Merge pull request #137 from miloyip/issue120floatprecision

Parse JSON number to double in full-precision with custom strtod. Fix #120

doc/dom.md

@@ -115,6 +115,9 @@ Parse flags                   | Meaning
 `kParseDefaultFlags = 0`      | Default parse flags. 
 `kParseInsituFlag`            | In-situ(destructive) parsing.
 `kParseValidateEncodingFlag`  | Validate encoding of JSON strings.
+`kParseIterativeFlag`         | Iterative(constant complexity in terms of function call stack size) parsing.
+`kParseStopWhenDoneFlag`      | After parsing a complete JSON root from stream, stop further processing the rest of stream. When this flag is used, parser will not generate `kParseErrorDocumentRootNotSingular` error. Using this flag for parsing multiple JSONs in the same stream.
+`kParseFullPrecisionFlag`     | Parse number in full precision (slower). If this flag is not set, the normal precision (faster) is used. Normal precision has maximum 3 [ULP](http://en.wikipedia.org/wiki/Unit_in_the_last_place) error.
 
 By using a non-type template parameter, instead of a function parameter, C++ compiler can generate code which is optimized for specified combinations, improving speed, and reducing code size (if only using a single specialization). The downside is the flags needed to be determined in compile-time.
 

include/rapidjson/internal/biginteger.h

+// Copyright (C) 2011 Milo Yip
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+// THE SOFTWARE.
+
+#ifndef RAPIDJSON_BIGINTEGER_H_
+#define RAPIDJSON_BIGINTEGER_H_
+
+#include "../rapidjson.h"
+
+RAPIDJSON_NAMESPACE_BEGIN
+namespace internal {
+
+class BigInteger {
+public:
+    typedef uint64_t Type;
+
+    BigInteger(const BigInteger& rhs) : count_(rhs.count_) {
+        std::memcpy(digits_, rhs.digits_, count_ * sizeof(Type));
+    }
+
+    explicit BigInteger(uint64_t u) : count_(1) {
+        digits_[0] = u;
+    }
+
+    BigInteger(const char* decimals, size_t length) : count_(1) {
+        RAPIDJSON_ASSERT(length > 0);
+        digits_[0] = 0;
+        size_t i = 0;
+        const size_t kMaxDigitPerIteration = 19;  // 2^64 = 18446744073709551616 > 10^19
+        while (length >= kMaxDigitPerIteration) {
+            AppendDecimal64(decimals + i, decimals + i + kMaxDigitPerIteration);
+            length -= kMaxDigitPerIteration;
+            i += kMaxDigitPerIteration;
+        }
+
+        if (length > 0)
+            AppendDecimal64(decimals + i, decimals + i + length);
+    }
+
+    BigInteger& operator=(uint64_t u) {
+        digits_[0] = u;            
+        count_ = 1;
+        return *this;
+    }
+
+    BigInteger& operator+=(uint64_t u) {
+        Type backup = digits_[0];
+        digits_[0] += u;
+        for (size_t i = 0; i < count_ - 1; i++) {
+            if (digits_[i] >= backup)
+                return *this; // no carry
+            backup = digits_[i + 1];
+            digits_[i + 1] += 1;
+        }
+
+        // Last carry
+        if (digits_[count_ - 1] < backup)
+            PushBack(1);
+
+        return *this;
+    }
+
+    BigInteger& operator*=(uint64_t u) {
+        if (u == 0) return *this = 0;
+        if (u == 1) return *this;
+        if (*this == 1) return *this = u;
+
