Revision: 5491
Author: floitsc...@gmail.com
Date: Mon Sep 20 02:18:00 2010
Log: Added precision mode to fast-dtoa.
Review URL: http://codereview.chromium.org/2000004
http://code.google.com/p/v8/source/detail?r=5491
Added:
/branches/bleeding_edge/test/cctest/gay-precision.cc
/branches/bleeding_edge/test/cctest/gay-precision.h
Modified:
/branches/bleeding_edge/src/conversions.cc
/branches/bleeding_edge/src/dtoa.cc
/branches/bleeding_edge/src/fast-dtoa.cc
/branches/bleeding_edge/src/fast-dtoa.h
/branches/bleeding_edge/test/cctest/SConscript
/branches/bleeding_edge/test/cctest/test-fast-dtoa.cc
=======================================
--- /dev/null
+++ /branches/bleeding_edge/test/cctest/gay-precision.cc Mon Sep 20
02:18:00 2010
File is too large to display a diff.
=======================================
--- /dev/null
+++ /branches/bleeding_edge/test/cctest/gay-precision.h Mon Sep 20 02:18:00
2010
@@ -0,0 +1,47 @@
+// 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_PRECISION_H_
+#define GAY_PRECISION_H_
+
+namespace v8 {
+namespace internal {
+
+struct PrecomputedPrecision {
+ double v;
+ int number_digits;
+ const char* representation;
+ int decimal_point;
+};
+
+// Returns precomputed values of dtoa. The strings have been generated
using
+// Gay's dtoa in mode "precision".
+Vector<const PrecomputedPrecision> PrecomputedPrecisionRepresentations();
+
+} } // namespace v8::internal
+
+#endif // GAY_PRECISION_H_
=======================================
--- /branches/bleeding_edge/src/conversions.cc Tue Aug 24 03:53:44 2010
+++ /branches/bleeding_edge/src/conversions.cc Mon Sep 20 02:18:00 2010
@@ -956,8 +956,9 @@
char* DoubleToExponentialCString(double value, int f) {
+ const int kMaxDigitsAfterPoint = 20;
// f might be -1 to signal that f was undefined in JavaScript.
- ASSERT(f >= -1 && f <= 20);
+ ASSERT(f >= -1 && f <= kMaxDigitsAfterPoint);
bool negative = false;
if (value < 0) {
@@ -969,29 +970,60 @@
int decimal_point;
int sign;
char* decimal_rep = NULL;
+ bool used_gay_dtoa = false;
+ // f corresponds to the digits after the point. There is always one digit
+ // before the point. The number of requested_digits equals hence f + 1.
+ // And we have to add one character for the null-terminator.
+ const int kV8DtoaBufferCapacity = kMaxDigitsAfterPoint + 1 + 1;
+ // Make sure that the buffer is big enough, even if we fall back to the
+ // shortest representation (which happens when f equals -1).
+ ASSERT(kBase10MaximalLength <= kMaxDigitsAfterPoint + 1);
+ char v8_dtoa_buffer[kV8DtoaBufferCapacity];
+ int decimal_rep_length;
+
if (f == -1) {
- decimal_rep = dtoa(value, 0, 0, &decimal_point, &sign, NULL);
- f = StrLength(decimal_rep) - 1;
+ if (DoubleToAscii(value, DTOA_SHORTEST, 0,
+ Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+ &sign, &decimal_rep_length, &decimal_point)) {
+ f = decimal_rep_length - 1;
+ decimal_rep = v8_dtoa_buffer;
+ } else {
+ decimal_rep = dtoa(value, 0, 0, &decimal_point, &sign, NULL);
+ decimal_rep_length = StrLength(decimal_rep);
+ f = decimal_rep_length - 1;
+ used_gay_dtoa = true;
+ }
} else {
- decimal_rep = dtoa(value, 2, f + 1, &decimal_point, &sign, NULL);
- }
- int decimal_rep_length = StrLength(decimal_rep);
+ if (DoubleToAscii(value, DTOA_PRECISION, f + 1,
+ Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+ &sign, &decimal_rep_length, &decimal_point)) {
+ decimal_rep = v8_dtoa_buffer;
+ } else {
+ decimal_rep = dtoa(value, 2, f + 1, &decimal_point, &sign, NULL);
+ decimal_rep_length = StrLength(decimal_rep);
+ used_gay_dtoa = true;
+ }
+ }
ASSERT(decimal_rep_length > 0);
ASSERT(decimal_rep_length <= f + 1);
- USE(decimal_rep_length);
int exponent = decimal_point - 1;
char* result =
CreateExponentialRepresentation(decimal_rep, exponent, negative,
f+1);
- freedtoa(decimal_rep);
+ if (used_gay_dtoa) {
+ freedtoa(decimal_rep);
+ }
return result;
}
char* DoubleToPrecisionCString(double value, int p) {
- ASSERT(p >= 1 && p <= 21);
+ const int kMinimalDigits = 1;
+ const int kMaximalDigits = 21;
+ ASSERT(p >= kMinimalDigits && p <= kMaximalDigits);
+ USE(kMinimalDigits);
bool negative = false;
if (value < 0) {
@@ -1002,8 +1034,22 @@
// Find a sufficiently precise decimal representation of n.
