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Semantics64

Exec64-div

Semanics of the DIV instruction [ISA:13.2].

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

We read two signed 64-bit integers from rs1 and rs2. We divide the first by the second, rounding towards 0; if the divisor is 0, the result is -1 (see Table 11 in [ISA:13.2]). We write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec64-div

(defun exec64-div (rd rs1 rs2 stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state64p stat))))
  (let ((__function__ 'exec64-div))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read64-xreg-signed rs1 stat))
         (rs2-operand (read64-xreg-signed rs2 stat))
         (result (if (= rs2-operand 0)
                     -1
                   (truncate rs1-operand rs2-operand)))
         (stat (write64-xreg rd result stat))
         (stat (inc64-pc stat)))
      stat)))

Theorem: state64p-of-exec64-div

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

Theorem: exec64-div-of-ubyte5-fix-rd

(defthm exec64-div-of-ubyte5-fix-rd
  (equal (exec64-div (ubyte5-fix rd)
                     rs1 rs2 stat)
         (exec64-div rd rs1 rs2 stat)))

Theorem: exec64-div-ubyte5-equiv-congruence-on-rd

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

Theorem: exec64-div-of-ubyte5-fix-rs1

(defthm exec64-div-of-ubyte5-fix-rs1
  (equal (exec64-div rd (ubyte5-fix rs1)
                     rs2 stat)
         (exec64-div rd rs1 rs2 stat)))

Theorem: exec64-div-ubyte5-equiv-congruence-on-rs1

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

Theorem: exec64-div-of-ubyte5-fix-rs2

(defthm exec64-div-of-ubyte5-fix-rs2
  (equal (exec64-div rd rs1 (ubyte5-fix rs2)
                     stat)
         (exec64-div rd rs1 rs2 stat)))

Theorem: exec64-div-ubyte5-equiv-congruence-on-rs2

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

Theorem: exec64-div-of-state64-fix-stat

(defthm exec64-div-of-state64-fix-stat
  (equal (exec64-div rd rs1 rs2 (state64-fix stat))
         (exec64-div rd rs1 rs2 stat)))

Theorem: exec64-div-state64-equiv-congruence-on-stat

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