Fast double-to-ascii conversion.

Review URL: http://codereview.chromium.org/866002

git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@4106 ce2b1a6d-e550-0410-aec6-3dcde31c8c00

src/SConscript

@@ -63,6 +63,7 @@ SOURCES = {
     full-codegen.cc
     func-name-inferrer.cc
     global-handles.cc
+    grisu3.cc
     handles.cc
     hashmap.cc
     heap-profiler.cc

src/cached_powers.h

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef V8_CACHED_POWERS_H_
+#define V8_CACHED_POWERS_H_
+
+#include "diy_fp.h"
+
+namespace v8 {
+namespace internal {
+
+struct CachedPower {
+  uint64_t significand;
+  int16_t binary_exponent;
+  int16_t decimal_exponent;
+};
+
+// The following defines implement the interface between this file and the
+// generated 'powers_ten.h'.
+// GRISU_CACHE_NAME(1) contains all possible cached powers.
+// GRISU_CACHE_NAME(i) contains GRISU_CACHE_NAME(1) where only every 'i'th
+// element is kept. More formally GRISU_CACHE_NAME(i) contains the elements j*i
+// with 0 <= j < k with k such that j*k < the size of GRISU_CACHE_NAME(1).
+// The higher 'i' is the fewer elements we use.
+// Given that there are less elements, the exponent-distance between two
+// elements in the cache grows. The variable GRISU_CACHE_MAX_DISTANCE(i) stores
+// the maximum distance between two elements.
+#define GRISU_CACHE_STRUCT CachedPower
+#define GRISU_CACHE_NAME(i) kCachedPowers##i
+#define GRISU_CACHE_MAX_DISTANCE(i) kCachedPowersMaxDistance##i
+#define GRISU_CACHE_OFFSET kCachedPowerOffset
+#define GRISU_UINT64_C V8_2PART_UINT64_C
+// The following include imports the precompiled cached powers.
+#include "powers_ten.h"  // NOLINT
+
+static const double kD_1_LOG2_10 = 0.30102999566398114;  //  1 / lg(10)
+
+// We can't use a function since we reference variables depending on the 'i'.
+// This way the compiler is able to see at compile time that only one
+// cache-array variable is used and thus can remove all the others.
+#define COMPUTE_FOR_CACHE(i) \
+  if (!found && (gamma - alpha + 1 >= GRISU_CACHE_MAX_DISTANCE(i))) {   \
+    int kQ = DiyFp::kSignificandSize;                                   \
+    double k = ceiling((alpha - e + kQ - 1) * kD_1_LOG2_10);            \
+    int index = (GRISU_CACHE_OFFSET + static_cast<int>(k) - 1) / i + 1; \
+    cached_power = GRISU_CACHE_NAME(i)[index];                          \
+    found = true;                                                       \
+  }                                                                     \
+
+static void GetCachedPower(int e, int alpha, int gamma, int* mk, DiyFp* c_mk) {
+  // The following if statement should be optimized by the compiler so that only
+  // one array is referenced and the others are not included in the object file.
+  bool found = false;
+  CachedPower cached_power;
+  COMPUTE_FOR_CACHE(20);
+  COMPUTE_FOR_CACHE(19);
+  COMPUTE_FOR_CACHE(18);
+  COMPUTE_FOR_CACHE(17);
+  COMPUTE_FOR_CACHE(16);
+  COMPUTE_FOR_CACHE(15);
+  COMPUTE_FOR_CACHE(14);
+  COMPUTE_FOR_CACHE(13);
+  COMPUTE_FOR_CACHE(12);
+  COMPUTE_FOR_CACHE(11);
+  COMPUTE_FOR_CACHE(10);
+  COMPUTE_FOR_CACHE(9);
+  COMPUTE_FOR_CACHE(8);
+  COMPUTE_FOR_CACHE(7);
+  COMPUTE_FOR_CACHE(6);
+  COMPUTE_FOR_CACHE(5);
+  COMPUTE_FOR_CACHE(4);
+  COMPUTE_FOR_CACHE(3);
+  COMPUTE_FOR_CACHE(2);
+  COMPUTE_FOR_CACHE(1);
+  if (!found) {
+    UNIMPLEMENTED();
+    // Silence compiler warnings.
+    cached_power.significand = 0;
+    cached_power.binary_exponent = 0;
+    cached_power.decimal_exponent = 0;
+  }
+  *c_mk = DiyFp(cached_power.significand, cached_power.binary_exponent);
+  *mk = cached_power.decimal_exponent;
+  ASSERT((alpha <= c_mk->e() + e) && (c_mk->e() + e <= gamma));
+}
+#undef GRISU_REDUCTION
+#undef GRISU_CACHE_STRUCT
+#undef GRISU_CACHE_NAME
+#undef GRISU_CACHE_MAX_DISTANCE
+#undef GRISU_CACHE_OFFSET
+#undef GRISU_UINT64_C
+
+} }  // namespace v8::internal
+
+#endif  // V8_CACHED_POWERS_H_

src/checks.h

@@ -80,6 +80,7 @@ static inline void CheckEqualsHelper(const char* file, int line,
   }
 }
 
+
 // Helper function used by the CHECK_EQ function when given int64_t
 // arguments.  Should not be called directly.
 static inline void CheckEqualsHelper(const char* file, int line,
@@ -202,6 +203,27 @@ static inline void CheckEqualsHelper(const char* file,
 }
 
 
+static inline void CheckNonEqualsHelper(const char* file,
+                                     int line,
+                                     const char* expected_source,
+                                     double expected,
+                                     const char* value_source,
+                                     double value) {
+  // Force values to 64 bit memory to truncate 80 bit precision on IA32.
+  volatile double* exp = new double[1];
+  *exp = expected;
+  volatile double* val = new double[1];
+  *val = value;
+  if (*exp == *val) {
+    V8_Fatal(file, line,
+             "CHECK_NE(%s, %s) failed\n#   Value: %f",
+             expected_source, value_source, *val);
+  }
+  delete[] exp;
+  delete[] val;
+}
+
+
 namespace v8 {
   class Value;
   template <class T> class Handle;

src/conversions.cc

@@ -31,6 +31,7 @@
 
 #include "conversions-inl.h"
 #include "factory.h"
+#include "grisu3.h"
 #include "scanner.h"
 
 namespace v8 {
@@ -382,8 +383,17 @@ const char* DoubleToCString(double v, Vector<char> buffer) {
       int decimal_point;
       int sign;
 
-      char* decimal_rep = dtoa(v, 0, 0, &decimal_point, &sign, NULL);
-      int length = StrLength(decimal_rep);
+      char* decimal_rep;
+      bool used_dtoa = false;
+      char grisu_buffer[kGrisu3MaximalLength + 1];
+      int length;
+      if (grisu3(v, grisu_buffer, &sign, &length, &decimal_point)) {
+        decimal_rep = grisu_buffer;
+      } else {
+        decimal_rep = dtoa(v, 0, 0, &decimal_point, &sign, NULL);
+        used_dtoa = true;
+        length = StrLength(decimal_rep);
+      }
 
       if (sign) builder.AddCharacter('-');
 
@@ -418,7 +428,7 @@ const char* DoubleToCString(double v, Vector<char> buffer) {
         builder.AddFormatted("%d", exponent);
       }
 