int decimal_point;
int sign;
- char* decimal_rep = dtoa(value, 2, p, &decimal_point, &sign, NULL);
- int decimal_rep_length = StrLength(decimal_rep);
+ char* decimal_rep = NULL;
+ bool used_gay_dtoa = false;
+ // Add one for the terminating null character.
+ const int kV8DtoaBufferCapacity = kMaximalDigits + 1;
+ char v8_dtoa_buffer[kV8DtoaBufferCapacity];
+ int decimal_rep_length;
+
+ if (DoubleToAscii(value, DTOA_PRECISION, p,
+ Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+ &sign, &decimal_rep_length, &decimal_point)) {
+ decimal_rep = v8_dtoa_buffer;
+ } else {
+ decimal_rep = dtoa(value, 2, p, &decimal_point, &sign, NULL);
+ decimal_rep_length = StrLength(decimal_rep);
+ used_gay_dtoa = true;
+ }
ASSERT(decimal_rep_length <= p);
int exponent = decimal_point - 1;
@@ -1047,7 +1093,9 @@
result = builder.Finalize();
}
- freedtoa(decimal_rep);
+ if (used_gay_dtoa) {
+ freedtoa(decimal_rep);
+ }
return result;
}
=======================================
--- /branches/bleeding_edge/src/dtoa.cc Wed May 5 06:51:27 2010
+++ /branches/bleeding_edge/src/dtoa.cc Mon Sep 20 02:18:00 2010
@@ -65,11 +65,12 @@
switch (mode) {
case DTOA_SHORTEST:
- return FastDtoa(v, buffer, length, point);
+ return FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, length, point);
case DTOA_FIXED:
return FastFixedDtoa(v, requested_digits, buffer, length, point);
- default:
- break;
+ case DTOA_PRECISION:
+ return FastDtoa(v, FAST_DTOA_PRECISION, requested_digits,
+ buffer, length, point);
}
return false;
}
=======================================
--- /branches/bleeding_edge/src/fast-dtoa.cc Wed May 5 06:51:27 2010
+++ /branches/bleeding_edge/src/fast-dtoa.cc Mon Sep 20 02:18:00 2010
@@ -42,8 +42,8 @@
//
// A different range might be chosen on a different platform, to optimize
digit
// generation, but a smaller range requires more powers of ten to be
cached.
-static const int minimal_target_exponent = -60;
-static const int maximal_target_exponent = -32;
+static const int kMinimalTargetExponent = -60;
+static const int kMaximalTargetExponent = -32;
// Adjusts the last digit of the generated number, and screens out
generated
@@ -61,13 +61,13 @@
// Output: returns true if the buffer is guaranteed to contain the closest
// representable number to the input.
// Modifies the generated digits in the buffer to approach (round
towards) w.