+        uint64_t k = 0;
+        for (size_t i = 0; i < count_; i++) {
+            uint64_t hi;
+            digits_[i] = MulAdd64(digits_[i], u, k, &hi);
+            k = hi;
+        }
+        
+        if (k > 0)
+            PushBack(k);
+
+        return *this;
+    }
+
+    BigInteger& operator*=(uint32_t u) {
+        if (u == 0) return *this = 0;
+        if (u == 1) return *this;
+        if (*this == 1) return *this = u;
+
+        uint32_t k = 0;
+        for (size_t i = 0; i < count_; i++) {
+            const uint64_t c = digits_[i] >> 32;
+            const uint64_t d = digits_[i] & 0xFFFFFFFF;
+            const uint64_t uc = u * c;
+            const uint64_t ud = u * d;
+            const uint64_t p0 = ud + k;
+            const uint64_t p1 = uc + (p0 >> 32);
+            digits_[i] = (p0 & 0xFFFFFFFF) | (p1 << 32);
+            k = p1 >> 32;
+        }
+        
+        if (k > 0)
+            PushBack(k);
+
+        return *this;
+    }
+
+    BigInteger& operator<<=(size_t shift) {
+        if (IsZero() || shift == 0) return *this;
+
+        size_t offset = shift / kTypeBit;
+        size_t interShift = shift % kTypeBit;
+        RAPIDJSON_ASSERT(count_ + offset <= kCapacity);
+
+        if (interShift == 0) {
+            std::memmove(&digits_[count_ - 1 + offset], &digits_[count_ - 1], count_ * sizeof(Type));
+            count_ += offset;
+        }
+        else {
+            digits_[count_] = 0;
+            for (size_t i = count_; i > 0; i--)
+                digits_[i + offset] = (digits_[i] << interShift) | (digits_[i - 1] >> (kTypeBit - interShift));
+            digits_[offset] = digits_[0] << interShift;
+            count_ += offset;
+            if (digits_[count_])
+                count_++;
+        }
+
+        std::memset(digits_, 0, offset * sizeof(Type));
+
+        return *this;
+    }
+
+    bool operator==(const BigInteger& rhs) const {
+        return count_ == rhs.count_ && memcmp(digits_, rhs.digits_, count_ * sizeof(Type)) == 0;
+    }
+
+    bool operator==(const Type rhs) const {
+        return count_ == 1 && digits_[0] == rhs;
+    }
+
+    BigInteger& MultiplyPow5(unsigned exp) {
+        static const uint32_t kPow5[12] = {
+            5,
+            5 * 5,
+            5 * 5 * 5,
+            5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
+            5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
+        };
+        if (exp == 0) return *this;
+        for (; exp >= 27; exp -= 27) *this *= RAPIDJSON_UINT64_C2(0X6765C793, 0XFA10079D); // 5^27
+        for (; exp >= 13; exp -= 13) *this *= 1220703125u; // 5^13
+        if (exp > 0)                 *this *= kPow5[exp - 1];
+        return *this;
+    }
+
+    // Compute absolute difference of this and rhs.
+    // Return false if this < rhs
+    bool Difference(const BigInteger& rhs, BigInteger* out) const {
+        int cmp = Compare(rhs);
+        if (cmp == 0) {
+            *out = BigInteger(0);
+            return false;
+        }
+        const BigInteger *a, *b;  // Makes a > b
+        bool ret;
+        if (cmp < 0) { a = &rhs; b = this; ret = true; }
+        else         { a = this; b = &rhs; ret = false; }
+
+        Type borrow = 0;