-      freedtoa(decimal_rep);
+      if (used_dtoa) freedtoa(decimal_rep);
     }
   }
   return builder.Finalize();

src/diy_fp.h

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef V8_DIY_FP_H_
+#define V8_DIY_FP_H_
+
+namespace v8 {
+namespace internal {
+
+// This "Do It Yourself Floating Point" class implements a floating-point number
+// with a uint64 significand and an int exponent. Normalized DiyFp numbers will
+// have the most significant bit of the significand set.
+// Multiplication and Subtraction do not normalize their results.
+// DiyFp are not designed to contain special doubles (NaN and Infinity).
+class DiyFp {
+ public:
+  static const int kSignificandSize = 64;
+
+  DiyFp() : f_(0), e_(0) {}
+  DiyFp(uint64_t f, int e) : f_(f), e_(e) {}
+
+  // this = this - other.
+  // The exponents of both numbers must be the same and the significand of this
+  // must be bigger than the significand of other.
+  // The result will not be normalized.
+  void Subtract(const DiyFp& other) {
+    ASSERT(e_ == other.e_);
+    ASSERT(f_ >= other.f_);
+    f_ -= other.f_;
+  }
+
+  // Returns a - b.
+  // The exponents of both numbers must be the same and this must be bigger
+  // than other. The result will not be normalized.
+  static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Subtract(b);
+    return result;
+  }
+
+
+  // this = this * other.
+  void Multiply(const DiyFp& other) {
+    // Simply "emulates" a 128 bit multiplication.
+    // However: the resulting number only contains 64 bits. The least
+    // significant 64 bits are only used for rounding the most significant 64
+    // bits.
+    const uint64_t kM32 = 0xFFFFFFFFu;
+    uint64_t a = f_ >> 32;
+    uint64_t b = f_ & kM32;
+    uint64_t c = other.f_ >> 32;
+    uint64_t d = other.f_ & kM32;
+    uint64_t ac = a * c;
+    uint64_t bc = b * c;
+    uint64_t ad = a * d;
+    uint64_t bd = b * d;
+    uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32);
+    tmp += 1U << 31;  // round
+    uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
+    e_ += other.e_ + 64;
+    f_ = result_f;
+  }
+
+  // returns a * b;
+  static DiyFp Times(const DiyFp& a, const DiyFp& b) {
+    DiyFp result = a;
+    result.Multiply(b);
+    return result;
+  }
+
+  void Normalize() {
+    ASSERT(f_ != 0);
+    uint64_t f = f_;
+    int e = e_;
+
+    // This method is mainly called for normalizing boundaries. In general
+    // boundaries need to be shifted by 10 bits. We thus optimize for this case.
+    const uint64_t k10MSBits = V8_2PART_UINT64_C(0xFFC00000, 00000000);
+    while ((f & k10MSBits) == 0) {
+      f <<= 10;
+      e -= 10;
+    }
+    while ((f & kUint64MSB) == 0) {
+      f <<= 1;
+      e--;
+    }
+    f_ = f;
+    e_ = e;
+  }
+
+  static DiyFp Normalize(const DiyFp& a) {
+    DiyFp result = a;
+    result.Normalize();
+    return result;
+  }
+
+  uint64_t f() const { return f_; }
+  int e() const { return e_; }
+
+  void set_f(uint64_t new_value) { f_ = new_value; }
+  void set_e(int new_value) { e_ = new_value; }
+
+ private:
+  static const uint64_t kUint64MSB = V8_2PART_UINT64_C(0x80000000, 00000000);
+
+  uint64_t f_;
+  int e_;
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_DIY_FP_H_

src/double.h

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef V8_DOUBLE_H_
+#define V8_DOUBLE_H_
+
+#include "diy_fp.h"
+
+namespace v8 {
+namespace internal {
+
+// We assume that doubles and uint64_t have the same endianness.
+static uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
+static double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
+
+// Helper functions for doubles.
+class Double {
+ public:
+  static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000);
+  static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000);
+  static const uint64_t kSignificandMask =
+      V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+  static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000);
+
+  Double() : d64_(0) {}
+  explicit Double(double d) : d64_(double_to_uint64(d)) {}
+  explicit Double(uint64_t d64) : d64_(d64) {}
+
+  DiyFp AsDiyFp() const {
+    ASSERT(!IsSpecial());
+    return DiyFp(Significand(), Exponent());
+  }
+
+  // this->Significand() must not be 0.
+  DiyFp AsNormalizedDiyFp() const {
+    uint64_t f = Significand();
+    int e = Exponent();
+
+    ASSERT(f != 0);
+
+    // The current double could be a denormal.
+    while ((f & kHiddenBit) == 0) {
+      f <<= 1;
+      e--;
+    }
+    // Do the final shifts in one go. Don't forget the hidden bit (the '-1').
+    f <<= DiyFp::kSignificandSize - kSignificandSize - 1;
+    e -= DiyFp::kSignificandSize - kSignificandSize - 1;
+    return DiyFp(f, e);
+  }
+
+  // Returns the double's bit as uint64.
+  uint64_t AsUint64() const {
+    return d64_;
+  }
+
+  int Exponent() const {
+    if (IsDenormal()) return kDenormalExponent;
+
+    uint64_t d64 = AsUint64();
+    int biased_e = static_cast<int>((d64 & kExponentMask) >> kSignificandSize);
+    return biased_e - kExponentBias;
+  }
+
+  uint64_t Significand() const {
+    uint64_t d64 = AsUint64();
+    uint64_t significand = d64 & kSignificandMask;
+    if (!IsDenormal()) {
+      return significand + kHiddenBit;
+    } else {
+      return significand;
+    }
+  }
+
+  // Returns true if the double is a denormal.
+  bool IsDenormal() const {
+    uint64_t d64 = AsUint64();
+    return (d64 & kExponentMask) == 0;
+  }
+
+  // We consider denormals not to be special.
+  // Hence only Infinity and NaN are special.
+  bool IsSpecial() const {
+    uint64_t d64 = AsUint64();
+    return (d64 & kExponentMask) == kExponentMask;
+  }
+
+  bool IsNan() const {
+    uint64_t d64 = AsUint64();
+    return ((d64 & kExponentMask) == kExponentMask) &&
+        ((d64 & kSignificandMask) != 0);
+  }
+
+
+  bool IsInfinite() const {
+    uint64_t d64 = AsUint64();
+    return ((d64 & kExponentMask) == kExponentMask) &&
+        ((d64 & kSignificandMask) == 0);
+  }
+
+
+  int Sign() const {
+    uint64_t d64 = AsUint64();
+    return (d64 & kSignMask) == 0? 1: -1;
+  }
+
+
+  // Returns the two boundaries of this.
+  // The bigger boundary (m_plus) is normalized. The lower boundary has the same
+  // exponent as m_plus.
+  void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
+    DiyFp v = this->AsDiyFp();
+    bool significand_is_zero = (v.f() == kHiddenBit);
+    DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
+    DiyFp m_minus;
+    if (significand_is_zero && v.e() != kDenormalExponent) {
+      // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
+      // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
+      // at a distance of 1e8.
+      // The only exception is for the smallest normal: the largest denormal is
+      // at the same distance as its successor.
+      // Note: denormals have the same exponent as the smallest normals.
+      m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
+    } else {
+      m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
+    }
+    m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
+    m_minus.set_e(m_plus.e());
+    *out_m_plus = m_plus;
+    *out_m_minus = m_minus;
+  }
+
+  double value() const { return uint64_to_double(d64_); }
+
+ private:
+  static const int kSignificandSize = 52;  // Excludes the hidden bit.
+  static const int kExponentBias = 0x3FF + kSignificandSize;
+  static const int kDenormalExponent = -kExponentBias + 1;
+
+  uint64_t d64_;
+};
+
+} }  // namespace v8::internal
+
+#endif  // V8_DOUBLE_H_

src/globals.h

@@ -98,6 +98,11 @@ typedef byte* Address;
 #define V8_PTR_PREFIX ""
 #endif  // V8_HOST_ARCH_64_BIT
 
