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- /*
- * 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 "src/utils/SkFloatToDecimal.h"
- #include <cfloat>
- #include <climits>
- #include <cmath>
- #include "include/core/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 output, including a terminating '\0' (for
- unit testing). Return strlen(output) (for SkWStream::write) The
- resulting string will be in the form /[-]?([0-9]*.)?[0-9]+/ and
- sscanf(output, "%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 output[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_ptr = &output[0];
- const char* const end = &output[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 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_ptr++ = '0';
- *output_ptr = '\0';
- return static_cast<unsigned>(output_ptr - output);
- }
- if (value < 0.0) {
- *output_ptr++ = '-';
- 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_ptr++ = '0' + buffer[bufferIndex];
- } while (bufferIndex);
- for (int i = 0; i < decimalShift; ++i) {
- *output_ptr++ = '0';
- }
- } else {
- int placesBeforeDecimal = bufferIndex + decimalShift;
- if (placesBeforeDecimal > 0) {
- while (placesBeforeDecimal-- > 0) {
- --bufferIndex;
- *output_ptr++ = '0' + buffer[bufferIndex];
- }
- *output_ptr++ = '.';
- } else {
- *output_ptr++ = '.';
- int placesAfterDecimal = -placesBeforeDecimal;
- while (placesAfterDecimal-- > 0) {
- *output_ptr++ = '0';
- }
- }
- while (bufferIndex > 0) {
- --bufferIndex;
- *output_ptr++ = '0' + buffer[bufferIndex];
- if (output_ptr == 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_ptr <= end);
- *output_ptr = '\0';
- return static_cast<unsigned>(output_ptr - output);
- }
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