float.h(3head)

1float.h(3HEAD)                      Headers                     float.h(3HEAD)
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NAME

6       float.h, float - floating types
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SYNOPSIS

9       #include <float.h>
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DESCRIPTION

13       The  characteristics  of floating types are defined in terms of a model
14       that describes a representation of floating-point  numbers  and  values
15       that  provide  information  about  an  implementation's  floating-point
16       arithmetic.
17
18
19       The following parameters are used to define the model for  each  float‐
20       ing-point type:
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22       s     sign (±1)
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25       b     base or radix of exponent representation (an integer >1)
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28       e     exponent  (an  integer  between  a  minimum  e(min) and a maximum
29             e(max))
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32       p     precision (the number of base-b digits in the significand)
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35       f(k)  non-negative integers less than b (the significand digits)
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39       In addition to  normalized  floating-point  numbers  (f(1)>0  if  x≠0),
40       floating  types  might be able to contain other kinds of floating-point
41       numbers, such  as  subnormal  floating-point  numbers  (x≠0,  e=e(min),
42       f(1)=0)   and   unnormalized  floating-point  numbers  (x≠0,  e=e(min),
43       f(1)=0), and values  that  are  not  floating-point  numbers,  such  as
44       infinities  and  NaNs.  A NaN is an encoding signifying Not-a-Number. A
45       quiet NaN propagates through almost every arithmetic operation  without
46       raising  a floating-point exception; a signaling NaN generally raises a
47       floating-point exception when occurring as an arithmetic operand.
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50       The accuracy  of  the  library  functions  in  math.h(3HEAD)  and  com‐
51       plex.h(3HEAD)  that  return  floating-point  results  is defined on the
52       libm(3LIB) manual page.
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55       All integer values in the <float.h> header, except FLT_ROUNDS, are con‐
56       stant expressions suitable for use in #if preprocessing directives; all
57       floating values  are  constant  expressions.  All  except  DECIMAL_DIG,
58       FLT_EVAL_METHOD,  FLT_RADIX, and FLT_ROUNDS have separate names for all
59       three floating-point types. The floating-point model representation  is
60       provided for all values except FLT_EVAL_METHOD and FLT_ROUNDS.
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63       The  rounding  mode for floating-point addition is characterized by the
64       value of FLT_ROUNDS:
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66       -1    Indeterminable.
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69       0     Toward zero.
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72       1     To nearest.
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75       2     Toward positive infinity.
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78       3     Toward negative infinity.
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82       The values of operations with floating operands and values  subject  to
83       the  usual  arithmetic conversions and of floating constants are evalu‐
84       ated to a format whose  range  and  precision  might  be  greater  than
85       required by the type. The use of evaluation formats is characterized by
86       the architecture-dependent value of FLT_EVAL_METHOD:
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88       -1    Indeterminable.
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91       0     Evaluate all operations and constants just to the range and  pre‐
92             cision of the type.
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95       1     Evaluate operations and constants of type float and double to the
96             range and precision of the  double  type;  evaluate  long  double
97             operations  and  constants to the range and precision of the long
98             double type.
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101       2     Evaluate all operations and constants to the range and  precision
102             of the long double type.
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105
106       The values given in the following list are defined as constants.
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108           o      Radix of exponent representation, b.
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110                    FLT_RADIX
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113           o      Number  of  base-FLT_RADIX digits in the floating-point sig‐
114                  nificand, p.
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116                    FLT_MANT_DIG
117                    DBL_MANT_DIG
118                    LDBL_MANT_DIG
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120
121           o      Number of decimal digits, n, such  that  any  floating-point
122                  number  in  the  widest  supported floating type with p(max)
123                  radix b digits can be rounded  to  a  floating-point  number
124                  with  n  decimal digits and back again without change to the
125                  value.
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127                    DECIMAL_DIG
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130           o      Number of decimal digits, q, such  that  any  floating-point
131                  number with q decimal digits can be rounded into a floating-
132                  point number with p radix b digits and  back  again  without
133                  change to the q decimal digits.
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135                    FLT_DIG
136                    DBL_DIG
137                    LDBL_DIG
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139
140           o      Minimum  negative integer such that FLT_RADIX raised to that
141                  power minus 1 is a normalized floating-point number, e(min).
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143                    FLT_MIN_EXP
144                    DBL_MIN_EXP
145                    LDBL_MIN_EXP
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148           o      Minimum negative integer such that 10 raised to  that  power
149                  is in the range of normalized floating-point numbers.
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151                    FLT_MIN_10_EXP
152                    DBL_MIN_10_EXP
153                    LDBL_MIN_10_EXP
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155
156           o      Maximum  integer  such  that  FLT_RADIX raised to that power
157                  minus 1 is a  representable  finite  floating-point  number,
158                  e(max).
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160                    FLT_MAX_EXP
161                    DBL_MAX_EXP
162                    LDBL_MAX_EXP
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164
165           o      Maximum  integer such that 10 raised to that power is in the
166                  range of representable finite floating-point numbers.
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168                    FLT_MAX_10_EXP
169                    DBL_MAX_10_EXP
170                    LDBL_MAX_10_EXP
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174       The values given in the following list are defined as constant  expres‐
175       sions with values that are greater than or equal to those shown:
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177           o      Maximum representable finite floating-point number.
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179                    FLT_MAX
180                    DBL_MAX
181                    LDBL_MAX
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184
185       The  values given in the following list are defined as constant expres‐
186       sions with implementation-defined (positive) values that are less  than
187       or equal to those shown:
188
189           o      The  difference between 1 and the least value greater than 1
190                  that is representable in the given floating-point type,  b^1
191                  - p.
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193                    FLT_EPSILON
194                    DBL_EPSILON
195                    LDBL_EPSILON
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197
198           o      Minimum    normalized    positive   floating-point   number,
199                  b^e(min)^-1.
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201                    FLT_MIN
202                    DBL_MIN
203                    LDBL_MIN
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ATTRIBUTES

207       See attributes(5) for descriptions of the following attributes:
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212       ┌─────────────────────────────┬─────────────────────────────┐
213       │      ATTRIBUTE TYPE         │      ATTRIBUTE VALUE        │
214       ├─────────────────────────────┼─────────────────────────────┤
215       │Interface Stability          │Standard                     │
216       └─────────────────────────────┴─────────────────────────────┘
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NAME

SYNOPSIS

DESCRIPTION

ATTRIBUTES

SEE ALSO