SymbolsABCDEFGHIJKLMNOPQRSTUVWXYZAPDA format conventions for this book
IEEE standard$IEEE Standard 754. See IEEE standardPowerPC NumericsSANEaccuracy of basic arithmetic operationsarithmetic, IEEE standard&computer approximation of real numbersdecimal fractionsdivisionby zero2elementary functions. See transcendental functionsexception handlingexceptional events
exceptionsIEEE arithmetic
advantages
advantagesIEEE Standard 854-IEEE standard arithmetic. See IEEE arithmetic
Infinitiesas alternative to stoppinginterval arithmeticinverse operationsNaNsas alternative to stopping
advantages precision real numberscomputer approximationroundingdefinedrounding directioncontroltranscendental functionsdefinedzero division by∞. See Infinities ±0. See zerobias of exponents data formatschoosingdiagrams
double formatdouble-double format precision ofrange of
single formatdenormalized numbers
density ofdouble-double format density of denormalized numbers#density of single-precision numbers
double formatdiagramrangedouble-double formatcompared to extended formatdiagraminterpretation of values precisionrangeexponentdefinedextended data type compared to double-double format-floating-point data formats. See data formats#floating-point values, interpretingflush-to-zero systemsformats. See data formatsfraction fielddefinedgradual underflowIEEE data formats'. See also single format, double format data formatsdouble-double formatnegativepositive
integer types"interpreting floating-point valuesinvalid exceptionsignaling NaN, result ofdouble-double formatquiet signaling!negative Infinity. See Infinitiesnegative zero. See zeronormalized numbers compared to denormalized numbersdouble-double formatNot-a-Number. See NaNs!positive Infinity. See Infinitiespositive zero. See zero data formatsof data formats
quiet NaNsrange of data formats(roundoff error with denormalized numberssign bit sign of zerosignaling NaNs significand
single formatdiagramrange$single-precision numbers, density of small valuesand error analysis representingtypes. See data formats underflowgradualvalues, interpreting variable types. See data formats–0 as a resultdouble-double formatsign of expression evaluation format
semantic typeevaluation formatminimum expression evaluation format expression evaluation methodswidest-need evaluationidest-need evaluationlanguage#function calls, conversions duringminimum evaluation formatexamples perations!subject to arithmetic conversionsrithmetic operationsautomatic type conversions
fabs function+floating-point environment. See environment)floating-point exceptions. See exceptions
exceptionsrounding direction modes . See also rounding directionrounding precision modesinexact exceptionintegers, convertingrounding2invalid-operation exception. See invalid exceptionoverflowenvironmental controls result, tinydefaultdownward
to nearest toward zeroupwardrounding downwarddefined&rounding modes. See rounding directionrounding precision modesrounding to integerrounding to nearest valuerounding toward zerodefinedrounding upwarddefinedinvalid exception tiny resultto-nearest rounding)toward –∞ rounding. See downward rounding'toward +∞ rounding. See upward roundingtoward-zero roundingdefinedupward roundingrounding toward decimal to binary conversions binary to decimal conversionsstrings
structures conversions accuracy of decimal to binarybetween decimal formats between floating-point formatsdouble-double to decimalinexact exceptioninvalid exceptionconverting betweendecform structure!decimal data, reading and writing decimal formatting structuredecimal stringsdecimal structure decimal to binary conversionsstrings
structures decimal to decimal conversionsconverting to decimalconversions required conversionsconverting to integer conversionsconverting to integerconversions supportedstring conversions* (multiply) operator+ (plus) operator/ (divide) operatoradditionargument reductionarithmetic operationsadditiondivisionmultiplication remainder square rootauxiliary functions&comparison operations. See comparisonscomparison operators comparisonsinvolving Infinitiesinvolving NaNs
sqrt functionsqrtl functionsquare root operationdefined nan function
C languagedata types, new double type. See double format float type. See single format*long double type. See double-double formatcompilerwidening for efficiency double type. See double formatdouble_t typedef9in definitions of float_t and double_t[extended data type$definitions of float_t and double_t] float type. See single formatfloat_t typedefFPCE technical report
data typesINFINITY constant*long double type. See double-double formatMathLibdata types, new NAN constant nan functionPowerPC Numerics
nanf function
nanl functioncreatingtagp parameterwidening for efficiencyaccessing the environment C functionsatomic operationsenvironmental controlscontrolling the environment C functions accessing C functionsC functions, types restoringcompilersavingsetting (compiler)environmental access switchpurpose, note on C functions C functionsclearingcompilerraisingcompilerrestoring (compiler)savingsettingspurioustestingfeclearexcept functionfegetenv function
definition%difference from feholdexcept functionfegetexcept function
definitionwith fesetexcept functionfegetround function
ceil functiondecimal to binary C functionsfloating-point to integerfloor functioninteger to floating-pointrinttol functionround functionroundtol functionrinttol functiondec2str function
definition digits field style fielddecimal output fixed-stylefloating-style
