[Notes] Floating Point Semantics in Compiler

10 Nov 2024

Floating Point Semantics

Floating Point Algebra
- limitation Computer Representation of FP and real world Real Numbers
  - Base, Precision
  - infinity
  - NaN
  - Denormal
  - SubNormal
  - Normal
  - Sized Zero
  - Exception
    - Overflow
    - Underflow
    - Divide by zero
    - Invalid
    - Inexact
- Exception
- Traps and floating point status register
- Rounding Errors
  - Important because results need to be consistent across machines
  - Relative Error Method (IEEE FP standard)
  - ULP Method
  - Rounding Modes
    - Nearest
    - Positive INF
    - Negative INF
    - Zero
IEEE 754 compliance
FP model
Fast Math

Reference