Interval Arithmetic Programming Reference

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

Index

Symbols

.CEQ., 1

.CGE., 1

.CGT., 1

.CLE., 1

.CLT., 1

.CNE., 1

.DJ., 1, 2

.EQ., 1

.IH., 1, 2

.IN., 1, 2

.INT., 1

.IX., 1, 2

.NEQ., 1

.PEQ., 1

.PGT., 1

.PLE., 1

.PLT., 1

.PNE., 1

.PSB., 1, 2

.PSP., 1, 2

.SB., 1, 2

.SEQ., 1

.SGE., 1

.SGT., 1

.SLE., 1

.SLT., 1

.SNE., 1

.SP., 1, 2

A

ABS, 1, 2

ACOS, 1, 2

affirmative relation, 1

affirmative relational operators, 1

AINT, 1, 2

ALLOCATED, 1

ANINT, 1, 2

-ansi, 1

anti-affirmative relation, 1

anti-affirmative relational operator, 1

arithmetic expressions, 1

arithmetic operations

containment set, 1

arithmetic operators, 1

formulas, 1

arrays

INTERVAL, 1

see also INTERVAL array functions, 1

ASIN, 1, 2

assignment statement, 1

assignment statements

evaluating with widest-need, 1

INTERVAL, 1

ASSOCIATED, 1

ATAN, 1, 2

ATAN2, 1, 2

indeterminate forms, 1

attribute

PARAMETER, 1

attributes

IMPLICIT, 1

-autopar, 1

B

base conversion, 1, 2

binary files, 1

BZ edit descriptor, 1

C

CEILING, 1, 2

certainly relational operators, 1, 2

certainly-relation, 1

character set notation

constants, 1

closed interval, 1

closed mathematical system, 1, 2

closed set, 1

closure of expression, 1

code examples

location, 1

naming convention, 1

command-line macro, 1

command-line options

-ansi, 1

-autopar, 1

effect on KTPV, 1

-explicitpar, 1

-fns, 1

-fround, 1

-fsimple, 1

-ftrap, 1

-r8const, 1

-xia, 1, 2

-xia=strict, 1

-xia=widestneed, 1

-xinterval, 1

-xtypemap, 1

composite expression, 1

connected set, 1

constant expression, 1

constants

character set notation, 1

external value, 1

literal, 1

named, 1, 2

strict interval expression processing, 1

constructor functions

KTPV-specific names, 1

containment constraint, 1, 2

containment failure, 1, 2

errors, 1

containment set, 1, 2

arithmetic operations, 1

containment set equivalent, 1

containment set evaluation theorem, 1

containment-set closure identity, 1

context-dependent INTERVAL constant, 1

COS, 1, 2

COSH, 1, 2

cset(expression, set)

