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Semantics

Exec-jalr

Semantics of the JALR instruction [ISA:2.5.1].

Signature
(exec-jalr rd rs1 imm pc stat feat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte12p imm).; stat — Guard (statp stat).; feat — Guard (featp feat).
Returns: new-stat — Type (statp new-stat).

We read an unsigned XLEN-bit integer from rs1. We sign-extend the 12-bit immediate to XLEN bits, obtaining an unsigned XLEN-bit offset. We add the offset to the integer from the register, and set the least significant bit to 0; this is the jump target. We write the address of the instruction just after this to rd; since instructions are 32-bit long, the address of the next instruction is obtained by adding 4 to pc, which is the address of this instruction, passed as input to this function. We write the jump target to the program counter.

Definitions and Theorems

Function: exec-jalr

(defun exec-jalr (rd rs1 imm pc stat feat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte12p imm)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (and (stat-validp stat feat)
                              (cond ((feat-32p feat) (ubyte32p pc))
                                    ((feat-64p feat) (ubyte64p pc))
                                    (t (impossible))))))
  (let ((__function__ 'exec-jalr))
    (declare (ignorable __function__))
    (b* ((base (read-xreg-unsigned (ubyte5-fix rs1)
                                   stat feat))
         (offset (loghead (feat->xlen feat)
                          (logext 12 (ubyte12-fix imm))))
         (mask (cond ((feat-32p feat) 4294967294)
                     ((feat-64p feat) 18446744073709551614)
                     (t (impossible))))
         (target-pc (logand mask (+ base offset)))
         (next-pc (+ pc 4))
         (stat (write-xreg (ubyte5-fix rd)
                           next-pc stat feat))
         (stat (write-pc target-pc stat feat)))
      stat)))

Theorem: statp-of-exec-jalr

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

Theorem: stat-validp-of-exec-jalr

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

Theorem: exec-jalr-of-ubyte5-fix-rd

(defthm exec-jalr-of-ubyte5-fix-rd
  (equal (exec-jalr (ubyte5-fix rd)
                    rs1 imm pc stat feat)
         (exec-jalr rd rs1 imm pc stat feat)))

Theorem: exec-jalr-ubyte5-equiv-congruence-on-rd

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

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

(defthm exec-jalr-of-ubyte5-fix-rs1
  (equal (exec-jalr rd (ubyte5-fix rs1)
                    imm pc stat feat)
         (exec-jalr rd rs1 imm pc stat feat)))

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

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

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

(defthm exec-jalr-of-ubyte12-fix-imm
  (equal (exec-jalr rd rs1 (ubyte12-fix imm)
                    pc stat feat)
         (exec-jalr rd rs1 imm pc stat feat)))

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

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

Theorem: exec-jalr-of-stat-fix-stat

(defthm exec-jalr-of-stat-fix-stat
  (equal (exec-jalr rd rs1 imm pc (stat-fix stat)
                    feat)
         (exec-jalr rd rs1 imm pc stat feat)))

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

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

Theorem: exec-jalr-of-feat-fix-feat

(defthm exec-jalr-of-feat-fix-feat
  (equal (exec-jalr rd rs1 imm pc stat (feat-fix feat))
         (exec-jalr rd rs1 imm pc stat feat)))

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

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