1 /* floating point to accurate string
2
3 Copyright (C) 2010-2023 Free Software Foundation, Inc.
4
5 This program is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
9
10 This program is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
14
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <https://www.gnu.org/licenses/>. */
17
18 /* Written by Paul Eggert. */
19
20 #ifndef _GL_FTOASTR_H
21 #define _GL_FTOASTR_H
22
23 #include "intprops.h"
24 #include <float.h>
25 #include <stddef.h>
26
27 /* Store into BUF (of size BUFSIZE) an accurate minimal-precision
28 string representation of a floating point number. FLAGS affect the
29 formatting of the number. Pad the output string with spaces as
30 necessary to width WIDTH bytes, in the style of printf. WIDTH must
31 be nonnegative. X is the floating-point number to be converted.
32
33 Return the number of bytes stored into BUF, not counting the
34 terminating null. However, do not overrun BUF: if BUF is too
35 small, return a fairly tight (but not necessarily exact) upper
36 bound on the value that would have been returned if BUF had been
37 big enough. If SIZE is zero, BUF may be a null pointer. On error
38 (e.g., returned value would exceed INT_MAX), return -1 and set
39 errno.
40
41 Example:
42
43 char buf[DBL_BUFSIZE_BOUND];
44 int r = dtoastr (buf, sizeof buf, 0, 0, 0.1);
45
46 In the C locale, this sets R to 3 and stores "0.1" into BUF. */
47
48 int ftoastr (char *buf, size_t bufsize, int flags, int width, float x);
49 int dtoastr (char *buf, size_t bufsize, int flags, int width, double x);
50 int ldtoastr (char *buf, size_t bufsize, int flags, int width, long double x);
51
52 /* The last two functions except that the formatting takes place in
53 the C locale. */
54 int c_dtoastr (char *buf, size_t bufsize, int flags, int width, double x);
55 int c_ldtoastr (char *buf, size_t bufsize, int flags, int width, long double x);
56
57
58 /* Flag values for ftoastr etc. These can be ORed together. */
59 enum
60 {
61 /* Left justify within the width; the default is right justification. */
62 FTOASTR_LEFT_JUSTIFY = 1,
63
64 /* Output "+" before positive numbers; the default outputs nothing. */
65 FTOASTR_ALWAYS_SIGNED = 2,
66
67 /* Output " " before positive numbers; ignored if
68 FTOASTR_ALWAYS_SIGNED is also given. */
69 FTOASTR_SPACE_POSITIVE = 4,
70
71 /* Pad with zeros instead of spaces; ignored if FTOASTR_LEFT_JUSTIFY
72 is also given. */
73 FTOASTR_ZERO_PAD = 8,
74
75 /* Use 'E' instead of 'e' before the exponent. */
76 FTOASTR_UPPER_E = 16
77 };
78
79
80 /* _GL_FLT_PREC_BOUND is an upper bound on the precision needed to
81 represent a float value without losing information. Likewise for
82 _GL_DBL_PREC_BOUND and double, and _GL_LDBL_PREC_BOUND and long double.
