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Semantics32

Exec32-divu

Semanics of the DIVU instruction [ISA:13.2].

Signature
(exec32-divu 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 two unsigned 32-bit integers from rs1 and rs2. We divide the first by the second, rounding towards 0; if the divisor is 0, the result is 2^{32}-1 (see Table 11 in [ISA:13.2]). We write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec32-divu

(defun exec32-divu (rd rs1 rs2 stat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (state32p stat))))
  (let ((__function__ 'exec32-divu))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read32-xreg-unsigned rs1 stat))
         (rs2-operand (read32-xreg-unsigned rs2 stat))
         (result (if (= rs2-operand 0)
                     (1- (expt 2 32))
                   (truncate rs1-operand rs2-operand)))
         (stat (write32-xreg rd result stat))
         (stat (inc32-pc stat)))
      stat)))

Theorem: state32p-of-exec32-divu

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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