SymbolsABCDEFGHIJKLMNOPQRSTUVWXYZAPDA format conventions for this bookIEEE standard$IEEE Standard 754. See IEEE standardPowerPC NumericsSANE 680x0-based Macintosh computersnumerics environmentaccuracy of basic arithmetic operations ANSI X3J11.1arithmetic, IEEE standard
C languageconformance to IEEE 754&computer approximation of real numbersdecimal fractionsdivisionby zero2elementary functions. See transcendental functionsexception handlingexceptional events
exceptionsFPCE technical reportIEEE arithmetic
advantages
advantages
C languageIEEE Standard 854-IEEE standard arithmetic. See IEEE arithmetic
Infinitiesas alternative to stoppinginterval arithmeticinverse operationsMathLibNaNsas alternative to stoppingNCEG Numerical C Extensions Group
advantagesSANE, compared to precision real numberscomputer approximationroundingdefinedrounding directioncontrol compared to PowerPC Numericstranscendental functionsdefinedzero division by∞. See Infinities ±0. See zerobias of exponents!classes of floating-point numbers data formatschoosingclasses of numbersdiagramsdiagrams, symbols used indouble formatdouble-double format precision ofrange ofsingle formatdenormalized numbers
density ofdouble-double format density of denormalized numbers#density of single-precision numbersdouble formatcompilerdiagramdiagram, symbols used in precisionrangerepresentation of valuesdouble-double formatcompared to extended formatcompilerdiagramdiagram, symbols used ininterpretation of values precisionrangeexponentdefinedextended data type compared to double-double format-floating-point data formats. See data formatsfloating-point numbers
classes of#floating-point values, interpretingflush-to-zero systemsformats. See data formatsfraction fielddefinedgradual underflowIEEE data formats'. See also single format, double format data formatsdouble-double formatnegativepositiveinteger types"interpreting floating-point valuesinvalid exceptionsignaling NaN, result ofdouble-double formatquiet signaling!negative Infinity. See Infinitiesnegative zero. See zeronormalized numbers compared to denormalized numbersdouble-double formatNot-a-Number. See NaNsnumbers, classes of!positive Infinity. See Infinitiespositive zero. See zero data formatsof data formats
quiet NaNsrange of data formats(roundoff error with denormalized numberssign bit sign of zerosignaling NaNs significandsingle formatcompilerdiagramdiagram, symbols used in precisionrangerepresentation of values$single-precision numbers, density of small valuesand error analysis representingsymbols in format diagramstypes. See data formats underflowgradualvalues, interpreting variable types. See data formats–0 as a resultdouble-double formatsign ofarithmetic operationsautomatic type conversions#function calls, conversions during conversions during expression evaluation expression evaluation formatminimum evaluation formatsemantic typeevaluation formatminimum widest need expression evaluation format expression evaluation methodscomparedexamples minimum evaluation format onlywidest-need evaluation&floating-point expressions, evaluatingminimum evaluation format"compared to widest-need evaluationexamples
operations!subject to arithmetic conversionsexpression evaluationof expression evaluationsemantic typewidest-need evaluation compared to minimum evaluationexamplesabsolute valueaddition invalid exception, generating comparisons invalid exception, generatinginvalid exceptioncopysign functioninvalid exceptioncurrent rounding directiondefault environmentdefault rounding directiondivide-by-zero exceptiondefined invalid exception, generatingdownward roundingdefined environmentdefaultenvironmental controlsdescriptions ofdivide-by-zeroinexactinvalidoverflow underflowfabs function+floating-point environment. See environment)floating-point exceptions. See exceptionsintegers, converting to
truncating
exceptionsrounding direction modes . See also rounding directionrounding precision modesinexact exceptionintegers, convertingrounding
truncating2invalid-operation exception. See invalid exceptionmultiplication invalid exception, generatingoverflowenvironmental controlsremainder function invalid exception, generating result, tinydefaultdownward
to nearest toward zeroupwardrounding downwarddefined&rounding modes. See rounding directionrounding precision modesrounding to integerrounding to nearest valuerounding toward zerodefinedrounding upwarddefinedinvalid exceptionsquare root operation invalid exception, generating tiny resultto-nearest rounding)toward –∞ rounding. See downward rounding'toward +∞ rounding. See upward roundingtoward-zero roundingdefined$truncating floating-point to integerupward roundingrounding toward decimal to binary conversions binary to decimal conversionsdouble-double formatstrings
structures accuracy of decimal to binarybetween decimal formats between floating-point formatsbinary to decimaldecimal to binarydouble-double formatdouble-double to decimalfloating-point to integerinexact exceptioninteger to floating-pointoverflow exceptionunderflow exceptionconverting betweendecform structure!decimal data, reading and writing decimal formatting structuredecimal stringsdecimal structure decimal to binary conversionsdouble-double formatstrings
