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Semantics64

Exec64-beq

Semantics of the BEQ instruction [ISA:2.5.2].

Signature
(exec64-beq rs1 rs2 imm pc stat) → new-stat
Arguments: rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; imm — Guard (ubyte12p imm).; pc — Guard (ubyte64p pc).; stat — Guard (state64p stat).
Returns: new-stat — Type (state64p new-stat).

We read two unsigned 64-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 64 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.

Definitions and Theorems

Function: exec64-beq

(defun exec64-beq (rs1 rs2 imm pc stat)
  (declare (xargs :guard (and (ubyte5p rs1)
                              (ubyte5p rs2)
                              (ubyte12p imm)
                              (ubyte64p pc)
                              (state64p stat))))
  (let ((__function__ 'exec64-beq))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read64-xreg-unsigned rs1 stat))
         (rs2-operand (read64-xreg-unsigned rs2 stat))
         (offset (loghead 64
                          (logext 13 (ash (ubyte12-fix imm) 1))))
         (target-pc (+ (ubyte64-fix pc) offset))
         (stat (if (= rs1-operand rs2-operand)
                   (write64-pc target-pc stat)
                 (inc64-pc stat))))
      stat)))

Theorem: state64p-of-exec64-beq

(defthm state64p-of-exec64-beq
  (b* ((new-stat (exec64-beq rs1 rs2 imm pc stat)))
    (state64p new-stat))
  :rule-classes :rewrite)

Theorem: exec64-beq-of-ubyte5-fix-rs1

(defthm exec64-beq-of-ubyte5-fix-rs1
  (equal (exec64-beq (ubyte5-fix rs1)
                     rs2 imm pc stat)
         (exec64-beq rs1 rs2 imm pc stat)))

Theorem: exec64-beq-ubyte5-equiv-congruence-on-rs1

(defthm exec64-beq-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec64-beq rs1 rs2 imm pc stat)
                  (exec64-beq rs1-equiv rs2 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec64-beq-of-ubyte5-fix-rs2

(defthm exec64-beq-of-ubyte5-fix-rs2
  (equal (exec64-beq rs1 (ubyte5-fix rs2)
                     imm pc stat)
         (exec64-beq rs1 rs2 imm pc stat)))

Theorem: exec64-beq-ubyte5-equiv-congruence-on-rs2

(defthm exec64-beq-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec64-beq rs1 rs2 imm pc stat)
                  (exec64-beq rs1 rs2-equiv imm pc stat)))
  :rule-classes :congruence)

Theorem: exec64-beq-of-ubyte12-fix-imm

(defthm exec64-beq-of-ubyte12-fix-imm
  (equal (exec64-beq rs1 rs2 (ubyte12-fix imm)
                     pc stat)
         (exec64-beq rs1 rs2 imm pc stat)))

Theorem: exec64-beq-ubyte12-equiv-congruence-on-imm

(defthm exec64-beq-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec64-beq rs1 rs2 imm pc stat)
                  (exec64-beq rs1 rs2 imm-equiv pc stat)))
  :rule-classes :congruence)

Theorem: exec64-beq-of-ubyte64-fix-pc

(defthm exec64-beq-of-ubyte64-fix-pc
  (equal (exec64-beq rs1 rs2 imm (ubyte64-fix pc)
                     stat)
         (exec64-beq rs1 rs2 imm pc stat)))

Theorem: exec64-beq-ubyte64-equiv-congruence-on-pc

(defthm exec64-beq-ubyte64-equiv-congruence-on-pc
  (implies (acl2::ubyte64-equiv pc pc-equiv)
           (equal (exec64-beq rs1 rs2 imm pc stat)
                  (exec64-beq rs1 rs2 imm pc-equiv stat)))
  :rule-classes :congruence)

Theorem: exec64-beq-of-state64-fix-stat

(defthm exec64-beq-of-state64-fix-stat
  (equal (exec64-beq rs1 rs2 imm pc (state64-fix stat))
         (exec64-beq rs1 rs2 imm pc stat)))

Theorem: exec64-beq-state64-equiv-congruence-on-stat

(defthm exec64-beq-state64-equiv-congruence-on-stat
  (implies (state64-equiv stat stat-equiv)
           (equal (exec64-beq rs1 rs2 imm pc stat)
                  (exec64-beq rs1 rs2 imm pc stat-equiv)))
  :rule-classes :congruence)