Extended Precision Arithmetic - Revision history

Mr z: Protected "Extended Precision Arithmetic" ([edit=autoconfirmed] (indefinite) [move=autoconfirmed] (indefinite))

2010-12-04T08:22:51Z

Protected "Extended Precision Arithmetic" ([edit=autoconfirmed] (indefinite) [move=autoconfirmed] (indefinite))

2006-01-08T21:34:03Z

‎Subtraction

2005-01-12T19:06:58Z

‎Comparison

2005-01-12T19:05:40Z

‎Subtraction

2005-01-12T10:17:35Z

‎Addition and Subtraction

2005-01-12T04:53:51Z

‎Comparison

2005-01-12T04:53:21Z

‎Addition and Subtraction

2005-01-12T00:22:48Z

‎Comparison

2005-01-12T00:11:41Z

‎Addition and Subtraction

2005-01-12T00:07:35Z

‎Addition and Subtraction

@@ Line 101: / Line 101: @@
 (R3 is the most signficant word, and R0 is the least significant.)
     SUB@ R4, R0    ; Subtract bits 0..15.
     DECR R1        ; \_ propagate the borrow to bits 16..31
@@ Line 113: / Line 114: @@
     DECR R3        ; \_ propagate the borrow to bits 48..63
     ADCR R3        ; /
-    ADD@ R4, R2    ; Subtract bits 32..47.
+    SUB@ R4, R2    ; Subtract bits 32..47.
     DECR R3        ; \_ propagate the borrow to bits 48..63
     ADCR R3        ; /
-   ADD@ R4, R3    ; Subtract bits 48..63 onboard planes to
+    SUB@ R4, R3    ; Subtract bits 48..63
 ==Comparison==

@@ Line 154: / Line 154: @@
 ==Comparison==
-For Addition and Subtraction, one works from the low end of the number towards the high end.  For comparisons, however, the opposite is true.  To compare two large numbers, one first compares the most significant words.  If they compare as equal, the process moves to the next most significant words.  The process continues until two corresponding words miscompare&mdash;at which point the program has established one number as larger than the other&mdash;or the program reaches the end of both numbers, indicating they are equal.
+For Addition and Subtraction, one usually works from the low end of the number towards the high end.  For comparisons, however, the opposite is true.  To compare two large numbers, one first compares the most significant words.  If they compare as equal, the process moves to the next most significant words.  The process continues until two corresponding words miscompare&mdash;at which point the program has established one number as larger than the other&mdash;or the program reaches the end of both numbers, indicating they are equal.
 The process works identically regardless of whether the two numbers are signed or unsigned.  The only difference between signed and unsigned comparison is whether one uses BGT/BLT (signed numbers) or BNEQ/BNC (unsigned numbers).

@@ Line 29: / Line 29: @@
 ==Subtraction==
-Subtraction is similar to addition, except that "borrows" take the place of "carries."  When subtracting two numbers that are larger than 16 bits, it's important to realize that all the "internal" portions of the subtract are effectively "unsigned."  Thus, the [[Carry Flag]] can be thought of as a "Not Borrow" bit for the lower order terms.  To subtract two extended precision numbers, one must include one additional step to correctly handle borrowing.
+Subtraction is similar to addition, except that "borrows" take the place of "carries."  When subtracting two numbers that are larger than 16 bits, it's important to realize that all the "internal" portions of the subtract are effectively "unsigned," even if the overall number is signed.  Thus, the [[Carry Flag]] can be thought of as a "Not Borrow" bit for the lower order terms.  To subtract two extended precision numbers, one must include one additional step to correctly handle borrowing.
 The following example illustrates subtracting the 32 bit number in R1:R0 from R3:R2.  The upper halves of the numbers are in R1 and R3.  The lower halves are in R0 and R2.

@@ Line 62: / Line 62: @@
 ==Comparison==
-For Addition and Subtraction, one works from the low end of the number towards the high end.  For comparison, the opposite is true.  To compare two large numbers, one first compares the most significant words.  If they compare as equal, the process moves to the next most significant words.  The process continues until two corresponding words miscompare&mdash;at which point the program has established one number as larger than the other&mdash;or the program reaches the end of both numbers, indicating they are equal.
+For Addition and Subtraction, one works from the low end of the number towards the high end.  For comparisons, however, the opposite is true.  To compare two large numbers, one first compares the most significant words.  If they compare as equal, the process moves to the next most significant words.  The process continues until two corresponding words miscompare&mdash;at which point the program has established one number as larger than the other&mdash;or the program reaches the end of both numbers, indicating they are equal.
 The process works identically regardless of whether the two numbers are signed or unsigned.  The only difference between signed and unsigned comparison is whether one uses BGT/BLT (signed numbers) or BNEQ/BNC (unsigned numbers).

@@ Line 40: / Line 40: @@
     DECR R3        ; Decrement R3 if we borrowed
     SUBR R1, R3    ; Subtract the upper halves.
 Subtracting longer numbers has the same complications as adding longer numbers.  The following example illustrates subtracting two 64 bit numbers.  This time, the first number is stored in memory pointed to by R4, and the difference is held in R3:R2:R1:R0.  The most significant portion is in R3, and the least significant portion is in R0.  This code moves all the DECRs to a set of subtracts up front.

← Older revision	Revision as of 08:22, 4 December 2010
(No difference)

@@ Line 30: / Line 30: @@
     SUBR R0, R2    ; Subtract the lower halves.  This may "borrow" from the upper half
-    ADCR R3        ; \_ Subtract 1 if we need to borrow, otherwise
+    ADCR R3        ; \_ Subtract 1 if we need to borrow, otherwise leave R3 alone.
-    DECR R3        ; /  leave R3 alone
+    DECR R3        ; /  (ADCR and DECR cancel in the not-borrow case.)
     SUBR R1, R3    ; Subtract the upper halves.

@@ Line 25: / Line 25: @@
     ADD@ R4, R3    ; Add bits 48..63 together.
-Subtraction is similar to addition.  When subtracting two numbers that are larger than 16 bits, it's important to realize that all the "internal" portions of the subtract are effectively "unsigned."  Thus, the [[Carry Bit]] can be thought of as a "Not Borrow" bit for the lower order terms.  To subtract two extended precision numbers, one must include one additional step to correctly handle borrowing.
+Subtraction is similar to addition.  When subtracting two numbers that are larger than 16 bits, it's important to realize that all the "internal" portions of the subtract are effectively "unsigned."  Thus, the [[Carry Flag]] can be thought of as a "Not Borrow" bit for the lower order terms.  To subtract two extended precision numbers, one must include one additional step to correctly handle borrowing.
 The following example illustrates subtracting the 32 bit number in R1:R0 from R3:R2.  The upper halves of the numbers are in R1 and R3.  The lower halves are in R0 and R2.
@@ Line 56: / Line 56: @@
     ADCR R3        ; propagate the not-borrow to bits 48..63
     SUB@ R4, R3    ; Subtract bits 0..15 from each other.
 ==Comparison==