Programming Lab 8A Zeller’s Rule

Programming Lab 8A
Zeller’s Rule
Topics: Replacing division by reciprocal multiplication, replacing multiplication by a sequence
of addition, subtraction and shift instructions.
Prerequisite Reading: Chapters 1-8
Revised: January 21, 2021
Click to download
Lab8A-Main.c
Background1
: The following formula is named Zeller's Rule and may be used
to convert a date into a day of the week.
𝑓 = 𝑘 +
13𝑚 − 1
5
+ 𝐷 +
𝐷
4
+
𝐶
4
− 2𝐶
Where:
𝒌 is the day of the month.
𝒎 is the month number. Months must be counted differently for Zeller's
Rule: March is 1, April is 2, and so on to February, which is 12. (This
makes the formula simpler, because on leap years February 29 is counted
as the last day of the year.) Thus, January and February are always
counted as the 11th and 12th months of the previous year.
𝑫 is the last two digits of the year.
𝑪 is the century - the first two digits of the year.
Example: January 29, 2064
𝑓 = 29 +
13 × 11 − 1
5
+ 63 +
63
4
+
20
4
− 2 × 20
= 29 + 28 + 63 + 15 + 5 − 40 = 100
Note: 𝐷 = 63 even though the year is 2064 because the month is January (see above). All the divisions above are unsigned
integer divisions that discard any fractional part. We then use signed integer division to get the remainder of 𝑓 divided by 7
since 𝑓 can be negative. If the remainder is negative, add 7. (This result is what your assembly language functions must
return.) A result of 0 means Sunday, 1 means Monday, etc. For our example, 100/7 = 14, remainder 2, so January 29,
2064 falls on a Tuesday.
Assignment: The main program will compile and run without writing any assembly. However, your task is to create
equivalent replacements in assembly language for the following three functions found in the C main program. The original
C versions have been defined as “weak” so that the linker will automatically replace them in the executable image by those
you create in assembly; you do not need to remove the C versions. This allows you to create and test your assembly language
functions one at a time. All three functions share a common set of parameters and return value. However, Zeller2 may
not contain any divide instructions (SDIV or UDIV) and Zeller3 may not contain any multiply instructions (MUL, MLS,
etc.):
uint32_t Zeller1(uint32_t k, uint32_t m, uint32_t D, uint32_t C) ;
uint32_t Zeller2(uint32_t k, uint32_t m, uint32_t D, uint32_t C) ;
uint32_t Zeller3(uint32_t k, uint32_t m, uint32_t D, uint32_t C) ;
Use this webpage to find instruction sequences that will divide by a constant without using a divide instruction. Test your
code with the main program. If your code is correct, the display should look like the image shown above. Use the touchscreen
to adjust the date and see the corresponding day of the week. Errors will be displayed as white text on a red background.
1 Adapted from http://mathforum.org/dr.math/faq/faq.calendar.html