Prayer Times Calculations: Pure C++ Code

[25-March-2017] Update: For brothers and sisters in Indonesia or any country below the equator, thanks to Reza's comment,  the code now works correctly.
[18-January-2012 Update: I refined the code to make it easier and more elegant to use]
[06-July-2011 Update: I found this page http://praytimes.org/calculation#Implementation ]

This idea came to me when a friend of mine was asking for an 'offline database' for prayer times. I searched for algorithms to make my own database and almost all search results lead to the same algorithm. And all codes are divided into two categories: a simple but approximate one, and a complicated but precise one. I tried with the complicated one to understand it but it needs more time because of its nested functions and -unfortunately- it is not a priority right now. So I went with the easy one as a start.

One thing I noticed is that every person is trying to make the ultimate use of the framework he is working on (mostly dotNet). But come on, it is all about calculations. Why don't you make a code that can be easily converted from one language/platform to another? That's why I wanted to make that code. It has a major problem till now as it produces times later than my Egyptian calendar up to 5 minutes !!! Only later not earlier.

Anyways, here is the code, and I hope I can reach better results in the near future (in-sha'a Allah).


 The parameters needed are:

• Year/Month/Day of the desired day.
• Longitude/Latitude/Time Zone of the desired place.
• Fajr Twilight/ Esha Twilight which differ in calculations from one country to another.

Organization	Angle of the sun under the Horizon (Fajr)	Angle of the sun under the Horizon (Isha)	Region
University Of Islamic Sciences, Karachi	18 Degrees	18 Degrees	Pakistan, Bangladesh, India, Afghanistan, Parts of Europe
North America	15 Degrees	15 Degrees	Parts of the USA, Canada, Parts of the UK
Muslim World League	18 Degrees	17 Degrees	Europe, The Far East, Parts of the USA
Umm Al-Qura Committee	19 Degrees	90 minutes after the Sunset Prayer 120 minutes (in Ramadan only)	The Arabian Peninsula
Egyptian General Authority of Survey	19.5 Degrees	17.5 Degrees	Africa, Syria, Iraq, Lebanon, Malaysia, Parts of the USA

The only library used in this function was

#include <math.h>

to use the trigonometric functions (sin, cos,...)


The function takes the data of Year/Month/Day/Longitude/Latitude/TimeZone/FajrTwilight/IshaTwilight plus 6 references to double variables (Fajr/SunRise/Zuhr/Asr/Maghrib/Isha). These 6 variables are the ones to return data into. I also added some supporting functions to help in some number conversions (for example, Radians to Degrees and vise versa).

//convert Degree to Radian
double degToRad(double degree)
{
    return ((3.1415926 / 180) * degree);
}

//convert Radian to Degree
double radToDeg(double radian)
{
    return (radian * (180/3.1415926));
}

//make sure a value is between 0 and 360
double moreLess360(double value)
{
    while(value > 360 || value < 0)
    {
        if(value > 360)
            value -= 360;

        else if (value <0)
            value += 360;
    }

    return value;
}

//make sure a value is between 0 and 24
double moreLess24(double value)
{
    while(value > 24 || value < 0)
    {
        if(value > 24)
            value -= 24;

        else if (value <0)
            value += 24;
    }

    return value;
}

//convert the double number to Hours and Minutes
void doubleToHrMin(double number, int &hours, int &minutes)
{
    hours = floor(moreLess24(number));
    minutes = floor(moreLess24(number - hours) * 60);
}

void calcPrayerTimes(int year, int month, int day,
                     double longitude, double latitude, int timeZone,
                     double fajrTwilight, double ishaTwilight,
                     double &fajrTime, double &sunRiseTime, double &zuhrTime,
                     double &asrTime, double &maghribTime, double &ishaTime)
{
    double D = (367 * year) - ((year + (int)((month + 9) / 12)) * 7 / 4) + (((int)(275 * month / 9)) + day - 730531.5);

    double L = 280.461 + 0.9856474 * D;
    L = moreLess360(L);

    double M = 357.528 + (0.9856003) * D;
    M = moreLess360(M);

    double Lambda = L + 1.915 * sin(degToRad(M)) + 0.02 * sin(degToRad(2 * M));
    Lambda = moreLess360(Lambda);

    double Obliquity = 23.439 - 0.0000004 * D;
    double Alpha = radToDeg(atan((cos(degToRad(Obliquity)) * tan(degToRad(Lambda)))));
    Alpha = moreLess360(Alpha);

