Theory FpSem

chapter ‹Generated by Lem from ‹semantics/fpSem.lem›.›

theory "FpSem" 

imports
  Main
  "HOL-Library.Datatype_Records"
  "LEM.Lem_pervasives"
  "Lib"
  "IEEE_Floating_Point.FP64"

begin 

― ‹‹open import Pervasives››
― ‹‹open import Lib››

― ‹‹open import {hol} `machine_ieeeTheory`››
― ‹‹open import {isabelle} `IEEE_Floating_Point.FP64`››

― ‹‹type rounding››

datatype fp_cmp_op = FP_Less | FP_LessEqual | FP_Greater | FP_GreaterEqual | FP_Equal
datatype fp_uop_op = FP_Abs | FP_Neg | FP_Sqrt
datatype fp_bop_op = FP_Add | FP_Sub | FP_Mul | FP_Div

― ‹‹val fp64_lessThan     : word64 -> word64 -> bool››
― ‹‹val fp64_lessEqual    : word64 -> word64 -> bool››
― ‹‹val fp64_greaterThan  : word64 -> word64 -> bool››
― ‹‹val fp64_greaterEqual : word64 -> word64 -> bool››
― ‹‹val fp64_equal        : word64 -> word64 -> bool››

― ‹‹val fp64_abs    : word64 -> word64››
― ‹‹val fp64_negate : word64 -> word64››
― ‹‹val fp64_sqrt   : rounding -> word64 -> word64››

― ‹‹val fp64_add : rounding -> word64 -> word64 -> word64››
― ‹‹val fp64_sub : rounding -> word64 -> word64 -> word64››
― ‹‹val fp64_mul : rounding -> word64 -> word64 -> word64››
― ‹‹val fp64_div : rounding -> word64 -> word64 -> word64››

― ‹‹val roundTiesToEven : rounding››

― ‹‹val fp_cmp : fp_cmp -> word64 -> word64 -> bool››
fun fp_cmp  :: " fp_cmp_op ⇒ 64 word ⇒ 64 word ⇒ bool "  where 
     " fp_cmp FP_Less = ( fp64_lessThan )"
|" fp_cmp FP_LessEqual = ( fp64_lessEqual )"
|" fp_cmp FP_Greater = ( fp64_greaterThan )"
|" fp_cmp FP_GreaterEqual = ( fp64_greaterEqual )"
|" fp_cmp FP_Equal = ( fp64_equal )"


― ‹‹val fp_uop : fp_uop -> word64 -> word64››
fun fp_uop  :: " fp_uop_op ⇒ 64 word ⇒ 64 word "  where 
     " fp_uop FP_Abs = ( fp64_abs )"
|" fp_uop FP_Neg = ( fp64_negate )"
|" fp_uop FP_Sqrt = ( fp64_sqrt To_nearest )"


― ‹‹val fp_bop : fp_bop -> word64 -> word64 -> word64››
fun fp_bop  :: " fp_bop_op ⇒ 64 word ⇒ 64 word ⇒ 64 word "  where 
     " fp_bop FP_Add = ( fp64_add To_nearest )"
|" fp_bop FP_Sub = ( fp64_sub To_nearest )"
|" fp_bop FP_Mul = ( fp64_mul To_nearest )"
|" fp_bop FP_Div = ( fp64_div To_nearest )"

end