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Semantics32

Eff32-addr

Effective address for a load or store instruction [ISA:2.6].

Signature
(eff32-addr rs1 imm stat) → addr
Arguments: rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte12p imm).; stat — Guard (state32p stat).
Returns: addr — Type (integerp addr).

We read an unsigned 32-bit integer from rs1; this is the base. We sign-extend the 12-bit immediate to 32 bits; this is the offset. We return the sum of base and offset, as an integer; the functions to read and write memory use the low 32 bits of this integer.

Definitions and Theorems

Function: eff32-addr

(defun eff32-addr (rs1 imm stat)
  (declare (xargs :guard (and (ubyte5p rs1)
                              (ubyte12p imm)
                              (state32p stat))))
  (let ((__function__ 'eff32-addr))
    (declare (ignorable __function__))
    (b* ((base (read32-xreg-unsigned rs1 stat))
         (offset (loghead 32 (logext 12 (ubyte12-fix imm)))))
      (+ base offset))))

Theorem: integerp-of-eff32-addr

(defthm integerp-of-eff32-addr
  (b* ((addr (eff32-addr rs1 imm stat)))
    (integerp addr))
  :rule-classes :rewrite)

Theorem: eff32-addr-of-ubyte5-fix-rs1

(defthm eff32-addr-of-ubyte5-fix-rs1
  (equal (eff32-addr (ubyte5-fix rs1) imm stat)
         (eff32-addr rs1 imm stat)))

Theorem: eff32-addr-ubyte5-equiv-congruence-on-rs1

(defthm eff32-addr-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (eff32-addr rs1 imm stat)
                  (eff32-addr rs1-equiv imm stat)))
  :rule-classes :congruence)

Theorem: eff32-addr-of-ubyte12-fix-imm

(defthm eff32-addr-of-ubyte12-fix-imm
  (equal (eff32-addr rs1 (ubyte12-fix imm) stat)
         (eff32-addr rs1 imm stat)))

Theorem: eff32-addr-ubyte12-equiv-congruence-on-imm

(defthm eff32-addr-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (eff32-addr rs1 imm stat)
                  (eff32-addr rs1 imm-equiv stat)))
  :rule-classes :congruence)

Theorem: eff32-addr-of-state32-fix-stat

(defthm eff32-addr-of-state32-fix-stat
  (equal (eff32-addr rs1 imm (state32-fix stat))
         (eff32-addr rs1 imm stat)))

Theorem: eff32-addr-state32-equiv-congruence-on-stat

(defthm eff32-addr-state32-equiv-congruence-on-stat
  (implies (state32-equiv stat stat-equiv)
           (equal (eff32-addr rs1 imm stat)
                  (eff32-addr rs1 imm stat-equiv)))
  :rule-classes :congruence)