Originální popis anglicky:
float.h - floating types
Návod, kniha: POSIX Programmer's Manual
#include <float.h>
The characteristics of floating types are defined in terms of a model that
describes a representation of floating-point numbers and values that provide
information about an implementation's floating-point arithmetic.
The following parameters are used to define the model for each floating-point
type:
- s
- Sign (±1).
- b
- Base or radix of exponent representation (an integer
>1).
- e
- Exponent (an integer between a minimum e_min and a
maximum e_max).
- p
- Precision (the number of base-b digits in the
significand).
- f_k
- Non-negative integers less than b (the significand
digits).
A floating-point number
x is defined by the following model:
In addition to normalized floating-point numbers (
f_1>0 if
x!=0), floating types may be able to contain other kinds of
floating-point numbers, such as subnormal floating-point numbers (
x!=0,
e=
e_min,
f_1=0) and unnormalized
floating-point numbers (
x!=0,
e>
e_min,
f_1=0), and values that are not floating-point numbers, such as
infinities and NaNs. A
NaN is an encoding signifying Not-a-Number. A
quiet NaN propagates through almost every arithmetic operation without
raising a floating-point exception; a
signaling NaN generally raises a
floating-point exception when occurring as an arithmetic operand.
The accuracy of the floating-point operations (
'+' ,
'-' ,
'*' ,
'/' ) and of the library functions in
<math.h> and
<complex.h> that return floating-point
results is implementation-defined. The implementation may state that the
accuracy is unknown.
All integer values in the
<float.h> header, except FLT_ROUNDS,
shall be constant expressions suitable for use in
#if preprocessing
directives; all floating values shall be constant expressions. All except
DECIMAL_DIG, FLT_EVAL_METHOD, FLT_RADIX, and FLT_ROUNDS have separate names
for all three floating-point types. The floating-point model representation is
provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
The rounding mode for floating-point addition is characterized by the
implementation-defined value of FLT_ROUNDS:
- -1
- Indeterminable.
- 0
- Toward zero.
- 1
- To nearest.
- 2
- Toward positive infinity.
- 3
- Toward negative infinity.
All other values for FLT_ROUNDS characterize implementation-defined rounding
behavior.
The values of operations with floating operands and values subject to the usual
arithmetic conversions and of floating constants are evaluated to a format
whose range and precision may be greater than required by the type. The use of
evaluation formats is characterized by the implementation-defined value of
FLT_EVAL_METHOD:
- -1
- Indeterminable.
- 0
- Evaluate all operations and constants just to the range and
precision of the type.
- 1
- Evaluate operations and constants of type float and
double to the range and precision of the double type;
evaluate long double operations and constants to the range and
precision of the long double type.
- 2
- Evaluate all operations and constants to the range and
precision of the long double type.
All other negative values for FLT_EVAL_METHOD characterize
implementation-defined behavior.
The values given in the following list shall be defined as constant expressions
with implementation-defined values that are greater or equal in magnitude
(absolute value) to those shown, with the same sign.
- *
- Radix of exponent representation, b.
- FLT_RADIX
2
- *
- Number of base-FLT_RADIX digits in the floating-point
significand, p.
- FLT_MANT_DIG
- DBL_MANT_DIG
- LDBL_MANT_DIG
-
- *
- Number of decimal digits, n, such that any
floating-point number in the widest supported floating type with
p_max radix b digits can be rounded to a floating-point
number with n decimal digits and back again without change to the
value.
- DECIMAL_DIG
10
- *
- Number of decimal digits, q, such that any
floating-point number with q decimal digits can be rounded into a
floating-point number with p radix b digits and back again
without change to the q decimal digits.
- FLT_DIG
6
- DBL_DIG
10
- LDBL_DIG
10
- *
- Minimum negative integer such that FLT_RADIX raised to that
power minus 1 is a normalized floating-point number, e_min.
- FLT_MIN_EXP
- DBL_MIN_EXP
- LDBL_MIN_EXP
-
- *
- Minimum negative integer such that 10 raised to that power
is in the range of normalized floating-point numbers.
- FLT_MIN_10_EXP
-37
- DBL_MIN_10_EXP
-37
- LDBL_MIN_10_EXP
-37
- *
- Maximum integer such that FLT_RADIX raised to that power
minus 1 is a representable finite floating-point number,
e_max.
- FLT_MAX_EXP
- DBL_MAX_EXP
- LDBL_MAX_EXP
-
- *
- Maximum integer such that 10 raised to that power is in the
range of representable finite floating-point numbers.
- FLT_MAX_10_EXP
+37
- DBL_MAX_10_EXP
+37
- LDBL_MAX_10_EXP
+37
The values given in the following list shall be defined as constant expressions
with implementation-defined values that are greater than or equal to those
shown:
- *
- Maximum representable finite floating-point number.
- FLT_MAX
1E+37
- DBL_MAX
1E+37
- LDBL_MAX
1E+37
The values given in the following list shall be defined as constant expressions
with implementation-defined (positive) values that are less than or equal to
those shown:
- *
- The difference between 1 and the least value greater than 1
that is representable in the given floating-point type,
b**1-p.
- FLT_EPSILON
1E-5
- DBL_EPSILON
1E-9
- LDBL_EPSILON
1E-9
- *
- Minimum normalized positive floating-point number,
b** e_min.
- FLT_MIN
1E-37
- DBL_MIN
1E-37
- LDBL_MIN
1E-37
The following sections are informative.
None.
None.
None.
<complex.h> ,
<math.h>
Portions of this text are reprinted and reproduced in electronic form from IEEE
Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable
Operating System Interface (POSIX), The Open Group Base Specifications Issue
6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics
Engineers, Inc and The Open Group. In the event of any discrepancy between
this version and the original IEEE and The Open Group Standard, the original
IEEE and The Open Group Standard is the referee document. The original
Standard can be obtained online at http://www.opengroup.org/unix/online.html
.
