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• Semantics

Exec-branch

Semantics of the instructions with the BRANCH opcode [ISA:2.5.2].

Signature

(exec-branch funct rs1 rs2 imm pc stat feat) → new-stat

Arguments

funct — Guard (branch-funct-p funct).

rs1 — Guard (ubyte5p rs1).

rs2 — Guard (ubyte5p rs2).

imm — Guard (ubyte12p imm).

stat — Guard (statp stat).

feat — Guard (featp feat).

Returns

new-stat — Type (statp new-stat).

Definitions and Theorems

Function: exec-branch

(defun exec-branch (funct rs1 rs2 imm pc stat feat)
  (declare (xargs :guard (and (branch-funct-p funct)
                              (ubyte5p rs1)
                              (ubyte5p rs2)
                              (ubyte12p imm)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (and (stat-validp stat feat)
                              (cond ((feat-32p feat) (ubyte32p pc))
                                    ((feat-64p feat) (ubyte64p pc))
                                    (t (impossible))))))
  (let ((__function__ 'exec-branch))
    (declare (ignorable __function__))
    (branch-funct-case funct
                       :beq (exec-beq rs1 rs2 imm pc stat feat)
                       :bne (exec-bne rs1 rs2 imm pc stat feat)
                       :blt (exec-blt rs1 rs2 imm pc stat feat)
                       :bltu (exec-bltu rs1 rs2 imm pc stat feat)
                       :bge (exec-bge rs1 rs2 imm pc stat feat)
                       :bgeu (exec-bgeu rs1 rs2 imm pc stat feat))))

Theorem: statp-of-exec-branch

(defthm statp-of-exec-branch
  (b* ((new-stat (exec-branch funct rs1 rs2 imm pc stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: stat-validp-of-exec-branch

(defthm stat-validp-of-exec-branch
 (implies
      (stat-validp stat feat)
      (b* ((?new-stat (exec-branch funct rs1 rs2 imm pc stat feat)))
        (stat-validp new-stat feat))))

Theorem: exec-branch-of-branch-funct-fix-funct

(defthm exec-branch-of-branch-funct-fix-funct
  (equal (exec-branch (branch-funct-fix funct)
                      rs1 rs2 imm pc stat feat)
         (exec-branch funct rs1 rs2 imm pc stat feat)))

Theorem: exec-branch-branch-funct-equiv-congruence-on-funct

(defthm exec-branch-branch-funct-equiv-congruence-on-funct
  (implies
       (branch-funct-equiv funct funct-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct-equiv rs1 rs2 imm pc stat feat)))
  :rule-classes :congruence)

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

(defthm exec-branch-of-ubyte5-fix-rs1
  (equal (exec-branch funct (ubyte5-fix rs1)
                      rs2 imm pc stat feat)
         (exec-branch funct rs1 rs2 imm pc stat feat)))

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

(defthm exec-branch-ubyte5-equiv-congruence-on-rs1
  (implies
       (ubyte5-equiv rs1 rs1-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct rs1-equiv rs2 imm pc stat feat)))
  :rule-classes :congruence)

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

(defthm exec-branch-of-ubyte5-fix-rs2
  (equal (exec-branch funct rs1 (ubyte5-fix rs2)
                      imm pc stat feat)
         (exec-branch funct rs1 rs2 imm pc stat feat)))

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

(defthm exec-branch-ubyte5-equiv-congruence-on-rs2
  (implies
       (ubyte5-equiv rs2 rs2-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct rs1 rs2-equiv imm pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-branch-of-ubyte12-fix-imm

(defthm exec-branch-of-ubyte12-fix-imm
  (equal (exec-branch funct rs1 rs2 (ubyte12-fix imm)
                      pc stat feat)
         (exec-branch funct rs1 rs2 imm pc stat feat)))

Theorem: exec-branch-ubyte12-equiv-congruence-on-imm

(defthm exec-branch-ubyte12-equiv-congruence-on-imm
  (implies
       (acl2::ubyte12-equiv imm imm-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct rs1 rs2 imm-equiv pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-branch-of-stat-fix-stat

(defthm exec-branch-of-stat-fix-stat
  (equal (exec-branch funct rs1 rs2 imm pc (stat-fix stat)
                      feat)
         (exec-branch funct rs1 rs2 imm pc stat feat)))

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

(defthm exec-branch-stat-equiv-congruence-on-stat
  (implies
       (stat-equiv stat stat-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct rs1 rs2 imm pc stat-equiv feat)))
  :rule-classes :congruence)

Theorem: exec-branch-of-feat-fix-feat

(defthm exec-branch-of-feat-fix-feat
  (equal (exec-branch funct
                      rs1 rs2 imm pc stat (feat-fix feat))
         (exec-branch funct rs1 rs2 imm pc stat feat)))

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

(defthm exec-branch-feat-equiv-congruence-on-feat
  (implies
       (feat-equiv feat feat-equiv)
       (equal (exec-branch funct rs1 rs2 imm pc stat feat)
              (exec-branch funct rs1 rs2 imm pc stat feat-equiv)))
  :rule-classes :congruence)