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Semantics32

Exec32-mulhsu

Semanics of the MULHSU instruction [ISA:13.1].

Signature
(exec32-mulhsu rd rs1 rs2 stat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (state32p stat).
Returns: new-stat — Type (state32p new-stat).

We read a signed 32-bit integer from rs1 and an unsigned 32-bit integer from rs2. We multiply them, we shift the product right by 32 bits, and we write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec32-mulhsu

(defun exec32-mulhsu (rd rs1 rs2 stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state32p stat))))
  (let ((__function__ 'exec32-mulhsu))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read32-xreg-signed rs1 stat))
         (rs2-operand (read32-xreg-unsigned rs2 stat))
         (product (* rs1-operand rs2-operand))
         (result (ash product 32))
         (stat (write32-xreg rd result stat))
         (stat (inc32-pc stat)))
      stat)))

Theorem: state32p-of-exec32-mulhsu

(defthm state32p-of-exec32-mulhsu
  (b* ((new-stat (exec32-mulhsu rd rs1 rs2 stat)))
    (state32p new-stat))
  :rule-classes :rewrite)

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: exec32-mulhsu-of-state32-fix-stat

(defthm exec32-mulhsu-of-state32-fix-stat
  (equal (exec32-mulhsu rd rs1 rs2 (state32-fix stat))
         (exec32-mulhsu rd rs1 rs2 stat)))

Theorem: exec32-mulhsu-state32-equiv-congruence-on-stat

(defthm exec32-mulhsu-state32-equiv-congruence-on-stat
  (implies (state32-equiv stat stat-equiv)
           (equal (exec32-mulhsu rd rs1 rs2 stat)
                  (exec32-mulhsu rd rs1 rs2 stat-equiv)))
  :rule-classes :congruence)