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Added reciprocal functions, and added atan(x).
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@ZCG-coder
ZCG-coder committed Jun 11, 2024
1 parent b78b72b commit 263f544
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Showing 2 changed files with 165 additions and 5 deletions.
44 changes: 44 additions & 0 deletions include/fn/basicArithm.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -271,6 +271,50 @@ namespace steppable::__internals::arithmetic
*/
std::string tan(const std::string& x, int decimals, int mode = 0);

/**
* @brief Calculates the secant of a number.
*
* @param x The number to calculate the secant of.
* @param decimals The number of decimal places to round off to.
* @param mode The mode to calculate the secant in. 0 = radians (default), 1 = degrees, 2 = gradians.
*
* @return The secant of the number.
*/
std::string sec(const std::string& x, int decimals, int mode = 0);

/**
* @brief Calculates the cosecant of a number.
*
* @param x The number to calculate the cosecant of.
* @param decimals The number of decimal places to round off to.
* @param mode The mode to calculate the cosecant in. 0 = radians (default), 1 = degrees, 2 = gradians.
*
* @return The cosecant of the number.
*/
std::string csc(const std::string& x, int decimals, int mode = 0);

/**
* @brief Calculates the cotangent of a number.
*
* @param x The number to calculate the cotangent of.
* @param decimals The number of decimal places to round off to.
* @param mode The mode to calculate the cotangent in. 0 = radians (default), 1 = degrees, 2 = gradians.
*
* @return The cotangent of the number.
*/
std::string cot(const std::string& x, int decimals, int mode = 0);

/**
* @brief Calculates the arc tangent of a number.
*
* @param x The number to calculate the arc tangent of.
* @param decimals The number of decimal places to round off to.
* @param mode The mode to calculate the arc tangent in. 0 = radians (default), 1 = degrees, 2 = gradians.
*
* @return The arc tangent of the number.
*/
std::string atan(const std::string& x, int decimals, int mode = 0);

/**
* @brief Executes a given predicate function a specified number of times.
*
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126 changes: 121 additions & 5 deletions src/trig/trig.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -47,19 +47,42 @@ namespace steppable::__internals::arithmetic
std::string degToRad(const std::string& _deg)
{
// rad = deg * (pi / 180)
auto deg = divideWithQuotient(_deg, "180").remainder;
auto deg = divideWithQuotient(_deg, "360").remainder;
auto rad = multiply(deg, constants::PI_OVER_180, 0);
return rad;
}

std::string gradToRad(const std::string& _grad)
{
// rad = grad * (pi / 200)
auto grad = divideWithQuotient(_grad, "200").remainder;
auto grad = divideWithQuotient(_grad, "400").remainder;
auto rad = multiply(grad, constants::PI_OVER_200, 0);
return rad;
}

std::string radToDeg(const std::string& _rad)
{
// deg = rad * (180 / pi)
auto rad = divideWithQuotient(_rad, static_cast<std::string>(constants::TWO_PI)).remainder;
auto deg = divide(rad, constants::PI_OVER_180, 0);
return deg;
}

std::string radToGrad(const std::string& _rad)
{
// grad = rad * (200 / pi)
auto rad = divideWithQuotient(_rad, static_cast<std::string>(constants::TWO_PI)).remainder;
auto grad = divide(rad, constants::PI_OVER_200, 0);
return grad;
}

std::string gradToDeg(const std::string& _grad)
{
// deg = grad * (9 / 10)
auto deg = divideWithQuotient(_grad, "400").remainder;
return deg;
}

