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• Effective-address-computations

X86-effective-addr-16-disp

Calculate the displacement for 16-bit effective address calculation.

Signature

(x86-effective-addr-16-disp proc-mode temp-rip mod x86) 
  → 
(mv flg disp increment-rip-by x86)

Arguments

mod — mod field of ModR/M byte.

Returns

disp — Type (i16p disp), given (x86p x86).

increment-rip-by — Type (natp increment-rip-by).

x86 — Type (x86p x86), given (x86p x86).

This is according to Intel manual, Mar'17, Vol. 2, Table 2-1.

The displacement is absent (i.e. 0) when Mod is 00b. An exception to this is when R/M is 110b, in which case there is a 16-bit displacement that is added to the index. This case is not handled by this function, but is instead handled in its caller function x86-effective-addr-16.

The displacement is a signed 8-bit value when Mod is 01b. The displacement is a signed 16-bit value when Mod is 10b. This function is not called when Mod is 11b.

If an error occurs when trying to read the displacement, 0 is returned as displacement, but the caller ignores the returned displacement given the error.

This function is called only when the address size is 16 bits.

Definitions and Theorems

Function: x86-effective-addr-16-disp

(defun x86-effective-addr-16-disp (proc-mode temp-rip mod x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (integer 0 4) proc-mode)
           (type (signed-byte 48) temp-rip)
           (type (unsigned-byte 2) mod))
  (declare (xargs :guard (2bits-p mod)))
  (let ((__function__ 'x86-effective-addr-16-disp))
    (declare (ignorable __function__))
    (case mod
      (0 (mv nil 0 0 x86))
      (1 (b* (((mv flg byte x86)
               (rime-size-opt proc-mode 1 temp-rip 1 :x nil x86
                              :mem-ptr? nil))
              ((when flg) (mv flg 0 0 x86)))
           (mv nil byte 1 x86)))
      (2 (b* (((mv flg word x86)
               (rime-size-opt proc-mode 2 temp-rip 1 :x nil x86
                              :mem-ptr? nil))
              ((when flg) (mv flg 0 0 x86)))
           (mv nil word 2 x86)))
      (otherwise (mv 'mod-value-wrong 0 0 x86)))))

Theorem: i16p-of-x86-effective-addr-16-disp.disp

(defthm i16p-of-x86-effective-addr-16-disp.disp
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (i16p disp)))
 :rule-classes :rewrite)

Theorem: natp-of-x86-effective-addr-16-disp.increment-rip-by

(defthm natp-of-x86-effective-addr-16-disp.increment-rip-by
  (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
        (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
    (natp increment-rip-by))
  :rule-classes :rewrite)

Theorem: x86p-of-x86-effective-addr-16-disp.x86

(defthm x86p-of-x86-effective-addr-16-disp.x86
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (x86p x86)))
 :rule-classes :rewrite)

Theorem: integerp-of-x86-effective-addr-16-disp.disp

(defthm integerp-of-x86-effective-addr-16-disp.disp
 (implies
     (x86p x86)
     (b* (((mv ?flg ?disp ?increment-rip-by ?x86)
           (x86-effective-addr-16-disp proc-mode temp-rip mod x86)))
       (integerp disp)))
 :rule-classes :type-prescription)

Theorem: mv-nth-2-x86-effective-addr-16-disp-<=-4

(defthm mv-nth-2-x86-effective-addr-16-disp-<=-4
 (<=
    (mv-nth 2
            (x86-effective-addr-16-disp proc-mode temp-rip mod x86))
    4)
 :rule-classes :linear)