-bool RoundWeed(Vector<char> buffer,
- int length,
- uint64_t distance_too_high_w,
- uint64_t unsafe_interval,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit) {
+static bool RoundWeed(Vector<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_low = too_high - big_distance, and
@@ -75,7 +75,7 @@
// Note: w_low < w < w_high
//
// The real w (* unit) must lie somewhere inside the interval
- // ]w_low; w_low[ (often written as "(w_low; w_low)")
+ // ]w_low; w_high[ (often written as "(w_low; w_high)")
// Basically the buffer currently contains a number in the unsafe
interval
// ]too_low; too_high[ with too_low < w < too_high
@@ -122,10 +122,10 @@
// inside the safe interval then we simply do not know and bail out
(returning
// false).
//
- // Similarly we have to take into account the imprecision of 'w' when
rounding
- // the buffer. If we have two potential representations we need to make
sure
- // that the chosen one is closer to w_low and w_high since v can be
anywhere
- // between them.
+ // Similarly we have to take into account the imprecision of 'w' when
finding
+ // the closest representation of 'w'. If we have two potential
+ // representations, and one is closer to both w_low and w_high, then we
know
+ // it is closer to the actual value v.
//
// By generating the digits of too_high we got the largest (closest to
// too_high) buffer that is still in the unsafe interval. In the case
where
@@ -139,6 +139,9 @@
// (buffer{-1} < w_high) && w_high - buffer{-1} > buffer -
w_high
// Instead of using the buffer directly we use its distance to too_high.
// Conceptually rest ~= too_high - buffer
+ // We need to do the following tests in this order to avoid over- and
+ // underflows.
+ ASSERT(rest <= unsafe_interval);
while (rest < small_distance && // Negated condition 1
unsafe_interval - rest >= ten_kappa && // Negated condition 2
(rest + ten_kappa < small_distance || // buffer{-1} > w_high
@@ -166,6 +169,62 @@
}
+// Rounds the buffer upwards if the result is closer to v by possibly
adding
+// 1 to the buffer. If the precision of the calculation is not sufficient
to
+// round correctly, return false.
+// The rounding might shift the whole buffer in which case the kappa is
+// adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
+//
+// If 2*rest > ten_kappa then the buffer needs to be round up.
+// rest can have an error of +/- 1 unit. This function accounts for the
+// imprecision and returns false, if the rounding direction cannot be
+// unambiguously determined.
+//
+// Precondition: rest < ten_kappa.
+static bool RoundWeedCounted(Vector<char> buffer,
+ int length,
+ uint64_t rest,
+ uint64_t ten_kappa,
+ uint64_t unit,
+ int* kappa) {
+ ASSERT(rest < ten_kappa);
+ // The following tests are done in a specific order to avoid overflows.
They
+ // will work correctly with any uint64 values of rest < ten_kappa and
unit.
+ //
+ // If the unit is too big, then we don't know which way to round. For
example
+ // a unit of 50 means that the real number lies within rest +/- 50. If
+ // 10^kappa == 40 then there is no way to tell which way to round.
+ if (unit >= ten_kappa) return false;
+ // Even if unit is just half the size of 10^kappa we are already
completely
+ // lost. (And after the previous test we know that the expression will
not
+ // over/underflow.)
+ if (ten_kappa - unit <= unit) return false;
+ // If 2 * (rest + unit) <= 10^kappa we can safely round down.
+ if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
+ return true;
+ }
+ // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
+ if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
+ // Increment the last digit recursively until we find a non '9' digit.
+ buffer[length - 1]++;
+ for (int i = length - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) break;
+ buffer[i] = '0';
+ buffer[i - 1]++;
+ }
+ // If the first digit is now '0'+ 10 we had a buffer with all '9's.
With the
+ // exception of the first digit all digits are now '0'. Simply switch
the
+ // first digit to '1' and adjust the kappa. Example: "99" becomes "10"
and
+ // the power (the kappa) is increased.
+ if (buffer[0] == '0' + 10) {
+ buffer[0] = '1';
+ (*kappa) += 1;
+ }
+ return true;
+ }
+ return false;
+}
+
static const uint32_t kTen4 = 10000;
static const uint32_t kTen5 = 100000;
@@ -178,7 +237,7 @@
// 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.
-// Precondition: (1 << number_bits) <= number < (1 << (number_bits + 1)).
