* Document Number: WG14 N792/J11 97-156
C9X Revision Proposal
* Title: C9X and LIA-1 informative annex.
Author: Fred J. Tydeman
Author Affiliation: Tydeman Consulting
Postal Address: 3711 Del Robles Dr., Austin, Texas, 78727, USA
E-mail Address: firstname.lastname@example.org
Telephone Number: +1 (512) 255-8696
Fax Number: +1 (512) 255-8696
Document History: WG14 N758/J11 97-121.
Y_ Editorial change/non-normative contribution
__ New feature
__ Addition to obsolescent feature list
__ Addition to Future Directions
__ Other (please specify) ______________________________
Area of Standard Affected:
__ Macro/typedef/tag name
Y_ Other (please specify) Annex_________________________
Prior Art: None.____________________________________________
Target Audience: Programmers writing programs that perform a
significant amount of numeric processing.___________________
Related Documents (if any):
WG14/N758 C9X and LIA-1 informative annex,
WG14/N756 LIA-1 Binding: Arithmetic exception => SIGFPE,
WG14/N755 LIA-1 Binding: <fenv.h> to <stdmath.h>,
WG14/N753 LIA-1 Binding: Rationale,
WG14/N752 LIA-1 Binding: Optional parts annex,
WG14/N751 LIA-1 Binding: Combined LIA-1 + IEC-559 annex,
WG14/N750 LIA-1 Binding: LIA-1 annex.
WG14/N749 LIA-1 Binding: <stdlia.h>,
WG14/N748 LIA-1 Binding: Adding 'pole' from LIA-2,
WG14/N747 IEC 559 Binding: Signaling NaNs,
WG14/N528 C Binding for LIA-1,
WG14/N488 LIA-2 (math library),
WG14/N487 LIA-1 (arithmetic),
WG14/N486 LIA Overview,
WG14/N463 Impact of adding LIA-1,
WG14/N461 C Binding of LIA-1,
Defect Report 152 longjmp from a signal handler,
Defect Report 099 Narrowing of FP expression,
Defect Report 056/063 Accuracy of floating-point,
Defect Report 036 Representation of FP constants,
Defect Report 025 Floating-point representation.
Proposal Attached: _Y Yes __ No, but what's your interest?
Abstract: This is an informative annex to C9X to document
the extent to which the C language currently supports the
LIA-1 requirements. It is NOT a binding bewteen C and LIA-1.
The other proposals should be considered a starting point
of the LIA-1 to C binding (if that binding is wanted).
Note: The '*' characters in the lefthand column are not part
of the proposal (they are useful for emacs M-x outline mode)
In the following, bold text, italic text,
<TT>code sample</TT> are the conventions used to indicate
text different from normal.
* -- Add to Annex A Bibliography:
ISO/IEC 10967-1:1994(E) Information technology --
Language independent arithmetic -- Part 1: Integer and
floating point arithmetic.
* -- Add a new annex, here called H, after annex G IEC
559-compatible complex arithmetic:
Language independent arithmetic
** H.1 Introduction
This annex documents the extent to which the C language
supports the standard: ISO/IEC 10967-1 Language independent
arithmetic, part 1, integer and floating-point arithmetic
(LIA-1). LIA-1 is more general than IEC 559 (annex F) in
that it covers integer and diverse floating-point arithmetics.
** H.2 Types
The relevant C arithmetic types meet the requirements of LIA-1
types if an implementation adds notification of exceptional
arithmetic operations and meets the 1-ULP accuracy requirement.
*** H.2.1 Boolean Type
The LIA-1 data type Boolean is implemented by the C data
type bool with values of true and
false, all from <stdbool.h>.
*** H.2.2 Integer Types
The signed C integer types int, long,
long long and the corresponding unsigned types are
compatible with LIA-1. If an implementation adds support
for the LIA-1 exceptional values integer_overflow
and undefined, then those types are LIA-1 conformant
types. C's unsigned integer types are "modulo" in the LIA-1
sense in that overflows or out-of-bounds results silently wrap.
An implementation that defines signed integer types as also
being modulo need not detect integer overflow, in which case,
only integer divide-by-zero need be detected.
The parameters for the integer data types can be
accessed by the following:
maxint INT_MAX, LONG_MAX, LLONG_MAX,
UINT_MAX, ULONG_MAX, ULLONG_MAX
minint INT_MIN, LONG_MIN, LLONG_MIN
The parameter "bounded" is always true, and is not provided.
The parameter "minint" is always 0 for the unsigned types, and
is not provided for those types.
**** H.2.2.2 Integer Operations
The integer operations on integer types are the following:
addI x + y
subI x - y
mulI x * y
divI, divtI x / y
remI, remtI x % y
negI - x
absI abs(x), labs(x), llabs(x)
eqI x == y
neqI x != y
lssI x < y
leqI x <= y
gtrI x > y
geqI x >= y
where x and y are expressions of the same integer type.
*** H.2.3 Floating-Point Types
The C floating-point types float, double, and long double
are compatible with LIA-1. If an implementation adds
support for the LIA-1 exceptional values underflow,
floating_overflow, and undefined, then those
types are conformant with LIA-1. An implementation that
uses IEC 559 floating-point formats and operations (see
Annex F) along with IEC 559 status flags and traps has
LIA-1 conformant types.