+// The following macro works on both 32 and 64-bit platforms.
+// Usage: instead of writing 0x1234567890123456
+//      write V8_2PART_UINT64_C(0x12345678,90123456);
+#define V8_2PART_UINT64_C(a, b) (((static_cast<uint64_t>(a) << 32) + 0x##b##u))
+
 #define V8PRIxPTR V8_PTR_PREFIX "x"
 #define V8PRIdPTR V8_PTR_PREFIX "d"
 

src/grisu3.cc

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#include "v8.h"
+
+#include "grisu3.h"
+
+#include "cached_powers.h"
+#include "diy_fp.h"
+#include "double.h"
+
+namespace v8 {
+namespace internal {
+
+template <int alpha = -60, int gamma = -32>
+class Grisu3 {
+ public:
+  // Provides a decimal representation of v.
+  // Returns true if it succeeds, otherwise the result can not be trusted.
+  // There will be *length digits inside the buffer (not null-terminated).
+  // If the function returns true then
+  //        v == (double) (buffer * 10^decimal_exponent).
+  // The digits in the buffer are the shortest representation possible: no
+  // 0.099999999999 instead of 0.1.
+  // The last digit will be closest to the actual v. That is, even if several
+  // digits might correctly yield 'v' when read again, the closest will be
+  // computed.
+  static bool grisu3(double v,
+                     char* buffer, int* length, int* decimal_exponent);
+
+ private:
+  // Rounds the buffer according to the rest.
+  // If there is too much imprecision to round then false is returned.
+  // Similarily false is returned when the buffer is not within Delta.
+  static bool RoundWeed(char* buffer, int len, uint64_t wp_W, uint64_t Delta,
+                        uint64_t rest, uint64_t ten_kappa, uint64_t ulp);
+  // Dispatches to the a specialized digit-generation routine. The chosen
+  // routine depends on w.e (which in turn depends on alpha and gamma).
+  // Currently there is only one digit-generation routine, but it would be easy
+  // to add others.
+  static bool DigitGen(DiyFp low, DiyFp w, DiyFp high,
+                       char* buffer, int* len, int* kappa);
+  // Generates w's digits. The result is the shortest in the interval low-high.
+  // All DiyFp are assumed to be imprecise and this function takes this
+  // imprecision into account. If the function cannot compute the best
+  // representation (due to the imprecision) then false is returned.
+  static bool DigitGen_m60_m32(DiyFp low, DiyFp w, DiyFp high,
+                               char* buffer, int* length, int* kappa);
+};
+
+
+template<int alpha, int gamma>
+bool Grisu3<alpha, gamma>::grisu3(double v,
+                                  char* buffer,
+                                  int* length,
+                                  int* decimal_exponent) {
+  DiyFp w = Double(v).AsNormalizedDiyFp();
+  // boundary_minus and boundary_plus are the boundaries between v and its
+  // neighbors. Any number strictly between boundary_minus and boundary_plus
+  // will round to v when read as double.
+  // Grisu3 will never output representations that lie exactly on a boundary.
+  DiyFp boundary_minus, boundary_plus;
+  Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  ASSERT(boundary_plus.e() == w.e());
+  DiyFp ten_mk;  // Cached power of ten: 10^-k
+  int mk;        // -k
+  GetCachedPower(w.e() + DiyFp::kSignificandSize, alpha, gamma, &mk, &ten_mk);
+  ASSERT(alpha <= w.e() + ten_mk.e() + DiyFp::kSignificandSize &&
+         gamma >= w.e() + ten_mk.e() + DiyFp::kSignificandSize);
+  // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
+  // 64 bit significand and ten_mk is thus only precise up to 64 bits.
+
+  // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
+  // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
+  // off by a small amount.
+  // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
+  // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
+  //           (f-1) * 2^e < w*10^k < (f+1) * 2^e
+  DiyFp scaled_w = DiyFp::Times(w, ten_mk);
+  ASSERT(scaled_w.e() ==
+         boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
+  // In theory it would be possible to avoid some recomputations by computing
+  // the difference between w and boundary_minus/plus (a power of 2) and to
+  // compute scaled_boundary_minus/plus by subtracting/adding from
+  // scaled_w. However the code becomes much less readable and the speed
+  // enhancements are not terriffic.
+  DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
+  DiyFp scaled_boundary_plus  = DiyFp::Times(boundary_plus,  ten_mk);
+
+  // DigitGen will generate the digits of scaled_w. Therefore we have
+  // v == (double) (scaled_w * 10^-mk).
+  // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
+  // integer than it will be updated. For instance if scaled_w == 1.23 then
+  // the buffer will be filled with "123" und the decimal_exponent will be
+  // decreased by 2.
+  int kappa;
+  bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
+                         buffer, length, &kappa);
+  *decimal_exponent = -mk + kappa;
+  return result;
+}
+
+// Generates the digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by alpha and gamma. Typically alpha >= -63
+// and gamma <= 3.
+// Returns false if it fails, in which case the generated digits in the buffer
+// should not be used.
+// Preconditions:
+//  * low, w and high are correct up to 1 ulp (unit in the last place). That
+//    is, their error must be less that a unit of their last digits.
+//  * low.e() == w.e() == high.e()
+//  * low < w < high, and taking into account their error: low~ <= high~
+//  * alpha <= w.e() <= gamma
+// Postconditions: returns false if procedure fails.
+//   otherwise:
+//     * buffer is not null-terminated, but len contains the number of digits.
+//     * buffer contains the shortest possible decimal digit-sequence
+//       such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
+//       correct values of low and high (without their error).
+//     * if more than one decimal representation gives the minimal number of
+//       decimal digits then the one closest to W (where W is the correct value
+//       of w) is chosen.
+// Remark: this procedure takes into account the imprecision of its input
+//   numbers. If the precision is not enough to guarantee all the postconditions
+//   then false is returned. This usually happens rarely (~0.5%).
+template<int alpha, int gamma>
+bool Grisu3<alpha, gamma>::DigitGen(DiyFp low,
+                                    DiyFp w,
+                                    DiyFp high,
+                                    char* buffer,
+                                    int* len,
+                                    int* kappa) {
+  ASSERT(low.e() == w.e() && w.e() == high.e());
+  ASSERT(low.f() + 1 <= high.f() - 1);
+  ASSERT(alpha <= w.e() && w.e() <= gamma);
+  // The following tests use alpha and gamma to avoid unnecessary dynamic tests.
+  if ((alpha >= -60 && gamma <= -32) ||  // -60 <= w.e() <= -32
+      (alpha <= -32 && gamma >= -60 &&   // Alpha/gamma overlaps -60/-32 region.
+       -60 <= w.e() && w.e() <= -32)) {
+    return DigitGen_m60_m32(low, w, high, buffer, len, kappa);
+  } else {
+    // A simple adaption of the special case -60/-32 would allow greater ranges
+    // of alpha/gamma and thus reduce the number of precomputed cached powers of
+    // ten.
+    UNIMPLEMENTED();
+    return false;
+  }
+}
+
+static const uint32_t kTen4 = 10000;
+static const uint32_t kTen5 = 100000;
+static const uint32_t kTen6 = 1000000;
+static const uint32_t kTen7 = 10000000;
+static const uint32_t kTen8 = 100000000;
+static const uint32_t kTen9 = 1000000000;
+
+// Returns the biggest power of ten that is <= than the given number. We
+// furthermore receive the maximum number of bits 'number' has.
+// If number_bits == 0 then 0^-1 is returned
+// The number of bits must be <= 32.
+static void BiggestPowerTen(uint32_t number,
+                            int number_bits,
+                            uint32_t* power,
+                            int* exponent) {
+  switch (number_bits) {
+    case 32:
+    case 31:
+    case 30:
+      if (kTen9 <= number) {
+        *power = kTen9;
+        *exponent = 9;
+        break;
+      }  // else fallthrough
+    case 29:
+    case 28:
+    case 27:
+      if (kTen8 <= number) {
+        *power = kTen8;
+        *exponent = 8;
+        break;
+      }  // else fallthrough
+    case 26:
+    case 25:
+    case 24:
+      if (kTen7 <= number) {
+        *power = kTen7;
+        *exponent = 7;
+        break;
+      }  // else fallthrough
+    case 23:
+    case 22:
+    case 21:
+    case 20:
+      if (kTen6 <= number) {
+        *power = kTen6;
+        *exponent = 6;
+        break;
+      }  // else fallthrough
+    case 19:
+    case 18:
+    case 17:
+      if (kTen5 <= number) {
+        *power = kTen5;
+        *exponent = 5;
+        break;
+      }  // else fallthrough
+    case 16:
+    case 15:
+    case 14:
+      if (kTen4 <= number) {
+        *power = kTen4;
+        *exponent = 4;
+        break;
+      }  // else fallthrough
+    case 13:
+    case 12:
+    case 11:
+    case 10:
+      if (1000 <= number) {
+        *power = 1000;
+        *exponent = 3;
+        break;
+      }  // else fallthrough
+    case 9:
+    case 8:
+    case 7:
+      if (100 <= number) {
+        *power = 100;
+        *exponent = 2;
+        break;
+      }  // else fallthrough
+    case 6:
+    case 5:
+    case 4:
+      if (10 <= number) {
+        *power = 10;
+        *exponent = 1;
+        break;
+      }  // else fallthrough
+    case 3:
+    case 2:
+    case 1:
+      if (1 <= number) {
+        *power = 1;
+        *exponent = 0;
+        break;
+      }  // else fallthrough
+    case 0:
+      *power = 0;
+      *exponent = -1;
+      break;
+    default:
+      // Following assignments are here to silence compiler warnings.
+      *power = 0;
+      *exponent = 0;
+      UNREACHABLE();
+  }
+}
+
+
+// Same comments as for DigitGen but with additional precondition:
+//    -60 <= w.e() <= -32
+//
+// Say, for the sake of example, that
+//   w.e() == -48, and w.f() == 0x1234567890abcdef
+// w's value can be computed by w.f() * 2^w.e()
+// We can obtain w's integral digits by simply shifting w.f() by -w.e().
+//  -> w's integral part is 0x1234
+//  w's fractional part is therefore 0x567890abcdef.
+// Printing w's integral part is easy (simply print 0x1234 in decimal).
+// In order to print its fraction we repeatedly multiply the fraction by 10 and
+// get each digit. Example the first digit after the comma would be computed by
+//   (0x567890abcdef * 10) >> 48. -> 3
+// The whole thing becomes slightly more complicated because we want to stop
+// once we have enough digits. That is, once the digits inside the buffer
+// represent 'w' we can stop. Everything inside the interval low - high
+// represents w. However we have to pay attention to low, high and w's
+// imprecision.
+template<int alpha, int gamma>
+bool Grisu3<alpha, gamma>::DigitGen_m60_m32(DiyFp low,
+                                            DiyFp w,
+                                            DiyFp high,
+                                            char* buffer,
+                                            int* length,
+                                            int* kappa) {
+  // low, w and high are imprecise, but by less than one ulp (unit in the last
+  // place).
+  // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
+  // the new numbers are outside of the interval we want the final
+  // representation to lie in.
+  // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
+  // numbers that are certain to lie in the interval. We will use this fact
+  // later on.
+  // We will now start by generating the digits within the uncertain
+  // interval. Later we will weed out representations that lie outside the safe
+  // interval and thus _might_ lie outside the correct interval.
+  uint64_t unit = 1;
+  DiyFp too_low = DiyFp(low.f() - unit, low.e());
+  DiyFp too_high = DiyFp(high.f() + unit, high.e());
+  // too_low and too_high are guaranteed to lie outside the interval we want the
+  // generated number in.
+  DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
+  // We now cut the input number into two parts: the integral digits and the
+  // fractionals. We will not write any decimal separator though, but adapt
+  // kappa instead.
+  // Reminder: we are currently computing the digits (stored inside the buffer)
+  // such that:   too_low < buffer * 10^kappa < too_high
+  // We use too_high for the digit_generation and stop as soon as possible.
+  // If we stop early we effectively round down.
+  DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
+  // Division by one is a shift.
+  uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
+  // Modulo by one is an and.
+  uint64_t fractionals = too_high.f() & (one.f() - 1);
+  uint32_t divider;
+  int divider_exponent;
+  BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+                  &divider, &divider_exponent);
+  *kappa = divider_exponent + 1;
+  *length = 0;
+  // Loop invariant: buffer = too_high / 10^kappa  (integer division)
+  // The invariant holds for the first iteration: kappa has been initialized
+  // with the divider exponent + 1. And the divider is the biggest power of ten
+  // that is smaller than integrals.
+  while (*kappa > 0) {
+    int digit = integrals / divider;
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    integrals %= divider;
+    (*kappa)--;
+    // Note that kappa now equals the exponent of the divider and that the
+    // invariant thus holds again.
+    uint64_t rest =
+        (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+    // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
+    // Reminder: unsafe_interval.e() == one.e()
+    if (rest < unsafe_interval.f()) {
+      // Rounding down (by not emitting the remaining digits) yields a number
+      // that lies within the unsafe interval.
+      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
+                       unsafe_interval.f(), rest,
+                       static_cast<uint64_t>(divider) << -one.e(), unit);
+    }
+    divider /= 10;
+  }
+
+  // The integrals have been generated. We are at the point of the decimal
+  // separator. In the following loop we simply multiply the remaining digits by
+  // 10 and divide by one. We just need to pay attention to multiply associated
+  // data (like the interval or 'unit'), too.
+  // Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
+  // increase its (imaginary) exponent. At the same time we decrease the
+  // divider's (one's) exponent and shift its significand.
+  // Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
+  //      fractionals.f *= 10;
+  //      fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
+  //      one.f >>= 1; one.e++;                 // value remains unchanged.
+  //      and we have again fractionals.e == one.e which allows us to divide
+  //           fractionals.f() by one.f()
+  // We simply combine the *= 10 and the >>= 1.
+  while (true) {
+    fractionals *= 5;
+    unit *= 5;
+    unsafe_interval.set_f(unsafe_interval.f() * 5);
+    unsafe_interval.set_e(unsafe_interval.e() + 1);  // Will be optimized out.
+    one.set_f(one.f() >> 1);
+    one.set_e(one.e() + 1);
+    // Integer division by one.
+    int digit = static_cast<int>(fractionals >> -one.e());
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    fractionals &= one.f() - 1;  // Modulo by one.
+    (*kappa)--;
+    if (fractionals < unsafe_interval.f()) {
+      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
+                       unsafe_interval.f(), fractionals, one.f(), unit);
+    }
+  }
+}
+
+
+// Rounds the given generated digits in the buffer and weeds out generated
+// digits that are not in the safe interval, or where we cannot find a rounded
+// representation.
+// Input: * buffer containing the digits of too_high / 10^kappa
+//        * the buffer's length
+//        * distance_too_high_w == (too_high - w).f() * unit
+//        * unsafe_interval == (too_high - too_low).f() * unit
+//        * rest = (too_high - buffer * 10^kappa).f() * unit
+//        * ten_kappa = 10^kappa * unit
+//        * unit = the common multiplier
+// Output: returns true on success.
+//    Modifies the generated digits in the buffer to approach (round towards) w.
+template<int alpha, int gamma>
+bool Grisu3<alpha, gamma>::RoundWeed(char* buffer,
+                                     int length,
+                                     uint64_t distance_too_high_w,
+                                     uint64_t unsafe_interval,
+                                     uint64_t rest,
+                                     uint64_t ten_kappa,
+                                     uint64_t unit) {
+  uint64_t small_distance = distance_too_high_w - unit;
+  uint64_t big_distance = distance_too_high_w + unit;
+  // Let w- = too_high - big_distance, and
+  //     w+ = too_high - small_distance.
+  // Note: w- < w < w+
+  //
+  // The real w (* unit) must lie somewhere inside the interval
+  // ]w-; w+[ (often written as "(w-; w+)")
+
+  // Basically the buffer currently contains a number in the unsafe interval
+  // ]too_low; too_high[ with too_low < w < too_high
+  //
+  // By generating the digits of too_high we got the biggest last digit.
+  // In the case that w+ < buffer < too_high we try to decrement the buffer.
+  // This way the buffer approaches (rounds towards) w.
+  // There are 3 conditions that stop the decrementation process:
+  //   1) the buffer is already below w+
+  //   2) decrementing the buffer would make it leave the unsafe interval
+  //   3) decrementing the buffer would yield a number below w+ and farther away
+  //      than the current number. In other words:
+  //                       (buffer{-1} < w+) && w+ - buffer{-1} > buffer - w+
+  // Instead of using the buffer directly we use its distance to too_high.
+  // Conceptually rest ~= too_high - buffer
+  while (rest < small_distance &&  // Negated condition 1
+         unsafe_interval - rest >= ten_kappa &&  // Negated condition 2
+         (rest + ten_kappa < small_distance ||  // buffer{-1} > w+
+          small_distance - rest >= rest + ten_kappa - small_distance)) {
+    buffer[length - 1]--;
+    rest += ten_kappa;
+  }
+
+  // We have approached w+ as much as possible. We now test if approaching w-
+  // would require changing the buffer. If yes, then we have two possible
+  // representations close to w, but we cannot decide which one is closer.
+  if (rest < big_distance &&
+      unsafe_interval - rest >= ten_kappa &&
+      (rest + ten_kappa < big_distance ||
+       big_distance - rest > rest + ten_kappa - big_distance)) {
+    return false;
+  }
+
+  // Weeding test.
+  //   The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
+  //   Since too_low = too_high - unsafe_interval this is equivalent too
+  //      [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
+  //   Conceptually we have: rest ~= too_high - buffer
+  return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
+}
+
+
+bool grisu3(double v, char* buffer, int* sign, int* length, int* point) {
+  ASSERT(v != 0);
+  ASSERT(!Double(v).IsSpecial());
+
+  if (v < 0) {
+    v = -v;
+    *sign = 1;
+  } else {
+    *sign = 0;
+  }
+  int decimal_exponent;
+  bool result = Grisu3<-60, -32>::grisu3(v, buffer, length, &decimal_exponent);
+  *point = *length + decimal_exponent;
+  buffer[*length] = '\0';
+  return result;
+}
+
+} }  // namespace v8::internal