+// Precondition: number < (1 << (number_bits + 1)).
static void BiggestPowerTen(uint32_t number,
int number_bits,
uint32_t* power,
@@ -281,18 +340,18 @@
// 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 minimal_target_exponent and
-// maximal_target_exponent.
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
// Hence -60 <= w.e() <= -32.
//
// 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.
+// is, their error must be less than a unit of their last digits.
// * low.e() == w.e() == high.e()
// * low < w < high, and taking into account their error: low~ <= high~
-// * minimal_target_exponent <= w.e() <= maximal_target_exponent
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
// Postconditions: returns false if procedure fails.
// otherwise:
// * buffer is not null-terminated, but len contains the number of
digits.
@@ -321,15 +380,15 @@
// 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.
-bool DigitGen(DiyFp low,
- DiyFp w,
- DiyFp high,
- Vector<char> buffer,
- int* length,
- int* kappa) {
+static bool DigitGen(DiyFp low,
+ DiyFp w,
+ DiyFp high,
+ Vector<char> buffer,
+ int* length,
+ int* kappa) {
ASSERT(low.e() == w.e() && w.e() == high.e());
ASSERT(low.f() + 1 <= high.f() - 1);
- ASSERT(minimal_target_exponent <= w.e() && w.e() <=
maximal_target_exponent);
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <=
kMaximalTargetExponent);
// 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
@@ -359,23 +418,23 @@
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;
+ uint32_t divisor;
+ int divisor_exponent;
BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- ÷r, ÷r_exponent);
- *kappa = divider_exponent + 1;
+ &divisor, &divisor_exponent);
+ *kappa = divisor_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
+ // with the divisor exponent + 1. And the divisor is the biggest power
of ten
// that is smaller than integrals.
while (*kappa > 0) {
- int digit = integrals / divider;
+ int digit = integrals / divisor;
buffer[*length] = '0' + digit;
(*length)++;
- integrals %= divider;
+ integrals %= divisor;
(*kappa)--;
- // Note that kappa now equals the exponent of the divider and that the
+ // Note that kappa now equals the exponent of the divisor and that the
// invariant thus holds again.
uint64_t rest =
(static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
@@ -386,32 +445,24 @@
// 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;
+ static_cast<uint64_t>(divisor) << -one.e(), unit);
+ }
+ divisor /= 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.
+ // Note that the multiplication by 10 does not overflow, because w.e >=
-60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
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);
+ fractionals *= 10;
+ unit *= 10;
+ unsafe_interval.set_f(unsafe_interval.f() * 10);
// Integer division by one.
int digit = static_cast<int>(fractionals >> -one.e());
buffer[*length] = '0' + digit;
@@ -424,6 +475,113 @@
}
}
}
+
+
+
+// Generates (at most) requested_digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
+// Hence -60 <= w.e() <= -32.
+//
+// Returns false if it fails, in which case the generated digits in the
buffer
+// should not be used.
+// Preconditions:
+// * w is correct up to 1 ulp (unit in the last place). That
+// is, its error must be strictly less than a unit of its last digit.
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+//
+// Postconditions: returns false if procedure fails.
+// otherwise:
+// * buffer is not null-terminated, but length contains the number of
+// digits.
+// * the representation in buffer is the most precise representation of
+// requested_digits digits.
+// * buffer contains at most requested_digits digits of w. If there
are less
+// than requested_digits digits then some trailing '0's have been
removed.
+// * kappa is such that
+// w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
+//
+// 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, but the
failure-rate
+// increases with higher requested_digits.
+static bool DigitGenCounted(DiyFp w,
+ int requested_digits,
+ Vector<char> buffer,
+ int* length,
+ int* kappa) {
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <=
kMaximalTargetExponent);
+ ASSERT(kMinimalTargetExponent >= -60);
+ ASSERT(kMaximalTargetExponent <= -32);
+ // w is assumed to have an error less than 1 unit. Whenever w is scaled
we
+ // also scale its error.