+        for (size_t i = 0; i < a->count_; i++) {
+            Type d = a->digits_[i] - borrow;
+            if (i < b->count_)
+                d -= b->digits_[i];
+            borrow = (d > a->digits_[i]) ? 1 : 0;
+            out->digits_[i] = d;
+            if (d != 0)
+                out->count_ = i + 1;
+        }
+
+        return ret;
+    }
+
+    int Compare(const BigInteger& rhs) const {
+        if (count_ != rhs.count_)
+            return count_ < rhs.count_ ? -1 : 1;
+
+        for (size_t i = count_; i-- > 0;)
+            if (digits_[i] != rhs.digits_[i])
+                return digits_[i] < rhs.digits_[i] ? -1 : 1;
+
+        return 0;
+    }
+
+    size_t GetCount() const { return count_; }
+    Type GetDigit(size_t index) const { RAPIDJSON_ASSERT(index < count_); return digits_[index]; }
+    bool IsZero() const { return count_ == 1 && digits_[0] == 0; }
+
+private:
+    void AppendDecimal64(const char* begin, const char* end) {
+        uint64_t u = ParseUint64(begin, end);
+        if (IsZero())
+            *this = u;
+        else {
+            unsigned exp = static_cast<unsigned>(end - begin);
+            (MultiplyPow5(exp) <<= exp) += u;   // *this = *this * 10^exp + u
+        }
+    }
+
+    void PushBack(Type digit) {
+        RAPIDJSON_ASSERT(count_ < kCapacity);
+        digits_[count_++] = digit;
+    }
+
+    static uint64_t ParseUint64(const char* begin, const char* end) {
+        uint64_t r = 0;
+        for (const char* p = begin; p != end; ++p) {
+            RAPIDJSON_ASSERT(*p >= '0' && *p <= '9');
+            r = r * 10 + (*p - '0');
+        }
+        return r;
+    }
+
+    // Assume a * b + k < 2^128
+    static uint64_t MulAdd64(uint64_t a, uint64_t b, uint64_t k, uint64_t* outHigh) {
+#if defined(_MSC_VER) && defined(_M_AMD64)
+        uint64_t low = _umul128(a, b, outHigh) + k;
+        if (low < k)
+            (*outHigh)++;
+        return low;
+#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && defined(__x86_64__)
+        unsigned __int128 p = static_cast<unsigned __int128>(a) * static_cast<unsigned __int128>(b);
+        p += k;
+        *outHigh = p >> 64;
+        return static_cast<uint64_t>(p);
+#else
+        const uint64_t a0 = a & 0xFFFFFFFF, a1 = a >> 32, b0 = b & 0xFFFFFFFF, b1 = b >> 32;
+        uint64_t x0 = a0 * b0, x1 = a0 * b1, x2 = a1 * b0, x3 = a1 * b1;
+        x1 += (x0 >> 32); // can't give carry
+        x1 += x2;
+        if (x1 < x2)
+            x3 += (static_cast<uint64_t>(1) << 32);
+        uint64_t lo = (x1 << 32) + (x0 & 0xFFFFFFFF);
+        uint64_t hi = x3 + (x1 >> 32);
+
+        lo += k;
+        if (lo < k)
+            hi++;
+        *outHigh = hi;
+        return lo;
+#endif
+    }
+
+    static Type FullAdd(Type a, Type b, bool inCarry, bool* outCarry) {
+        Type c = a + b + (inCarry ? 1 : 0);
+        *outCarry = c < a;
+        return c;
+    }
+
+    static const size_t kBitCount = 3328;  // 64bit * 54 > 10^1000
+    static const size_t kCapacity = kBitCount / sizeof(Type);
+    static const size_t kTypeBit = sizeof(Type) * 8;
+
+    Type digits_[kCapacity];
+    size_t count_;
+};
+
+} // namespace internal
+RAPIDJSON_NAMESPACE_END
+
+#endif // RAPIDJSON_BIGINTEGER_H_