src/grisu3.h

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef V8_GRISU3_H_
+#define V8_GRISU3_H_
+
+namespace v8 {
+namespace internal {
+
+// Grisu3 will produce at most kGrisu3MaximalLength digits. This does not
+// include the terminating '\0' character.
+static const int kGrisu3MaximalLength = 17;
+
+// Provides a decimal representation of v.
+//   v must satisfy v != 0 and it must not be Infinity or NaN.
+// Returns true if it succeeds, otherwise the result can not be trusted.
+// There will be *length digits inside the buffer followed by a null terminator.
+// If the function returns true then
+//   v == (double) (buffer * 10^(decimal-point - length)).
+// The digits in the buffer are the shortest representation possible: no
+// 0.099999999999 instead of 0.1.
+// The last digit will be closest to the actual v. That is, even if several
+// digits might correctly yield 'v' when read again, the buffer will contain the
+// one closest to v.
+// The variable 'sign' will be '0' if the given number is positive, and '1'
+//   otherwise.
+bool grisu3(double d, char* buffer, int* sign, int* length, int* decimal_point);
+
+} }  // namespace v8::internal
+
+#endif  // V8_GRISU3_H_

test/cctest/SConscript

@@ -34,6 +34,7 @@ Import('context object_files')
 
 SOURCES = {
   'all': [
+    'gay_shortest.cc',
     'test-accessors.cc',
     'test-alloc.cc',
     'test-api.cc',
@@ -43,8 +44,11 @@ SOURCES = {
     'test-dataflow.cc',
     'test-debug.cc',
     'test-decls.cc',
+    'test-diy_fp.cc',
+    'test-double.cc',
     'test-flags.cc',
     'test-func-name-inference.cc',
+    'test-grisu3.cc',
     'test-hashmap.cc',
     'test-heap.cc',
     'test-heap-profiler.cc',

test/cctest/gay_shortest.h

+// Copyright 2006-2008 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef GAY_SHORTEST_H_
+#define GAY_SHORTEST_H_
+
+namespace v8 {
+namespace internal {
+
+struct GayShortest {
+  double v;
+  const char* representation;
+  int decimal_point;
+};
+
+Vector<const GayShortest> PrecomputedShortestRepresentations();
+
+} }  // namespace v8::internal
+
+#endif  // GAY_SHORTEST_H_

test/cctest/test-diy_fp.cc

+// Copyright 2006-2008 the V8 project authors. All rights reserved.
+
+#include <stdlib.h>
+
+#include "v8.h"
+
+#include "platform.h"
+#include "cctest.h"
+#include "diy_fp.h"
+
+
+using namespace v8::internal;
+
+
+TEST(Subtract) {
+  DiyFp diy_fp1 = DiyFp(3, 0);
+  DiyFp diy_fp2 = DiyFp(1, 0);
+  DiyFp diff = DiyFp::Minus(diy_fp1, diy_fp2);
+
+  CHECK(2 == diff.f());  // NOLINT
+  CHECK_EQ(0, diff.e());
+  diy_fp1.Subtract(diy_fp2);
+  CHECK(2 == diy_fp1.f());  // NOLINT
+  CHECK_EQ(0, diy_fp1.e());
+}
+
+
+TEST(Multiply) {
+  DiyFp diy_fp1 = DiyFp(3, 0);
+  DiyFp diy_fp2 = DiyFp(2, 0);
+  DiyFp product = DiyFp::Times(diy_fp1, diy_fp2);
+
+  CHECK(0 == product.f());  // NOLINT
+  CHECK_EQ(64, product.e());
+  diy_fp1.Multiply(diy_fp2);
+  CHECK(0 == diy_fp1.f());  // NOLINT
+  CHECK_EQ(64, diy_fp1.e());
+
+  diy_fp1 = DiyFp(V8_2PART_UINT64_C(0x80000000, 00000000), 11);
+  diy_fp2 = DiyFp(2, 13);
+  product = DiyFp::Times(diy_fp1, diy_fp2);
+  CHECK(1 == product.f());  // NOLINT
+  CHECK_EQ(11 + 13 + 64, product.e());
+
+  // Test rounding.
+  diy_fp1 = DiyFp(V8_2PART_UINT64_C(0x80000000, 00000001), 11);
+  diy_fp2 = DiyFp(1, 13);
+  product = DiyFp::Times(diy_fp1, diy_fp2);
+  CHECK(1 == product.f());  // NOLINT
+  CHECK_EQ(11 + 13 + 64, product.e());
+
+  diy_fp1 = DiyFp(V8_2PART_UINT64_C(0x7fffffff, ffffffff), 11);
+  diy_fp2 = DiyFp(1, 13);
+  product = DiyFp::Times(diy_fp1, diy_fp2);
+  CHECK(0 == product.f());  // NOLINT
+  CHECK_EQ(11 + 13 + 64, product.e());
+
+  // Halfway cases are allowed to round either way. So don't check for it.
+
+  // Big numbers.
+  diy_fp1 = DiyFp(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF), 11);
+  diy_fp2 = DiyFp(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF), 13);
+  // 128bit result: 0xfffffffffffffffe0000000000000001
+  product = DiyFp::Times(diy_fp1, diy_fp2);
+  CHECK(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFe) == product.f());
+  CHECK_EQ(11 + 13 + 64, product.e());
+}

