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    • States

    Write-xreg

    Write an integer to an x register.

    Signature
    (write-xreg reg val stat feat) → new-stat
    Arguments
    reg — Guard (natp reg).
    val — Guard (integerp val).
    stat — Guard (statp stat).
    feat — Guard (featp feat).
    Returns
    new-stat — Type (statp new-stat).

    The integer may have any size: we only keep its low XLEN bits, and write those to the register.

    The index must be less than the number n of registers, so that the registers x0 to x<n-1> can be indexed.

    As explained in stat, x0 is not modeled explicitly, since it is hardwired to 0. Thus, the 0 index is treated separately; the other cases are handled by decrementing the index by 1.

    Definitions and Theorems

    Function: write-xreg

    (defun write-xreg (reg val stat feat)
     (declare (xargs :guard (and (natp reg)
                                 (integerp val)
                                 (statp stat)
                                 (featp feat))))
     (declare (xargs :guard (and (stat-validp stat feat)
                                 (< (lnfix reg) (feat->xnum feat)))))
     (let ((__function__ 'write-xreg))
      (declare (ignorable __function__))
      (b* ((reg (lnfix reg)))
       (if (= reg 0)
           (stat-fix stat)
         (change-stat stat
                      :xregs (update-nth (1- reg)
                                         (loghead (feat->xlen feat) val)
                                         (stat->xregs stat)))))))

    Theorem: statp-of-write-xreg

    (defthm statp-of-write-xreg
      (b* ((new-stat (write-xreg reg val stat feat)))
        (statp new-stat))
      :rule-classes :rewrite)

    Theorem: stat-validp-of-write-xreg

    (defthm stat-validp-of-write-xreg
      (implies (and (stat-validp stat feat)
                    (< (lnfix reg) (feat->xnum feat)))
               (b* ((?new-stat (write-xreg reg val stat feat)))
                 (stat-validp new-stat feat))))

    Theorem: write-xreg-of-x0

    (defthm write-xreg-of-x0
      (equal (write-xreg 0 val stat feat)
             (stat-fix stat)))

    Theorem: write-xreg-of-nfix-reg

    (defthm write-xreg-of-nfix-reg
      (equal (write-xreg (nfix reg) val stat feat)
             (write-xreg reg val stat feat)))

    Theorem: write-xreg-nat-equiv-congruence-on-reg

    (defthm write-xreg-nat-equiv-congruence-on-reg
      (implies (acl2::nat-equiv reg reg-equiv)
               (equal (write-xreg reg val stat feat)
                      (write-xreg reg-equiv val stat feat)))
      :rule-classes :congruence)

    Theorem: write-xreg-of-ifix-val

    (defthm write-xreg-of-ifix-val
      (equal (write-xreg reg (ifix val) stat feat)
             (write-xreg reg val stat feat)))

    Theorem: write-xreg-int-equiv-congruence-on-val

    (defthm write-xreg-int-equiv-congruence-on-val
      (implies (acl2::int-equiv val val-equiv)
               (equal (write-xreg reg val stat feat)
                      (write-xreg reg val-equiv stat feat)))
      :rule-classes :congruence)

    Theorem: write-xreg-of-stat-fix-stat

    (defthm write-xreg-of-stat-fix-stat
      (equal (write-xreg reg val (stat-fix stat)
                         feat)
             (write-xreg reg val stat feat)))

    Theorem: write-xreg-stat-equiv-congruence-on-stat

    (defthm write-xreg-stat-equiv-congruence-on-stat
      (implies (stat-equiv stat stat-equiv)
               (equal (write-xreg reg val stat feat)
                      (write-xreg reg val stat-equiv feat)))
      :rule-classes :congruence)

    Theorem: write-xreg-of-feat-fix-feat

    (defthm write-xreg-of-feat-fix-feat
      (equal (write-xreg reg val stat (feat-fix feat))
             (write-xreg reg val stat feat)))

    Theorem: write-xreg-feat-equiv-congruence-on-feat

    (defthm write-xreg-feat-equiv-congruence-on-feat
      (implies (feat-equiv feat feat-equiv)
               (equal (write-xreg reg val stat feat)
                      (write-xreg reg val stat feat-equiv)))
      :rule-classes :congruence)