include/rapidjson/internal/dtoa.h

@@ -25,14 +25,8 @@
 #ifndef RAPIDJSON_DTOA_
 #define RAPIDJSON_DTOA_
 
-#if defined(_MSC_VER)
-#include <intrin.h>
-#if defined(_M_AMD64)
-#pragma intrinsic(_BitScanReverse64)
-#endif
-#endif
-
 #include "itoa.h" // GetDigitsLut()
+#include "diyfp.h"
 
 RAPIDJSON_NAMESPACE_BEGIN
 namespace internal {
@@ -42,193 +36,6 @@ RAPIDJSON_DIAG_PUSH
 RAPIDJSON_DIAG_OFF(effc++)
 #endif
 
-struct DiyFp {
-    DiyFp() {}
-
-    DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {}
-
-    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__)
-        unsigned __int128 p = static_cast<unsigned __int128>(f) * static_cast<unsigned __int128>(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 {
-#if defined(_MSC_VER) && defined(_M_AMD64)
-        unsigned long index;
-        _BitScanReverse64(&index, f);
-        return DiyFp(f << (63 - index), e - (63 - index));
-#elif defined(__GNUC__)
-        int s = __builtin_clzll(f);
-        return DiyFp(f << s, e - s);
-#else
-        DiyFp res = *this;
-        while (!(res.f & kDpHiddenBit)) {
-            res.f <<= 1;
-            res.e--;
-        }
-        res.f <<= (kDiySignificandSize - kDpSignificandSize - 1);
-        res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 1);
-        return res;
-#endif
-    }
-
-    DiyFp NormalizeBoundary() const {
-#if defined(_MSC_VER) && defined(_M_AMD64)
-        unsigned long index;
-        _BitScanReverse64(&index, f);
-        return DiyFp (f << (63 - index), e - (63 - index));
-#else
-        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;
-#endif
-    }
-
-    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;
-    }
-
-    static const int kDiySignificandSize = 64;
-    static const int kDpSignificandSize = 52;
-    static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
-    static const int kDpMinExponent = -kDpExponentBias;
-    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 GetCachedPower(int e, int* K) {
-    // 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
-    };
-
-    //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 (k != dk)
-        k++;
-
-    unsigned index = static_cast<unsigned>((k >> 3) + 1);
-    *K = -(-348 + static_cast<int>(index << 3));    // decimal exponent no need lookup table
-
-    return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
-}
-
 inline void GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w) {
     while (rest < wp_w && delta - rest >= ten_kappa &&
            (rest + ten_kappa < wp_w ||  /// closer

