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.
17 static 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. */
58 unsigned 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