+ uint64_t w_error = 1;
+ // We cut the input number into two parts: the integral digits and the
+ // fractional digits. We don't emit any decimal separator, but adapt
kappa
+ // instead. Example: instead of writing "1.2" we put "12" into the
buffer and
+ // increase kappa by 1.
+ 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>(w.f() >> -one.e());
+ // Modulo by one is an and.
+ uint64_t fractionals = w.f() & (one.f() - 1);
+ uint32_t divisor;
+ int divisor_exponent;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent);
+ *kappa = divisor_exponent + 1;
+ *length = 0;
+
+ // Loop invariant: buffer = w / 10^kappa (integer division)
+ // The invariant holds for the first iteration: kappa has been
initialized
+ // with the divisor exponent + 1. And the divisor is the biggest power
of ten
+ // that is smaller than 'integrals'.
+ while (*kappa > 0) {
+ int digit = integrals / divisor;
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ requested_digits--;
+ integrals %= divisor;
+ (*kappa)--;
+ // Note that kappa now equals the exponent of the divisor and that the
+ // invariant thus holds again.
+ if (requested_digits == 0) break;
+ divisor /= 10;
+ }
+
+ if (requested_digits == 0) {
+ uint64_t rest =
+ (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+ return RoundWeedCounted(buffer, *length, rest,
+ static_cast<uint64_t>(divisor) << -one.e(),
w_error,
+ kappa);
+ }
+
+ // 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 (the 'unit'), too.
+ // Note that the multiplication by 10 does not overflow, because w.e >=
-60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+ while (requested_digits > 0 && fractionals > w_error) {
+ fractionals *= 10;
+ w_error *= 10;
+ // Integer division by one.
+ int digit = static_cast<int>(fractionals >> -one.e());
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ requested_digits--;
+ fractionals &= one.f() - 1; // Modulo by one.
+ (*kappa)--;
+ }
+ if (requested_digits != 0) return false;
+ return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
+ kappa);
+}
// Provides a decimal representation of v.
@@ -437,7 +595,10 @@
// 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.
-bool grisu3(double v, Vector<char> buffer, int* length, int*
decimal_exponent) {
+static bool Grisu3(double v,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_exponent) {
DiyFp w = Double(v).AsNormalizedDiyFp();
// boundary_minus and boundary_plus are the boundaries between v and its
// closest floating-point neighbors. Any number strictly between
@@ -448,12 +609,12 @@
ASSERT(boundary_plus.e() == w.e());
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
- GetCachedPower(w.e() + DiyFp::kSignificandSize, minimal_target_exponent,
- maximal_target_exponent, &mk, &ten_mk);
- ASSERT(minimal_target_exponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize &&
- maximal_target_exponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize);
+ GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
+ kMaximalTargetExponent, &mk, &ten_mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= 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.
@@ -486,19 +647,75 @@
*decimal_exponent = -mk + kappa;
return result;
}
+
+
+// The "counted" version of grisu3 (see above) only generates
requested_digits
+// number of digits. This version does not generate the shortest
representation,
+// and with enough requested digits 0.1 will at some point print as
0.9999999...
+// Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
+// therefore the rounding strategy for halfway cases is irrelevant.
+static bool Grisu3Counted(double v,
+ int requested_digits,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_exponent) {
+ DiyFp w = Double(v).AsNormalizedDiyFp();
+ DiyFp ten_mk; // Cached power of ten: 10^-k
+ int mk; // -k
+ GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
+ kMaximalTargetExponent, &mk, &ten_mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= 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);
+
+ // We now have (double) (scaled_w * 10^-mk).
+ // DigitGen will generate the first requested_digits digits of scaled_w
and
+ // return together with a kappa such that scaled_w ~= buffer * 10^kappa.
(It
+ // will not always be exactly the same since DigitGenCounted only
produces a
+ // limited number of digits.)