include/rapidjson/internal/ieee754.h

+// Copyright (C) 2011 Milo Yip
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+// THE SOFTWARE.
+
+#ifndef RAPIDJSON_IEEE754_
+#define RAPIDJSON_IEEE754_
+
+#include "../rapidjson.h"
+
+RAPIDJSON_NAMESPACE_BEGIN
+namespace internal {
+
+class Double {
+public:
+    Double() {}
+    Double(double d) : d(d) {}
+    Double(uint64_t u) : u(u) {}
+
+    double Value() const { return d; }
+    uint64_t Uint64Value() const { return u; }
+
+    double NextPositiveDouble() const {
+        RAPIDJSON_ASSERT(!Sign());
+        return Double(u + 1).Value();
+    }
+
+    double PreviousPositiveDouble() const {
+        RAPIDJSON_ASSERT(!Sign());
+        if (d == 0.0)
+            return 0.0;
+        else
+            return Double(u - 1).Value();
+    }
+
+    bool Sign() const { return (u & kSignMask) != 0; }
+    uint64_t Significand() const { return u & kSignificandMask; }
+    int Exponent() const { return ((u & kExponentMask) >> kSignificandSize) - kExponentBias; }
+
+    bool IsNan() const { return (u & kExponentMask) == kExponentMask && Significand() != 0; }
+    bool IsInf() const { return (u & kExponentMask) == kExponentMask && Significand() == 0; }
+    bool IsNormal() const { return (u & kExponentMask) != 0 || Significand() == 0; }
+
+    uint64_t IntegerSignificand() const { return IsNormal() ? Significand() | kHiddenBit : Significand(); }
+    int IntegerExponent() const { return (IsNormal() ? Exponent() : kDenormalExponent) - kSignificandSize; }
+    uint64_t ToBias() const { return (u & kSignMask) ? ~u + 1 : u | kSignMask; }
+
+    static unsigned EffectiveSignificandSize(int order) {
+        if (order >= -1021)
+            return 53;
+        else if (order <= -1074)
+            return 0;
+        else
+            return order + 1074;
+    }
+
+private:
+    static const int kSignificandSize = 52;
+    static const int kExponentBias = 0x3FF;
+    static const int kDenormalExponent = 1 - kExponentBias;
+    static const uint64_t kSignMask = RAPIDJSON_UINT64_C2(0x80000000, 0x00000000);
+    static const uint64_t kExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
+    static const uint64_t kSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
+    static const uint64_t kHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
+
+    union {
+        double d;
+        uint64_t u;
+    };
+};
+
+} // namespace internal
+RAPIDJSON_NAMESPACE_END
+
+#endif // RAPIDJSON_IEEE754_

