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Semantics

Exec-slt

Semantics of the SLT instruction [ISA:2.4.2].

Signature
(exec-slt 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 compare the two signed 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-slt

(defun exec-slt (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-slt))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read-xreg-signed (ubyte5-fix rs1)
                                        stat feat))
         (rs2-operand (read-xreg-signed (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-slt

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

Theorem: stat-validp-of-exec-slt

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: exec-slt-of-stat-fix-stat

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

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

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

Theorem: exec-slt-of-feat-fix-feat

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

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

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