test/cctest/test-double.cc

+// Copyright 2006-2008 the V8 project authors. All rights reserved.
+
+#include <stdlib.h>
+
+#include "v8.h"
+
+#include "platform.h"
+#include "cctest.h"
+#include "diy_fp.h"
+#include "double.h"
+
+
+using namespace v8::internal;
+
+
+TEST(Uint64Conversions) {
+  // Start by checking the byte-order.
+  uint64_t ordered = V8_2PART_UINT64_C(0x01234567, 89ABCDEF);
+  CHECK_EQ(3512700564088504e-318, Double(ordered).value());
+
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  CHECK_EQ(5e-324, Double(min_double64).value());
+
+  uint64_t max_double64 = V8_2PART_UINT64_C(0x7fefffff, ffffffff);
+  CHECK_EQ(1.7976931348623157e308, Double(max_double64).value());
+}
+
+TEST(AsDiyFp) {
+  uint64_t ordered = V8_2PART_UINT64_C(0x01234567, 89ABCDEF);
+  DiyFp diy_fp = Double(ordered).AsDiyFp();
+  CHECK_EQ(0x12 - 0x3FF - 52, diy_fp.e());
+  // The 52 mantissa bits, plus the implicit 1 in bit 52 as a UINT64.
+  CHECK(V8_2PART_UINT64_C(0x00134567, 89ABCDEF) == diy_fp.f());  // NOLINT
+
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  diy_fp = Double(min_double64).AsDiyFp();
+  CHECK_EQ(-0x3FF - 52 + 1, diy_fp.e());
+  // This is a denormal; so no hidden bit.
+  CHECK(1 == diy_fp.f());  // NOLINT
+
+  uint64_t max_double64 = V8_2PART_UINT64_C(0x7fefffff, ffffffff);
+  diy_fp = Double(max_double64).AsDiyFp();
+  CHECK_EQ(0x7FE - 0x3FF - 52, diy_fp.e());
+  CHECK(V8_2PART_UINT64_C(0x001fffff, ffffffff) == diy_fp.f());  // NOLINT
+}
+
+
+TEST(AsNormalizedDiyFp) {
+  uint64_t ordered = V8_2PART_UINT64_C(0x01234567, 89ABCDEF);
+  DiyFp diy_fp = Double(ordered).AsNormalizedDiyFp();
+  CHECK_EQ(0x12 - 0x3FF - 52 - 11, diy_fp.e());
+  CHECK((V8_2PART_UINT64_C(0x00134567, 89ABCDEF) << 11) ==
+        diy_fp.f());  // NOLINT
+
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  diy_fp = Double(min_double64).AsNormalizedDiyFp();
+  CHECK_EQ(-0x3FF - 52 + 1 - 63, diy_fp.e());
+  // This is a denormal; so no hidden bit.
+  CHECK(V8_2PART_UINT64_C(0x80000000, 00000000) == diy_fp.f());  // NOLINT
+
+  uint64_t max_double64 = V8_2PART_UINT64_C(0x7fefffff, ffffffff);
+  diy_fp = Double(max_double64).AsNormalizedDiyFp();
+  CHECK_EQ(0x7FE - 0x3FF - 52 - 11, diy_fp.e());
+  CHECK((V8_2PART_UINT64_C(0x001fffff, ffffffff) << 11) ==
+        diy_fp.f());  // NOLINT
+}
+
+
+TEST(IsDenormal) {
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  CHECK(Double(min_double64).IsDenormal());
+  uint64_t bits = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+  CHECK(Double(bits).IsDenormal());
+  bits = V8_2PART_UINT64_C(0x00100000, 00000000);
+  CHECK(!Double(bits).IsDenormal());
+}
+
+
+TEST(IsSpecial) {
+  CHECK(Double(V8_INFINITY).IsSpecial());
+  CHECK(Double(-V8_INFINITY).IsSpecial());
+  CHECK(Double(OS::nan_value()).IsSpecial());
+  uint64_t bits = V8_2PART_UINT64_C(0xFFF12345, 00000000);
+  CHECK(Double(bits).IsSpecial());
+  // Denormals are not special:
+  CHECK(!Double(5e-324).IsSpecial());
+  CHECK(!Double(-5e-324).IsSpecial());
+  // And some random numbers:
+  CHECK(!Double(0.0).IsSpecial());
+  CHECK(!Double(-0.0).IsSpecial());
+  CHECK(!Double(1.0).IsSpecial());
+  CHECK(!Double(-1.0).IsSpecial());
+  CHECK(!Double(1000000.0).IsSpecial());
+  CHECK(!Double(-1000000.0).IsSpecial());
+  CHECK(!Double(1e23).IsSpecial());
+  CHECK(!Double(-1e23).IsSpecial());
+  CHECK(!Double(1.7976931348623157e308).IsSpecial());
+  CHECK(!Double(-1.7976931348623157e308).IsSpecial());
+}
+
+
+TEST(IsInfinite) {
+  CHECK(Double(V8_INFINITY).IsInfinite());
+  CHECK(Double(-V8_INFINITY).IsInfinite());
+  CHECK(!Double(OS::nan_value()).IsInfinite());
+  CHECK(!Double(0.0).IsInfinite());
+  CHECK(!Double(-0.0).IsInfinite());
+  CHECK(!Double(1.0).IsInfinite());
+  CHECK(!Double(-1.0).IsInfinite());
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  CHECK(!Double(min_double64).IsInfinite());
+}
+
+
+TEST(IsNan) {
+  CHECK(Double(OS::nan_value()).IsNan());
+  uint64_t other_nan = V8_2PART_UINT64_C(0xFFFFFFFF, 00000001);
+  CHECK(Double(other_nan).IsNan());
+  CHECK(!Double(V8_INFINITY).IsNan());
+  CHECK(!Double(-V8_INFINITY).IsNan());
+  CHECK(!Double(0.0).IsNan());
+  CHECK(!Double(-0.0).IsNan());
+  CHECK(!Double(1.0).IsNan());
+  CHECK(!Double(-1.0).IsNan());
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  CHECK(!Double(min_double64).IsNan());
+}
+
+
+TEST(Sign) {
+  CHECK_EQ(1, Double(1.0).Sign());
+  CHECK_EQ(1, Double(V8_INFINITY).Sign());
+  CHECK_EQ(-1, Double(-V8_INFINITY).Sign());
+  CHECK_EQ(1, Double(0.0).Sign());
+  CHECK_EQ(-1, Double(-0.0).Sign());
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  CHECK_EQ(1, Double(min_double64).Sign());
+}
+
+
+TEST(NormalizedBoundaries) {
+  DiyFp boundary_plus;
+  DiyFp boundary_minus;
+  DiyFp diy_fp = Double(1.5).AsNormalizedDiyFp();
+  Double(1.5).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  // 1.5 does not have a significand of the form 2^p (for some p).
+  // Therefore its boundaries are at the same distance.
+  CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f());
+  CHECK((1 << 10) == diy_fp.f() - boundary_minus.f());  // NOLINT
+
+  diy_fp = Double(1.0).AsNormalizedDiyFp();
+  Double(1.0).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  // 1.0 does have a significand of the form 2^p (for some p).
+  // Therefore its lower boundary is twice as close as the upper boundary.
+  CHECK_GT(boundary_plus.f() - diy_fp.f(), diy_fp.f() - boundary_minus.f());
+  CHECK((1 << 9) == diy_fp.f() - boundary_minus.f());  // NOLINT
+  CHECK((1 << 10) == boundary_plus.f() - diy_fp.f());  // NOLINT
+
+  uint64_t min_double64 = V8_2PART_UINT64_C(0x00000000, 00000001);
+  diy_fp = Double(min_double64).AsNormalizedDiyFp();
+  Double(min_double64).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  // min-value does not have a significand of the form 2^p (for some p).
+  // Therefore its boundaries are at the same distance.
+  CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f());
+  // Denormals have their boundaries much closer.
+  CHECK((static_cast<uint64_t>(1) << 62) ==
+        diy_fp.f() - boundary_minus.f());  // NOLINT
+
+  uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
+  diy_fp = Double(smallest_normal64).AsNormalizedDiyFp();
+  Double(smallest_normal64).NormalizedBoundaries(&boundary_minus,
+                                                 &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  // Even though the significand is of the form 2^p (for some p), its boundaries
+  // are at the same distance. (This is the only exception).
+  CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f());
+  CHECK((1 << 10) == diy_fp.f() - boundary_minus.f());  // NOLINT
+
+  uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+  diy_fp = Double(largest_denormal64).AsNormalizedDiyFp();
+  Double(largest_denormal64).NormalizedBoundaries(&boundary_minus,
+                                                  &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f());
+  CHECK((1 << 11) == diy_fp.f() - boundary_minus.f());  // NOLINT
+
+  uint64_t max_double64 = V8_2PART_UINT64_C(0x7fefffff, ffffffff);
+  diy_fp = Double(max_double64).AsNormalizedDiyFp();
+  Double(max_double64).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  CHECK_EQ(diy_fp.e(), boundary_minus.e());
+  CHECK_EQ(diy_fp.e(), boundary_plus.e());
+  // max-value does not have a significand of the form 2^p (for some p).
+  // Therefore its boundaries are at the same distance.
+  CHECK(diy_fp.f() - boundary_minus.f() == boundary_plus.f() - diy_fp.f());
+  CHECK((1 << 10) == diy_fp.f() - boundary_minus.f());  // NOLINT
+}