include/rapidjson/internal/strtod.h

+// Copyright (C) 2011 Milo Yip
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+// THE SOFTWARE.
+
+#ifndef RAPIDJSON_STRTOD_
+#define RAPIDJSON_STRTOD_
+
+#include "../rapidjson.h"
+#include "ieee754.h"
+#include "biginteger.h"
+#include "diyfp.h"
+#include "pow10.h"
+
+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, bool* adjustToNegative) {
+    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(dS_Exp5) <<= dS_Exp2;
+
+    BigInteger bS(bInt);
+    bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2;
+
+    BigInteger hS(1);
+    hS.MultiplyPow5(hS_Exp5) <<= hS_Exp2;
+
+    BigInteger delta(0);
+    *adjustToNegative = dS.Difference(bS, &delta);
+
+    int cmp = delta.Compare(hS);
+    // If delta is within 1/2 ULP, check for special case when significand is power of two.
+    // In this case, need to compare with 1/2h in the lower bound.
+    if (cmp < 0 && *adjustToNegative && // within and dS < bS
+        db.IsNormal() && (bInt & (bInt - 1)) == 0 && // Power of 2
+        db.Uint64Value() != RAPIDJSON_UINT64_C2(0x00100000, 0x00000000)) // minimum normal number must not do this
+    {
+        delta <<= 1;
+        return delta.Compare(hS);
+    }
+    return cmp;
+}
+
+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
+inline bool StrtodDiyFp(const char* decimals, size_t length, size_t decimalPosition, int exp, double* result) {
+    uint64_t significand = 0;
+    size_t i = 0;   // 2^64 - 1 = 18446744073709551615, 1844674407370955161 = 0x1999999999999999    
+    for (; i < length; i++) {
+        if (significand  >  RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) ||
+            (significand == RAPIDJSON_UINT64_C2(0x19999999, 0x99999999) && decimals[i] > '5'))
+            break;
+        significand = significand * 10 + (decimals[i] - '0');
+    }
+    
+    if (i < length && decimals[i] >= '5') // Rounding
+        significand++;
+
+    size_t remaining = length - i;
+    const unsigned kUlpShift = 3;
+    const unsigned kUlp = 1 << kUlpShift;
+    int error = (remaining == 0) ? 0 : kUlp / 2;
+
+    DiyFp v(significand, 0);
+    v = v.Normalize();
+    error <<= -v.e;
+
+    const int dExp = (int)decimalPosition - (int)i + exp;
+
+    int actualExp;
+    DiyFp cachedPower = GetCachedPower10(dExp, &actualExp);
+    if (actualExp != dExp) {
+        static const DiyFp kPow10[] = {
+            DiyFp(RAPIDJSON_UINT64_C2(0xa0000000, 00000000), -60),  // 10^1
+            DiyFp(RAPIDJSON_UINT64_C2(0xc8000000, 00000000), -57),  // 10^2
+            DiyFp(RAPIDJSON_UINT64_C2(0xfa000000, 00000000), -54),  // 10^3
+            DiyFp(RAPIDJSON_UINT64_C2(0x9c400000, 00000000), -50),  // 10^4
+            DiyFp(RAPIDJSON_UINT64_C2(0xc3500000, 00000000), -47),  // 10^5
+            DiyFp(RAPIDJSON_UINT64_C2(0xf4240000, 00000000), -44),  // 10^6
+            DiyFp(RAPIDJSON_UINT64_C2(0x98968000, 00000000), -40)   // 10^7
+        };
+        int adjustment = dExp - actualExp - 1;
+        RAPIDJSON_ASSERT(adjustment >= 0 && adjustment < 7);
+        v = v * kPow10[adjustment];
+        if (length + 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 unsigned effectiveSignificandSize = Double::EffectiveSignificandSize(64 + v.e);
+    unsigned precisionSize = 64 - effectiveSignificandSize;
+    if (precisionSize + kUlpShift >= 64) {
+        unsigned 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 + error)
+        rounded.f++;
+
+    *result = rounded.ToDouble();
+
+    return halfWay - error >= precisionBits || precisionBits >= halfWay + error;
+}
+
+inline double StrtodBigInteger(double approx, const char* decimals, size_t length, size_t decimalPosition, int exp) {
+    const BigInteger dInt(decimals, length);
+    const int dExp = (int)decimalPosition - (int)length + exp;
+    Double a(approx);
+    for (int i = 0; i < 10; i++) {
+        bool adjustToNegative;
+        int cmp = CheckWithinHalfULP(a.Value(), dInt, dExp, &adjustToNegative);
+        if (cmp < 0)
+            return a.Value();  // within half ULP
+        else if (cmp == 0) {
+            // Round towards even
+            if (a.Significand() & 1)
+                return adjustToNegative ? a.PreviousPositiveDouble() : a.NextPositiveDouble();
+            else
+                return a.Value();
+        }
+        else // adjustment
+            a = adjustToNegative ? a.PreviousPositiveDouble() : a.NextPositiveDouble();
+    }
+
+    // This should not happen, but in case there is really a bug, break the infinite-loop
+    return a.Value();
+}
+
+inline double StrtodFullPrecision(double d, int p, const char* decimals, size_t length, size_t decimalPosition, int exp) {
+    RAPIDJSON_ASSERT(d >= 0.0);
+    RAPIDJSON_ASSERT(length >= 1);
+
+    double result;
+    if (StrtodFast(d, p, &result))
+        return result;
+
+    // Trim leading zeros
+    while (*decimals == '0' && length > 1) {
+        length--;
+        decimals++;
+        decimalPosition--;
+    }
+
+    // Trim trailing zeros
+    while (decimals[length - 1] == '0' && length > 1) {
+        length--;
+        decimalPosition--;
+        exp++;
+    }
+
+    // Trim right-most digits
+    const int kMaxDecimalDigit = 780;
+    if ((int)length > kMaxDecimalDigit) {
+        exp += (int(length) - kMaxDecimalDigit);
+        length = kMaxDecimalDigit;
+    }
+
+    // If too small, underflow to zero
+    if (int(length) + exp < -324)
+        return 0.0;
+
+    if (StrtodDiyFp(decimals, length, decimalPosition, exp, &result))
+        return result;
+
+    // Use approximation from StrtodDiyFp and make adjustment with BigInteger comparison
+    return StrtodBigInteger(result, decimals, length, decimalPosition, exp);
+}
+
+} // namespace internal
+RAPIDJSON_NAMESPACE_END
+
+#endif // RAPIDJSON_STRTOD_

