--- /dev/null
+// 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.
+//
+// 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.
+
+#ifndef RAPIDJSON_STRTOD_
+#define RAPIDJSON_STRTOD_
+
+#include "ieee754.h"
+#include "biginteger.h"
+#include "diyfp.h"
+#include "pow10.h"
+#include <climits>
+#include <limits>
+
+RAPIDJSON_NAMESPACE_BEGIN
+namespace internal {
+
+inline double FastPath(double significand, int exp) {
+ if (exp < -308)
+ return 0.0;
+ else if (exp >= 0)
+ return significand * internal::Pow10(exp);
+ else
+ return significand / internal::Pow10(-exp);
+}
+
+inline double StrtodNormalPrecision(double d, int p) {
+ if (p < -308) {
+ // Prevent expSum < -308, making Pow10(p) = 0
+ d = FastPath(d, -308);
+ d = FastPath(d, p + 308);
+ }
+ else
+ d = FastPath(d, p);
+ return d;
+}
+
+template <typename T>
+inline T Min3(T a, T b, T c) {
+ T m = a;
+ if (m > b) m = b;
+ if (m > c) m = c;
+ return m;
+}
+
+inline int CheckWithinHalfULP(double b, const BigInteger& d, int dExp) {
+ const Double db(b);
+ const uint64_t bInt = db.IntegerSignificand();
+ const int bExp = db.IntegerExponent();
+ const int hExp = bExp - 1;
+
+ int dS_Exp2 = 0, dS_Exp5 = 0, bS_Exp2 = 0, bS_Exp5 = 0, hS_Exp2 = 0, hS_Exp5 = 0;
+
+ // Adjust for decimal exponent
+ if (dExp >= 0) {
+ dS_Exp2 += dExp;
+ dS_Exp5 += dExp;
+ }
+ else {
+ bS_Exp2 -= dExp;
+ bS_Exp5 -= dExp;
+ hS_Exp2 -= dExp;
+ hS_Exp5 -= dExp;
+ }
+
+ // Adjust for binary exponent
+ if (bExp >= 0)
+ bS_Exp2 += bExp;
+ else {
+ dS_Exp2 -= bExp;
+ hS_Exp2 -= bExp;
+ }
+
+ // Adjust for half ulp exponent
+ if (hExp >= 0)
+ hS_Exp2 += hExp;
+ else {
+ dS_Exp2 -= hExp;
+ bS_Exp2 -= hExp;
+ }
+
+ // Remove common power of two factor from all three scaled values
+ int common_Exp2 = Min3(dS_Exp2, bS_Exp2, hS_Exp2);
+ dS_Exp2 -= common_Exp2;
+ bS_Exp2 -= common_Exp2;
+ hS_Exp2 -= common_Exp2;
+
+ BigInteger dS = d;
+ dS.MultiplyPow5(static_cast<unsigned>(dS_Exp5)) <<= static_cast<unsigned>(dS_Exp2);
+
+ BigInteger bS(bInt);
+ bS.MultiplyPow5(static_cast<unsigned>(bS_Exp5)) <<= static_cast<unsigned>(bS_Exp2);
+
+ BigInteger hS(1);
+ hS.MultiplyPow5(static_cast<unsigned>(hS_Exp5)) <<= static_cast<unsigned>(hS_Exp2);
+
+ BigInteger delta(0);
+ dS.Difference(bS, &delta);
+
+ return delta.Compare(hS);
+}
+
+inline bool StrtodFast(double d, int p, double* result) {
+ // Use fast path for string-to-double conversion if possible
+ // see http://www.exploringbinary.com/fast-path-decimal-to-floating-point-conversion/
+ if (p > 22 && p < 22 + 16) {
+ // Fast Path Cases In Disguise
+ d *= internal::Pow10(p - 22);
+ p = 22;
+ }
+
+ if (p >= -22 && p <= 22 && d <= 9007199254740991.0) { // 2^53 - 1
+ *result = FastPath(d, p);
+ return true;
+ }
+ else
+ return false;
+}
+
+// Compute an approximation and see if it is within 1/2 ULP
+template<typename Ch>
+inline bool StrtodDiyFp(const Ch* decimals, int dLen, int dExp, double* result) {
+ uint64_t significand = 0;
+ int i = 0; // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999
+ for (; i < dLen; i++) {
+ if (significand > RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
+ (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > Ch('5')))
+ break;
+ significand = significand * 10u + static_cast<unsigned>(decimals[i] - Ch('0'));
+ }
+
+ if (i < dLen && decimals[i] >= Ch('5')) // Rounding
+ significand++;
+
+ int remaining = dLen - i;
+ const int kUlpShift = 3;
+ const int kUlp = 1 << kUlpShift;
+ int64_t error = (remaining == 0) ? 0 : kUlp / 2;
+
+ DiyFp v(significand, 0);
+ v = v.Normalize();
+ error <<= -v.e;
+
+ dExp += remaining;
+
+ int actualExp;
+ DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
+ if (actualExp != dExp) {
+ static const DiyFp kPow10[] = {
+ DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 0x00000000), -60), // 10^1
+ DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 0x00000000), -57), // 10^2
+ DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 0x00000000), -54), // 10^3
+ DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), -50), // 10^4
+ DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 0x00000000), -47), // 10^5
+ DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 0x00000000), -44), // 10^6
+ DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 0x00000000), -40) // 10^7
+ };
+ int adjustment = dExp - actualExp;
+ RAPIDJSON_ASSERT(adjustment >= 1 && adjustment < 8);
+ v = v * kPow10[adjustment - 1];
+ if (dLen + adjustment > 19) // has more digits than decimal digits in 64-bit
+ error += kUlp / 2;
+ }
+
+ v = v * cachedPower;
+
+ error += kUlp + (error == 0 ? 0 : 1);
+
+ const int oldExp = v.e;
+ v = v.Normalize();
+ error <<= oldExp - v.e;
+
+ const int effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
+ int precisionSize = 64 - effectiveSignificandSize;
+ if (precisionSize + kUlpShift >= 64) {
+ int scaleExp = (precisionSize + kUlpShift) - 63;
+ v.f >>= scaleExp;
+ v.e += scaleExp;
+ error = (error >> scaleExp) + 1 + kUlp;
+ precisionSize -= scaleExp;
+ }
+
+ DiyFp rounded(v.f >> precisionSize, v.e + precisionSize);
+ const uint64_t precisionBits = (v.f & ((uint64_t(1) << precisionSize) - 1)) * kUlp;
+ const uint64_t halfWay = (uint64_t(1) << (precisionSize - 1)) * kUlp;
+ if (precisionBits >= halfWay + static_cast<unsigned>(error)) {
+ rounded.f++;
+ if (rounded.f & (DiyFp::kDpHiddenBit << 1)) { // rounding overflows mantissa (issue #340)
+ rounded.f >>= 1;
+ rounded.e++;
+ }
+ }
+
+ *result = rounded.ToDouble();
+
+ return halfWay - static_cast<unsigned>(error) >= precisionBits || precisionBits >= halfWay + static_cast<unsigned>(error);
+}
+
+template<typename Ch>
+inline double StrtodBigInteger(double approx, const Ch* decimals, int dLen, int dExp) {
+ RAPIDJSON_ASSERT(dLen >= 0);
+ const BigInteger dInt(decimals, static_cast<unsigned>(dLen));
+ Double a(approx);
+ int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp);
+ if (cmp < 0)
+ return a.Value(); // within half ULP
+ else if (cmp == 0) {
+ // Round towards even
+ if (a.Significand() & 1)
+ return a.NextPositiveDouble();
+ else
+ return a.Value();
+ }
+ else // adjustment
+ return a.NextPositiveDouble();
+}
+
+template<typename Ch>
+inline double StrtodFullPrecision(double d, int p, const Ch* decimals, size_t length, size_t decimalPosition, int exp) {
+ RAPIDJSON_ASSERT(d >= 0.0);
+ RAPIDJSON_ASSERT(length >= 1);
+
+ double result = 0.0;
+ if (StrtodFast(d, p, &result))
+ return result;
+
+ RAPIDJSON_ASSERT(length <= INT_MAX);
+ int dLen = static_cast<int>(length);
+
+ RAPIDJSON_ASSERT(length >= decimalPosition);
+ RAPIDJSON_ASSERT(length - decimalPosition <= INT_MAX);
+ int dExpAdjust = static_cast<int>(length - decimalPosition);
+
+ RAPIDJSON_ASSERT(exp >= INT_MIN + dExpAdjust);
+ int dExp = exp - dExpAdjust;
+
+ // Make sure length+dExp does not overflow
+ RAPIDJSON_ASSERT(dExp <= INT_MAX - dLen);
+
+ // Trim leading zeros
+ while (dLen > 0 && *decimals == '0') {
+ dLen--;
+ decimals++;
+ }
+
+ // Trim trailing zeros
+ while (dLen > 0 && decimals[dLen - 1] == '0') {
+ dLen--;
+ dExp++;
+ }
+
+ if (dLen == 0) { // Buffer only contains zeros.
+ return 0.0;
+ }
+
+ // Trim right-most digits
+ const int kMaxDecimalDigit = 767 + 1;
+ if (dLen > kMaxDecimalDigit) {
+ dExp += dLen - kMaxDecimalDigit;
+ dLen = kMaxDecimalDigit;
+ }
+
+ // If too small, underflow to zero.
+ // Any x <= 10^-324 is interpreted as zero.
+ if (dLen + dExp <= -324)
+ return 0.0;
+
+ // If too large, overflow to infinity.
+ // Any x >= 10^309 is interpreted as +infinity.
+ if (dLen + dExp > 309)
+ return std::numeric_limits<double>::infinity();
+
+ if (StrtodDiyFp(decimals, dLen, dExp, &result))
+ return result;
+
+ // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
+ return StrtodBigInteger(result, decimals, dLen, dExp);
+}
+
+} // namespace internal
+RAPIDJSON_NAMESPACE_END
+
+#endif // RAPIDJSON_STRTOD_
projects / ceph.git / blobdiff