std::string _cos(const std::string& x, const int decimals)
{
// .,,. ., /=====================================================================\
Expand Down Expand Up @@ -103,7 +126,7 @@ namespace steppable::__internals::arithmetic
{
case 0:
{
result = _cos(x, decimals);
result = _cos(divideWithQuotient(x, static_cast<std::string>(constants::TWO_PI)).remainder, decimals);
break;
}
case 1:
Expand Down Expand Up @@ -137,7 +160,10 @@ namespace steppable::__internals::arithmetic
{
case 0:
{
result = cos(subtract(x, constants::PI_OVER_2, 0), decimals);
result = cos(subtract(divideWithQuotient(x, static_cast<std::string>(constants::TWO_PI)).remainder,
constants::PI_OVER_2,
0),
decimals);
break;
}
case 1:
Expand Down Expand Up @@ -171,7 +197,7 @@ namespace steppable::__internals::arithmetic
{
case 0:
{
auto cosX = cos(x, decimals + 1);
auto cosX = cos(divideWithQuotient(x, static_cast<std::string>(constants::TWO_PI)).remainder, decimals + 1);
if (isZeroString(cosX))
{
error("trig::tan"s, "Tangent is undefined here."s);
Expand Down Expand Up @@ -214,6 +240,88 @@ namespace steppable::__internals::arithmetic
return roundOff(result, decimals);
}

std::string csc(const std::string& x, const int decimals, const int mode)
{
auto sinX = sin(x, decimals + 1, mode);
if (isZeroString(sinX))
{
error("trig::csc"s, "Cosecant is undefined here."s);
return "Infinity";
}
return divide("1", sinX, 0, decimals);
}

std::string sec(const std::string& x, const int decimals, const int mode)
{
auto cosX = cos(x, decimals + 1, mode);
if (isZeroString(cosX))
{
error("trig::sec"s, "Secant is undefined here."s);
return "Infinity";
}
return divide("1", cosX, 0, decimals);
}

std::string cot(const std::string& x, const int decimals, const int mode)
{
auto tanX = tan(x, decimals + 1, mode);
if (isZeroString(tanX))
{
error("trig::cot"s, "Cotangent is undefined here."s);
return "Infinity";
}
return divide("1", tanX, 0, decimals);
}

std::string atan(const std::string& _x, const int decimals, const int mode)
{
auto x = _x;
bool isReduced = false;
if (compare(abs(x, 0), "1", 0) != "0")
{
isReduced = true;
// Reduce x to a small number
x = divide("1", x, 0, decimals * 2);
}
// Otherwise, use Padé series.
// (https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-017-1310-6/tables/1)
// 3
// 55x + 105x
// ------------------ ~= arctan(x)
// 4 2
// 9x + 90x + 105
auto x2 = power(x, "2", 0);
auto x3 = multiply(x2, x, 0); // Use multiply to reduce the number of operations.
auto x4 = multiply(x3, x, 0);
auto numerator = add(multiply("55", x3, 0), multiply("105", x, 0), 0);
auto denominator = add(add(x4, multiply("90", x2, 0), 0), "105", 0);
auto result = standardizeNumber(divide(numerator, denominator, 0, decimals * 2));

if (isReduced)
{
// If x was reduced, use the identity
// arctan(1/x) = pi/2 - arctan(x)
result = subtract(constants::PI_OVER_2, result, 0);
}
result = roundOff(result, decimals);

// Convert the result as needed.
switch (mode)
{
case 1:
result = radToDeg(result);
break;
case 2:
result = radToGrad(result);
break;
default:
break;
}

return result;
}

// std::string asin(const std::string& x, const int decimals, const int mode) {}
} // namespace steppable::__internals::arithmetic

#ifndef NO_MAIN
Expand Down Expand Up @@ -242,6 +350,14 @@ int main(int _argc, const char* _argv[])
std::cout << cos(arg, decimals, mode) << '\n';
else if (command == "tan")
std::cout << tan(arg, decimals, mode) << '\n';
else if (command == "csc")
std::cout << csc(arg, decimals, mode) << '\n';
else if (command == "sec")
std::cout << sec(arg, decimals, mode) << '\n';
else if (command == "cot")
std::cout << cot(arg, decimals, mode) << '\n';
else if (command == "atan")
std::cout << atan(arg, decimals, mode) << '\n';
else
error("trig::main", "Invalid command."s);
}
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