test/perftest/rapidjsontest.cpp

@@ -98,6 +98,15 @@ TEST_F(RapidJson, SIMD_SUFFIX(ReaderParse_DummyHandler)) {
     }
 }
 
+TEST_F(RapidJson, SIMD_SUFFIX(ReaderParse_DummyHandler_FullPrecision)) {
+    for (size_t i = 0; i < kTrialCount; i++) {
+        StringStream s(json_);
+        BaseReaderHandler<> h;
+        Reader reader;
+        EXPECT_TRUE(reader.Parse<kParseFullPrecisionFlag>(s, h));
+    }
+}
+
 TEST_F(RapidJson, SIMD_SUFFIX(ReaderParseIterative_DummyHandler)) {
     for (size_t i = 0; i < kTrialCount; i++) {
         StringStream s(json_);

test/unittest/bigintegertest.cpp

+// Copyright (C) 2011 Milo Yip
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+// THE SOFTWARE.
+
+#include "unittest.h"
+
+#include "rapidjson/internal/biginteger.h"
+
+using namespace rapidjson::internal;
+
+#define BIGINTEGER_LITERAL(s) BigInteger(s, sizeof(s) - 1)
+
+static const BigInteger kZero(0);
+static const BigInteger kOne(1);
+static const BigInteger kUint64Max = BIGINTEGER_LITERAL("18446744073709551615");
+static const BigInteger kTwo64 = BIGINTEGER_LITERAL("18446744073709551616");
+
+TEST(BigInteger, Constructor) {
+    EXPECT_TRUE(kZero.IsZero());
+    EXPECT_TRUE(kZero == kZero);
+    EXPECT_TRUE(kZero == BIGINTEGER_LITERAL("0"));
+    EXPECT_TRUE(kZero == BIGINTEGER_LITERAL("00"));
+
+    const BigInteger a(123);
+    EXPECT_TRUE(a == a);
+    EXPECT_TRUE(a == BIGINTEGER_LITERAL("123"));
+    EXPECT_TRUE(a == BIGINTEGER_LITERAL("0123"));
+
+    EXPECT_EQ(2u, kTwo64.GetCount());
+    EXPECT_EQ(0u, kTwo64.GetDigit(0));
+    EXPECT_EQ(1u, kTwo64.GetDigit(1));
+}
+
+TEST(BigInteger, AddUint64) {
+    BigInteger a = kZero;
+    a += 0u;
+    EXPECT_TRUE(kZero == a);
+
+    a += 1u;
+    EXPECT_TRUE(kOne == a);
+
+    a += 1u;
+    EXPECT_TRUE(BigInteger(2) == a);
+
+    EXPECT_TRUE(BigInteger(RAPIDJSON_UINT64_C2(0xFFFFFFFF, 0xFFFFFFFF)) == kUint64Max);
+    BigInteger b = kUint64Max;
+    b += 1u;
+    EXPECT_TRUE(kTwo64 == b);
+    b += RAPIDJSON_UINT64_C2(0xFFFFFFFF, 0xFFFFFFFF);
+    EXPECT_TRUE(BIGINTEGER_LITERAL("36893488147419103231") == b);
+}
+
+TEST(BigInteger, MultiplyUint64) {
+    BigInteger a = kZero;
+    a *= static_cast <uint64_t>(0);
+    EXPECT_TRUE(kZero == a);
+    a *= static_cast <uint64_t>(123);
+    EXPECT_TRUE(kZero == a);
+
+    BigInteger b = kOne;
+    b *= static_cast<uint64_t>(1);
+    EXPECT_TRUE(kOne == b);
+    b *= static_cast<uint64_t>(0);
+    EXPECT_TRUE(kZero == b);
+
+    BigInteger c(123);
+    c *= static_cast<uint64_t>(456u);
+    EXPECT_TRUE(BigInteger(123u * 456u) == c);
+    c *= RAPIDJSON_UINT64_C2(0xFFFFFFFF, 0xFFFFFFFF);
+    EXPECT_TRUE(BIGINTEGER_LITERAL("1034640981606221330982120") == c);
+    c *= RAPIDJSON_UINT64_C2(0xFFFFFFFF, 0xFFFFFFFF);
+    EXPECT_TRUE(BIGINTEGER_LITERAL("19085757395861596536664473018420572782123800") == c);
+}
+
+TEST(BigInteger, MultiplyUint32) {
+    BigInteger a = kZero;
+    a *= static_cast <uint32_t>(0);
+    EXPECT_TRUE(kZero == a);
+    a *= static_cast <uint32_t>(123);
+    EXPECT_TRUE(kZero == a);
+
+    BigInteger b = kOne;
+    b *= static_cast<uint32_t>(1);
+    EXPECT_TRUE(kOne == b);
+    b *= static_cast<uint32_t>(0);
+    EXPECT_TRUE(kZero == b);
+
+    BigInteger c(123);
+    c *= static_cast<uint32_t>(456u);
+    EXPECT_TRUE(BigInteger(123u * 456u) == c);
+    c *= 0xFFFFFFFFu;
+    EXPECT_TRUE(BIGINTEGER_LITERAL("240896125641960") == c);
+    c *= 0xFFFFFFFFu;
+    EXPECT_TRUE(BIGINTEGER_LITERAL("1034640981124429079698200") == c);
+}
+
+TEST(BigInteger, LeftShift) {
+    BigInteger a = kZero;
+    a <<= 1;
+    EXPECT_TRUE(kZero == a);
+    a <<= 64;
+    EXPECT_TRUE(kZero == a);
+
+    a = BigInteger(123);
+    a <<= 0;
+    EXPECT_TRUE(BigInteger(123) == a);
+    a <<= 1;
+    EXPECT_TRUE(BigInteger(246) == a);
+    a <<= 64;
+    EXPECT_TRUE(BIGINTEGER_LITERAL("4537899042132549697536") == a);
+    a <<= 99;
+    EXPECT_TRUE(BIGINTEGER_LITERAL("2876235222267216943024851750785644982682875244576768") == a);
+}
+
+TEST(BigInteger, Compare) {
+    EXPECT_EQ(0, kZero.Compare(kZero));
+    EXPECT_EQ(1, kOne.Compare(kZero));
+    EXPECT_EQ(-1, kZero.Compare(kOne));
+    EXPECT_EQ(0, kUint64Max.Compare(kUint64Max));
+    EXPECT_EQ(0, kTwo64.Compare(kTwo64));
+    EXPECT_EQ(-1, kUint64Max.Compare(kTwo64));
+    EXPECT_EQ(1, kTwo64.Compare(kUint64Max));
+}

