Ring/Lessons/Mathematical Functions

Mathematical Functions In this chapter we are going to learn about the mathematical functions List of functions The Ring programming language comes with the next mathematical functions =============== ============================================================================= Function Description =============== ============================================================================= sin(x) Returns the sine of an angle of x radians cos(x) Returns the cosine of an angle of x radians tan(x) Returns the tangent of an angle of x radians asin(x) Returns the principal value of the arc sine of x, expressed in radians acos(x) Returns the principal value of the arc cosine of x, expressed in radians atan(x) Returns the principal value of the arc tangent of x, expressed in radians atan2(y,x) Returns the principal arc tangent of y/x, in the interval [-pi,+pi] radians sinh(x) Returns the hyperbolic sine of x radians cosh(x) Returns the hyperbolic cosine of x radians tanh(x) Returns the hyperbolic tangent of x radians exp(x) Returns the value of e raised to the xth power log(x) Returns the natural logarithm of x log10(x) Returns the common logarithm (base-10 logarithm) of x ceil(x) Returns the smallest integer value greater than or equal to x floor(x) Returns the largest integer value less than or equal to x fabs(x) Returns the absolute value of x. pow(x,y) Returns x raised to the power of y sqrt(x) Returns the square root of x random(x) Returns a random number in the range [0,x] unsigned(n,n,c) Perform operation using unsigned numbers decimals(n) Determine the decimals digits after the point in float/double numbers =============== ============================================================================= Example See "Mathematical Functions" + nl See "Sin(0) = " + sin(0) + nl See "Sin(90) radians = " + sin(90) + nl See "Sin(90) degree = " + sin(90*3.14/180) + nl See "Cos(0) = " + cos(0) + nl See "Cos(90) radians = " + cos(90) + nl See "Cos(90) degree = " + cos(90*3.14/180) + nl See "Tan(0) = " + tan(0) + nl See "Tan(90) radians = " + tan(90) + nl See "Tan(90) degree = " + tan(90*3.14/180) + nl See "asin(0) = " + asin(0) + nl See "acos(0) = " + acos(0) + nl See "atan(0) = " + atan(0) + nl See "atan2(1,1) = " + atan2(1,1) + nl See "sinh(0) = " + sinh(0) + nl See "sinh(1) = " + sinh(1) + nl See "cosh(0) = " + cosh(0) + nl See "cosh(1) = " + cosh(1) + nl See "tanh(0) = " + tanh(0) + nl See "tanh(1) = " + tanh(1) + nl See "exp(0) = " + exp(0) + nl See "exp(1) = " + exp(1) + nl See "log(1) = " + log(1) + nl See "log(2) = " + log(2) + nl See "log10(1) = " + log10(1) + nl See "log10(2) = " + log10(2) + nl See "log10(10) = " + log10(10) + nl See "Ceil(1.12) = " + Ceil(1.12) + nl See "Ceil(1.72) = " + Ceil(1.72) + nl See "Floor(1.12) = " + floor(1.12) + nl See "Floor(1.72) = " + floor(1.72) + nl See "fabs(1.12) = " + fabs(1.12) + nl See "fabs(1.72) = " + fabs(1.72) + nl See "pow(2,3) = " + pow(2,3) + nl see "sqrt(16) = " + sqrt(16) + nl Program Output: Mathematical Functions Sin(0) = 0 Sin(90) radians = 0.89 Sin(90) degree = 1.00 Cos(0) = 1 Cos(90) radians = -0.45 Cos(90) degree = 0.00 Tan(0) = 0 Tan(90) radians = -2.00 Tan(90) degree = 1255.77 asin(0) = 0 acos(0) = 1.57 atan(0) = 0 atan2(1,1) = 0.79 sinh(0) = 0 sinh(1) = 1.18 cosh(0) = 1 cosh(1) = 1.54 tanh(0) = 0 tanh(1) = 0.76 exp(0) = 1 exp(1) = 2.72 log(1) = 0 log(2) = 0.69 log10(1) = 0 log10(2) = 0.30 log10(10) = 1 Ceil(1.12) = 2 Ceil(1.72) = 2 Floor(1.12) = 1 Floor(1.72) = 1 fabs(1.12) = 1.12 fabs(1.72) = 1.72 pow(2,3) = 8 sqrt(16) = 4 Random() Function The Random() function generate a random number and we can set the maximum value (optional). Syntax: Random(x) ---> Random number in the range [0,x] Example: for x = 1 to 20 see "Random number : " + random() + nl + "Random number Max (100) : " + random(100) + nl next Program Output: Random number : 31881 Random number Max (100) : 80 Random number : 5573 Random number Max (100) : 63 Random number : 2231 Random number Max (100) : 43 Random number : 12946 Random number Max (100) : 39 Random number : 22934 Random number Max (100) : 48 Random number : 4690 Random number Max (100) : 52 Random number : 13196 Random number Max (100) : 65 Random number : 30390 Random number Max (100) : 87 Random number : 4327 Random number Max (100) : 77 Random number : 12456 Random number Max (100) : 17 Random number : 28438 Random number Max (100) : 13 Random number : 30503 Random number Max (100) : 6 Random number : 31769 Random number Max (100) : 94 Random number : 8274 Random number Max (100) : 65 Random number : 14390 Random number Max (100) : 90 Random number : 28866 Random number Max (100) : 12 Random number : 24558 Random number Max (100) : 70 Random number : 29981 Random number Max (100) : 77 Random number : 12847 Random number Max (100) : 63 Random number : 6632 Random number Max (100) : 60 Unsigned() Function We can use unsigned numbers using the Unsigned() function. Syntax: Unsigned(nNum1,nNum2,cOperator) --> result of cOperator operation on nNum1,nNum2 Example: see oat_hash("hello") + nl # Jenkins hash function - https://en.wikipedia.org/wiki/Jenkins_hash_function func oat_hash cKey h = 0 for x in cKey h = unsigned(h,ascii(x),"+") h = unsigned(h,unsigned(h,10,"<<"),"+") r = unsigned(h,6,">>") h = unsigned(h, r,"^") next h = unsigned(h,unsigned(h,3,"<<"),"+") h = unsigned(h,unsigned(h,11,">>"),"^") h = unsigned(h,unsigned(h,15,"<<"),"+") return h Output: 3372029979.00 Decimals() Functions We can determine the decimals numbers count after the point in float/double numbers using the decimals() function. Syntax: Decimals(nDecimalsCount) Example: x = 1.1234567890123 for d = 0 to 14 decimals(d) see x + nl next Output: 1 1.1 1.12 1.123 1.1235 1.12346 1.123457 1.1234568 1.12345679 1.123456789 1.1234567890 1.12345678901 1.123456789012 1.1234567890123 1.12345678901230 Ring programming language