Стандарт языка Си С99 TC (1113411), страница 8
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A NaN is an encoding signifying Not-a-Number. A quiet NaN propagatesthrough almost every arithmetic operation without raising a floating-point exception; asignaling NaN generally raises a floating-point exception when occurring as an15) See 6.2.5.16) The floating-point model is intended to clarify the description of each floating-point characteristic anddoes not require the floating-point arithmetic of the implementation to be identical.§5.2.4.2.2Environment23ISO/IEC 9899:TC3Committee Draft — Septermber 7, 2007WG14/N1256arithmetic operand.17)4An implementation may give zero and non-numeric values (such as infinities and NaNs) asign or may leave them unsigned.
Wherever such values are unsigned, any requirementin this International Standard to retrieve the sign shall produce an unspecified sign, andany requirement to set the sign shall be ignored.5The accuracy of the floating-point operations (+, -, *, /) and of the library functions in<math.h> and <complex.h> that return floating-point results is implementationdefined, as is the accuracy of the conversion between floating-point internalrepresentations and string representations performed by the library functions in<stdio.h>, <stdlib.h>, and <wchar.h>. The implementation may state that theaccuracy is unknown.6All integer values in the <float.h> header, except FLT_ROUNDS, shall be constantexpressions suitable for use in #if preprocessing directives; all floating values shall beconstant expressions.
All except DECIMAL_DIG, FLT_EVAL_METHOD, FLT_RADIX,and FLT_ROUNDS have separate names for all three floating-point types. The floatingpoint model representation is provided for all values except FLT_EVAL_METHOD andFLT_ROUNDS.7The rounding mode for floating-point addition is characterized by the implementationdefined value of FLT_ROUNDS:18)-10123indeterminabletoward zeroto nearesttoward positive infinitytoward negative infinityAll other values for FLT_ROUNDS characterize implementation-defined roundingbehavior.8Except for assignment and cast (which remove all extra range and precision), the valuesof operations with floating operands and values subject to the usual arithmeticconversions and of floating constants are evaluated to a format whose range and precisionmay be greater than required by the type. The use of evaluation formats is characterizedby the implementation-defined value of FLT_EVAL_METHOD:19)17) IEC 60559:1989 specifies quiet and signaling NaNs.
For implementations that do not supportIEC 60559:1989, the terms quiet NaN and signaling NaN are intended to apply to encodings withsimilar behavior.18) Evaluation of FLT_ROUNDS correctly reflects any execution-time change of rounding mode throughthe function fesetround in <fenv.h>.24Environment§5.2.4.2.2WG14/N1256-1Committee Draft — Septermber 7, 2007ISO/IEC 9899:TC3indeterminable;0evaluate all operations and constants just to the range and precision of thetype;1evaluate operations and constants of type float and double to therange and precision of the double type, evaluate long doubleoperations and constants to the range and precision of the long doubletype;2evaluate all operations and constants to the range and precision of thelong double type.All other negative values for FLT_EVAL_METHOD characterize implementation-definedbehavior.9The values given in the following list shall be replaced by constant expressions withimplementation-defined values that are greater or equal in magnitude (absolute value) tothose shown, with the same sign:— radix of exponent representation, bFLT_RADIX2— number of base-FLT_RADIX digits in the floating-point significand, pFLT_MANT_DIGDBL_MANT_DIGLDBL_MANT_DIG— number of decimal digits, n, such that any floating-point number in the widestsupported floating type with pmax radix b digits can be rounded to a floating-pointnumber with n decimal digits and back again without change to the value, pmax log10 bif b is a power of 10 1 + pmax log10 b otherwiseDECIMAL_DIG10— number of decimal digits, q, such that any floating-point number with q decimal digitscan be rounded into a floating-point number with p radix b digits and back againwithout change to the q decimal digits,19) The evaluation method determines evaluation formats of expressions involving all floating types, notjust real types.
