mirror of https://github.com/axmolengine/axmol.git
291 lines
8.8 KiB
C++
291 lines
8.8 KiB
C++
// Tencent is pleased to support the open source community by making RapidJSON available.
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//
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// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved.
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//
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// Licensed under the MIT License (the "License"); you may not use this file except
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// in compliance with the License. You may obtain a copy of the License at
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//
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// http://opensource.org/licenses/MIT
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//
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// Unless required by applicable law or agreed to in writing, software distributed
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// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
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// CONDITIONS OF ANY KIND, either express or implied. See the License for the
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// specific language governing permissions and limitations under the License.
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#ifndef RAPIDJSON_STRTOD_
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#define RAPIDJSON_STRTOD_
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#include "ieee754.h"
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#include "biginteger.h"
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#include "diyfp.h"
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#include "pow10.h"
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#include <climits>
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#include <limits>
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RAPIDJSON_NAMESPACE_BEGIN
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namespace internal {
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inline double FastPath(double significand, int exp) {
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if (exp < -308)
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return 0.0;
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else if (exp >= 0)
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return significand * internal::Pow10(exp);
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else
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return significand / internal::Pow10(-exp);
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}
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inline double StrtodNormalPrecision(double d, int p) {
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if (p < -308) {
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// Prevent expSum < -308, making Pow10(p) = 0
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d = FastPath(d, -308);
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d = FastPath(d, p + 308);
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}
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else
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d = FastPath(d, p);
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return d;
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}
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template <typename T>
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inline T Min3(T a, T b, T c) {
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T m = a;
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if (m > b) m = b;
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if (m > c) m = c;
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return m;
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}
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inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
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const Double db(b);
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const uint64_t bInt = db.IntegerSignificand();
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const int bExp = db.IntegerExponent();
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const int hExp = bExp - 1;
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int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
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// Adjust for decimal exponent
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if (dExp >= 0) {
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dS_Exp2 += dExp;
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dS_Exp5 += dExp;
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}
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else {
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bS_Exp2 -= dExp;
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bS_Exp5 -= dExp;
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hS_Exp2 -= dExp;
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hS_Exp5 -= dExp;
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}
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// Adjust for binary exponent
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if (bExp >= 0)
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bS_Exp2 += bExp;
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else {
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dS_Exp2 -= bExp;
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hS_Exp2 -= bExp;
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}
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// Adjust for half ulp exponent
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if (hExp >= 0)
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hS_Exp2 += hExp;
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else {
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dS_Exp2 -= hExp;
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bS_Exp2 -= hExp;
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}
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// Remove common power of two factor from all three scaled values
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int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
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dS_Exp2 -= common_Exp2;
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bS_Exp2 -= common_Exp2;
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hS_Exp2 -= common_Exp2;
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BigInteger dS = d;
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dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
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BigInteger bS(bInt);
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bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
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BigInteger hS(1);
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hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
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BigInteger delta(0);
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dS.Difference(bS, &delta);
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return delta.Compare(hS);
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}
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inline bool StrtodFast(double d, int p, double* result) {
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// Use fast path for string-to-double conversion if possible
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// see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
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if (p > 22 && p < 22 + 16) {
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// Fast Path Cases In Disguise
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d *= internal::Pow10(p - 22);
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p = 22;
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}
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if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
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*result = FastPath(d, p);
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return true;
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}
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else
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return false;
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}
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// Compute an approximation and see if it is within 1/2 ULP
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inline bool StrtodDiyFp(const char* decimals, int dLen, int dExp, double* result) {
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uint64_t significand = 0;
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int i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
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for (; i < dLen; i++) {
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if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
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(significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
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break;
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significand = significand * 10u + static_cast<unsigned>(decimals[i] - '0');
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}
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if (i < dLen && decimals[i] >= '5') // Rounding
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significand++;
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int remaining = dLen - i;
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const int kUlpShift = 3;
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const int kUlp = 1 << kUlpShift;
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int64_t error = (remaining == 0) ? 0 : kUlp / 2;
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DiyFp v(significand, 0);
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v = v.Normalize();
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error <<= -v.e;
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dExp += remaining;
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int actualExp;
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DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
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if (actualExp != dExp) {
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static const DiyFp kPow10[] = {
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DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60), // 10^1
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DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57), // 10^2
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DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54), // 10^3
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DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50), // 10^4
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DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47), // 10^5
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DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44), // 10^6
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DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40) // 10^7
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};
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int adjustment = dExp - actualExp;
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RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
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v = v * kPow10[adjustment - 1];
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if (dLen + adjustment > 19) // has more digits than decimal digits in 64-bit
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error += kUlp / 2;
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}
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v = v * cachedPower;
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error += kUlp + (error == 0 ? 0 : 1);
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const int oldExp = v.e;
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v = v.Normalize();
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error <<= oldExp - v.e;
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const int effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
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int precisionSize = 64 - effectiveSignificandSize;
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if (precisionSize + kUlpShift >= 64) {
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int scaleExp = (precisionSize + kUlpShift) - 63;
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v.f >>= scaleExp;
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v.e += scaleExp;
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error = (error >> scaleExp) + 1 + kUlp;
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precisionSize -= scaleExp;
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}
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DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
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const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
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const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
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if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
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rounded.f++;
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if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
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rounded.f >>= 1;
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rounded.e++;
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}
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}
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*result = rounded.ToDouble();
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return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
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}
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inline double StrtodBigInteger(double approx, const char* decimals, int dLen, int dExp) {
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RAPIDJSON_ASSERT(dLen >= 0);
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const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
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Double a(approx);
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int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
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if (cmp < 0)
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return a.Value(); // within half ULP
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else if (cmp == 0) {
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// Round towards even
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if (a.Significand() & 1)
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return a.NextPositiveDouble();
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else
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return a.Value();
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}
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else // adjustment
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return a.NextPositiveDouble();
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}
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inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
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RAPIDJSON_ASSERT(d >= 0.0);
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RAPIDJSON_ASSERT(length >= 1);
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double result = 0.0;
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if (StrtodFast(d, p, &result))
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return result;
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RAPIDJSON_ASSERT(length <= INT_MAX);
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int dLen = static_cast<int>(length);
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RAPIDJSON_ASSERT(length >= decimalPosition);
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RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
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int dExpAdjust = static_cast<int>(length - decimalPosition);
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RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
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int dExp = exp - dExpAdjust;
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// Make sure length+dExp does not overflow
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RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);
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// Trim leading zeros
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while (dLen > 0 && *decimals == '0') {
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dLen--;
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decimals++;
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}
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// Trim trailing zeros
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while (dLen > 0 && decimals[dLen - 1] == '0') {
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dLen--;
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dExp++;
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}
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if (dLen == 0) { // Buffer only contains zeros.
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return 0.0;
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}
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// Trim right-most digits
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const int kMaxDecimalDigit = 767 + 1;
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if (dLen > kMaxDecimalDigit) {
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dExp += dLen - kMaxDecimalDigit;
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dLen = kMaxDecimalDigit;
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}
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// If too small, underflow to zero.
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// Any x <= 10^-324 is interpreted as zero.
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if (dLen + dExp <= -324)
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return 0.0;
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// If too large, overflow to infinity.
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// Any x >= 10^309 is interpreted as +infinity.
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if (dLen + dExp > 309)
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return std::numeric_limits<double>::infinity();
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if (StrtodDiyFp(decimals, dLen, dExp, &result))
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return result;
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// Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
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return StrtodBigInteger(result, decimals, dLen, dExp);
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}
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} // namespace internal
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RAPIDJSON_NAMESPACE_END
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#endif // RAPIDJSON_STRTOD_
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