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Semantics32

Exec32-bltu

Semantics of the BLTU instruction [ISA:2.5.2].

Signature
(exec32-bltu rs1 rs2 imm pc stat) → new-stat
Arguments: rs1 — Guard (ubyte5p rs1).; rs2 — Guard (ubyte5p rs2).; imm — Guard (ubyte12p imm).; pc — Guard (ubyte32p pc).; stat — Guard (stat32ip stat).
Returns: new-stat — Type (stat32ip new-stat).

We read two unsigned 32-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 32 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 unsigned integers from the registers: if the first one is less than the second one, we write the branch target to the program counter; otherwise, we increment the program counter.

Definitions and Theorems

Function: exec32-bltu

(defun exec32-bltu (rs1 rs2 imm pc stat)
  (declare (xargs :guard (and (ubyte5p rs1)
                              (ubyte5p rs2)
                              (ubyte12p imm)
                              (ubyte32p pc)
                              (stat32ip stat))))
  (let ((__function__ 'exec32-bltu))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read32-xreg-unsigned rs1 stat))
         (rs2-operand (read32-xreg-unsigned rs2 stat))
         (offset (loghead 32
                          (logext 13 (ash (ubyte12-fix imm) 1))))
         (target-pc (+ (ubyte32-fix pc) offset))
         (stat (if (< rs1-operand rs2-operand)
                   (write32-pc target-pc stat)
                 (inc32-pc stat))))
      stat)))

Theorem: stat32ip-of-exec32-bltu

(defthm stat32ip-of-exec32-bltu
  (b* ((new-stat (exec32-bltu rs1 rs2 imm pc stat)))
    (stat32ip new-stat))
  :rule-classes :rewrite)

Theorem: exec32-bltu-of-ubyte5-fix-rs1

(defthm exec32-bltu-of-ubyte5-fix-rs1
  (equal (exec32-bltu (ubyte5-fix rs1)
                      rs2 imm pc stat)
         (exec32-bltu rs1 rs2 imm pc stat)))

Theorem: exec32-bltu-ubyte5-equiv-congruence-on-rs1

(defthm exec32-bltu-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec32-bltu rs1 rs2 imm pc stat)
                  (exec32-bltu rs1-equiv rs2 imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-bltu-of-ubyte5-fix-rs2

(defthm exec32-bltu-of-ubyte5-fix-rs2
  (equal (exec32-bltu rs1 (ubyte5-fix rs2)
                      imm pc stat)
         (exec32-bltu rs1 rs2 imm pc stat)))

Theorem: exec32-bltu-ubyte5-equiv-congruence-on-rs2

(defthm exec32-bltu-ubyte5-equiv-congruence-on-rs2
  (implies (ubyte5-equiv rs2 rs2-equiv)
           (equal (exec32-bltu rs1 rs2 imm pc stat)
                  (exec32-bltu rs1 rs2-equiv imm pc stat)))
  :rule-classes :congruence)

Theorem: exec32-bltu-of-ubyte12-fix-imm

(defthm exec32-bltu-of-ubyte12-fix-imm
  (equal (exec32-bltu rs1 rs2 (ubyte12-fix imm)
                      pc stat)
         (exec32-bltu rs1 rs2 imm pc stat)))

Theorem: exec32-bltu-ubyte12-equiv-congruence-on-imm

(defthm exec32-bltu-ubyte12-equiv-congruence-on-imm
  (implies (acl2::ubyte12-equiv imm imm-equiv)
           (equal (exec32-bltu rs1 rs2 imm pc stat)
                  (exec32-bltu rs1 rs2 imm-equiv pc stat)))
  :rule-classes :congruence)

Theorem: exec32-bltu-of-ubyte32-fix-pc

(defthm exec32-bltu-of-ubyte32-fix-pc
  (equal (exec32-bltu rs1 rs2 imm (ubyte32-fix pc)
                      stat)
         (exec32-bltu rs1 rs2 imm pc stat)))

Theorem: exec32-bltu-ubyte32-equiv-congruence-on-pc

(defthm exec32-bltu-ubyte32-equiv-congruence-on-pc
  (implies (acl2::ubyte32-equiv pc pc-equiv)
           (equal (exec32-bltu rs1 rs2 imm pc stat)
                  (exec32-bltu rs1 rs2 imm pc-equiv stat)))
  :rule-classes :congruence)

Theorem: exec32-bltu-of-stat32i-fix-stat

(defthm exec32-bltu-of-stat32i-fix-stat
  (equal (exec32-bltu rs1 rs2 imm pc (stat32i-fix stat))
         (exec32-bltu rs1 rs2 imm pc stat)))

Theorem: exec32-bltu-stat32i-equiv-congruence-on-stat

(defthm exec32-bltu-stat32i-equiv-congruence-on-stat
  (implies (stat32i-equiv stat stat-equiv)
           (equal (exec32-bltu rs1 rs2 imm pc stat)
                  (exec32-bltu rs1 rs2 imm pc stat-equiv)))
  :rule-classes :congruence)