Index

Numbers and Symbols

-fastSubnormal Numbers and Nonstandard Arithmetic

-fnonstdSubnormal Numbers and Nonstandard Arithmetic

A

abort on exception

C exampleieee_handler: Abort on Exceptions

abrupt underflowUnderflow Thresholds

flush underflow results

Two Examples of Gradual Underflow Versus Abrupt Underflow

Gaps Between Representable Single-Format Floating-Point Numbers

accuracy

floating-point operationsWhat Is IEEE Arithmetic?

significant digits (number of)Ranges and Precisions in Decimal Representation

thresholdDoes Underflow Matter?

addrans

random number utilitiesRandom Number Facilities

argument reduction

trigonometric functionsArgument Reduction for Trigonometric Functions

B

base conversion

base 10 to base 2Base Conversion in the Oracle Solaris Environment

base 2 to base 10Base Conversion in the Oracle Solaris Environment

formatted I/OBase Conversion in the Oracle Solaris Environment

C

C driver

example, call FORTRAN subroutines from CCalling Fortran From C

clock speedfpversion(1) Function: Finding Information About the FPU

conversion between number setsComparison of a Set of Numbers Defined by Digital and Binary Representation

conversions between decimal strings and binary floating-point numbersWhat Is IEEE Arithmetic?

convert_external

binary floating-pointData Conversion Routines

data conversionData Conversion Routines

D

data types

relation to IEEE formatsStorage Formats

dbxUsing the Debugger to Locate an Exception

decimal representation

maximum positive normal numberRanges and Precisions in Decimal Representation

minimum positive normal numberRanges and Precisions in Decimal Representation

precisionRanges and Precisions in Decimal Representation

rangesRanges and Precisions in Decimal Representation

double-precision representation

C exampleIEEE Arithmetic

FORTRAN exampleDouble Precision Example

E

examine the accrued exception bits

C exampleieee_flags — Accrued Exceptions

examine the accrued exception flags

C exampleExamining the Accrued Exception Flags

F

floating-point

exceptions listWhat Is IEEE Arithmetic?

rounding directionWhat Is IEEE Arithmetic?

rounding precisionWhat Is IEEE Arithmetic?

floating-point accuracy

decimal strings and binary floating-point numbersWhat Is IEEE Arithmetic?

floating-point exceptionsFloating-Point Environment

abort on exceptionsieee_handler: Abort on Exceptions

accrued exception bitsieee_flags — Accrued Exceptions

common exceptionsWhat Is an Exception?

default resultIEEE Floating-Point Exceptions

definitionWhat Is an Exception?

flagsDetecting Exceptions

accruedDetecting Exceptions

currentDetecting Exceptions

ieee_functionsieee_sun(3m)

ieee_retrospectiveieee_retrospective(3m)

list of exceptionsWhat Is an Exception?

priorityNotes for Table 4-1

trap precedenceNotes for Table 4-1

floating-point queue (FQ)Floating-Point Status Register and Queue

floating-point status register (FSR)

Floating-Point Status Register and Queue

Some Debugging Commands (SPARC)

floatingpoint.h

define handler types

C and C++ieee_handler (3m)

flush to zero (seeabrupt underflow)Underflow Thresholds

G

generate an array of numbers

FORTRAN exampleRandom Number Generator

gradual underflow

error propertiesError Properties of Gradual Underflow

I

IEEE double extended format

biased exponent

x86 architectureDouble-Extended Format (x86)

bit-field assignment

x86 architectureDouble-Extended Format (x86)

fraction

x86 architectureDouble-Extended Format (x86)

Inf

SPARC architectureValues Represented by Bit Patterns

x86 architectureValues Represented by Bit Patterns (x86)

NaN

x86 architectureBit Patterns in Double-Extended Format and Their Values (x86)

normal number

SPARC architectureValues Represented by Bit Patterns

x86 architectureValues Represented by Bit Patterns (x86)

quadruple precision

SPARC architectureQuadruple Format

sign bit

x86 architectureDouble-Extended Format (x86)

significand

explicit leading bit (x86 architecture)Double-Extended Format (x86)

subnormal number

SPARC architectureValues Represented by Bit Patterns

x86 architectureValues Represented by Bit Patterns (x86)

IEEE double format

biased exponentDouble Format

bit patterns and equivalent valuesValues Represented by Bit Patterns in IEEE Double Format

bit-field assignmentDouble Format

denormalized numberValues Represented by Bit Patterns in IEEE Double Format

fraction

Double Format

Double Format

storage on SPARCDouble Format

storage on x86Double Format

implicit bitValues Represented by Bit Patterns in IEEE Double Format

Inf, infinityValues Represented by Bit Patterns in IEEE Double Format

NaN, not a numberBit Patterns in Double-Storage Format and Their IEEE Values

normal numberValues Represented by Bit Patterns in IEEE Double Format

precisionValues Represented by Bit Patterns in IEEE Double Format

sign bitDouble Format

significandValues Represented by Bit Patterns in IEEE Double Format

subnormal numberValues Represented by Bit Patterns in IEEE Double Format

IEEE formats

relation to language data typesStorage Formats

IEEE single format

biased exponentSingle Format

biased exponent,implicit bitValues Represented by Bit Patterns in IEEE Single Format

bit assignmentsSingle Format

bit patterns and equivalent valuesValues Represented by Bit Patterns in IEEE Single Format

bit-field assignmentSingle Format

denormalized numberValues Represented by Bit Patterns in IEEE Single Format

fractionSingle Format

Inf, negative infinityValues Represented by Bit Patterns in IEEE Single Format

Inf,positive infinityValues Represented by Bit Patterns in IEEE Single Format

mixed number, significandValues Represented by Bit Patterns in IEEE Single Format