see also containment set1

CSHIFT, 1

D

D edit descriptor, 1

DATA, 1

data

INTERVAL data type, 1

representing intervals, 1

dbx, 1, 2

debugging tools

dbx, 1, 2

GPC, 1, 2

default INTEGER KTPV, 1

default KTPV, 1

degenerate interval, 1, 2

representation, 1

DINTERVAL, 1, 2

directed rounding, 1, 2, 3

disjoint interval, 1

disjoint set relation, 1

display format

inf, sup, 1

DOT_PRODUCT, 1

E

E edit descriptor, 1

edit descriptors

BZ, 1

D, 1

E, 1

F, 1

forms, 1

G, 1

input fields, 1

list-directed output, 1, 2

P, 1

repeatable, 1

summary, 1

VE, 1

VEN, 1

VES, 1

VF, 1

VG, 1

w, d, e parameters, 1

element set relation, 1

empty interval, 1, 2

empty set, 1

endpoint type

internal type conversions, 1

EOSHIFT, 1

EQUIVALENCE statement, 1

restrictions, 1

errors

containment failure, 1

error detection, 1

integer overflow, 1

ev(literal_constant), 1

exceptions, 1

exchangeable expression, 1

EXP, 1, 2

-explicitpar, 1

expression context, 1, 2

expression evaluation

mixed-type, 1

expression processing

mixed-mode, 1

strict, 1

widest-need, 1

expressions

composite, 1

constant, 1

INTERVAL, 1

INTERVAL constant, 1

mixed type and KTPV, 1

extended interval, 1

extended operators

widest-need expression processing, 1

extending intrinsic INTERVAL operators, 1

external functions, 1

external representation, 1

external value, 1, 2, 3

notation, 1

F

F edit descriptor, 1

f95 interval support features, 1

FLOOR, 1, 2

-fns, 1

FORMAT, 1, 2

formatted input, 1

Fortran INTERVAL extensions, 1

-fround, 1

-fsimple, 1

-ftrap, 1

FUNCTION, 1

functions

constructor, 1

external, 1

statement, 1

G

G edit descriptor, 1

global program checking (GPC), 1, 2

H

hull

see INTERVAL hull1

I

implementation quality, 1

IMPLICIT attribute, 1

indeterminate forms

ATAN2, 1

power operator, 1

INF, 1, 2

inf, sup display format, 1

infima, 1

infimum, 1, 2

input list, 1

input/output

entering INTERVAL data, 1

formatted input, 1

list-directed input, 1

list-directed output, 1

single number, 1, 2, 3

single-number, 1

unformatted input/output, 1

INT, 1

integer overflow, 1

INTERFACE, 1

interior set relation, 1

internal approximation, 1, 2

intersection set theoretic operator, 1, 2

INTERVAL, 1, 2, 3, 4

alignment, 1

arrays, 1

assignment statements, 1

expressions, 1

size, 1

interval algorithm, 1

interval arithmetic, 1, 2

INTERVAL arithmetic functions

ABS, 1

AINT, 1

ANINT, 1

MAX, 1, 2

MIN, 1, 2

MOD, 1

SIGN, 1

VDABS, 1

VDINT, 1

VDMOD, 1

VDNINT, 1

VDSIGN, 1

VQABS, 1

VQINT, 1

VQNINT, 1

VSABS, 1

VSINT, 1

VSMOD, 1

VSNINT, 1

VSSIGN, 1

INTERVAL arithmetic operations, 1

INTERVAL array functions, 1

ABS, 1

ACOS, 1

AINT, 1

ALLOCATED, 1

ANINT, 1

ASIN, 1

ASSOCIATED, 1

ATAN, 1

ATAN2, 1

CEILING, 1

COS, 1

COSH, 1

CSHIFT, 1

DINTERVAL, 1

DOT_PRODUCT, 1

EOSHIFT, 1

EXP, 1

FLOOR, 1

INF, 1

INT, 1

INTERVAL, 1

KIND, 1

LBOUND, 1

LOG, 1

LOG10, 1

MAG, 1

MATMUL, 1

MAX, 1

MAXLOC, 1

MAXVAL, 1

MERGE, 1

MID, 1

MIG, 1

MIN, 1

MINLOC, 1

MINVAL, 1

MOD, 1

NDIGITS, 1

NULL, 1

PACK, 1

PRODUCT, 1

QINTERVAL, 1

RESHAPE, 1

SHAPE, 1

SIGN, 1

SIN, 1

SINH, 1

SINTERVAL, 1

SIZE, 1

SPREAD, 1

SQRT, 1

SUM, 1

SUP, 1

TAN, 1

TANH, 1

TRANSPOSE, 1

UBOUND, 1

UNPACK, 1

WID, 1

INTERVAL assignment statements, 1, 2

interval box, 1

INTERVAL constant expressions, 1

INTERVAL constants, 1, 2

external value, 1

internal approximation, 1, 2

KTPV, 1