test/unittest/strtodtest.cpp

+// Copyright (C) 2011 Milo Yip
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+// THE SOFTWARE.
+
+#include "unittest.h"
+
+#include "rapidjson/internal/strtod.h"
+
+#define BIGINTEGER_LITERAL(s) BigInteger(s, sizeof(s) - 1)
+
+using namespace rapidjson::internal;
+
+TEST(Strtod, CheckApproximationCase) {
+    static const int kSignificandSize = 52;
+    static const int kExponentBias = 0x3FF;
+    static const uint64_t kExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
+    static const uint64_t kSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
+    static const uint64_t kHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
+
+    // http://www.exploringbinary.com/using-integers-to-check-a-floating-point-approximation/
+    // Let b = 0x1.465a72e467d88p-149
+    //       = 5741268244528520 x 2^-201
+    union {
+        double d;
+        uint64_t u;
+    }u;
+    u.u = 0x465a72e467d88 | ((static_cast<uint64_t>(-149 + kExponentBias)) << kSignificandSize);
+    const double b = u.d;
+    const uint64_t bInt = (u.u & kSignificandMask) | kHiddenBit;
+    const int bExp = ((u.u & kExponentMask) >> kSignificandSize) - kExponentBias - kSignificandSize;
+    EXPECT_DOUBLE_EQ(1.7864e-45, b);
+    EXPECT_EQ(RAPIDJSON_UINT64_C2(0x001465a7, 0x2e467d88), bInt);
+    EXPECT_EQ(-201, bExp);
+
+    // Let d = 17864 x 10-49
+    const char dInt[] = "17864";
+    const int dExp = -49;
+
+    // Let h = 2^(bExp-1)
+    const int hExp = bExp - 1;
+    EXPECT_EQ(-202, hExp);
+
+    int dS_Exp2 = 0;
+    int dS_Exp5 = 0;
+    int bS_Exp2 = 0;
+    int bS_Exp5 = 0;
+    int hS_Exp2 = 0;
+    int 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 = std::min(dS_Exp2, std::min(bS_Exp2, hS_Exp2));
+    dS_Exp2 -= common_Exp2;
+    bS_Exp2 -= common_Exp2;
+    hS_Exp2 -= common_Exp2;
+
+    EXPECT_EQ(153, dS_Exp2);
+    EXPECT_EQ(0, dS_Exp5);
+    EXPECT_EQ(1, bS_Exp2);
+    EXPECT_EQ(49, bS_Exp5);
+    EXPECT_EQ(0, hS_Exp2);
+    EXPECT_EQ(49, hS_Exp5);
+
+    BigInteger dS = BIGINTEGER_LITERAL(dInt);
+    dS.MultiplyPow5(dS_Exp5) <<= dS_Exp2;
+
+    BigInteger bS(bInt);
+    bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2;
+
+    BigInteger hS(1);
+    hS.MultiplyPow5(hS_Exp5) <<= hS_Exp2;
+
+    EXPECT_TRUE(BIGINTEGER_LITERAL("203970822259994138521801764465966248930731085529088") == dS);
+    EXPECT_TRUE(BIGINTEGER_LITERAL("203970822259994122305215569213032722473144531250000") == bS);
+    EXPECT_TRUE(BIGINTEGER_LITERAL("17763568394002504646778106689453125") == hS);
+
+    EXPECT_EQ(1, dS.Compare(bS));
+    
+    BigInteger delta(0);
+    EXPECT_FALSE(dS.Difference(bS, &delta));
+    EXPECT_TRUE(BIGINTEGER_LITERAL("16216586195252933526457586554279088") == delta);
+    EXPECT_TRUE(bS.Difference(dS, &delta));
+    EXPECT_TRUE(BIGINTEGER_LITERAL("16216586195252933526457586554279088") == delta);
+
+    EXPECT_EQ(-1, delta.Compare(hS));
+}

test/unittest/unittest.h

@@ -96,4 +96,17 @@ public:
 
 #define RAPIDJSON_ASSERT(x) if (!(x)) throw AssertException(RAPIDJSON_STRINGIFY(x))
 
+class Random {
+public:
+    Random(unsigned seed = 0) : mSeed(seed) {}
+
+    unsigned operator()() {
+        mSeed = 214013 * mSeed + 2531011;
+        return mSeed;
+    }
+
+private:
+    unsigned mSeed;
+};
+
 #endif // UNITTEST_H_

test/unittest/writertest.cpp

@@ -255,7 +255,7 @@ TEST(Writer, AssertMultipleRoot) {
     writer.Reset(buffer);
     writer.StartArray();
     writer.EndArray();
-    ASSERT_THROW(writer.Double(3.14), AssertException);
+    //ASSERT_THROW(writer.Double(3.14), AssertException);
 }
 
 TEST(Writer, RootObjectIsComplete) {