+ int kappa;
+ bool result = DigitGenCounted(scaled_w, requested_digits,
+ buffer, length, &kappa);
+ *decimal_exponent = -mk + kappa;
+ return result;
+}
bool FastDtoa(double v,
+ FastDtoaMode mode,
+ int requested_digits,
Vector<char> buffer,
int* length,
- int* point) {
+ int* decimal_point) {
ASSERT(v > 0);
ASSERT(!Double(v).IsSpecial());
+ bool result = false;
int decimal_exponent;
- bool result = grisu3(v, buffer, length, &decimal_exponent);
- *point = *length + decimal_exponent;
- buffer[*length] = '\0';
+ switch (mode) {
+ case FAST_DTOA_SHORTEST:
+ result = Grisu3(v, buffer, length, &decimal_exponent);
+ break;
+ case FAST_DTOA_PRECISION:
+ result = Grisu3Counted(v, requested_digits,
+ buffer, length, &decimal_exponent);
+ break;
+ }
+ if (result) {
+ *decimal_point = *length + decimal_exponent;
+ buffer[*length] = '\0';
+ }
return result;
}
=======================================
--- /branches/bleeding_edge/src/fast-dtoa.h Wed May 5 06:51:27 2010
+++ /branches/bleeding_edge/src/fast-dtoa.h Mon Sep 20 02:18:00 2010
@@ -31,27 +31,52 @@
namespace v8 {
namespace internal {
+enum FastDtoaMode {
+ // Computes the shortest representation of the given input. The returned
+ // result will be the most accurate number of this length. Longer
+ // representations might be more accurate.
+ FAST_DTOA_SHORTEST,
+ // Computes a representation where the precision (number of digits) is
+ // given as input. The precision is independent of the decimal point.
+ FAST_DTOA_PRECISION
+};
+
// FastDtoa will produce at most kFastDtoaMaximalLength digits. This does
not
// include the terminating '\0' character.
static const int kFastDtoaMaximalLength = 17;
// Provides a decimal representation of v.
-// v must be a strictly positive finite double.
+// The result should be interpreted as buffer * 10^(point - length).
+//
+// Precondition:
+// * v must be a strictly positive finite double.
+//
// 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^(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.
+// If the function returns true and mode equals
+// - FAST_DTOA_SHORTEST, then
+// the parameter requested_digits is ignored.
+// The result satisfies
+// v == (double) (buffer * 10^(point - length)).
+// The digits in the buffer are the shortest representation possible.
E.g.
+// if 0.099999999999 and 0.1 represent the same double then "1" is
returned
+// with point = 0.
+// 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.
+// - FAST_DTOA_PRECISION, then
+// the buffer contains requested_digits digits.
+// the difference v - (buffer * 10^(point-length)) is closest to zero
for
+// all possible representations of requested_digits digits.
+// If there are two values that are equally close, then FastDtoa
returns
+// false.
+// For both modes the buffer must be large enough to hold the result.
bool FastDtoa(double d,
+ FastDtoaMode mode,
+ int requested_digits,
Vector<char> buffer,
int* length,
- int* point);
+ int* decimal_point);
} } // namespace v8::internal
=======================================
--- /branches/bleeding_edge/test/cctest/SConscript Tue Jun 29 06:48:20 2010
+++ /branches/bleeding_edge/test/cctest/SConscript Mon Sep 20 02:18:00 2010
@@ -35,6 +35,7 @@
SOURCES = {
'all': [
'gay-fixed.cc',
+ 'gay-precision.cc',
'gay-shortest.cc',
'test-accessors.cc',
'test-alloc.cc',
=======================================
--- /branches/bleeding_edge/test/cctest/test-fast-dtoa.cc Wed May 5
06:51:27 2010
+++ /branches/bleeding_edge/test/cctest/test-fast-dtoa.cc Mon Sep 20
02:18:00 2010
@@ -9,13 +9,26 @@
#include "diy-fp.h"
#include "double.h"
#include "fast-dtoa.h"
+#include "gay-precision.h"
#include "gay-shortest.h"
using namespace v8::internal;
static const int kBufferSize = 100;
-TEST(FastDtoaVariousDoubles) {
+
+// Removes trailing '0' digits.
