C issue 0286: Correctly rounded and rounding direction/mode

This issue has been automatically converted from the original issue lists and some formatting may not have been preserved.

Authors: WG 14, Fred Tydeman (USA)
Date: 2003-04-13
Submitted against: C99
Status: Fixed
Fixed in: C99 TC3
Converted from: summary-c99.htm, dr_286.htm

Summary

    effective rounding
    current rounding
    rounding mode characterized by the value of FLT_ROUNDS

    rounding direction mode
    rounding direction
    rounding mode
    directed-rounding control mode
    directed rounding mode
    rounding control mode

Details

3.9 correctly rounded result: representation in the result format that is nearest in value, subject to the effective rounding mode, to what the result would be given unlimited range and precision

5.2.4.2.2 Characteristics of floating types <float.h>: Paragraph 6: The rounding mode for floating-point addition is characterized by the implementation-defined value of FLT_ROUNDS:18)

18) Evaluation of FLT_ROUNDS correctly reflects any execution-time change of rounding mode through the function fesetround in <fenv.h>.

Paragraph 1: The header <fenv.h> declares two types and several macros and functions to provide access to the floating-point environment. The floating-point environment refers collectively to any floating-point status flags and control modes supported by the implementation.173)

173) This header is designed to support the floating-point exception status flags and directed-rounding control modes required by IEC 60559, and other similar floating-point state information.

Paragraph 7 Each of the macros: FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD; is defined if and only if the implementation supports getting and setting the represented rounding direction by means of the fegetround and fesetround functions.

7.6.3 Rounding: Paragraph 1 The fegetround and fesetround functions provide control of rounding direction modes.

7.12.9.3 The nearbyint functions: Paragraph 2: The nearbyint functions round their argument to an integer value in floating-point format, using the current rounding direction and without raising the inexact floating-point exception.

7.12.9.5 The lrint and llrint functions: Paragraph 2: The lrint and llrint functions round their argument to the nearest integer value, rounding according to the current rounding direction.

7.12.9.6 The round functions: Paragraph 2: The round functions round their argument to the nearest integer value in floating-point format, rounding halfway cases away from zero, regardless of the current rounding direction.

7.12.9.7 The lround and llround functions: Paragraph 2: The lround and llround functions round their argument to the nearest integer value, rounding halfway cases away from zero, regardless of the current rounding direction.

Footnote 203) When y != 0, the remainder r = x REM y is defined regardless of the rounding mode ...

7.12.13.1 The fma functions: Paragraph 2: The fma functions compute (x*y)+z, rounded as one ternary operation: they compute the value (as if) to infinite precision and round once to the result format, according to the rounding mode characterized by the value of FLT_ROUNDS.

Paragraph 12: ... error should have a correct sign for the current rounding direction.

Paragraph 13: ... error should have a correct sign for the current rounding direction.

Paragraph 8: ... error should have a correct sign for the current rounding direction.

Paragraph 9: ... according to the current rounding direction, ... ... should have a correct sign for the current rounding direction.

Paragraph 12: ... error should have a correct sign for the current rounding direction.

Paragraph 13: ... the error should have a correct sign for the current rounding direction.

Paragraph 8: ... the error should have a correct sign for the current rounding direction.

Paragraph 9: ... according to the current rounding direction, with the extra stipulation that the error with respect to D should have a correct sign for the current rounding direction.

Annex F.3 Operators and functions: Paragraph 1: The fegetround and fesetround functions in <fenv.h> provide the facility to select among the IEC 60559 directed rounding modes represented by the rounding direction macros in <fenv.h> (FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO) and the values 0, 1, 2, and 3 of FLT_ROUNDS are the IEC 60559 directed rounding modes.

Paragraph 2: Conversions involving IEC 60559 formats follow all pertinent recommended practice. In particular, conversion between any supported IEC 60559 format and decimal with DECIMAL_DIG or fewer significant digits is correctly rounded, which assures that conversion from the widest supported IEC 60559 format to decimal with DECIMAL_DIG digits and back is the identity function.

Paragraph 3: 3 Functions such as strtod that convert character sequences to floating types honor the rounding direction. Hence, if the rounding direction might be upward or downward, the implementation cannot convert a minus-signed sequence by negating the converted unsigned sequence.

Annex F.6 Contracted expressions: Paragraph 1: A contracted expression treats infinities, NaNs, signed zeros, subnormals, and the rounding directions in a manner consistent with the basic arithmetic operations covered by IEC 60559.

Annex F.7 Floating-point environment: Paragraph 1: The floating-point environment defined in <fenv.h> includes the IEC 60559 floating-point exception status flags and directed-rounding control modes.

Annex F.7.1 Environment management: Paragraph 1: IEC 60559 requires that floating-point operations implicitly raise floating-point exception status flags, and that rounding control modes can be set explicitly to affect result values of floating-point operations.

Annex F.7.2 Translation: Paragraph 1: During translation the IEC 60559 default modes are in effect: The rounding direction mode is rounding to nearest.

Footnote 306) As floating constants are converted to appropriate internal representations at translation time, their conversion is subject to default rounding modes ...

Annex F.7.3 Execution: Paragraph 1: At program startup the floating-point environment is initialized as prescribed by IEC 60559: All floating-point exception status flags are cleared. The rounding direction mode is rounding to nearest.

Footnote 307) Where the state for the FENV_ACCESS pragma is "on", results of inexact expressions like 1.0/3.0 are affected by rounding modes set at execution time, ...

Annex F.8.2 Expression transformations: has in several places: default rounding direction.

Annex F.8.4 Constant arithmetic: Paragraph 1: ... changing the rounding direction to downward ...

Footnote 311) 0-0 yields -0 instead of +0 just when the rounding direction is downward.

Paragraph 10: Whether the functions honor the rounding direction mode is implementation-defined.

Annex F.9.6.3 The nearbyint functions: Paragraph 1: The nearbyint functions use IEC 60559 rounding according to the current rounding direction.

Annex F.9.6.5 The lrint and llrint functions: Paragraph 1: The lrint and llrint functions provide floating-to-integer conversion as prescribed by IEC 60559. They round according to the current rounding direction.

Annex F.9.6.7 The lround and llround functions: Paragraph 1: The lround and llround functions differ from the lrint and llrint functions with the default rounding direction ...

Annex F.9.6.8 The trunc functions: Paragraph 1: The trunc functions use IEC 60559 rounding toward zero (regardless of the current rounding direction).

Annex J.3.6 Floating point: Paragraph 1: Additional floating-point exceptions, rounding modes, environments, and classifications, and their macro names (7.6, 7.12).

Annex J.3.12 Library functions: Whether the functions in <math.h> honor the rounding direction mode in an IEC 60559 conformant implementation (F.9).

Suggested Technical Corrigendum

Of the six 'equivalent' phrases that involve 'rounding', 'direction', 'control', and 'mode', pick one ('rounding mode' is the submitter's choice) and change the others to it thruout the C99 standard.

Change 7.12.13.1 The fma functions: '... the rounding mode characterized by the value of FLT_ROUNDS' to '... the current rounding mode'.

Change Annex F.5 Binary-decimal conversion: Paragraph 2: 'correctly rounded' to 'correctly rounded (which honors the current rounding mode)'. Note: Once 'effective rounding mode' is changed to 'current rounding mode', is this change really needed (since correctly rounded implies honors the current rounding mode)?

Committee Discussion

This needs to be passed by the original authors to see if there is some rationale for the multiple terminology. No real opposition to the Suggested Technical Corrigendum, the Committee does not feel a need to rush this change.

Technical Corrigendum