1<float.h>(0P) POSIX Programmer's Manual <float.h>(0P)
2
6 float.h - floating types
7
9 #include <float.h>
10
12 The characteristics of floating types are defined in terms of a model
13 that describes a representation of floating-point numbers and values
14 that provide information about an implementation's floating-point
15 arithmetic.
16 The following parameters are used to define the model for each float‐
18 ing-point type:
19 s Sign (±1).
21 b Base or radix of exponent representation (an integer >1).
23 e Exponent (an integer between a minimum e_min and a maximum
25 e_max).
26 p Precision (the number of base-b digits in the significand).
28 f_k Non-negative integers less than b (the significand digits).
30 A floating-point number x is defined by the following model:
33 In addition to normalized floating-point numbers (f_1>0 if x!=0),
35 floating types may be able to contain other kinds of floating-point
36 numbers, such as subnormal floating-point numbers ( x!=0, e= e_min,
37 f_1=0) and unnormalized floating-point numbers ( x!=0, e> e_min,
38 f_1=0), and values that are not floating-point numbers, such as infini‐
39 ties and NaNs. A NaN is an encoding signifying Not-a-Number. A quiet
40 NaN propagates through almost every arithmetic operation without rais‐
41 ing a floating-point exception; a signaling NaN generally raises a
42 floating-point exception when occurring as an arithmetic operand.
43 The accuracy of the floating-point operations ( '+', '-', '*', '/' )
45 and of the library functions in <math.h> and <complex.h> that return
46 floating-point results is implementation-defined. The implementation
47 may state that the accuracy is unknown.
48 All integer values in the <float.h> header, except FLT_ROUNDS, shall be
50 constant expressions suitable for use in #if preprocessing directives;
51 all floating values shall be constant expressions. All except DECI‐
52 MAL_DIG, FLT_EVAL_METHOD, FLT_RADIX, and FLT_ROUNDS have separate names
53 for all three floating-point types. The floating-point model represen‐
54 tation is provided for all values except FLT_EVAL_METHOD and
55 FLT_ROUNDS.
56 The rounding mode for floating-point addition is characterized by the
58 implementation-defined value of FLT_ROUNDS:
59 -1 Indeterminable.
61 0 Toward zero.
63 1 To nearest.
65 2 Toward positive infinity.
67 3 Toward negative infinity.
69 All other values for FLT_ROUNDS characterize implementation-defined
72 rounding behavior.
73 The values of operations with floating operands and values subject to
75 the usual arithmetic conversions and of floating constants are evalu‐
76 ated to a format whose range and precision may be greater than required
77 by the type. The use of evaluation formats is characterized by the
78 implementation-defined value of FLT_EVAL_METHOD:
79 -1 Indeterminable.
81 0 Evaluate all operations and constants just to the range and pre‐
83 cision of the type.
84 1 Evaluate operations and constants of type float and double to
86 the range and precision of the double type; evaluate long double
87 operations and constants to the range and precision of the long
88 double type.
89 2 Evaluate all operations and constants to the range and precision
91 of the long double type.
92 All other negative values for FLT_EVAL_METHOD characterize implementa‐
95 tion-defined behavior.
96 The values given in the following list shall be defined as constant
98 expressions with implementation-defined values that are greater or
99 equal in magnitude (absolute value) to those shown, with the same sign.
100 * Radix of exponent representation, b.
102 FLT_RADIX
104 2
105 * Number of base-FLT_RADIX digits in the floating-point significand,
108 p.
109 FLT_MANT_DIG
111 DBL_MANT_DIG
113 LDBL_MANT_DIG
115 * Number of decimal digits, n, such that any floating-point number in
118 the widest supported floating type with p_max radix b digits can be
119 rounded to a floating-point number with n decimal digits and back
120 again without change to the value.
121 DECIMAL_DIG
123 10
124 * Number of decimal digits, q, such that any floating-point number
127 with q decimal digits can be rounded into a floating-point number
128 with p radix b digits and back again without change to the q decimal
129 digits.
130 FLT_DIG
132 6
133 DBL_DIG
135 10
136 LDBL_DIG
138 10
139 * Minimum negative integer such that FLT_RADIX raised to that power
142 minus 1 is a normalized floating-point number, e_min.
143 FLT_MIN_EXP
145 DBL_MIN_EXP
147 LDBL_MIN_EXP
149 * Minimum negative integer such that 10 raised to that power is in the
152 range of normalized floating-point numbers.
153 FLT_MIN_10_EXP
155 -37
156 DBL_MIN_10_EXP
158 -37
159 LDBL_MIN_10_EXP
161 -37
162 * Maximum integer such that FLT_RADIX raised to that power minus 1 is
165 a representable finite floating-point number, e_max.
166 FLT_MAX_EXP
168 DBL_MAX_EXP
170 LDBL_MAX_EXP
172 * Maximum integer such that 10 raised to that power is in the range of
175 representable finite floating-point numbers.
176 FLT_MAX_10_EXP
178 +37
179 DBL_MAX_10_EXP
181 +37
182 LDBL_MAX_10_EXP
184 +37
185 The values given in the following list shall be defined as constant
188 expressions with implementation-defined values that are greater than or
189 equal to those shown:
190 * Maximum representable finite floating-point number.
192 FLT_MAX
194 1E+37
195 DBL_MAX
197 1E+37
198 LDBL_MAX
200 1E+37
201 The values given in the following list shall be defined as constant
204 expressions with implementation-defined (positive) values that are less
205 than or equal to those shown:
206 * The difference between 1 and the least value greater than 1 that is
208 representable in the given floating-point type, b**1-p.
209 FLT_EPSILON
211 1E-5
212 DBL_EPSILON
214 1E-9
215 LDBL_EPSILON
217 1E-9
218 * Minimum normalized positive floating-point number, b**e_min.
221 FLT_MIN
223 1E-37
224 DBL_MIN
226 1E-37
227 LDBL_MIN
229 1E-37
230 The following sections are informative.
233
235 None.
236
238 None.
239
241 None.
242
244 <complex.h>, <math.h>
245
247 Portions of this text are reprinted and reproduced in electronic form
248 from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
249 -- Portable Operating System Interface (POSIX), The Open Group Base
250 Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
251 Electrical and Electronics Engineers, Inc and The Open Group. In the
252 event of any discrepancy between this version and the original IEEE and
253 The Open Group Standard, the original IEEE and The Open Group Standard
254 is the referee document. The original Standard can be obtained online
255 at http://www.opengroup.org/unix/online.html .
256IEEE/The Open Group 2003 <float.h>(0P)