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Rv32im-le-semantics

Exec32-lui

Semantics of the LUI instruction [ISA:2.4.1].

Signature
(exec32-lui rd imm stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; imm — Guard (ubyte20p imm).; stat — Guard (stat32p stat).
Returns: new-stat — Type (stat32p new-stat).

We use the 20 bits of the immediate as the high bits of an unsigned 32-bit integer, whose low bits are 0. We write the integer to rd. We increment the program counter.

Definitions and Theorems

Function: exec32-lui

(defun exec32-lui (rd imm stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte20p imm)
                              (stat32p stat))))
  (b* ((result (ash (ubyte20-fix imm) 12))
       (stat (write32-xreg rd result stat))
       (stat (inc32-pc stat)))
    stat))

Theorem: stat32p-of-exec32-lui

(defthm stat32p-of-exec32-lui
  (b* ((new-stat (exec32-lui rd imm stat)))
    (stat32p new-stat))
  :rule-classes :rewrite)

Theorem: exec32-lui-of-ubyte5-fix-rd

(defthm exec32-lui-of-ubyte5-fix-rd
  (equal (exec32-lui (ubyte5-fix rd) imm stat)
         (exec32-lui rd imm stat)))

Theorem: exec32-lui-ubyte5-equiv-congruence-on-rd

(defthm exec32-lui-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec32-lui rd imm stat)
                  (exec32-lui rd-equiv imm stat)))
  :rule-classes :congruence)

Theorem: exec32-lui-of-ubyte20-fix-imm

(defthm exec32-lui-of-ubyte20-fix-imm
  (equal (exec32-lui rd (ubyte20-fix imm) stat)
         (exec32-lui rd imm stat)))

Theorem: exec32-lui-ubyte20-equiv-congruence-on-imm

(defthm exec32-lui-ubyte20-equiv-congruence-on-imm
  (implies (acl2::ubyte20-equiv imm imm-equiv)
           (equal (exec32-lui rd imm stat)
                  (exec32-lui rd imm-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-lui-of-stat32-fix-stat

(defthm exec32-lui-of-stat32-fix-stat
  (equal (exec32-lui rd imm (stat32-fix stat))
         (exec32-lui rd imm stat)))

Theorem: exec32-lui-stat32-equiv-congruence-on-stat

(defthm exec32-lui-stat32-equiv-congruence-on-stat
  (implies (stat32-equiv stat stat-equiv)
           (equal (exec32-lui rd imm stat)
                  (exec32-lui rd imm stat-equiv)))
  :rule-classes :congruence)