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Modern Language Tools
      and 754R


      E. Jason Riedy
      UC Berkeley
Current State:

     HW Designers                        SW Designers
●
    Can implement                         ●
                                              Few implementation
    anything!                                           options.
    No feedback on                                     No access to
                           Languages
●                                                  ●


    trade-offs.                                           features.

                     ●
                         Not bridging the gap.


                 ●
                     What can 754R do?
●
    Current 754 support is ad-hoc.
         ●
             C99, Fortran 2003 provide different
             descriptions for same model.
         ●
             Many languages provide no semantics.
         ●
             Compilers provide less...

●
    754R: Provide a language for languages.
     ●
         Not LIA: Describe 754 arithmetic, not all
         possible arithmetics.
     ●
         Use modern language tools: Type theory
         and inferencing.
Typing from 20k Feet

●
    Precisions ≈ data types



●
    Operations ≈ function types


●   Expression evaluation rules ⊂typing rules
Impact on 754R
●
    Provides a sound base for definitions.
●
    Could define typing hierarchy and “literal”
    type for wide expression evaluation.
    –   Assists interval arithmetic!
●
    Models modes and flags:
    –

●
    Possible problems:
    –   Comparison operators and wide eval?
    –   Compiler support?

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From ARITH-17: Intro slides for the panel on language interations with arithmetic

  • 1. Modern Language Tools and 754R E. Jason Riedy UC Berkeley
  • 2. Current State: HW Designers SW Designers ● Can implement ● Few implementation anything! options. No feedback on No access to Languages ● ● trade-offs. features. ● Not bridging the gap. ● What can 754R do?
  • 3. Current 754 support is ad-hoc. ● C99, Fortran 2003 provide different descriptions for same model. ● Many languages provide no semantics. ● Compilers provide less... ● 754R: Provide a language for languages. ● Not LIA: Describe 754 arithmetic, not all possible arithmetics. ● Use modern language tools: Type theory and inferencing.
  • 4. Typing from 20k Feet ● Precisions ≈ data types ● Operations ≈ function types ● Expression evaluation rules ⊂typing rules
  • 5. Impact on 754R ● Provides a sound base for definitions. ● Could define typing hierarchy and “literal” type for wide expression evaluation. – Assists interval arithmetic! ● Models modes and flags: – ● Possible problems: – Comparison operators and wide eval? – Compiler support?