Tomohiko Sakamoto’s Day-Of-Week Algorithm
June 17, 2016
Here is Sakamoto’s algorithm for calculating the day of the week, taken from the comment that introduces the code:
Jan 1st 1 AD is a Monday in Gregorian calendar.
So Jan 0th 1 AD is a Sunday [It does not exist technically].Every 4 years we have a leap year. But xy00 cannot be a leap unless xy divides 4 with reminder 0.
y/4 – y/100 + y/400 : this gives the number of leap years from 1AD to the given year. As each year has 365 days (divdes 7 with reminder 1), unless it is a leap year or the date is in Jan or Feb, the day of a given date changes by 1 each year. In other case it increases by 2.
y -= m So y + y/4 – y/100 + y/400 gives the day of Jan 0th (Dec 31st of prev year) of the year. (This gives the reminder with 7 of the number of days passed before the given year began.)
Array t: Number of days passed before the month ‘m+1’ begins.
So t[m-1]+d is the number of days passed in year ‘y’ upto the given date.
(y + y/4 – y/100 + y/400 + t[m-1] + d) % 7 is reminder of the number of days from Jan 0 1AD to the given date which will be the day (0=Sunday,6=Saturday).
int dow(int y, int m, int d) { static int t[] = {0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4}; y -= m < 3; return (y + y/4 - y/100 + y/400 + t[m-1] + d) % 7; }
Another description is given here.
Your task is to write a program that implements the day-of-week algorithm shown above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
A Haskell version, with a variant (dow’) that provides a little more type safety.
import Data.Vector t :: Vector Int t = fromList [0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4]; -- Given a year, month (1-12) and day of month return the day of the week (0-6). dow :: Int -> Int -> Int -> Int dow y m d = let y' = if m < 3 then y - 1 else y in (y' + y' `div` 4 - y' `div` 100 + y' `div` 400 + t ! (m-1) + d) `mod` 7 -- A slightly more typesafe variant. data Month = Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec deriving (Enum, Show) data Day = Sun | Mon | Tue | Wed | Thu | Fri | Sat deriving (Enum, Show) -- Given a year, month and day of month return the day of the week. dow' :: Int -> Month -> Int -> Day dow' y m d = toEnum $ dow y (fromEnum m + 1) d main :: IO () main = do print $ dow 2016 6 18 print $ dow' 2016 Jun 18Here’s a solution in x86 assembly.
/* dow.s */
.section .data
t:
.long 0,3,2,5,0,3,5,1,4,6,2,4
.section .text
.globl dow
.type dow,@function
# int dow(y, m, d);
dow:
# Save old base pointer
pushl %ebp
movl %esp, %ebp
# Create a local variable for
# the result.
# result: -4(%ebp)
subl $4, %esp
# Arguments:
# y: 8(%ebp)
# m: 12(%ebp)
# d: 16(%ebp)
# %ebp Offsets:
.equ result, -4
.equ y, 8
.equ m, 12
.equ d, 16
# if (m < 3) –y;
cmpl $3, m(%ebp)
jge proceed
decl y(%ebp)
proceed:
# result = y
movl y(%ebp), %ecx
movl %ecx, result(%ebp)
# result += y/4
movl $0, %edx
movl y(%ebp), %eax
movl $4, %ecx
divl %ecx
addl %eax, result(%ebp)
# result -= y/100
movl $0, %edx
movl y(%ebp), %eax
movl $100, %ecx
divl %ecx
subl %eax, result(%ebp)
# result += y/400
movl $0, %edx
movl y(%ebp), %eax
movl $400, %ecx
divl %ecx
addl %eax, result(%ebp)
# result += t[m-1]
movl m(%ebp), %ecx
decl %ecx
movl t(,%ecx,4), %ecx
addl %ecx, result(%ebp)
# result += d
movl d(%ebp), %ecx
addl %ecx, result(%ebp)
# result = result % 7
movl $0, %edx
movl result(%ebp), %eax
movl $7, %ecx
divl %ecx
movl %edx, result(%ebp)
# Save result
movl result(%ebp), %eax
# Restore old base pointer
movl %ebp, %esp
popl %ebp
ret
Here’s a C program that calls the day-of-week function.
/* main.c */ #include <stdio.h> #include <stdlib.h> int dow(int y, int m, int d); int main(int argc, char* argv[]) { if (argc != 4) { fprintf(stderr, "3 arguments are required (year, month, day)\n"); return 1; } int year = atoi(argv[1]); int month = atoi(argv[2]); int day = atoi(argv[3]); int day_of_week = dow(year, month, day); printf("%d\n", day_of_week); return 0; }Here’s example usage.
language=”asm” didn’t work for formatting my last post. Here’s the assembly code formatted with language=”text”.