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• 4vmask

4vec-mask-to-zero

Reduce a constant 4vec using a 4vmask; any irrelevant bits become 0s.

Signature

(4vec-mask-to-zero mask value) → masked-value

Arguments

mask — Mask of bits that we care about.
    Guard (4vmask-p mask).

value — Original value to be masked.
    Guard (4vec-p value).

Returns

masked-value — value with irrelevant bits replaced by 0s.
    Type (4vec-p masked-value).

Definitions and Theorems

Function: 4vec-mask-to-zero

(defun 4vec-mask-to-zero (mask value)
  (declare (xargs :guard (and (4vmask-p mask) (4vec-p value))))
  (let ((__function__ '4vec-mask-to-zero))
    (declare (ignorable __function__))
    (b* ((mask (sparseint-val (4vmask-fix mask)))
         ((4vec value) value))
      (4vec (logand mask value.upper)
            (logand mask value.lower)))))

Theorem: 4vec-p-of-4vec-mask-to-zero

(defthm 4vec-p-of-4vec-mask-to-zero
  (b* ((masked-value (4vec-mask-to-zero mask value)))
    (4vec-p masked-value))
  :rule-classes :rewrite)

Theorem: 4vec-mask-to-zero-of-4vmask-fix-mask

(defthm 4vec-mask-to-zero-of-4vmask-fix-mask
  (equal (4vec-mask-to-zero (4vmask-fix mask)
                            value)
         (4vec-mask-to-zero mask value)))

Theorem: 4vec-mask-to-zero-4vmask-equiv-congruence-on-mask

(defthm 4vec-mask-to-zero-4vmask-equiv-congruence-on-mask
  (implies (4vmask-equiv mask mask-equiv)
           (equal (4vec-mask-to-zero mask value)
                  (4vec-mask-to-zero mask-equiv value)))
  :rule-classes :congruence)

Theorem: 4vec-mask-to-zero-of-4vec-fix-value

(defthm 4vec-mask-to-zero-of-4vec-fix-value
  (equal (4vec-mask-to-zero mask (4vec-fix value))
         (4vec-mask-to-zero mask value)))

Theorem: 4vec-mask-to-zero-4vec-equiv-congruence-on-value

(defthm 4vec-mask-to-zero-4vec-equiv-congruence-on-value
  (implies (4vec-equiv value value-equiv)
           (equal (4vec-mask-to-zero mask value)
                  (4vec-mask-to-zero mask value-equiv)))
  :rule-classes :congruence)

Theorem: 4vec-mask-to-zero-idempotent

(defthm 4vec-mask-to-zero-idempotent
  (equal (4vec-mask-to-zero mask (4vec-mask-to-zero mask value))
         (4vec-mask-to-zero mask value)))

Theorem: 4vec-mask-to-zero-minus-1

(defthm 4vec-mask-to-zero-minus-1
  (equal (4vec-mask-to-zero -1 value)
         (4vec-fix value)))

Theorem: 4vec-mask-to-zero-zero

(defthm 4vec-mask-to-zero-zero
  (equal (4vec-mask-to-zero 0 value) 0))

Theorem: 4vec-mask-of-4vec-mask-to-zero

(defthm 4vec-mask-of-4vec-mask-to-zero
  (equal (4vec-mask mask (4vec-mask-to-zero mask value))
         (4vec-mask mask value)))