/*
* Copyright 2017 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkFloatToDecimal.h"
#include <cfloat>
#include <climits>
#include <cmath>
#include "SkTypes.h"
// returns `value * pow(base, e)`, assuming `e` is positive.
static double pow_by_squaring(double value, double base, int e) {
// https://en.wikipedia.org/wiki/Exponentiation_by_squaring
SkASSERT(e > 0);
while (true) {
if (e & 1) {
value *= base;
}
e >>= 1;
if (0 == e) {
return value;
}
base *= base;
}
}
// Return pow(10.0, e), optimized for common cases.
static double pow10(int e) {
switch (e) {
case 0: return 1.0; // common cases
case 1: return 10.0;
case 2: return 100.0;
case 3: return 1e+03;
case 4: return 1e+04;
case 5: return 1e+05;
case 6: return 1e+06;
case 7: return 1e+07;
case 8: return 1e+08;
case 9: return 1e+09;
case 10: return 1e+10;
case 11: return 1e+11;
case 12: return 1e+12;
case 13: return 1e+13;
case 14: return 1e+14;
case 15: return 1e+15;
default:
if (e > 15) {
return pow_by_squaring(1e+15, 10.0, e - 15);
} else {
SkASSERT(e < 0);
return pow_by_squaring(1.0, 0.1, -e);
}
}
}
/** Write a string into result, includeing a terminating '\0' (for
unit testing). Return strlen(result) (for SkWStream::write) The
resulting string will be in the form /[-]?([0-9]*.)?[0-9]+/ and
sscanf(result, "%f", &x) will return the original value iff the
value is finite. This function accepts all possible input values.
Motivation: "PDF does not support [numbers] in exponential format
(such as 6.02e23)." Otherwise, this function would rely on a
sprintf-type function from the standard library. */
unsigned SkFloatToDecimal(float value, char result[kMaximumSkFloatToDecimalLength]) {
/* The longest result is -FLT_MIN.
We serialize it as "-.0000000000000000000000000000000000000117549435"
which has 48 characters plus a terminating '\0'. */
static_assert(kMaximumSkFloatToDecimalLength == 49, "");
// 3 = '-', '.', and '\0' characters.
// 9 = number of significant digits
// abs(FLT_MIN_10_EXP) = number of zeros in FLT_MIN
static_assert(kMaximumSkFloatToDecimalLength == 3 + 9 - FLT_MIN_10_EXP, "");
/* section C.1 of the PDF1.4 spec (http://goo.gl/0SCswJ) says that
most PDF rasterizers will use fixed-point scalars that lack the
dynamic range of floats. Even if this is the case, I want to
serialize these (uncommon) very small and very large scalar
values with enough precision to allow a floating-point
rasterizer to read them in with perfect accuracy.
Experimentally, rasterizers such as pdfium do seem to benefit
from this. Rasterizers that rely on fixed-point scalars should
gracefully ignore these values that they can not parse. */
char* output = &result[0];
const char* const end = &result[kMaximumSkFloatToDecimalLength - 1];
// subtract one to leave space for '\0'.
/* This function is written to accept any possible input value,
including non-finite values such as INF and NAN. In that case,
we ignore value-correctness and and output a syntacticly-valid
number. */
if (value == INFINITY) {
value = FLT_MAX; // nearest finite float.
}
if (value == -INFINITY) {
value = -FLT_MAX; // nearest finite float.
}
if (!std::isfinite(value) || value == 0.0f) {
// NAN is unsupported in PDF. Always output a valid number.
// Also catch zero here, as a special case.
*output++ = '0';
*output = '\0';
return static_cast<unsigned>(output - result);
}
if (value < 0.0) {
*output++ = '-';
value = -value;
}
SkASSERT(value >= 0.0f);
int binaryExponent;
(void)std::frexp(value, &binaryExponent);
static const double kLog2 = 0.3010299956639812; // log10(2.0);
int decimalExponent = static_cast<int>(std::floor(kLog2 * binaryExponent));
int decimalShift = decimalExponent - 8;
double power = pow10(-decimalShift);
SkASSERT(value * power <= (double)INT_MAX);
int d = static_cast<int>(value * power + 0.5);
// SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
SkASSERT(d <= 999999999);
if (d > 167772159) { // floor(pow(10,1+log10(1<<24)))
// need one fewer decimal digits for 24-bit precision.
decimalShift = decimalExponent - 7;
// SkASSERT(power * 0.1 = pow10(-decimalShift));
// recalculate to get rounding right.
d = static_cast<int>(value * (power * 0.1) + 0.5);
SkASSERT(d <= 99999999);
}
while (d % 10 == 0) {
d /= 10;
++decimalShift;
}
SkASSERT(d > 0);
// SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
unsigned char buffer[9]; // decimal value buffer.
int bufferIndex = 0;
do {
buffer[bufferIndex++] = d % 10;
d /= 10;
} while (d != 0);
SkASSERT(bufferIndex <= (int)sizeof(buffer) && bufferIndex > 0);
if (decimalShift >= 0) {
do {
--bufferIndex;
*output++ = '0' + buffer[bufferIndex];
} while (bufferIndex);
for (int i = 0; i < decimalShift; ++i) {
*output++ = '0';
}
} else {
int placesBeforeDecimal = bufferIndex + decimalShift;
if (placesBeforeDecimal > 0) {
while (placesBeforeDecimal-- > 0) {
--bufferIndex;
*output++ = '0' + buffer[bufferIndex];
}
*output++ = '.';
} else {
*output++ = '.';
int placesAfterDecimal = -placesBeforeDecimal;
while (placesAfterDecimal-- > 0) {
*output++ = '0';
}
}
while (bufferIndex > 0) {
--bufferIndex;
*output++ = '0' + buffer[bufferIndex];
if (output == end) {
break; // denormalized: don't need extra precision.
// Note: denormalized numbers will not have the same number of
// significantDigits, but do not need them to round-trip.
}
}
}
SkASSERT(output <= end);
*output = '\0';
return static_cast<unsigned>(output - result);
}