**** H.2.3.1 Floating-Point Parameters
The parameters for a floating point data type can
be accessed by the following:
p FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG
emax FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP
emin FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP
The derived constants for the floating point
types are accessed by the following:
fmax FLT_MAX, DBL_MAX, LDBL_MAX
fminN FLT_MIN, DBL_MIN, LDBL_MIN
epsilon FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON
**** H.2.3.2 Floating-Point Operations
The floating-point operations on floating-point
types are the following:
addF x + y
subF x - y
mulF x * y
divF x / y
negF - x
absF fabsf(x), fabs(x), fabsl(x)
exponentF 1.f+logbf(x), 1.0+logb(x), 1.L+logbl(x)
scaleF scalbnf(x, n), scalbn(x, n), scalbnl(x, n)
scalblnf(x, li), scalbln(x, li), scalblnl(x, li)
intpartF modff(x, &y), modf(x, &y), modfl(x, &y)
fractpartF modff(x, &y), modf(x, &y), modfl(x, &y)
eqF x == y
neqF x != y
lssF x < y
leqF x <= y
gtrF x > y
geqF x >= y
where x and y are expressions of the same floating point
type, n is of type int, and li is of type long int.
**** H.2.3.3 Rounding Styles
The C Standard requires all floating types use the same
radix and rounding style, so that only one identifier for
each is provided to map to LIA-1.
The FLT_ROUNDS parameter can be used to indicate the LIA-1
truncate FLT_ROUNDS == 0
nearest FLT_ROUNDS == 1
other FLT_ROUNDS != 0 && FLT_ROUNDS != 1
provided that an implementation extends FLT_ROUNDS to cover
the rounding style used in all relevant LIA-1 operations, not
just addition as in C.
*** H.2.4 Type Conversions
The LIA-1 type conversions are the following type casts:
cvtI'->I (int)i, (long)i, (long long)i,
(unsigned int)i, (unsigned long)i,
(unsigned long long)i
cvtF->I (int) x,
(long long) x,
(unsigned int) x,
(unsigned long) x,
(unsigned long long) x
cvtI->F (float) i, (double) i, (long double) i
cvtF'->F (float) x, (double) x, (long double) x
In the above conversions from floating to integer, the use
of (cast)x can be replaced with (cast)round(x), (cast)rint(x)
(cast)nearbyint(x), (cast)trunc(x), (cast)ceil(x), or
(cast)floor(x) as they all meet LIA's requirements on
floating to integer rounding. The remainder() function is
useful for doing silent wrapping to unsigned integer types.
C's floating-point to integer conversion functions,
lrint(), llrint(), lround(), and llround(), can meet LIA-1's
requirements if an implementation handles out of range as
C's conversions (type casts) from floating-point to
floating-point can meet LIA-1 if an implementation uses
round to nearest.
C's conversions (type casts) from integer to floating-point
can meet LIA-1 if an implementation uses round to nearest.
** H.3 Notification
Notification is the process by which a user or program is
informed that an exceptional arithmetic operation has occured.
C's operations are compatible with LIA-1 in that C allows an
implementation to cause a notification to occur when any
arithmetic operation returns an exceptional value as
defined in LIA-1 clause 5.
*** H.3.1 Notification alternatives
LIA-1 requires at least the following two alternatives
for handling of notifications: setting indicators or
trap-and-terminate. LIA-1 allows a third alternative:
An implementation need only support a given notification
alternative for the entire program. An implementation may
support the ability to switch between notification
alternatives during execution, but is not required to do so.
An implementation can provide separate selection for each
kind of notification, but this is not required.
C allows an implementation to provide notification.
C's SIGFPE (for traps) and FE_INVALID, FE_DIVBYZERO,
FE_OVERFLOW, FE_UNDERFLOW (for indicators) can provide
C's signal handlers are compatible with LIA-1. Default
handling of SIGFPE can provide trap-and-terminate
behavior. User provided signal handlers for SIGFPE
allow for trap-and-resume behavior.
**** H.3.1.1 Indicators
C's <fenv.h> status flags are compatible with LIA's indicators.
The following mapping is for floating-point types:
undefined FE_INVALID, FE_DIVBYZERO
The floating-point indicator interrogation and manipulation
where i is an expression of type int representing a
LIA-1 indicator subset.
C allows an implementation to provide the following LIA-1
required behavior: at program termination if any indicator
is set the implementation shall send an unambiguous and
"hard to ignore" message (see LIA-1 subclause 6.1.2)
LIA-1 does not make the distinction between floating-point
and integer for undefined. This documentation is
making that distinction because <fenv.h> covers only the
**** H.3.1.2 Traps
C is compatible with LIA's trap requirements. An
implementation can provide an alternative of notification
through termination with a ``hard-to-ignore'' message
(see LIA-1 subclause 6.1.3).
LIA-1 does not require that traps be precise.
C does require that SIGFPE be the signal
corresponding to arithmetic exceptions, if there is any
signal raised for them.
C has signal handlers for SIGFPE and allows trapping
arithmetic exceptions. When arithmetic exceptions do trap,
C's signal-handler mechanism allows trap-and-terminate (either
default implementation behavior or user replacement for it)
and trap-and-resume, at the programmer's option.