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Semantics32

Exec32-add

Semantics of the ADD instruction [ISA:2.4.2].

Signature
(exec32-add rd rs1 rs2 stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (stat32ip stat).
Returns: new-stat — Type (stat32ip new-stat).

We read two unsigned 32-bit integers from rs1 and rs2. We add them, and write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec32-add

(defun exec32-add (rd rs1 rs2 stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (stat32ip stat))))
  (let ((__function__ 'exec32-add))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read32-xreg-signed rs1 stat))
         (rs2-operand (read32-xreg-signed rs2 stat))
         (result (+ rs1-operand rs2-operand))
         (stat (write32-xreg rd result stat))
         (stat (inc32-pc stat)))
      stat)))

Theorem: stat32ip-of-exec32-add

(defthm stat32ip-of-exec32-add
  (b* ((new-stat (exec32-add rd rs1 rs2 stat)))
    (stat32ip new-stat))
  :rule-classes :rewrite)

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

(defthm exec32-add-of-ubyte5-fix-rd
  (equal (exec32-add (ubyte5-fix rd)
                     rs1 rs2 stat)
         (exec32-add rd rs1 rs2 stat)))

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

(defthm exec32-add-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec32-add rd rs1 rs2 stat)
                  (exec32-add rd-equiv rs1 rs2 stat)))
  :rule-classes :congruence)

Theorem: exec32-add-of-ubyte5-fix-rs1

(defthm exec32-add-of-ubyte5-fix-rs1
  (equal (exec32-add rd (ubyte5-fix rs1)
                     rs2 stat)
         (exec32-add rd rs1 rs2 stat)))

Theorem: exec32-add-ubyte5-equiv-congruence-on-rs1

(defthm exec32-add-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec32-add rd rs1 rs2 stat)
                  (exec32-add rd rs1-equiv rs2 stat)))
  :rule-classes :congruence)

Theorem: exec32-add-of-ubyte5-fix-rs2

(defthm exec32-add-of-ubyte5-fix-rs2
  (equal (exec32-add rd rs1 (ubyte5-fix rs2)
                     stat)
         (exec32-add rd rs1 rs2 stat)))

Theorem: exec32-add-ubyte5-equiv-congruence-on-rs2

(defthm exec32-add-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec32-add rd rs1 rs2 stat)
                  (exec32-add rd rs1 rs2-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-add-of-stat32i-fix-stat

(defthm exec32-add-of-stat32i-fix-stat
  (equal (exec32-add rd rs1 rs2 (stat32i-fix stat))
         (exec32-add rd rs1 rs2 stat)))

Theorem: exec32-add-stat32i-equiv-congruence-on-stat

(defthm exec32-add-stat32i-equiv-congruence-on-stat
  (implies (stat32i-equiv stat stat-equiv)
           (equal (exec32-add rd rs1 rs2 stat)
                  (exec32-add rd rs1 rs2 stat-equiv)))
  :rule-classes :congruence)