test/cctest/test-grisu3.cc

+// Copyright 2006-2008 the V8 project authors. All rights reserved.
+
+#include <stdlib.h>
+
+#include "v8.h"
+
+#include "platform.h"
+#include "cctest.h"
+#include "diy_fp.h"
+#include "double.h"
+#include "gay_shortest.h"
+#include "grisu3.h"
+
+using namespace v8::internal;
+
+static const int kBufferSize = 100;
+
+TEST(GrisuVariousDoubles) {
+  char buffer[kBufferSize];
+  int sign;
+  int length;
+  int point;
+  int status;
+
+  double min_double = 5e-324;
+  status = grisu3(min_double, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("5", buffer);
+  CHECK_EQ(-323, point);
+
+  double max_double = 1.7976931348623157e308;
+  status = grisu3(max_double, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("17976931348623157", buffer);
+  CHECK_EQ(309, point);
+
+  status = grisu3(4294967272.0, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("4294967272", buffer);
+  CHECK_EQ(10, point);
+
+  status = grisu3(4.1855804968213567e298, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("4185580496821357", buffer);
+  CHECK_EQ(299, point);
+
+  status = grisu3(5.5626846462680035e-309, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("5562684646268003", buffer);
+  CHECK_EQ(-308, point);
+
+  status = grisu3(2147483648.0, buffer, &sign, &length, &point);
+  CHECK(status);
+  CHECK_EQ(0, sign);
+  CHECK_EQ("2147483648", buffer);
+  CHECK_EQ(10, point);
+
+  status = grisu3(3.5844466002796428e+298, buffer, &sign, &length, &point);
+  if (status) {  // Not all grisu3 variants manage to compute this number.
+    CHECK_EQ("35844466002796428", buffer);
+    CHECK_EQ(0, sign);
+    CHECK_EQ(299, point);
+  }
+
+  uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
+  double v = Double(smallest_normal64).value();
+  status = grisu3(v, buffer, &sign, &length, &point);
+  if (status) {
+    CHECK_EQ(0, sign);
+    CHECK_EQ("22250738585072014", buffer);
+    CHECK_EQ(-307, point);
+  }
+
+  uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+  v = Double(largest_denormal64).value();
+  status = grisu3(v, buffer, &sign, &length, &point);
+  if (status) {
+    CHECK_EQ(0, sign);
+    CHECK_EQ("2225073858507201", buffer);
+    CHECK_EQ(-307, point);
+  }
+}
+
+
+TEST(GrisuGayShortest) {
+  char buffer[kBufferSize];
+  bool status;
+  int sign;
+  int length;
+  int point;
+  int succeeded = 0;
+  int total = 0;
+  bool needed_max_length = false;
+
+  Vector<const GayShortest> precomputed = PrecomputedShortestRepresentations();
+  for (int i = 0; i < precomputed.length(); ++i) {
+    const GayShortest current_test = precomputed[i];
+    total++;
+    double v = current_test.v;
+    status = grisu3(v, buffer, &sign, &length, &point);
+    CHECK_GE(kGrisu3MaximalLength, length);
+    if (!status) continue;
+    if (length == kGrisu3MaximalLength) needed_max_length = true;
+    succeeded++;
+    CHECK_EQ(0, sign);  // All precomputed numbers are positive.
+    CHECK_EQ(current_test.decimal_point, point);
+    CHECK_EQ(current_test.representation, buffer);
+  }
+  CHECK_GT(succeeded*1.0/total, 0.99);
+  CHECK(needed_max_length);
+}