For example, if FLT_EVAL_METHOD is 1, then the product of two float_Complex operands is represented in the double _Complex format, and its parts are evaluated todouble.§5.2.4.2.2Environment25ISO/IEC 9899:TC3Committee Draft — Septermber 7, 2007WG14/N1256 p log10 bif b is a power of 10 ( p − 1) log10 b otherwiseFLT_DIG6DBL_DIG10LDBL_DIG10— minimum negative integer such that FLT_RADIX raised to one less than that power isa normalized floating-point number, eminFLT_MIN_EXPDBL_MIN_EXPLDBL_MIN_EXP— minimum negative integer such that 10 raised to that power is in the range ofnormalized floating-point numbers, log10 b emin −1 FLT_MIN_10_EXP-37DBL_MIN_10_EXP-37LDBL_MIN_10_EXP-37— maximum integer such that FLT_RADIX raised to one less than that power is arepresentable finite floating-point number, emaxFLT_MAX_EXPDBL_MAX_EXPLDBL_MAX_EXP— maximum integer such that 10 raised to that power is in the range of representablefinite floating-point numbers, log10 ((1 − b− p )b emax )FLT_MAX_10_EXPDBL_MAX_10_EXPLDBL_MAX_10_EXP10+37+37+37The values given in the following list shall be replaced by constant expressions withimplementation-defined values that are greater than or equal to those shown:— maximum representable finite floating-point number, (1 − b− p )b emaxFLT_MAXDBL_MAXLDBL_MAX111E+371E+371E+37The values given in the following list shall be replaced by constant expressions withimplementation-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 thegiven floating point type, b1− p26Environment§5.2.4.2.2WG14/N1256Committee Draft — Septermber 7, 2007FLT_EPSILONDBL_EPSILONLDBL_EPSILONISO/IEC 9899:TC31E-51E-91E-9— minimum normalized positive floating-point number, b emin −1FLT_MINDBL_MINLDBL_MIN1E-371E-371E-37Recommended practice12Conversion from (at least) double to decimal with DECIMAL_DIG digits and backshould be the identity function.13EXAMPLE 1 The following describes an artificial floating-point representation that meets the minimumrequirements of this International Standard, and the appropriate values in a <float.h> header for typefloat:x = s16e6f k 16−k ,Σk=1FLT_RADIXFLT_MANT_DIGFLT_EPSILONFLT_DIGFLT_MIN_EXPFLT_MINFLT_MIN_10_EXPFLT_MAX_EXPFLT_MAXFLT_MAX_10_EXP14−31 ≤ e ≤ +321669.53674316E-07F6-312.93873588E-39F-38+323.40282347E+38F+38EXAMPLE 2 The following describes floating-point representations that also meet the requirements forsingle-precision and double-precision normalized numbers in IEC 60559,20) and the appropriate values in a<float.h> header for types float and double:24x f = s2ef k 2−k ,Σk=1x d = s2ef k 2−k ,Σk=153FLT_RADIXDECIMAL_DIGFLT_MANT_DIGFLT_EPSILONFLT_EPSILON−125 ≤ e ≤ +128−1021 ≤ e ≤ +1024217241.19209290E-07F // decimal constant0X1P-23F // hex constant20) The floating-point model in that standard sums powers of b from zero, so the values of the exponentlimits are one less than shown here.§5.2.4.2.2Environment27ISO/IEC 9899:TC3Committee Draft — Septermber 7, 2007FLT_DIG6FLT_MIN_EXP-125FLT_MIN1.17549435E-38FFLT_MIN0X1P-126FFLT_MIN_10_EXP-37FLT_MAX_EXP+128FLT_MAX3.40282347E+38FFLT_MAX0X1.fffffeP127FFLT_MAX_10_EXP+38DBL_MANT_DIG53DBL_EPSILON 2.2204460492503131E-16DBL_EPSILON0X1P-52DBL_DIG15DBL_MIN_EXP-1021DBL_MIN2.2250738585072014E-308DBL_MIN0X1P-1022DBL_MIN_10_EXP-307DBL_MAX_EXP+1024DBL_MAX1.7976931348623157E+308DBL_MAX0X1.fffffffffffffP1023DBL_MAX_10_EXP+308WG14/N1256// decimal constant// hex constant// decimal constant// hex constant// decimal constant// hex constant// decimal constant// hex constant// decimal constant// hex constantIf a type wider than double were supported, then DECIMAL_DIG would be greater than 17.
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