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Semantics64

Exec64-op-32

Semantics of the instructions with the OP-32 opcode [ISA:4.2.2] [ISA:13.1] [ISA:13.2].

Signature
(exec64-op-32 funct rd rs1 rs2 stat) → new-stat
Arguments: funct — Guard (op-32-funct-p funct).; rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

Definitions and Theorems

Function: exec64-op-32

(defun exec64-op-32 (funct rd rs1 rs2 stat)
  (declare (xargs :guard (and (op-32-funct-p funct)
                              (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state64p stat))))
  (let ((__function__ 'exec64-op-32))
    (declare (ignorable __function__))
    (op-32-funct-case funct
                      :addw (exec64-addw rd rs1 rs2 stat)
                      :subw (exec64-subw rd rs1 rs2 stat)
                      :sllw (exec64-sllw rd rs1 rs2 stat)
                      :srlw (exec64-srlw rd rs1 rs2 stat)
                      :sraw (exec64-sraw rd rs1 rs2 stat)
                      :mulw (exec64-mulw rd rs1 rs2 stat)
                      :divw (exec64-divw rd rs1 rs2 stat)
                      :divuw (exec64-divuw rd rs1 rs2 stat)
                      :remw (exec64-remw rd rs1 rs2 stat)
                      :remuw (exec64-remuw rd rs1 rs2 stat))))

Theorem: state64p-of-exec64-op-32

(defthm state64p-of-exec64-op-32
  (b* ((new-stat (exec64-op-32 funct rd rs1 rs2 stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: exec64-op-32-of-op-32-funct-fix-funct

(defthm exec64-op-32-of-op-32-funct-fix-funct
  (equal (exec64-op-32 (op-32-funct-fix funct)
                       rd rs1 rs2 stat)
         (exec64-op-32 funct rd rs1 rs2 stat)))

Theorem: exec64-op-32-op-32-funct-equiv-congruence-on-funct

(defthm exec64-op-32-op-32-funct-equiv-congruence-on-funct
  (implies (op-32-funct-equiv funct funct-equiv)
           (equal (exec64-op-32 funct rd rs1 rs2 stat)
                  (exec64-op-32 funct-equiv rd rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-32-of-ubyte5-fix-rd

(defthm exec64-op-32-of-ubyte5-fix-rd
  (equal (exec64-op-32 funct (ubyte5-fix rd)
                       rs1 rs2 stat)
         (exec64-op-32 funct rd rs1 rs2 stat)))

Theorem: exec64-op-32-ubyte5-equiv-congruence-on-rd

(defthm exec64-op-32-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec64-op-32 funct rd rs1 rs2 stat)
                  (exec64-op-32 funct rd-equiv rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-32-of-ubyte5-fix-rs1

(defthm exec64-op-32-of-ubyte5-fix-rs1
  (equal (exec64-op-32 funct rd (ubyte5-fix rs1)
                       rs2 stat)
         (exec64-op-32 funct rd rs1 rs2 stat)))

Theorem: exec64-op-32-ubyte5-equiv-congruence-on-rs1

(defthm exec64-op-32-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec64-op-32 funct rd rs1 rs2 stat)
                  (exec64-op-32 funct rd rs1-equiv rs2 stat)))
  :rule-classes :congruence)

Theorem: exec64-op-32-of-ubyte5-fix-rs2

(defthm exec64-op-32-of-ubyte5-fix-rs2
  (equal (exec64-op-32 funct rd rs1 (ubyte5-fix rs2)
                       stat)
         (exec64-op-32 funct rd rs1 rs2 stat)))

Theorem: exec64-op-32-ubyte5-equiv-congruence-on-rs2

(defthm exec64-op-32-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec64-op-32 funct rd rs1 rs2 stat)
                  (exec64-op-32 funct rd rs1 rs2-equiv stat)))
  :rule-classes :congruence)

Theorem: exec64-op-32-of-state64-fix-stat

(defthm exec64-op-32-of-state64-fix-stat
  (equal (exec64-op-32 funct rd rs1 rs2 (state64-fix stat))
         (exec64-op-32 funct rd rs1 rs2 stat)))

Theorem: exec64-op-32-state64-equiv-congruence-on-stat

(defthm exec64-op-32-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (exec64-op-32 funct rd rs1 rs2 stat)
                  (exec64-op-32 funct rd rs1 rs2 stat-equiv)))
  :rule-classes :congruence)