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Semantics

Exec-sltu

Semantics of the SLTU instruction [ISA:2.4.2].

Signature
(exec-sltu 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 unsigned XLEN-bit integers from rs1 and rs2. We compare the two unsigned integers: if the first one is less than the second, the result is 1, otherwise it is 0. We write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec-sltu

(defun exec-sltu (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-sltu))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read-xreg-unsigned (ubyte5-fix rs1)
                                          stat feat))
         (rs2-operand (read-xreg-unsigned (ubyte5-fix rs2)
                                          stat feat))
         (result (if (< rs1-operand rs2-operand) 1 0))
         (stat (write-xreg (ubyte5-fix rd)
                           result stat feat))
         (stat (inc4-pc stat feat)))
      stat)))

Theorem: statp-of-exec-sltu

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

Theorem: stat-validp-of-exec-sltu

(defthm stat-validp-of-exec-sltu
  (implies (stat-validp stat feat)
           (b* ((?new-stat (exec-sltu rd rs1 rs2 stat feat)))
             (stat-validp new-stat feat))))

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: exec-sltu-of-stat-fix-stat

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

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

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

Theorem: exec-sltu-of-feat-fix-feat

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

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

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