X3J3/96-054

Date:     February 17, 1996
To:       X3J3
From:     Craig T. Dedo
Subject:  Evaluation of Intrinsic Procedures


NUMBER:        202
TITLE:         Evaluation of Intrinsic Procedures
KEYWORDS:      Algorithm, Mathematical, Computational
DEFECT TYPE:   Interpretation
STATUS:        X3J3 Consideration in Progress

QUESTION: 1.  When the standard specifies an algorithm for computing a
          mathematical procedure, must a processor use the specified
          algorithm?

          Example: ANINT is defined as INT (A + 0.5).  On some processors
          ANINT (16 000 001.0) evaluates to 16 000 002.0 using this algo-
          rithm.

          2.  May a processor return a mathematically equivalent result
          in the evaluation of a numeric intrinsic procedure?

          Example:  If ANINT (16 000 001.0) can be computed as the more
          expected 16 000 001.0, may a processor do so?

ANSWER:   1.  No, a processor is not required to use the algorithm
          from the standard.

          2.  Yes, a processor may return the mathematically equivalent
          result in the evaluation of any numeric intrinsic procedure.

DISCUSSION:  The use or specification of an algorithm in the standard is
          intended to specify the value and properties of the required
          end result.  It is not intended to require that a processor
          use a particular method of achieving that result.  Thus, an
          algorithm  specifies the mathematical results, not the computa-
          tional results, of the evaluation of intrinsic procedures.

          Although the standard does not directly address this issue, one
          may infer from several passages that the standard intends to
          permit a processor to use any mathematically equivalent method
          in the evaluation of intrinsic procedures.  This practice is
          expressly permitted for the evaluation of numeric intrinsic
          operations in 7.1.7.3 [81:17-19].
            The rules given in 7.2.1 specify the interpretation of a
            numeric intrinsic operation.  Once the interpretation has
            been established in accordance with those rules, the
            processor may evaluate any mathematically equivalent
            expression, provided that the integrity of parentheses
            is not violated.
          Further into the section are two tables specifying allowable
          and nonallowable alternative forms for certain mathematical
          expressions [81:30-40, 82:3-10].

          It is true that rule R701 in section 7.1.1.1 defines a
          <<function-reference>> as a <<primary>>.  However, section
          7.1.7, "Evaluation of operations", contains several references
          to rules concerning the evaluation of functions [79:40, 80:4-
          17, 81:1-8].  Thus the context indicates that the standard
          intends to permit a processor this freedom of operation in the
          evaluation of intrinsic procedures as well.

          The standard intends to permit a processor to use infinite
          accuracy if available.  Section 1.3.2, Exclusions, states in
          part, "This International Standard does not specify:  . . . (6)
          The physical properties of the representation of quantities and
          the method of rounding, approximating, or computing numeric
          values on a particular processor." [1:19, 1:29-30]

EDITS:    None.

SUBMITTED BY:  Keith H. Bierman

HISTORY:  95-247    m134 Submitted with proposed response, adopted 9-4
          95-256    m134 Ballot failed, 10-6
          95-260    m135 Proposed response, no action
          96-023    m136 Proposed response, no action
          96-054    m137 Proposed response

[End of 96-054]