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Semantics

Exec-beq

Semantics of the BEQ instruction [ISA:2.5.2].

Signature
(exec-beq rs1 rs2 imm pc stat feat) → new-stat
Arguments: rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; imm — Guard (ubyte12p imm).; pc — Guard (unsigned-byte-p (feat->xlen feat) pc).; stat — Guard (statp stat).; feat — Guard (featp feat).
Returns: new-stat — Type (statp new-stat).

We read two unsigned XLEN-bit integers from rs1 and rs2. We use the 12 bits of the immediate as the high bits of a 13-bit integer, whose low bit is 0 (i.e. the immediate measures multiples of 2); the unsigned 13-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 branch target. We compare the two integers from the registers: if they are equal, we write the branch target to the program counter; otherwise, we increment the program counter.

If the branch target is taken and is not aligned, we stop with an error. [ISA:2.2] clarifies that this happens at the branch instruction, not when trying to read the target instruction.

Definitions and Theorems

Function: exec-beq

(defun exec-beq (rs1 rs2 imm pc stat feat)
  (declare (xargs :guard (and (ubyte5p rs1)
                              (ubyte5p rs2)
                              (ubyte12p imm)
                              (statp stat)
                              (featp feat)
                              (unsigned-byte-p (feat->xlen feat)
                                               pc))))
  (declare (xargs :guard (and (stat-validp stat feat)
                              (< (lnfix rs1) (feat->xnum feat))
                              (< (lnfix rs2) (feat->xnum feat)))))
  (let ((__function__ 'exec-beq))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read-xreg-unsigned (ubyte5-fix rs1)
                                          stat feat))
         (rs2-operand (read-xreg-unsigned (ubyte5-fix rs2)
                                          stat feat))
         (offset (loghead (feat->xlen feat)
                          (logext 13 (ash (ubyte12-fix imm) 1))))
         (target-pc (+ pc offset))
         (stat (if (= rs1-operand rs2-operand)
                   (if (= (mod target-pc 4) 0)
                       (write-pc target-pc stat feat)
                     (error stat feat))
                 (inc4-pc stat feat))))
      stat)))

Theorem: statp-of-exec-beq

(defthm statp-of-exec-beq
  (b* ((new-stat (exec-beq rs1 rs2 imm pc stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: stat-validp-of-exec-beq

(defthm stat-validp-of-exec-beq
  (implies (stat-validp stat feat)
           (b* ((?new-stat (exec-beq rs1 rs2 imm pc stat feat)))
             (stat-validp new-stat feat))))

Theorem: exec-beq-of-ubyte5-fix-rs1

(defthm exec-beq-of-ubyte5-fix-rs1
  (equal (exec-beq (ubyte5-fix rs1)
                   rs2 imm pc stat feat)
         (exec-beq rs1 rs2 imm pc stat feat)))

Theorem: exec-beq-ubyte5-equiv-congruence-on-rs1

(defthm exec-beq-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec-beq rs1 rs2 imm pc stat feat)
                  (exec-beq rs1-equiv rs2 imm pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-beq-of-ubyte5-fix-rs2

(defthm exec-beq-of-ubyte5-fix-rs2
  (equal (exec-beq rs1 (ubyte5-fix rs2)
                   imm pc stat feat)
         (exec-beq rs1 rs2 imm pc stat feat)))

Theorem: exec-beq-ubyte5-equiv-congruence-on-rs2

(defthm exec-beq-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec-beq rs1 rs2 imm pc stat feat)
                  (exec-beq rs1 rs2-equiv imm pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-beq-of-ubyte12-fix-imm

(defthm exec-beq-of-ubyte12-fix-imm
  (equal (exec-beq rs1 rs2 (ubyte12-fix imm)
                   pc stat feat)
         (exec-beq rs1 rs2 imm pc stat feat)))

Theorem: exec-beq-ubyte12-equiv-congruence-on-imm

(defthm exec-beq-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec-beq rs1 rs2 imm pc stat feat)
                  (exec-beq rs1 rs2 imm-equiv pc stat feat)))
  :rule-classes :congruence)

Theorem: exec-beq-of-stat-fix-stat

(defthm exec-beq-of-stat-fix-stat
  (equal (exec-beq rs1 rs2 imm pc (stat-fix stat)
                   feat)
         (exec-beq rs1 rs2 imm pc stat feat)))

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

(defthm exec-beq-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (exec-beq rs1 rs2 imm pc stat feat)
                  (exec-beq rs1 rs2 imm pc stat-equiv feat)))
  :rule-classes :congruence)

Theorem: exec-beq-of-feat-fix-feat

(defthm exec-beq-of-feat-fix-feat
  (equal (exec-beq rs1 rs2 imm pc stat (feat-fix feat))
         (exec-beq rs1 rs2 imm pc stat feat)))

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

(defthm exec-beq-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (exec-beq rs1 rs2 imm pc stat feat)
                  (exec-beq rs1 rs2 imm pc stat feat-equiv)))
  :rule-classes :congruence)