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Semantics

Exec-jal

Semantics of the JAL instruction [ISA:2.5.1].

Signature
(exec-jal rd imm pc stat feat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; imm — Guard (ubyte20p imm).; stat — Guard (statp stat).; feat — Guard (featp feat).
Returns: new-stat — Type (statp new-stat).

We use the 20 bits of the immediate as the high bits of an unsigned 21-bit integer, whose low bit is 0 (i.e. the immediate measures multiples of 2); the unsigned 21-bit integer is sign-extended to XLEN bits, obtaining an offset. We add the offset to the address of the instruction, which is passed as the pc input to this function; this is the jump target. We write the address of the instruction just after this to rd; since instructions are 32-bit long, the address of the next instruction is obtained by adding 4 to pc. We write the jump target to the program counter.

Definitions and Theorems

Function: exec-jal

(defun exec-jal (rd imm pc stat feat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte20p 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)))
                              (< (lnfix rd) (feat->xnum feat)))))
  (let ((__function__ 'exec-jal))
    (declare (ignorable __function__))
    (b* ((offset (loghead (feat->xlen feat)
                          (logext 21 (ash (ubyte20-fix imm) 1))))
         (target-pc (+ pc offset))
         (next-pc (+ pc 4))
         (stat (write-xreg (ubyte5-fix rd)
                           next-pc stat feat))
         (stat (write-pc target-pc stat feat)))
      stat)))

Theorem: statp-of-exec-jal

(defthm statp-of-exec-jal
  (b* ((new-stat (exec-jal rd imm pc stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: stat-validp-of-exec-jal

(defthm stat-validp-of-exec-jal
  (implies (and (stat-validp stat feat)
                (< (lnfix rd) (feat->xnum feat)))
           (b* ((?new-stat (exec-jal rd imm pc stat feat)))
             (stat-validp new-stat feat))))

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

(defthm exec-jal-of-ubyte5-fix-rd
  (equal (exec-jal (ubyte5-fix rd)
                   imm pc stat feat)
         (exec-jal rd imm pc stat feat)))

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

(defthm exec-jal-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec-jal rd imm pc stat feat)
                  (exec-jal rd-equiv imm pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-jal-of-ubyte20-fix-imm

(defthm exec-jal-of-ubyte20-fix-imm
  (equal (exec-jal rd (ubyte20-fix imm)
                   pc stat feat)
         (exec-jal rd imm pc stat feat)))

Theorem: exec-jal-ubyte20-equiv-congruence-on-imm

(defthm exec-jal-ubyte20-equiv-congruence-on-imm
  (implies (acl2::ubyte20-equiv imm imm-equiv)
           (equal (exec-jal rd imm pc stat feat)
                  (exec-jal rd imm-equiv pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-jal-of-stat-fix-stat

(defthm exec-jal-of-stat-fix-stat
  (equal (exec-jal rd imm pc (stat-fix stat)
                   feat)
         (exec-jal rd imm pc stat feat)))

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

(defthm exec-jal-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (exec-jal rd imm pc stat feat)
                  (exec-jal rd imm pc stat-equiv feat)))
  :rule-classes :congruence)

Theorem: exec-jal-of-feat-fix-feat

(defthm exec-jal-of-feat-fix-feat
  (equal (exec-jal rd imm pc stat (feat-fix feat))
         (exec-jal rd imm pc stat feat)))

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

(defthm exec-jal-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (exec-jal rd imm pc stat feat)
                  (exec-jal rd imm pc stat feat-equiv)))
  :rule-classes :congruence)