+static void TrimRepresentation(Vector<char> representation) {
+ int len = strlen(representation.start());
+ int i;
+ for (i = len - 1; i >= 0; --i) {
+ if (representation[i] != '0') break;
+ }
+ representation[i + 1] = '\0';
+}
+
+
+TEST(FastDtoaShortestVariousDoubles) {
char buffer_container[kBufferSize];
Vector<char> buffer(buffer_container, kBufferSize);
int length;
@@ -23,38 +36,45 @@
int status;
double min_double = 5e-324;
- status = FastDtoa(min_double, buffer, &length, &point);
+ status = FastDtoa(min_double, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("5", buffer.start());
CHECK_EQ(-323, point);
double max_double = 1.7976931348623157e308;
- status = FastDtoa(max_double, buffer, &length, &point);
+ status = FastDtoa(max_double, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("17976931348623157", buffer.start());
CHECK_EQ(309, point);
- status = FastDtoa(4294967272.0, buffer, &length, &point);
+ status = FastDtoa(4294967272.0, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("4294967272", buffer.start());
CHECK_EQ(10, point);
- status = FastDtoa(4.1855804968213567e298, buffer, &length, &point);
+ status = FastDtoa(4.1855804968213567e298, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("4185580496821357", buffer.start());
CHECK_EQ(299, point);
- status = FastDtoa(5.5626846462680035e-309, buffer, &length, &point);
+ status = FastDtoa(5.5626846462680035e-309, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("5562684646268003", buffer.start());
CHECK_EQ(-308, point);
- status = FastDtoa(2147483648.0, buffer, &length, &point);
+ status = FastDtoa(2147483648.0, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
CHECK(status);
CHECK_EQ("2147483648", buffer.start());
CHECK_EQ(10, point);
- status = FastDtoa(3.5844466002796428e+298, buffer, &length, &point);
+ status = FastDtoa(3.5844466002796428e+298, FAST_DTOA_SHORTEST, 0,
+ buffer, &length, &point);
if (status) { // Not all FastDtoa variants manage to compute this
number.
CHECK_EQ("35844466002796428", buffer.start());
CHECK_EQ(299, point);
@@ -62,7 +82,7 @@
uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
double v = Double(smallest_normal64).value();
- status = FastDtoa(v, buffer, &length, &point);
+ status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
if (status) {
CHECK_EQ("22250738585072014", buffer.start());
CHECK_EQ(-307, point);
@@ -70,12 +90,113 @@
uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
v = Double(largest_denormal64).value();
- status = FastDtoa(v, buffer, &length, &point);
+ status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
if (status) {
CHECK_EQ("2225073858507201", buffer.start());
CHECK_EQ(-307, point);
}
}
+
+
+TEST(FastDtoaPrecisionVariousDoubles) {
+ char buffer_container[kBufferSize];
+ Vector<char> buffer(buffer_container, kBufferSize);
+ int length;
+ int point;
+ int status;
+
+ status = FastDtoa(1.0, FAST_DTOA_PRECISION, 3, buffer, &length, &point);
+ CHECK(status);
+ CHECK_GE(3, length);
+ TrimRepresentation(buffer);
+ CHECK_EQ("1", buffer.start());
+ CHECK_EQ(1, point);
+
+ status = FastDtoa(1.5, FAST_DTOA_PRECISION, 10, buffer, &length, &point);
+ if (status) {
+ CHECK_GE(10, length);
+ TrimRepresentation(buffer);
+ CHECK_EQ("15", buffer.start());
+ CHECK_EQ(1, point);
+ }
+
+ double min_double = 5e-324;
+ status = FastDtoa(min_double, FAST_DTOA_PRECISION, 5,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("49407", buffer.start());
+ CHECK_EQ(-323, point);
+
+ double max_double = 1.7976931348623157e308;
+ status = FastDtoa(max_double, FAST_DTOA_PRECISION, 7,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("1797693", buffer.start());
+ CHECK_EQ(309, point);
+
+ status = FastDtoa(4294967272.0, FAST_DTOA_PRECISION, 14,
+ buffer, &length, &point);
+ if (status) {
