1/*
2 * Copyright 2017 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#include "SkFloatToDecimal.h"
9
10#include <cfloat>
11#include <climits>
12#include <cmath>
13
14#include "SkTypes.h"
15
16// Return pow(10.0, e), optimized for common cases.
17static double pow10(int e) {
18    switch (e) {
19        case 0:  return 1.0;  // common cases
20        case 1:  return 10.0;
21        case 2:  return 100.0;
22        case 3:  return 1e+03;
23        case 4:  return 1e+04;
24        case 5:  return 1e+05;
25        case 6:  return 1e+06;
26        case 7:  return 1e+07;
27        case 8:  return 1e+08;
28        case 9:  return 1e+09;
29        case 10: return 1e+10;
30        case 11: return 1e+11;
31        case 12: return 1e+12;
32        case 13: return 1e+13;
33        case 14: return 1e+14;
34        case 15: return 1e+15;
35        default:
36            if (e > 15) {
37                double value = 1e+15;
38                while (e-- > 15) { value *= 10.0; }
39                return value;
40            } else {
41                SkASSERT(e < 0);
42                double value = 1.0;
43                while (e++ < 0) { value /= 10.0; }
44                return value;
45            }
46    }
47}
48
49/** Write a string into result, includeing a terminating '\0' (for
50    unit testing).  Return strlen(result) (for SkWStream::write) The
51    resulting string will be in the form /[-]?([0-9]*.)?[0-9]+/ and
52    sscanf(result, "%f", &x) will return the original value iff the
53    value is finite. This function accepts all possible input values.
54
55    Motivation: "PDF does not support [numbers] in exponential format
56    (such as 6.02e23)."  Otherwise, this function would rely on a
57    sprintf-type function from the standard library. */
58unsigned SkFloatToDecimal(float value, char result[kMaximumSkFloatToDecimalLength]) {
59    /* The longest result is -FLT_MIN.
60       We serialize it as "-.0000000000000000000000000000000000000117549435"
61       which has 48 characters plus a terminating '\0'. */
62
63    static_assert(kMaximumSkFloatToDecimalLength == 49, "");
64    // 3 = '-', '.', and '\0' characters.
65    // 9 = number of significant digits
66    // abs(FLT_MIN_10_EXP) = number of zeros in FLT_MIN
67    static_assert(kMaximumSkFloatToDecimalLength == 3 + 9 - FLT_MIN_10_EXP, "");
68
69    /* section C.1 of the PDF1.4 spec (http://goo.gl/0SCswJ) says that
70       most PDF rasterizers will use fixed-point scalars that lack the
71       dynamic range of floats.  Even if this is the case, I want to
72       serialize these (uncommon) very small and very large scalar
73       values with enough precision to allow a floating-point
74       rasterizer to read them in with perfect accuracy.
75       Experimentally, rasterizers such as pdfium do seem to benefit
76       from this.  Rasterizers that rely on fixed-point scalars should
77       gracefully ignore these values that they can not parse. */
78    char* output = &result[0];
79    const char* const end = &result[kMaximumSkFloatToDecimalLength - 1];
80    // subtract one to leave space for '\0'.
81
82    /* This function is written to accept any possible input value,
83       including non-finite values such as INF and NAN.  In that case,
84       we ignore value-correctness and and output a syntacticly-valid
85       number. */
86    if (value == INFINITY) {
87        value = FLT_MAX;  // nearest finite float.
88    }
89    if (value == -INFINITY) {
90        value = -FLT_MAX;  // nearest finite float.
91    }
92    if (!std::isfinite(value) || value == 0.0f) {
93        // NAN is unsupported in PDF.  Always output a valid number.
94        // Also catch zero here, as a special case.
95        *output++ = '0';
96        *output = '\0';
97        return static_cast<unsigned>(output - result);
98    }
99    if (value < 0.0) {
100        *output++ = '-';
101        value = -value;
102    }
103    SkASSERT(value >= 0.0f);
104
105    int binaryExponent;
106    (void)std::frexp(value, &binaryExponent);
107    static const double kLog2 = 0.3010299956639812;  // log10(2.0);
108    int decimalExponent = static_cast<int>(std::floor(kLog2 * binaryExponent));
109    int decimalShift = decimalExponent - 8;
110    double power = pow10(-decimalShift);
111    SkASSERT(value * power <= (double)INT_MAX);
112    int d = static_cast<int>(value * power + 0.5);
113    // SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
114    SkASSERT(d <= 999999999);
115    if (d > 167772159) {  // floor(pow(10,1+log10(1<<24)))
116       // need one fewer decimal digits for 24-bit precision.
117       decimalShift = decimalExponent - 7;
118       // SkASSERT(power * 0.1 = pow10(-decimalShift));
119       // recalculate to get rounding right.
120       d = static_cast<int>(value * (power * 0.1) + 0.5);
121       SkASSERT(d <= 99999999);
122    }
123    while (d % 10 == 0) {
124        d /= 10;
125        ++decimalShift;
126    }
127    SkASSERT(d > 0);
128    // SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
129    unsigned char buffer[9]; // decimal value buffer.
130    int bufferIndex = 0;
131    do {
132        buffer[bufferIndex++] = d % 10;
133        d /= 10;
134    } while (d != 0);
135    SkASSERT(bufferIndex <= (int)sizeof(buffer) && bufferIndex > 0);
136    if (decimalShift >= 0) {
137        do {
138            --bufferIndex;
139            *output++ = '0' + buffer[bufferIndex];
140        } while (bufferIndex);
141        for (int i = 0; i < decimalShift; ++i) {
142            *output++ = '0';
143        }
144    } else {
145        int placesBeforeDecimal = bufferIndex + decimalShift;
146        if (placesBeforeDecimal > 0) {
147            while (placesBeforeDecimal-- > 0) {
148                --bufferIndex;
149                *output++ = '0' + buffer[bufferIndex];
150            }
151            *output++ = '.';
152        } else {
153            *output++ = '.';
154            int placesAfterDecimal = -placesBeforeDecimal;
155            while (placesAfterDecimal-- > 0) {
156                *output++ = '0';
157            }
158        }
159        while (bufferIndex > 0) {
160            --bufferIndex;
161            *output++ = '0' + buffer[bufferIndex];
162            if (output == end) {
163                break;  // denormalized: don't need extra precision.
164                // Note: denormalized numbers will not have the same number of
165                // significantDigits, but do not need them to round-trip.
166            }
167        }
168    }
169    SkASSERT(output <= end);
170    *output = '\0';
171    return static_cast<unsigned>(output - result);
172}
173