.f <<= 1; + res.e--; + } + return res; +#endif + } + + DiyFp NormalizeBoundary() const { + DiyFp res = *this; + while (!(res.f & (kDpHiddenBit << 1))) { + res.f <<= 1; + res.e--; + } + res.f <<= (kDiySignificandSize - kDpSignificandSize - 2); + res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2); + return res; + } + + void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const { + DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary(); + DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1); + mi.f <<= mi.e - pl.e; + mi.e = pl.e; + *plus = pl; + *minus = mi; + } + + double ToDouble() const { + union { + double d; + uint64_t u64; + }u; + RAPIDJSON_ASSERT(f <= kDpHiddenBit + kDpSignificandMask); + if (e < kDpDenormalExponent) { + // Underflow. + return 0.0; + } + if (e >= kDpMaxExponent) { + // Overflow. + return std::numeric_limits<double>::infinity(); + } + const uint64_t be = (e == kDpDenormalExponent && (f & kDpHiddenBit) == 0) ? 0 : + static_cast<uint64_t>(e + kDpExponentBias); + u.u64 = (f & kDpSignificandMask) | (be << kDpSignificandSize); + return u.d; + } + + static const int kDiySignificandSize = 64; + static const int kDpSignificandSize = 52; + static const int kDpExponentBias = 0x3FF + kDpSignificandSize; + static const int kDpMaxExponent = 0x7FF - kDpExponentBias; + static const int kDpMinExponent = -kDpExponentBias; + static const int kDpDenormalExponent = -kDpExponentBias + 1; + static const uint64_t kDpExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000); + static const uint64_t kDpSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF); + static const uint64_t kDpHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000); + + uint64_t f; + int e; +}; + +inline DiyFp GetCachedPowerByIndex(size_t index) { + // 10^-348, 10^-340, ..., 10^340 + static const uint64_t kCachedPowers_F[] = { + RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288), RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76), + RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76), RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea), + RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d), RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df), + RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca), RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f), + RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c), RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c), + RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83), RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5), + RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb), RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d), + RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57), RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637), + RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f), RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7), + RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4), RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5), + RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e), RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b), + RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba), RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996), + RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584), RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6), + RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126), RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8), + RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b), RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053), + RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655), RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd), + RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94), + RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf), RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b), + RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6), RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac), + RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06), RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3), + RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e), RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb), + RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc), RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c), + RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000), + RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000), RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984), + RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3), RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70), + RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068), RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245), + RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27), RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8), + RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db), RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a), + RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758), RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea), + RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a), RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85), + RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877), RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2), + RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d), RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3), + RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3), RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25), + RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c), RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece), + RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2), RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5), + RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df), RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a), + RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396), RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c), + RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410), RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a), + RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c), RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129), + RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d), RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429), + RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85), RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d), + RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f), RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841), + RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9), RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9), + RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b) + }; + static const int16_t kCachedPowers_E[] = { + -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, + -954, -927, -901, -874, -847, -821, -794, -768, -741, -715, + -688, -661, -635, -608, -582, -555, -529, -502, -475, -449, + -422, -396, -369, -343, -316, -289, -263, -236, -210, -183, + -157, -130, -103, -77, -50, -24, 3, 30, 56, 83, + 109, 136, 162, 189, 216, 242, 269, 295, 322, 348, + 375, 402, 428, 455, 481, 508, 534, 561, 588, 614, + 641, 667, 694, 720, 747, 774, 800, 827, 853, 880, + 907, 933, 960, 986, 1013, 1039, 1066 + }; + RAPIDJSON_ASSERT(index < 87); + return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]); +} + +inline DiyFp GetCachedPower(int e, int* K) { + + //int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374; + double dk = (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive + int k = static_cast<int>(dk); + if (dk - k > 0.0) + k++; + + unsigned index = static_cast<unsigned>((k >> 3) + 1); + *K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table + + return GetCachedPowerByIndex(index); +} + +inline DiyFp GetCachedPower10(int exp, int *outExp) { + RAPIDJSON_ASSERT(exp >= -348); + unsigned index = static_cast<unsigned>(exp + 348) / 8u; + *outExp = -348 + static_cast<int>(index) * 8; + return GetCachedPowerByIndex(index); +} + +#ifdef __GNUC__ +RAPIDJSON_DIAG_POP +#endif + +#ifdef __clang__ +RAPIDJSON_DIAG_POP +RAPIDJSON_DIAG_OFF(padded) +#endif + +} // namespace internal +RAPIDJSON_NAMESPACE_END + +#endif // RAPIDJSON_DIYFP_H_ |