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States

Write-xreg-32

Write an integer to the low 32 bit of a 64-bit x register, sign-extending to the high 32 bits of the register.

Signature
(write-xreg-32 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).

This is is only defined when XLEN is 64; when it is 32, write-xreg already writes all 32 bits. When XLEN is 64, several instructions write to the low 32 bits of a register, sign-extending to the high 32 bits; so it is useful to introduce this abbreviation, which takes an integer of any size, keeps the low 32 bits, and writes their sign extension to the register.

Definitions and Theorems

Function: write-xreg-32

(defun write-xreg-32 (reg val stat feat)
  (declare (xargs :guard (and (natp reg)
                              (integerp val)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (and (stat-validp stat feat)
                              (feat-64p feat)
                              (< (lnfix reg) (feat->xnum feat)))))
  (let ((__function__ 'write-xreg-32))
    (declare (ignorable __function__))
    (write-xreg reg (logext 32 (lifix val))
                stat feat)))

Theorem: statp-of-write-xreg-32

(defthm statp-of-write-xreg-32
  (b* ((new-stat (write-xreg-32 reg val stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: stat-validp-of-write-xreg-32

(defthm stat-validp-of-write-xreg-32
  (implies (and (stat-validp stat feat)
                (< (lnfix reg) (feat->xnum feat)))
           (b* ((?new-stat (write-xreg-32 reg val stat feat)))
             (stat-validp new-stat feat))))

Theorem: write-xreg-32-of-nfix-reg

(defthm write-xreg-32-of-nfix-reg
  (equal (write-xreg-32 (nfix reg) val stat feat)
         (write-xreg-32 reg val stat feat)))

Theorem: write-xreg-32-nat-equiv-congruence-on-reg

(defthm write-xreg-32-nat-equiv-congruence-on-reg
  (implies (acl2::nat-equiv reg reg-equiv)
           (equal (write-xreg-32 reg val stat feat)
                  (write-xreg-32 reg-equiv val stat feat)))
  :rule-classes :congruence)

Theorem: write-xreg-32-of-ifix-val

(defthm write-xreg-32-of-ifix-val
  (equal (write-xreg-32 reg (ifix val) stat feat)
         (write-xreg-32 reg val stat feat)))

Theorem: write-xreg-32-int-equiv-congruence-on-val

(defthm write-xreg-32-int-equiv-congruence-on-val
  (implies (acl2::int-equiv val val-equiv)
           (equal (write-xreg-32 reg val stat feat)
                  (write-xreg-32 reg val-equiv stat feat)))
  :rule-classes :congruence)

Theorem: write-xreg-32-of-stat-fix-stat

(defthm write-xreg-32-of-stat-fix-stat
  (equal (write-xreg-32 reg val (stat-fix stat)
                        feat)
         (write-xreg-32 reg val stat feat)))

Theorem: write-xreg-32-stat-equiv-congruence-on-stat

(defthm write-xreg-32-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (write-xreg-32 reg val stat feat)
                  (write-xreg-32 reg val stat-equiv feat)))
  :rule-classes :congruence)

Theorem: write-xreg-32-of-feat-fix-feat

(defthm write-xreg-32-of-feat-fix-feat
  (equal (write-xreg-32 reg val stat (feat-fix feat))
         (write-xreg-32 reg val stat feat)))

Theorem: write-xreg-32-feat-equiv-congruence-on-feat

(defthm write-xreg-32-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (write-xreg-32 reg val stat feat)
                  (write-xreg-32 reg val stat feat-equiv)))
  :rule-classes :congruence)