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Missing-parents

Exec-mulh

Semanics of the MULH instruction [ISA:13.1].

Signature
(exec-mulh rd rs1 rs2 stat feat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; stat — Guard (statp stat).; feat — Guard (featp feat).
Returns: new-stat — Type (statp new-stat).

We read two signed XLEN-bit integers from rs1 and rs2. We multiply them, we shift the product right by XLEN bits, and we write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec-mulh

(defun exec-mulh (rd rs1 rs2 stat feat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (stat-validp stat feat)))
  (let ((__function__ 'exec-mulh))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read-xreg-signed (ubyte5-fix rs1)
                                        stat feat))
         (rs2-operand (read-xreg-signed (ubyte5-fix rs2)
                                        stat feat))
         (product (* rs1-operand rs2-operand))
         (result (ash product (feat->xlen feat)))
         (stat (write-xreg (ubyte5-fix rd)
                           result stat feat))
         (stat (inc4-pc stat feat)))
      stat)))

Theorem: statp-of-exec-mulh

(defthm statp-of-exec-mulh
  (b* ((new-stat (exec-mulh rd rs1 rs2 stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: exec-mulh-of-ubyte5-fix-rd

(defthm exec-mulh-of-ubyte5-fix-rd
  (equal (exec-mulh (ubyte5-fix rd)
                    rs1 rs2 stat feat)
         (exec-mulh rd rs1 rs2 stat feat)))

Theorem: exec-mulh-ubyte5-equiv-congruence-on-rd

(defthm exec-mulh-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec-mulh rd rs1 rs2 stat feat)
                  (exec-mulh rd-equiv rs1 rs2 stat feat)))
  :rule-classes :congruence)

Theorem: exec-mulh-of-ubyte5-fix-rs1

(defthm exec-mulh-of-ubyte5-fix-rs1
  (equal (exec-mulh rd (ubyte5-fix rs1)
                    rs2 stat feat)
         (exec-mulh rd rs1 rs2 stat feat)))

Theorem: exec-mulh-ubyte5-equiv-congruence-on-rs1

(defthm exec-mulh-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec-mulh rd rs1 rs2 stat feat)
                  (exec-mulh rd rs1-equiv rs2 stat feat)))
  :rule-classes :congruence)

Theorem: exec-mulh-of-ubyte5-fix-rs2

(defthm exec-mulh-of-ubyte5-fix-rs2
  (equal (exec-mulh rd rs1 (ubyte5-fix rs2)
                    stat feat)
         (exec-mulh rd rs1 rs2 stat feat)))

Theorem: exec-mulh-ubyte5-equiv-congruence-on-rs2

(defthm exec-mulh-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec-mulh rd rs1 rs2 stat feat)
                  (exec-mulh rd rs1 rs2-equiv stat feat)))
  :rule-classes :congruence)

Theorem: exec-mulh-of-stat-fix-stat

(defthm exec-mulh-of-stat-fix-stat
  (equal (exec-mulh rd rs1 rs2 (stat-fix stat)
                    feat)
         (exec-mulh rd rs1 rs2 stat feat)))

Theorem: exec-mulh-stat-equiv-congruence-on-stat

(defthm exec-mulh-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (exec-mulh rd rs1 rs2 stat feat)
                  (exec-mulh rd rs1 rs2 stat-equiv feat)))
  :rule-classes :congruence)

Theorem: exec-mulh-of-feat-fix-feat

(defthm exec-mulh-of-feat-fix-feat
  (equal (exec-mulh rd rs1 rs2 stat (feat-fix feat))
         (exec-mulh rd rs1 rs2 stat feat)))

Theorem: exec-mulh-feat-equiv-congruence-on-feat

(defthm exec-mulh-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (exec-mulh rd rs1 rs2 stat feat)
                  (exec-mulh rd rs1 rs2 stat feat-equiv)))
  :rule-classes :congruence)