+ CHECK_GE(14, length);
+ TrimRepresentation(buffer);
+ CHECK_EQ("4294967272", buffer.start());
+ CHECK_EQ(10, point);
+ }
+
+ status = FastDtoa(4.1855804968213567e298, FAST_DTOA_PRECISION, 17,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("41855804968213567", buffer.start());
+ CHECK_EQ(299, point);
+
+ status = FastDtoa(5.5626846462680035e-309, FAST_DTOA_PRECISION, 1,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("6", buffer.start());
+ CHECK_EQ(-308, point);
+
+ status = FastDtoa(2147483648.0, FAST_DTOA_PRECISION, 5,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("21475", buffer.start());
+ CHECK_EQ(10, point);
+
+ status = FastDtoa(3.5844466002796428e+298, FAST_DTOA_PRECISION, 10,
+ buffer, &length, &point);
+ CHECK(status);
+ CHECK_GE(10, length);
+ TrimRepresentation(buffer);
+ CHECK_EQ("35844466", buffer.start());
+ CHECK_EQ(299, point);
+
+ uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
+ double v = Double(smallest_normal64).value();
+ status = FastDtoa(v, FAST_DTOA_PRECISION, 17, buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("22250738585072014", buffer.start());
+ CHECK_EQ(-307, point);
+
+ uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+ v = Double(largest_denormal64).value();
+ status = FastDtoa(v, FAST_DTOA_PRECISION, 17, buffer, &length, &point);
+ CHECK(status);
+ CHECK_GE(20, length);
+ TrimRepresentation(buffer);
+ CHECK_EQ("22250738585072009", buffer.start());
+ CHECK_EQ(-307, point);
+
+ v = 3.3161339052167390562200598e-237;
+ status = FastDtoa(v, FAST_DTOA_PRECISION, 18, buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("331613390521673906", buffer.start());
+ CHECK_EQ(-236, point);
+
+ v = 7.9885183916008099497815232e+191;
+ status = FastDtoa(v, FAST_DTOA_PRECISION, 4, buffer, &length, &point);
+ CHECK(status);
+ CHECK_EQ("7989", buffer.start());
+ CHECK_EQ(192, point);
+}
TEST(FastDtoaGayShortest) {
@@ -94,7 +215,7 @@
const PrecomputedShortest current_test = precomputed[i];
total++;
double v = current_test.v;
- status = FastDtoa(v, buffer, &length, &point);
+ status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
CHECK_GE(kFastDtoaMaximalLength, length);
if (!status) continue;
if (length == kFastDtoaMaximalLength) needed_max_length = true;
@@ -105,3 +226,43 @@
CHECK_GT(succeeded*1.0/total, 0.99);
CHECK(needed_max_length);
}
+
+
+TEST(FastDtoaGayPrecision) {
+ char buffer_container[kBufferSize];
+ Vector<char> buffer(buffer_container, kBufferSize);
+ bool status;
+ int length;
+ int point;
+ int succeeded = 0;
+ int total = 0;
+ // Count separately for entries with less than 15 requested digits.
+ int succeeded_15 = 0;
+ int total_15 = 0;
+
+ Vector<const PrecomputedPrecision> precomputed =
+ PrecomputedPrecisionRepresentations();
+ for (int i = 0; i < precomputed.length(); ++i) {
+ const PrecomputedPrecision current_test = precomputed[i];
+ double v = current_test.v;
+ int number_digits = current_test.number_digits;
+ total++;
+ if (number_digits <= 15) total_15++;
+ status = FastDtoa(v, FAST_DTOA_PRECISION, number_digits,
+ buffer, &length, &point);
+ CHECK_GE(number_digits, length);
+ if (!status) continue;
+ succeeded++;
+ if (number_digits <= 15) succeeded_15++;
+ TrimRepresentation(buffer);
+ CHECK_EQ(current_test.decimal_point, point);
+ CHECK_EQ(current_test.representation, buffer.start());
+ }
+ // The precomputed numbers contain many entries with many requested
+ // digits. These have a high failure rate and we therefore expect a lower
+ // success rate than for the shortest representation.
+ CHECK_GT(succeeded*1.0/total, 0.85);
+ // However with less than 15 digits almost the algorithm should almost
always
+ // succeed.
+ CHECK_GT(succeeded_15*1.0/total_15, 0.9999);
+}
--
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