strict expression processing, 1

strict interval expression processing, 1

type, 1

widest-need interval expression processing, 1

INTERVAL data type, 1

INTERVAL expressions, 1, 2

INTERVAL hull, 1, 2

INTERVAL hull set theoretic operator, 1

INTERVAL input

input fields, 1

INTERVAL input/output, 1

INTERVAL library, 1

INTERVAL mathematical functions

EXP, 1

LOG, 1

LOG10, 1

SQRT, 1

VDEXP, 1

VDLOG, 1

VDLOG10, 1

VDSQRT, 1

VSEXP, 1

VSLOG, 1

VSLOG10, 1

VSSQRT, 1

interval order relations, 1

certainly, 1

definitions, 1

possibly, 1

set, 1

INTERVAL relational operators, 1, 2

.CEQ., 1

.CGE., 1

.CGT., 1

.CLE., 1

.CLT., 1

.CNE., 1

.DJ., 1

.EQ., 1

.IN., 1

.NEQ., 1

.PEQ., 1

.PGT., 1

.PLE., 1

.PLT., 1

.PNE., 1

.PSB., 1

.PSP., 1

.SB., 1

.SEQ., 1, 2

.SGE., 1

.SGT., 1

.SLE., 1

.SLT., 1

.SNE., 1

.SP., 1

interval resources

code examples, 1

email, 1

papers, 1

web sites, 1

INTERVAL- specific operators, 1

INTERVAL statements, 1, 2

interval support

performance, 1

INTERVAL support goals, 1

INTERVAL trigonometric functions

ACOS, 1

ASIN, 1

ATAN, 1

ATAN2, 1

COS, 1

COSH, 1

SIN, 1

SINH, 1

TAN, 1

TANH, 1

VDACOS, 1

VDASIN, 1

VDATAN, 1

VDATAN2, 1

VDCOS, 1

VDCOSH, 1

VDSIN, 1

VDSINH, 1

VDTAN, 1

VDTANH, 1

VSACOS, 1

VSASIN, 1

VSATAN, 1

VSATAN2, 1

VSCOS, 1

VSCOSH, 1

VSSIN, 1

VSSINH, 1

VSTAN, 1

VSTANH, 1

INTERVAL type conversion functions

DINTERVAL, 1

INTERVAL, 1

QINTERVAL, 1

SINTERVAL, 1

INTERVAL variables

declaring and initializing, 1

interval width, 1

narrow, 1, 2, 3

related to base conversion, 1

sharp, 1

intervals

f95 interval support features, 1

goals of compiler support, 1

input/output, 1

INTERVAL-specific functions, 1, 2, 3

CEILING, 1

FLOOR, 1

INF, 1

ISEMPTY, 1

MAG, 1

MID, 1

MIG, 1

NDIGITS, 1

PRECISION, 1

RANGE, 1

SUP, 1

VDINF, 1

VDISEMPTY, 1

VDMAG, 1

VDMID, 1

VDMIG, 1

VDSUP, 1

VDWID, 1

VQINF, 1

VQISEMPTY, 1

VQMAG, 1

VQMID, 1

VQMIG, 1

VQSUP, 1

VQWID, 1

VSINF, 1

VSISEMPTY, 1

VSMAG, 1

VSMID, 1

VSMIG, 1

VSSUP, 1

VSWID, 1

WID, 1

intrinsic f95 interval support, 1

intrinsic functions

INTERVAL, 1

properties, 1

standard, 1

VS,VD,VQ prefixes, 1

intrinsic INTERVAL data type, 1

intrinsic INTERVAL-specific function, 1

intrinsic operators, 1

arithmetic, 1

precedence of operators, 1

relational, 1

INTRINSIC statement, 1

ISEMPTY, 1

K

KIND, 1

kind type parameter value (KTPV), 1

alignment, 1

default values, 1, 2, 3

INTERVAL constant, 1

size, 1

specific constructor function names, 1

KTPV_max, 1, 2

L

LBOUND, 1

libraries

INTERVAL functions, 1

interval support, 1

list-directed input, 1

input list, 1

list-directed output, 1

literal constants, 1, 2, 3

external value, 1

internal approximation, 1

LOG, 1, 2

LOG10, 1, 2

M

MAG, 1, 2

mantissa, 1

MATMUL, 1

MAX, 1, 2, 3

MAXLOC, 1

MAXVAL, 1

MERGE, 1

MID, 1, 2

MIG, 1, 2

MIN, 1, 2, 3

MINLOC, 1

MINVAL, 1

mixed-KTPV INTERVAL expression, 1

mixed-mode expression evaluation, 1

mixed-mode expressions

non-INTERVAL named constant compiler warning, 1

type and KTPV, 1, 2

widest-need expression processing, 1

mixed-type expression evaluation, 1

mixed-type INTERVAL expressions, 1, 2

MOD, 1, 2

multiple-use expression (MUE), 1

N

named constant, 1, 2, 3

named constants, 1

NAMELIST statement, 1

narrow intervals, 1, 2, 3

NDIGITS, 1, 2

non-INTERVAL named constants

mixed-mode expressions, 1

NULL, 1

O

online interval resources, 1