NaN, not a numberBit Patterns in Single-Storage Format and Their IEEE Values

normal number

maximum positiveValues Represented by Bit Patterns in IEEE Single Format

normal number bit patternValues Represented by Bit Patterns in IEEE Single Format

precision, normal numberValues Represented by Bit Patterns in IEEE Single Format

sign bitSingle Format

subnormal number bit patternValues Represented by Bit Patterns in IEEE Single Format

IEEE Standard 754

double extended formatWhat Is IEEE Arithmetic?

double formatWhat Is IEEE Arithmetic?

single formatWhat Is IEEE Arithmetic?

ieee_flags

accrued exception flagieee_flags(3m)

examine accrued exception bits-C exampleieee_flags — Accrued Exceptions

rounding directionieee_flags(3m)

rounding precision

ieee_flags Input Values for the Rounding Direction

ieee_flags(3m)

set exception flags-C exampleExamining the Accrued Exception Flags – Fortran

truncate roundingParameter Values for ieee_flags

ieee_functions

bit mask operationsieee_functions(3m) and ieee_sun(3m)

floating-point exceptionsieee_sun(3m)

ieee_handlerieee_handler (3m)

abort on exception

FORTRAN exampleieee_handler: Abort on Exceptions

example, calling sequenceUsing dbx to Locate the Instruction Causing an Exception

trap on common exceptionsWhat Is an Exception?

trap on exception

C exampleieee_handler: Trapping Exceptions

ieee_retrospective

check underflow exception flagSubnormal Numbers and Nonstandard Arithmetic

floating-point exceptionsieee_retrospective(3m)

floating-point status register (FSR)ieee_retrospective(3m)

getting information about nonstandard IEEE modesieee_retrospective(3m)

getting information about outstanding exceptionsieee_retrospective(3m)

nonstandard_arithmetic in effectieee_retrospective(3m)

precisionieee_retrospective(3m)

roundingieee_retrospective(3m)

suppress exception messagesieee_retrospective(3m)

ieee_sun

IEEE classification functionsieee_functions(3m) and ieee_sun(3m)

ieee_values

quadruple-precision valuesieee_values(3m)

representing floating-point valuesieee_values(3m)

representing Infieee_values(3m)

representing NaNieee_values(3m)

representing normal numberieee_values(3m)

single-precision valuesieee_values(3m)

ieee_values functions

C exampleIEEE Special Values

Inf

Special Cases and libm Functions

Floating-Point Environment

default result of divide by zeroIEEE Floating-Point Exceptions

L

lcrans

random number utilitiesRandom Number Facilities

libm

list of functionsStandard Math Library

libm functions

double precisionCalling Single, Double, and Extended/Quadruple Functions

quadruple precisionCalling Single, Double, and Extended/Quadruple Functions

single precisionCalling Single, Double, and Extended/Quadruple Functions

libsunmath

list of functionsOracle Math Library

N

NaN

Special Cases and libm Functions

Bit Patterns in Quadruple Format

Floating-Point Environment

nonstandard_arithmetic

gradual underflownonstandard_arithmetic(3m)

turn off IEEE gradual underflowSubnormal Numbers and Nonstandard Arithmetic

underflownonstandard_arithmetic(3m)

normal number

maximum positiveValues Represented by Bit Patterns in IEEE Single Format

minimum positive

Gaps Between Representable Single-Format Floating-Point Numbers

Underflow Thresholds

number line

binary representationRanges and Precisions in Decimal Representation

decimal representationRanges and Precisions in Decimal Representation

powers of 2Number Line

O

operating system math library

libm.aStandard Math Library

P

pi

infinitely precise valueArgument Reduction for Trigonometric Functions

Q

quietNaN

default result of invalid operationIEEE Floating-Point Exceptions

R

random number generatorsRandom Number Generator

random number utilities

shufransRandom Number Facilities

represent double-precision value

C exampleDouble Precision Example

FORTRAN examplePrint Smallest Normal Numbers in Each Format (Continued)

represent single-precision value

C exampleDouble Precision Example

round-off error

accuracy

loss ofHow Does IEEE Arithmetic Treat Underflow?

rounding directionWhat Is IEEE Arithmetic?

C exampleieee_flags — Rounding Direction

rounding precisionWhat Is IEEE Arithmetic?

S

set exception flags

C exampleExamining the Accrued Exception Flags – Fortran

shufrans

shuffle pseudo-random numbersRandom Number Facilities

single formatSingle Format

single precision representation

C exampleIEEE Arithmetic

standard_arithmetic

turn on IEEE behaviorSubnormal Numbers and Nonstandard Arithmetic

subnormal numberGaps Between Representable Single-Format Floating-Point Numbers

floating-point calculationsUnderflow Thresholds

System V Interface Definition (SVID)Standards Compliance

T

trap

abort on exceptionieee_handler: Abort on Exceptions

ieee_retrospectiveieee_retrospective(3m)

trap on exception

C example

Trap on Underflow (SPARC)

ieee_handler: Trapping Exceptions

trap on floating-point exceptions

C exampleieee_handler: Trapping Exceptions

trigonometric functions

argument reduction

Argument Reduction for Trigonometric Functions

Argument Reduction for Trigonometric Functions

U

underflow

floating-point calculationsUnderflow Thresholds

gradualUnderflow Thresholds

nonstandard_arithmeticnonstandard_arithmetic(3m)

thresholdGaps Between Representable Single-Format Floating-Point Numbers

underflow thresholds

double extended precisionUnderflow Thresholds

double precisionUnderflow Thresholds

single precisionUnderflow Thresholds

unit in last place (ulp)About the Algorithms

unordered comparison

floating-point valuesNotes for Table 4-1

NaNNotes for Table 4-1