* 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: <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 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, <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: 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 typeboolwith values oftrueandfalse, all from <stdbool.h>. *** 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 typeint, and li is of typelong 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 viaSIGFPE(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 ofSIGFPEfor 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 typeintrepresenting a LIA-1 indicator subset. C does not require any of those indicators. C does support, via <fenv.h>, 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 <fenv.h> 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 thatSIGFPEbe 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) forSIGFPE, 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 forSIGFPEinvoked by means other thanraisethat doeslongjmp,exit,abort, orreturnis undefined behavior.