* Document Number: WG14 N758/J11 97-121
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, USA, 78727
E-mail Address: tydeman@tybor.com
Telephone Number: +1 (512) 255-8696
Fax Number: +1 (512) 255-8696
Sponsor: WG14
Date: 1997-09-22
Proposal Category:
Y_ Editorial change/non-normative contribution
__ Correction
__ New feature
__ Addition to obsolescent feature list
__ Addition to Future Directions
__ Other (please specify) ______________________________
Area of Standard Affected:
__ Environment
Y_ Language
__ Preprocessor
__ Library
__ Macro/typedef/tag name
__ Function
__ Header
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/N756 LIA-1 Binding: Arithmetic exception => SIGFPE,
WG14/N755 LIA-1 Binding: to ,
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: ,
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 expected that this annex will be
replaced by an amendment to C9X in a year or two that will
be the binding of LIA-1 to C9X.
The other proposals should be considered a starting point
of the LIA-1 amendment.
Proposal:
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*,
`code sample` 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:
Annex H
(informative)
Language Independent Arithmetic
** H.1 Introduction
This annex documents the extent to which the C language
currently supports the ISO/IEC 10967-1 Language Independent
Arithmetic, part 1, integer and floating-point arithmetic
(LIA-1) standard. It is expected that this annex will
eventually be replaced, by an amendment to the C language,
with a binding between LIA-1 and C. Part of the delay is
due to differences between LIA-1 and LIA-2 on the meaning of
pole and undefined exceptions.
For the rest of this annex, the term LIA-1-like will be used
to denote a C type that meets a LIA-1 type except for the
lack of notification of exceptional arithmetic operations.
** H.2 Types
*** 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 .
*** H.2.2 Integral Types
None of the unsigned or signed C integral types conform to
LIA-1 because they all lack the LIA-1 exceptional values
integer_overflow and undefined.[Footnote]
[Footnote: Exceptional values are used as part of the LIA-1
defining formalism only. They do not represent values of
any data types. There is no requirement that they be
represented or stored in a computing system. They are not
used in subsequent arithmetic operations.
The values Not-a-number and infinity of IEC 559 are not
considered exceptional values for LIA-1. They are
"continuation values" -- a value used in lieu of an
exceptional arithmetic operation; after a status flag has
been set to record the notification.]
The parameters for the LIA-1-like 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 LIA-1-like 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 integral type.
*** H.2.3 Floating-Point Types
None of the C floating-point types conform to LIA-1 because
they all lack the LIA-1 exceptional values underflow,
floating_overflow, and undefined.
**** H.2.3.1 Floating-Point Parameters
The parameters for a LIA-1-like floating point data type can
be accessed by the following:
r FLT_RADIX.
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 LIA-1-like 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.
rnd_style FLT_ROUNDS.
[Note: Defect Report 56/63, still open, is about the
accuracy of floating-point arithmetic, a concern of LIA-1
and LIA-2. Defect Report 25 is about floating-point
representation; has been answered, but did not result in a
change to the standard, may need to be revisited. Defect
Report 36 dealing with representation of floating-point
constants may need to be revisited for LIA-2. This Note is
not intended to be printed in the standard.]
**** H.2.3.2 Floating-Point Operations
The floating-point operations on LIA-1-like 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 in the LIA-1 binding.
The FLT_ROUNDS [footnote] parameter corresponds to the LIA-1
rounding styles:
truncate FLT_ROUNDS == 0.
nearest FLT_ROUNDS == 1.
other FLT_ROUNDS != 0 && FLT_ROUNDS != 1.
[footnote] The definition of FLT_ROUNDS has been extended to
cover the rounding style used in all LIA-1 operations, not
just addition. FLT_ROUNDS does not apply to type conversions.
*** H.2.4 Type Conversions
The LIA-1-like 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)round(x),
(long)round(x),
(long long)round(x),
(unsigned int)round(x),
(unsigned long)round(x),
(unsigned long long)round(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 integral, the use
of round() can be replaced with rint() or nearbyint() as
long as the current rounding direction is to nearest.
C's conversions (type casts) from floating-point to integral
do not meet LIA-1 as LIA-1 requires round to nearest and C
requires round to zero, also known as truncate.
None of C's floating-point to integral conversion functions,
lrint(), llrint(), lround(), and llround(), meet LIA-1's
requirements as the result is unspecified if the rounded
value is outside the integral range and also a range error may
happen.
C's conversions (type casts) from floating-point to
floating-point do not meet LIA-1 as LIA-1 requires round to
nearest and C leaves it as implementation defined as to the
rounding function.
C's conversions (type casts) from integral to floating-point
do not meet LIA-1 as LIA-1 requires round to nearest and C
leaves it as implementation defined as to the rounding
function.
C's round(), trunc(), ceil(), floor(), rint() and
nearbyint() are not covered by LIA-1 as they are not type
conversions.
** H.3 Notification
Notification is the process by which a user or program is
informed that an arithmetic operation cannot be performed.
Specifically, a notification shall occur when any arithmetic
operation returns an exceptional value as defined in LIA-1
clause 5.
*** H.3.1 Notification alternatives
The implementation shall provide at least the following two
alternatives for handling of notifications: setting
indicators or trap and terminate.
C does not require LIA-1 notification. However, to the
extent that notification occurs in implementations that
support it, it would be via **SIGFPE** (for traps) and
FE_INVALID, FE_DIVBYZERO, FE_OVERFLOW, FE_UNDERFLOW (for
indicators).
The notification alternative selected may influence code
generation. Because of this, an implementation need only
support a given 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 does not require any of those alternatives. "Trap and
terminate" is a good description of the default handling of
**SIGFPE** for some C implementations.
**** H.3.1.1 Indicators
The following floating-point indicators shall be provided.
They shall be clear at the start of the program. They are
set when any arithmetic operation returns an exceptional
value as defined in LIA-1 clause 5. Once set, an indicator
shall be cleared only by explicit action of the program
(that is, they are sticky).
The following mapping is for LIA-1-like floating-point
types:
undefined FE_INVALID, FE_DIVBYZERO
floating_overflow FE_OVERFLOW.
underflow FE_UNDERFLOW.
The values representing individual indicators shall be
distinct non-negative powers of two. The empty set is
denoted by 0. Other indicator subsets are named by
combining individual indicators using bit-or.
The floating-point indicator interrogation and manipulation
operations are:
set_indicators feraiseexcept(i)
clear_indicators feclearexcept(i)
test_indicators fetestexcept(i)
current_indicators fetestexcept(FE_ALL_EXCEPT)
where i is an expression of type **int** representing a
LIA-1 indicator subset.
C does not require any of those indicators. C does support,
via , indicators for IEC 559 exceptions. Those same
indicators could be used for other floating-point hardware.
C does not require that 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 only covers the
floating-point indicators.
**** H.3.1.2 Traps
The implementation shall provide an alternative of
notification through termination with a ``hard-to-ignore''
message (see LIA-1 subclause 6.1.3).
C does require that **SIGFPE** be the signal
corresponding to arithmetic exceptions, if there is any
signal raised for them.
C has signal handlers (both implementation provided default
and user provided) for **SIGFPE**, but C has no
requirement that arithmetic exceptions trap. When arithmetic
exceptions do trap, C's signal-handler mechanism supports
trap and terminate (either default implementation behavior
or user replacement for it) and trap and resume, at the
programmer's option.
But, it appears from the response to Defect Report 152 that
a signal handler for **SIGFPE** invoked by means other
than **raise** that does **longjmp**, **exit**,
**abort**, or **return** is undefined behavior.