definition exp field sgn field sig fieldfloor functionfloating-point numbersintegers, converting tocompilerfloor functionfloorl functionformatters, numericformatting outputfixed-style decimalfloating-style decimalnearbyint functionconverting to decimal converting to floating-pointconverting to stringcompilerconverting to decimal converting to floating-pointconverting to stringnearbyintl functionnum2dec function
definitionwith dec2str functionoutputfixed-style decimalfloating-style decimalrinttol functionrinttoll functionround functionfloor function
ceil functionroundl functionroundtol functionroundtoll functionscannersstr2dec function$truncating floating-point to integertruncl function
ceil functioncompiler,antilog functions. See exponential functionsscalingsign manipulationbase 2 exponentialcomparison functions C functionscopysignl function difference, positive function exp function
exp2 functionexp2l function
expl functionexpm1 functionexpm1l functiondetermining value ofexponential functionsbase 2 exponentialnatural exponentialnatural exponential – 1fabsl function
fdim functionfdiml function
fmax functionfmaxl function
fmin functionfminl functiondetermining value offrexp functionfrexpl function
comparison exponential logarithmicsign manipulationldexp functionldexpl function log functionlogarithmic functionsnatural
logl functionmaximum functionminimum functionnatural exponentialnatural exponential minus 1natural logarithm positive difference function pow functionPowerPC Numericspower function
asin functionasinh functionasinhl functionasinl function
atan functionatan2 functionatan2l functionatanh functionatanhl functionatanl functionexponent field, returnbinary logarithmcommon logarithm cos function
logb functionlog10 functionlog10l functionlog1p functionlog1pl function
log2 functionlog2l functionbinarycommon
logb functionlogbl function
modf functionmodfl function pi constant sin functionsinesine, hyperbolic
sinh functionsinhl function
sinl function tan functiontangenttangent, hyperbolic
tanh functiontanhl function
tanl functiontrigonometric functions#trigonometric functions, hyperbolicannuity functionnextafter functions complementary error functioncompound function erf function
erfc functionerror functionsfinancial functionserror financialgammagamma functiongamma functionshypot function
hypotenusehypotl functionlgamma functionlgammal function log of gammanextafter functionsPowerPC Numericsnextafterl functionrandom number generatorrandomx function address mode assembler data formatsCondition Register assemblerfloating-point registersFPSCRload assembler instructionsformats#PowerPC floating-point architecture data formats registersCondition Registerfloating-pointFPSCRspecial-purposespecial-purpose registers store assembler instructionsformatsenvironmental access branch assembler instructionsassembler instructionsCR. See Condition Register assemblerassembler instructionsassembler instructions assembler"enabling and disabling (assembler)
preserving assembler assembler assembler assemblertestingfloating-point result flags=Floating-Point Status and Control Register (FPSCR). See FPSCRexception bitsformat manipulation result flagsrounding directionmcrfs assembler instructionmffs assembler instruction mtfsb0 assembler instruction mtfsb1 assembler instructionmtfsf assembler instruction mtfsfi assembler instructionenvironmental access result flags assembler assembler assembler assembler assembleroperations supported assemblerassembler instructionsdifference operation assembler assemblerfcmpo assembler instructionfcmpu assembler instruction assembler#multiply-add assembler instructionsformat assembler assembler assemblerordered comparison assembleroperations supportedsubtraction operation assembler assembler 680x0-based Macintosh computers porting fromcomp data type (porting)"compatibility across architecturesSANESANESANESANE8in transcendental function declarations[double_t typedef%transcendental function declarations]SANESANEexp1 SANE functionSANE:in transcendental function declarations[extended data type%transcendental function declarations] fp.h file
porting toSANEipower SANE functionlog1 SANE function
porting toSANESANESANESANEpi SANE functionporting programs from SANESANESANE, compared toSANE, porting from compared to PowerPC Numerics conversions data formatsdenormalized numbers environmentexpression evaluation
InfinitiesNaNs
operationsporting programs fromtranscendental functions sane.h fileSANE4Standard Apple Numerics Environment (SANE). See SANESANE8087 coprocessorAINTBASIC
CDC computersCray computersuseevaluation rulesFortranHP Spectrum quad format IBM Q formatinstant roundingINTinvalid operation flagMC68881 coprocessor
mixed formatsporting programsPascalPDP-11C from non-Macintosh computersinstantSIGN(A) SIGN(A,B)stopping programtransported codeTrunc function VAX H format_MIN_EVAL_FORMAT macro_WIDEST_NEED_EVAL macroexpression evaluationcompiler optimizations5and evaluation of floating-point constant expressions and floating-point environmentand widest-need evaluationcontraction operators as minimum evaluation format as minimum evaluation formatignoringdefinedcompiler&floating-point expressions, evaluating(floating-point variables, initializationexpression evaluationfp_contract pragma"fp_wide_function_parameters pragma fp_wide_function_returns pragmafp_wide_variables pragma*initialization of floating-point variables expression evaluation extensionsenabling and disabling
optimizations5and evaluation of floating-point constant expressions and floating-point environmentand widest-need evaluationpragmas fenv_access fp_contractfp_wide_function_parametersfp_wide_function_returnsfp_wide_variables as minimum evaluation format