83 These are macros, not enums, to work around a bug in IBM xlc 12.1. */
84
85 #if FLT_RADIX == 10 /* decimal floating point */
86 # define _GL_FLT_PREC_BOUND FLT_MANT_DIG
87 # define _GL_DBL_PREC_BOUND DBL_MANT_DIG
88 # define _GL_LDBL_PREC_BOUND LDBL_MANT_DIG
89 #else
90
91 /* An upper bound on the number of bits needed to represent a single
92 digit in a floating-point fraction. */
93 # if FLT_RADIX == 2 /* IEEE 754 floating point, VAX floating point, etc. */
94 # define _GL_FLOAT_DIG_BITS_BOUND 1
95 # elif FLT_RADIX <= 16 /* IBM hex floating point has FLT_RADIX == 16. */
96 # define _GL_FLOAT_DIG_BITS_BOUND 4
97 # else /* no machine is this bad, but let's be complete */
98 # define _GL_FLOAT_DIG_BITS_BOUND ((int) TYPE_WIDTH (int) - 1)
99 # endif
100
101 /* An upper bound on the number of decimal digits needed to represent
102 a floating point number accurately, assuming a fraction contains
103 DIG digits. For why the "+ 1" is needed, see "Binary to Decimal
104 Conversion" in David Goldberg's paper "What Every Computer
105 Scientist Should Know About Floating-Point Arithmetic"
106 <https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html>. */
107 # define _GL_FLOAT_PREC_BOUND(dig) \
108 (INT_BITS_STRLEN_BOUND ((dig) * _GL_FLOAT_DIG_BITS_BOUND) + 1)
109
110 # define _GL_FLT_PREC_BOUND _GL_FLOAT_PREC_BOUND ( FLT_MANT_DIG)
111 # define _GL_DBL_PREC_BOUND _GL_FLOAT_PREC_BOUND ( DBL_MANT_DIG)
112 # define _GL_LDBL_PREC_BOUND _GL_FLOAT_PREC_BOUND (LDBL_MANT_DIG)
113 #endif
114
115
116 /* Bound on the number of bytes printed for an exponent in the range
117 MIN..MAX, where MIN < 0 < MAX; printf always prints a sign and at
118 least 2 digits. Although the maximum known exponent is 4932 for
119 IEEE 754 binary128, support tight bounds for exponents up to a
120 million, just in case. */
121 #define _GL_FLOAT_EXPONENT_STRLEN_BOUND(min, max) \
122 ( -100 < (min) && (max) < 100 ? 3 \
123 : -1000 < (min) && (max) < 1000 ? 4 \
124 : -10000 < (min) && (max) < 10000 ? 5 \
125 : -100000 < (min) && (max) < 100000 ? 6 \
126 : -1000000 < (min) && (max) < 1000000 ? 7 \
127 : INT_STRLEN_BOUND (int) /* not a tight bound */)
128
129 /* A reasonably tight bound on the length of a type-T floating value
130 formatted with ftoastr etc. Room is needed for sign, fraction
131 digits, decimal point, "e", and exponent. POINTLEN should be a
132 reasonably tight bound on the string length of the decimal
133 point. */
134 #define _GL_FLOAT_STRLEN_BOUND_L(t, pointlen) \
135 (1 + _GL_##t##_PREC_BOUND + pointlen + 1 \
136 + _GL_FLOAT_EXPONENT_STRLEN_BOUND (t##_MIN_10_EXP, t##_MAX_10_EXP))
137 #define FLT_STRLEN_BOUND_L(pointlen) _GL_FLOAT_STRLEN_BOUND_L ( FLT, pointlen)
138 #define DBL_STRLEN_BOUND_L(pointlen) _GL_FLOAT_STRLEN_BOUND_L ( DBL, pointlen)
139 #define LDBL_STRLEN_BOUND_L(pointlen) _GL_FLOAT_STRLEN_BOUND_L (LDBL, pointlen)
140
141 /* Looser bounds that are locale-independent and are integral constant
142 expressions. */
143 #define FLT_STRLEN_BOUND FLT_STRLEN_BOUND_L (MB_LEN_MAX)
144 #define DBL_STRLEN_BOUND DBL_STRLEN_BOUND_L (MB_LEN_MAX)
145 #define LDBL_STRLEN_BOUND LDBL_STRLEN_BOUND_L (MB_LEN_MAX)
146
147 /* Looser, locale-independent bounds that include the trailing null byte. */
148 #define FLT_BUFSIZE_BOUND ( FLT_STRLEN_BOUND + 1)
149 #define DBL_BUFSIZE_BOUND ( DBL_STRLEN_BOUND + 1)
150 #define LDBL_BUFSIZE_BOUND (LDBL_STRLEN_BOUND + 1)
151
152 #endif /* _GL_FTOASTR_H */