structures decimal to decimal conversions$converting from double-double format converting from single formatdefined"converting to double-double formatconverting to single formatdefined converting from double format converting from single formatconverting to decimalconverting to double formatconverting to single formatconversions required conversionsconverting to integer conversionsconverting to integer conversionsconversions supported converting from double formatdefined$converting from double-double formatconverting to double formatdefined"converting to double-double formatstring conversions conversions– (minus) operator ! !%! (not less or greater than) operator!= (not equal) operator!= (unordered) operator !> (not greater than) operator(!>= (not greater than or equal) operator (less or greater than) operator* (multiply) operator+ (plus) operator/ (divide) operator= (ordered) operator== (equal to) operatordefined> (greater than) operatordefined&>= (greater than or equal to) operatorargument reductionadditiondivisionmultiplication remainderround-to-integer square root subtractionauxiliary functions&comparison operations. See comparisonscomparison operatorsinvolving Infinitiesinvolving NaNsrint functionrint functiondifference operationdefinedequal to operatorconverting to integerfmod function functions auxiliarygreater than operator
operationsarithmetic operationsauxiliary functions comparisons comparisonsmodulo function comparisonsnot unordered comparison
arithmeticdefined
comparisondefinedcompilerordered comparisondefinedfunctions supportedoperations supportedorder ofrelational operatorsdefinedremainderl functionremquo functionremquol functionrint functionrintl functionround to integer operationcurrent comparisonssqrt functionsqrtl functiondefinedsubtraction operationdefinedunordered (comparison)defined nan functiondata types, new double type. See double format float type. See single format*long double type. See double-double formatcompilercompilercompilerwidening for efficiency double type. See double formatdouble_t typedef&in definitions of float_t and double_t float type. See single formatcompilerfloat_t typedef
data typesfpclassify macroINFINITY constantisfinite macro isnan macroisnormal macro*long double type. See double-double formatdata types, new NAN constant nan functionPowerPC Numericsnanf functionnanl functioncreatingcompilersignbit macrotagp parameterwidening for efficiencyaccessing the environment C functionsatomic operationsenvironmental controlscontrolling the environment C functions accessing C functionsC functions, types restoringcompilersavingcompilersetting (compiler)environmental access switchpurpose, note on C functions C functionsclearingcompiler
preservingcompilerraisingcompilerrestoring (compiler)savingcompilersettingcompilerspurioustestingcompilerfeclearexcept functionfegetenv function
definition%difference from feholdexcept functionfegetexcept function
definitionwith fesetexcept functionfegetround function
definitionwith fesetround functionfeholdexcept function fenv.h file fenv_t typeferaiseexcept functionfesetenv functionfesetexcept functionfesetround functionfetestexcept functionfeupdateenv function
definitionwith feholdexcept functionfexcept_t typeFE_ALL_EXCEPT constantFE_DFL_ENV constantFE_DIVBYZERO constantFE_DOWNWARD constantFE_INEXACT constantFE_INVALID constantFE_OVERFLOW constantFE_TONEAREST constantFE_TOWARDZERO constantFE_UNDERFLOW constantFE_UPWARD constantenvironmental accessenvironmental controlscompilersaving (compiler)settingcompilerexamplespurious exceptionsexample C functions conversionsceil functionceill function C functionsceil function C functionsfloor functionnearbyint functionrinttol functionround functionroundtol functiontrunc functionnearbyint functionrinttol functiondec2f functiondec2l functiondec2num functiondec2numl functiondec2s functiondec2str function
definition digits field style fielddecimal output fixed-stylefloating-style
definition exp field sgn field sig field C functionsfloor functioncompilerfloor functionfloorl functionformatters, numericformatting outputfixed-style decimalfloating-style decimal fp.h file functions conversionsnearbyint functionconverting to decimal converting to floating-pointconverting to stringcompiler conversionsconverting to decimal converting to floating-pointconverting to stringnearbyint functionnearbyintl functionnum2dec function
definitionwith dec2str function
conversioncompileroutputfixed-style decimalfloating-style decimalrinttol functionrinttoll functionround functionfloor functiontrunc functionceil functionroundl functionroundtol functionroundtoll functionscannersstr2dec functiontrunc functiontrunc functiontruncl functionceil functioncompiler,antilog functions. See exponential functionsscalingsign manipulationbase 2 exponentialtranscendental functionscomparison functions C functionscopysignl function difference, positive function exp functionexp2 functionexp2l functionexpl functionexpm1 functionexpm1l functiondetermining value ofexponential functionsbase 2 exponentialnatural exponentialnatural exponential – 1fabsl functionfdim functionfdiml functionfmax functionfmaxl functionfmin functionfminl functiontranscendental functionsdetermining value offrexp functionfrexpl function