tools/generate-ten-powers.scm

+;; Copyright 2010 the V8 project authors. All rights reserved.
+;; Redistribution and use in source and binary forms, with or without
+;; modification, are permitted provided that the following conditions are
+;; met:
+;;
+;;     * Redistributions of source code must retain the above copyright
+;;       notice, this list of conditions and the following disclaimer.
+;;     * Redistributions in binary form must reproduce the above
+;;       copyright notice, this list of conditions and the following
+;;       disclaimer in the documentation and/or other materials provided
+;;       with the distribution.
+;;     * Neither the name of Google Inc. nor the names of its
+;;       contributors may be used to endorse or promote products derived
+;;       from this software without specific prior written permission.
+;;
+;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+;; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+;; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+;; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+;; OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+;; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+;; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+;; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+;; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+;; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+;; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+;; This is a Scheme script for the Bigloo compiler. Bigloo must be compiled with
+;; support for bignums. The compilation of the script can be done as follows:
+;;   bigloo -static-bigloo -o generate-ten-powers generate-ten-powers.scm
+;;  
+;; Generate approximations of 10^k.
+
+(module gen-ten-powers
+   (static (class Cached-Fast
+	      v::bignum
+	      e::bint
+	      exact?::bool))
+   (main my-main))
+
+
+;;----------------bignum shifts -----------------------------------------------
+(define (bit-lshbx::bignum x::bignum by::bint)
+   (if (<fx by 0)
+       #z0
+       (*bx x (exptbx #z2 (fixnum->bignum by)))))
+
+(define (bit-rshbx::bignum x::bignum by::bint)
+   (if (<fx by 0)
+       #z0
+       (/bx x (exptbx #z2 (fixnum->bignum by)))))
+
+;;----------------the actual power generation -------------------------------
+
+;; e should be an indication. it might be too small.
+(define (round-n-cut n e nb-bits)
+   (define max-container (- (bit-lshbx #z1 nb-bits) 1))
+   (define (round n)
+      (case *round*
+	 ((down) n)
+	 ((up)
+	  (+bx n
+	       ;; with the -1 it will only round up if the cut off part is
+	       ;; non-zero
+	       (-bx (bit-lshbx #z1
+			       (-fx (+fx e nb-bits) 1))
+		    #z1)))
+	 ((round)
+	  (+bx n
+	       (bit-lshbx #z1
+			  (-fx (+fx e nb-bits) 2))))))
+   (let* ((shift (-fx (+fx e nb-bits) 1))
+	  (cut (bit-rshbx (round n) shift))
+	  (exact? (=bx n (bit-lshbx cut shift))))
+      (if (<=bx cut max-container)
+	  (values cut e exact?)
+	  (round-n-cut n (+fx e 1) nb-bits))))
+
+(define (rounded-/bx x y)
+   (case *round*
+      ((down)  (/bx x y))
+      ((up)    (+bx (/bx x y) #z1))
+      ((round) (let ((tmp (/bx (*bx #z2 x) y)))
+		  (if (zerobx? (remainderbx tmp #z2))
+		      (/bx tmp #z2)
+		      (+bx (/bx tmp #z2) #z1))))))
+
+(define (generate-powers from to mantissa-size)
+   (let* ((nb-bits mantissa-size)
+	  (offset (- from))
+	  (nb-elements (+ (- from) to 1))
+	  (vec (make-vector nb-elements))
+	  (max-container (- (bit-lshbx #z1 nb-bits) 1)))
+      ;; the negative ones. 10^-1, 10^-2, etc.
+      ;; We already know, that we can't be exact, so exact? will always be #f.
+      ;; Basically we will have a ten^i that we will *10 at each iteration. We
+      ;; want to create the matissa of 1/ten^i. However the mantissa must be
+      ;; normalized (start with a 1). -> we have to shift the number.
+      ;; We shift by multiplying with two^e. -> We encode two^e*(1/ten^i) ==
+      ;;  two^e/ten^i.
+      (let loop ((i 1)
+		 (ten^i #z10)
+		 (two^e #z1)
+		 (e 0))
+	 (unless (< (- i) from)
+	    (if (>bx (/bx (*bx #z2 two^e) ten^i) max-container)
+		;; another shift would make the number too big. We are
+		;; hence normalized now.
+		(begin
+		   (vector-set! vec (-fx offset i)
+				(instantiate::Cached-Fast
+				   (v (rounded-/bx two^e ten^i))
+				   (e (negfx e))
+				   (exact? #f)))
+		   (loop (+fx i 1) (*bx ten^i #z10) two^e e))
+		(loop i ten^i (bit-lshbx two^e 1) (+fx e 1)))))
+      ;; the positive ones 10^0, 10^1, etc.
+      ;; start with 1.0. mantissa: 10...0 (1 followed by nb-bits-1 bits)
+      ;;      -> e = -(nb-bits-1)
+      ;; exact? is true when the container can still hold the complete 10^i
+      (let loop ((i 0)
+		 (n (bit-lshbx #z1 (-fx nb-bits 1)))
+		 (e (-fx 1 nb-bits)))
+	 (when (<= i to)
+	    (receive (cut e exact?)
+	       (round-n-cut n e nb-bits)
+	       (vector-set! vec (+fx i offset)
+			    (instantiate::Cached-Fast
+			       (v cut)
+			       (e e)
+			       (exact? exact?)))
+	       (loop (+fx i 1) (*bx n #z10) e))))
+      vec))
+
+(define (print-c powers from to struct-type
+		 cache-name max-distance-name offset-name macro64)
+   (define (display-power power k)
+      (with-access::Cached-Fast power (v e exact?)
+	 (let ((tmp-p (open-output-string)))
+	    ;; really hackish way of getting the digits
+	    (display (format "~x" v) tmp-p)
+	    (let ((str (close-output-port tmp-p)))
+	       (printf "  {~a(0x~a, ~a), ~a, ~a},\n"
+		       macro64
+		       (substring str 0 8)
+		       (substring str 8 16)
+		       e
+		       k)))))
+   (define (print-powers-reduced n)
+      (print "static const " struct-type " " cache-name
+	     "(" n ")"
+	     "[] = {")
+      (let loop ((i 0)
+		 (nb-elements 0)
+		 (last-e 0)
+		 (max-distance 0))
+	 (cond
+	    ((>= i (vector-length powers))
+	     (print "  };")
+	     (print "static const int " max-distance-name "(" n ") = "
+		 max-distance ";")
+	     (print "// nb elements (" n "): " nb-elements))
+	    (else
+	     (let* ((power (vector-ref powers i))
+		    (e (Cached-Fast-e power)))
+	     (display-power power (+ i from))
+	     (loop (+ i n)
+		   (+ nb-elements 1)
+		   e
+		   (cond
+		      ((=fx i 0) max-distance)
+		      ((> (- e last-e) max-distance) (- e last-e))
+		      (else max-distance))))))))
+   (print "// Copyright 2010 the V8 project authors. All rights reserved.")
+   (print "// ------------ GENERATED FILE ----------------")
+   (print "// command used:")
+   (print "// "
+	  (apply string-append (map (lambda (str)
+				       (string-append " " str))
+				    *main-args*))
+	  "  // NOLINT")
+   (print)
+   (print
+    "// This file is intended to be included inside another .h or .cc files\n"
+    "// with the following defines set:\n"
+    "//  GRISU_CACHE_STRUCT: should expand to the name of a struct that will\n"
+    "//   hold the cached powers of ten. Each entry will hold a 64-bit\n"
+    "//   significand, a 16-bit signed binary exponent, and a 16-bit\n"
+    "//   signed decimal exponent. Each entry will be constructed as follows:\n"
+    "//      { significand, binary_exponent, decimal_exponent }.\n"
+    "//  GRISU_CACHE_NAME(i): generates the name for the different caches.\n"
+    "//   The parameter i will be a number in the range 1-20. A cache will\n"
+    "//   hold every i'th element of a full cache. GRISU_CACHE_NAME(1) will\n"
+    "//   thus hold all elements. The higher i the fewer elements it has.\n"
+    "//   Ideally the user should only reference one cache and let the\n"
+    "//   compiler remove the unused ones.\n"
+    "//  GRISU_CACHE_MAX_DISTANCE(i): generates the name for the maximum\n"
+    "//   binary exponent distance between all elements of a given cache.\n"
+    "//  GRISU_CACHE_OFFSET: is used as variable name for the decimal\n"
+    "//   exponent offset. It is equal to -cache[0].decimal_exponent.\n"
+    "//  GRISU_UINT64_C: used to construct 64-bit values in a platform\n"
+    "//   independent way. In order to encode 0x123456789ABCDEF0 the macro\n"
+    "//   will be invoked as follows: GRISU_UINT64_C(0x12345678,9ABCDEF0).\n")
+   (print)
+   (print-powers-reduced 1)
+   (print-powers-reduced 2)
+   (print-powers-reduced 3)
+   (print-powers-reduced 4)
+   (print-powers-reduced 5)
+   (print-powers-reduced 6)
+   (print-powers-reduced 7)
+   (print-powers-reduced 8)
+   (print-powers-reduced 9)
+   (print-powers-reduced 10)
+   (print-powers-reduced 11)
+   (print-powers-reduced 12)
+   (print-powers-reduced 13)
+   (print-powers-reduced 14)
+   (print-powers-reduced 15)
+   (print-powers-reduced 16)
+   (print-powers-reduced 17)
+   (print-powers-reduced 18)
+   (print-powers-reduced 19)
+   (print-powers-reduced 20)
+   (print "static const int GRISU_CACHE_OFFSET = " (- from) ";"))
+
+;;----------------main --------------------------------------------------------
+(define *main-args* #f)
+(define *mantissa-size* #f)
+(define *dest* #f)
+(define *round* #f)
+(define *from* #f)
+(define *to* #f)
+
+(define (my-main args)
+   (set! *main-args* args)
+   (args-parse (cdr args)
+      (section "Help")
+      (("?") (args-parse-usage #f))
+      ((("-h" "--help") (help "?, -h, --help" "This help message"))
+       (args-parse-usage #f))
+      (section "Misc")
+      (("-o" ?file (help "The output file"))
+       (set! *dest* file))
+      (("--mantissa-size" ?size (help "Container-size in bits"))
+       (set! *mantissa-size* (string->number size)))
+      (("--round" ?direction (help "Round bignums (down, round or up)"))
+       (set! *round* (string->symbol direction)))
+      (("--from" ?from (help "start at 10^from"))
+       (set! *from* (string->number from)))
+      (("--to" ?to (help "go up to 10^to"))
+       (set! *to* (string->number to)))
+      (else
+       (print "Illegal argument `" else "'. Usage:")
+       (args-parse-usage #f)))
+   (when (not *from*)
+      (error "generate-ten-powers"
+	     "Missing from"
+	     #f))
+   (when (not *to*)
+      (error "generate-ten-powers"
+	     "Missing to"
+	     #f))
+   (when (not *mantissa-size*)
+      (error "generate-ten-powers"
+	     "Missing mantissa size"
+	     #f))
+   (when (not (memv *round* '(up down round)))
+      (error "generate-ten-powers"
+	     "Missing round-method"
+	     *round*))
+
+   (let ((dividers (generate-powers *from* *to* *mantissa-size*))
+	 (p (if (not *dest*)
+		(current-output-port)
+		(open-output-file *dest*))))
+      (unwind-protect
+	 (with-output-to-port p
+	    (lambda ()
+	       (print-c dividers *from* *to*
+			"GRISU_CACHE_STRUCT" "GRISU_CACHE_NAME"
+			"GRISU_CACHE_MAX_DISTANCE" "GRISU_CACHE_OFFSET"
+			"GRISU_UINT64_C"
+			)))
+	 (if *dest*
+	     (close-output-port p)))))

tools/gyp/v8.gyp

@@ -229,6 +229,7 @@
         '../../src/builtins.cc',
         '../../src/builtins.h',
         '../../src/bytecodes-irregexp.h',
+        '../../src/cached_powers.h',
         '../../src/char-predicates-inl.h',
         '../../src/char-predicates.h',
         '../../src/checks.cc',
@@ -264,6 +265,8 @@
         '../../src/disassembler.cc',
         '../../src/disassembler.h',
         '../../src/dtoa-config.c',
+        '../../src/diy_fp.h',
+        '../../src/double.h',
         '../../src/execution.cc',
         '../../src/execution.h',
         '../../src/factory.cc',
@@ -284,6 +287,8 @@
         '../../src/global-handles.cc',
         '../../src/global-handles.h',
         '../../src/globals.h',
+        '../../src/grisu3.h',
+        '../../src/grisu3.cc',
         '../../src/handles-inl.h',
         '../../src/handles.cc',
         '../../src/handles.h',
@@ -330,6 +335,7 @@
         '../../src/parser.cc',
         '../../src/parser.h',
         '../../src/platform.h',
+        '../../src/powers_ten.h',
         '../../src/prettyprinter.cc',
         '../../src/prettyprinter.h',
         '../../src/property.cc',