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 // returns `value * pow(base, e)`, assuming `e` is positive.
pow_by_squaring(double value,double base,int e)17 static double pow_by_squaring(double value, double base, int e) {
18 // https://en.wikipedia.org/wiki/Exponentiation_by_squaring
19 SkASSERT(e > 0);
20 while (true) {
21 if (e & 1) {
22 value *= base;
23 }
24 e >>= 1;
25 if (0 == e) {
26 return value;
27 }
28 base *= base;
29 }
30 }
31
32 // Return pow(10.0, e), optimized for common cases.
pow10(int e)33 static double pow10(int e) {
34 switch (e) {
35 case 0: return 1.0; // common cases
36 case 1: return 10.0;
37 case 2: return 100.0;
38 case 3: return 1e+03;
39 case 4: return 1e+04;
40 case 5: return 1e+05;
41 case 6: return 1e+06;
42 case 7: return 1e+07;
43 case 8: return 1e+08;
44 case 9: return 1e+09;
45 case 10: return 1e+10;
46 case 11: return 1e+11;
47 case 12: return 1e+12;
48 case 13: return 1e+13;
49 case 14: return 1e+14;
50 case 15: return 1e+15;
51 default:
52 if (e > 15) {
53 return pow_by_squaring(1e+15, 10.0, e - 15);
54 } else {
55 SkASSERT(e < 0);
56 return pow_by_squaring(1.0, 0.1, -e);
57 }
58 }
59 }
60
61 /** Write a string into result, includeing a terminating '\0' (for
62 unit testing). Return strlen(result) (for SkWStream::write) The
63 resulting string will be in the form /[-]?([0-9]*.)?[0-9]+/ and
64 sscanf(result, "%f", &x) will return the original value iff the
65 value is finite. This function accepts all possible input values.
66
67 Motivation: "PDF does not support [numbers] in exponential format
68 (such as 6.02e23)." Otherwise, this function would rely on a
69 sprintf-type function from the standard library. */
SkFloatToDecimal(float value,char result[kMaximumSkFloatToDecimalLength])70 unsigned SkFloatToDecimal(float value, char result[kMaximumSkFloatToDecimalLength]) {
71 /* The longest result is -FLT_MIN.
72 We serialize it as "-.0000000000000000000000000000000000000117549435"
73 which has 48 characters plus a terminating '\0'. */
74
75 static_assert(kMaximumSkFloatToDecimalLength == 49, "");
76 // 3 = '-', '.', and '\0' characters.
77 // 9 = number of significant digits
78 // abs(FLT_MIN_10_EXP) = number of zeros in FLT_MIN
79 static_assert(kMaximumSkFloatToDecimalLength == 3 + 9 - FLT_MIN_10_EXP, "");
80
81 /* section C.1 of the PDF1.4 spec (http://goo.gl/0SCswJ) says that
82 most PDF rasterizers will use fixed-point scalars that lack the
83 dynamic range of floats. Even if this is the case, I want to
84 serialize these (uncommon) very small and very large scalar
85 values with enough precision to allow a floating-point
86 rasterizer to read them in with perfect accuracy.
87 Experimentally, rasterizers such as pdfium do seem to benefit
88 from this. Rasterizers that rely on fixed-point scalars should
89 gracefully ignore these values that they can not parse. */
90 char* output = &result[0];
91 const char* const end = &result[kMaximumSkFloatToDecimalLength - 1];
92 // subtract one to leave space for '\0'.
93
94 /* This function is written to accept any possible input value,
95 including non-finite values such as INF and NAN. In that case,
96 we ignore value-correctness and and output a syntacticly-valid
97 number. */
98 if (value == INFINITY) {
99 value = FLT_MAX; // nearest finite float.
100 }
101 if (value == -INFINITY) {
102 value = -FLT_MAX; // nearest finite float.
103 }
104 if (!std::isfinite(value) || value == 0.0f) {
105 // NAN is unsupported in PDF. Always output a valid number.
106 // Also catch zero here, as a special case.
107 *output++ = '0';
108 *output = '\0';
109 return static_cast<unsigned>(output - result);
110 }
111 if (value < 0.0) {
112 *output++ = '-';
113 value = -value;
114 }
115 SkASSERT(value >= 0.0f);
116
117 int binaryExponent;
118 (void)std::frexp(value, &binaryExponent);
119 static const double kLog2 = 0.3010299956639812; // log10(2.0);
120 int decimalExponent = static_cast<int>(std::floor(kLog2 * binaryExponent));
121 int decimalShift = decimalExponent - 8;
122 double power = pow10(-decimalShift);
123 SkASSERT(value * power <= (double)INT_MAX);
124 int d = static_cast<int>(value * power + 0.5);
125 // SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
126 SkASSERT(d <= 999999999);
127 if (d > 167772159) { // floor(pow(10,1+log10(1<<24)))
128 // need one fewer decimal digits for 24-bit precision.
129 decimalShift = decimalExponent - 7;
130 // SkASSERT(power * 0.1 = pow10(-decimalShift));
131 // recalculate to get rounding right.
132 d = static_cast<int>(value * (power * 0.1) + 0.5);
133 SkASSERT(d <= 99999999);
134 }
135 while (d % 10 == 0) {
136 d /= 10;
137 ++decimalShift;
138 }
139 SkASSERT(d > 0);
140 // SkASSERT(value == (float)(d * pow(10.0, decimalShift)));
141 unsigned char buffer[9]; // decimal value buffer.
142 int bufferIndex = 0;
143 do {
144 buffer[bufferIndex++] = d % 10;
145 d /= 10;
146 } while (d != 0);
147 SkASSERT(bufferIndex <= (int)sizeof(buffer) && bufferIndex > 0);
148 if (decimalShift >= 0) {
149 do {
150 --bufferIndex;
151 *output++ = '0' + buffer[bufferIndex];
152 } while (bufferIndex);
153 for (int i = 0; i < decimalShift; ++i) {
154 *output++ = '0';
155 }
156 } else {
157 int placesBeforeDecimal = bufferIndex + decimalShift;
158 if (placesBeforeDecimal > 0) {
159 while (placesBeforeDecimal-- > 0) {
160 --bufferIndex;
161 *output++ = '0' + buffer[bufferIndex];
162 }
163 *output++ = '.';
164 } else {
165 *output++ = '.';
166 int placesAfterDecimal = -placesBeforeDecimal;
167 while (placesAfterDecimal-- > 0) {
168 *output++ = '0';
169 }
170 }
171 while (bufferIndex > 0) {
172 --bufferIndex;
173 *output++ = '0' + buffer[bufferIndex];
174 if (output == end) {
175 break; // denormalized: don't need extra precision.
176 // Note: denormalized numbers will not have the same number of
177 // significantDigits, but do not need them to round-trip.
178 }
179 }
180 }
181 SkASSERT(output <= end);
182 *output = '\0';
183 return static_cast<unsigned>(output - result);
184 }
185