    Alpha = Alpha - (360 * (int)(Alpha / 360));
    Alpha = Alpha + 90 * (floor(Lambda / 90) - floor(Alpha / 90));

    double ST = 100.46 + 0.985647352 * D;
    double Dec = radToDeg(asin(sin(degToRad(Obliquity)) * sin(degToRad(Lambda))));
    double Durinal_Arc = radToDeg(acos((sin(degToRad(-0.8333)) - sin(degToRad(Dec)) * sin(degToRad(latitude))) / (cos(degToRad(Dec)) * cos(degToRad(latitude)))));

    double Noon = Alpha - ST;
    Noon = moreLess360(Noon);


    double UT_Noon = Noon - longitude;


    ////////////////////////////////////////////
    // Calculating Prayer Times Arcs & Times //
    //////////////////////////////////////////

    // 2) Zuhr Time [Local noon]
    zuhrTime = UT_Noon / 15 + timeZone;

    // Asr Hanafi
    //double Asr_Alt =radToDeg(atan(2 + tan(degToRad(abs(latitude - Dec)))));

    // Asr Shafii
    double Asr_Alt = radToDeg(atan(1 + tan(degToRad(abs(latitude - Dec)))));
    double Asr_Arc = radToDeg(acos((sin(degToRad(90 - Asr_Alt)) - sin(degToRad(Dec)) * sin(degToRad(latitude))) / (cos(degToRad(Dec)) * cos(degToRad(latitude)))));
    Asr_Arc = Asr_Arc / 15;
    // 3) Asr Time
    asrTime = zuhrTime + Asr_Arc;

    // 1) Shorouq Time
    sunRiseTime = zuhrTime - (Durinal_Arc / 15);

    // 4) Maghrib Time
    maghribTime = zuhrTime + (Durinal_Arc / 15);


    double Esha_Arc = radToDeg(acos((sin(degToRad(ishaTwilight)) - sin(degToRad(Dec)) * sin(degToRad(latitude))) / (cos(degToRad(Dec)) * cos(degToRad(latitude)))));
    // 5) Isha Time
    ishaTime = zuhrTime + (Esha_Arc / 15);

    // 0) Fajr Time
    double Fajr_Arc = radToDeg(acos((sin(degToRad(fajrTwilight)) - sin(degToRad(Dec)) * sin(degToRad(latitude))) / (cos(degToRad(Dec)) * cos(degToRad(latitude)))));
    fajrTime = zuhrTime - (Fajr_Arc / 15);

    return;
}

So, if I take Cairo as an example:

• Date: 18-1-2012
• Longitude: 30.2
• Latitude: 30
• Time Zone: +2 
• Fajr Twilight: -19.5
• Esha Twilight: -17.5

the function will be used like this:

double fajr, sunRise, zuhr, asr, maghrib, isha;
calcPrayerTimes(2012,1,18, 30.2, 30, 2, -19.5, -17.5, fajr, sunRise, zuhr, asr, maghrib, isha);

Note that these prayer times are still "double" and should be converted to a time format. I made the doubleToHrMin function (you can find it before the calcPrayerTimes fnction) which splits the number into Hours and Minutes. It takes the double and two references to int variables. Here is how to use it:

int hours, minutes;
doubleToHrMin(fajr, hours, minutes);

Now you have the prayer time as Hour/Minute to use it however you want.

So, in brief:
- I first add the above code block to my code, then use it whenever I want like this example:

double fajr, sunRise, zuhr, asr, maghrib, isha;
calcPrayerTimes(2012,1,18, 30.2, 30, 2, -19.5, -17.5,
                fajr, sunRise, zuhr, asr, maghrib, isha);

int hours, minutes;

doubleToHrMin(fajr, hours, minutes);
std::cout << "Fajr: " << hours << ":" << minutes << std::endl;

doubleToHrMin(sunRise, hours, minutes);
std::cout << "Sunrise: " << hours << ":" << minutes << std::endl;

doubleToHrMin(zuhr, hours, minutes);
std::cout << "Zuhr: " << hours << ":" << minutes << std::endl;

doubleToHrMin(asr, hours, minutes);
std::cout << "Asr: " << hours << ":" << minutes << std::endl;

doubleToHrMin(maghrib, hours, minutes);
std::cout << "Maghrib: " << hours << ":" << minutes << std::endl;

doubleToHrMin(isha, hours, minutes);
std::cout << "Isha: " << hours << ":" << minutes << std::endl;

(view the full prayer times example in this online IDE)

I hope it is useful to someone looking for the pure algorithm with no framework dependencies, and I hope I come back to it one more time to see the problem of these extra resulting minutes.


Resources:

جمعية الفلك بالقطيف
Muslim Programmers & Designers Community
Tanzil.info (1),(2)
PrayTime.info
IslamCity.com
IslamWare.com