opaque

data type, 1

INTERVAL type, 1

operator precedence, 1

operators

arithmetic, 1

extending, 1

intrinsic, 1

power, 1

relational, 1

P

P edit descriptor, 1

PACK, 1

PARAMETER, 1

PARAMETER attribute, 1

parameters

named constants, 1

performance, 1

point, 1

POINTER statement, 1

porting code, 1

possibly relational operators, 1, 2

possibly-relation, 1

power operator, 1

containment failure, 1

indeterminate forms, 1

singularities, 1

precedence of intrinsic operators, 1

PRECISION, 1

processing expressions

widest-need expression processing, 1

PRODUCT, 1

proper subset set relation, 1

proper superset set relation, 1

Q

QINTERVAL, 1, 2

quality of implementation, 1, 2

R

-r8const, 1

radix conversion, 1, 2

RANGE, 1

READ statement, 1

read-only variable, 1

relational operators, 1

certainly true, 1

possibly true, 1

set, 1

RESHAPE, 1

S

scale factor, 1

semantics, 1

set relational operators, 1, 2

set relations, 1

disjoint, 1

element, 1

interior, 1

proper subset, 1

proper superset, 1

subset, 1

superset, 1

set theoretic, 1

set theoretic operators, 1

INTERVAL hull, 1, 2

INTERVAL intersection, 1, 2

set-relations, 1

set-theoretic functions, 1

SHAPE, 1

sharp intervals, 1, 2

SIGN, 1, 2

SIN, 1, 2

single-number editing, 1

single-number input/output, 1, 2, 3, 4

single-number INTERVAL data conversion, 1

single-number interval format, 1

single-number interval representation

precision, 1

single-use expression

see SUE1

singularities

power operator, 1

SINH, 1, 2

SINTERVAL, 1, 2

SIZE, 1

SPREAD, 1

SQRT, 1, 2

standard intrinsic functions, 1

statement function, 1

statements

DATA, 1

EQUIVALENCE, 1

FORMAT, 1, 2

FUNCTION, 1

INTERFACE, 1

INTERVAL, 1, 2, 3, 4

INTRINSIC, 1

NAMELIST, 1

PARAMETER, 1

POINTER, 1

READ, 1

type, 1

WRITE, 1

strict expression processing, 1, 2, 3

subset set relation, 1

SUE, 1, 2

SUM, 1

SUP, 1, 2

superset set relation, 1

suprema, 1

supremum, 1, 2

syntax, 1

T

TAN, 1, 2

TANH, 1, 2

The, 1

TRANSPOSE, 1

type declaration, 1

type declaration statements

INTERVAL, 1

type statement, 1

U

UBOUND, 1

uld, 1, 2

ulp, 1, 2, 3

unformatted input/output, 1

unit in last digit

see uld1

unit in last place

see ulp1, 2

UNPACK, 1

V

valid interval result, 1

value assignment, 1, 2

variables

INTERVAL, 1

VDABS, 1

VDACOS, 1

VDASIN, 1

VDATAN, 1

VDATAN2, 1

VDCOS, 1

VDCOSH, 1

VDEXP, 1

VDINF, 1

VDINT, 1

VDISEMPTY, 1

VDLOG, 1

VDLOG10, 1

VDMAG, 1

VDMID, 1

VDMIG, 1

VDMOD, 1

VDNINT, 1

VDSIGN, 1

VDSIN, 1

VDSINH, 1

VDSQRT, 1

VDSUP, 1

VDTAN, 1

VDTANH, 1

VDWID, 1

VE edit descriptor, 1

VEN edit descriptor, 1

VES edit descriptor, 1

VF edit descriptor, 1

VG edit descriptor, 1

VQABS, 1

VQINF, 1

VQINT, 1

VQISEMPTY, 1

VQMAG, 1

VQMID, 1

VQMIG, 1

VQNINT, 1

VQSUP, 1

VQWID, 1

VSABS, 1

VSACOS, 1

VSASIN, 1

VSATAN, 1

VSATAN2, 1

VSCOS, 1

VSCOSH, 1

VSEXP, 1

VSINF, 1

VSINT, 1

VSISEMPTY, 1

VSLOG, 1

VSLOG10, 1

VSMAG, 1

VSMID, 1

VSMIG, 1

VSMOD, 1

VSNINT, 1

VSSIGN, 1

VSSIN, 1

VSSINH, 1

VSSQRT, 1

VSSUP, 1

VSTAN, 1

VSTANH, 1

VSWID, 1

W

WID, 1, 2

widest-need expression processing, 1, 2

command-line option, 1

evaluating assignment statements, 1

evaluating expressions, 1

extended operators, 1

limiting scope, 1

mixed-mode expressions, 1

scope, 1

steps, 1

WRITE statement, 1

X

X**N, 1

X**Y, 1

-xia, 1

-xinterval, 1

-xtypemap, 1

Y

Y edit descriptors

single-number editing, 1