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14.1.?CEL Mathematical Functions The following mathematical functions are available for use with all CEL expressions. Note: In the Function column in the table below, [a] denotes any dimension of the first operand. Table?14.1?Standard Mathematical CEL Functions Function Operand’s Values Result’s Dimensions abs( [a] ) Any [a] acos( [ ] ) Radians asin( [ ] ) Radians atan( [ ] )[a] Any Radians atan2( [a], [a] )[a] Any Radians besselJ( [ ], [ ] )[b] Dimensionless besselY( [ ], [ ] )[b] Dimensionless cos( [radians] ) Any Dimensionless cosh( [ ] ) Any Dimensionless exp( [ ] ) Any Dimensionless int([ ])[c] Dimensionless Dimensionless loge( [ ] )[d] Dimensionless log10( [ ] )[e] Dimensionless min( [a], [a] ) Any [a] max( [a], [a] ) Any [a] mod( [a], [a] )[f] Any [a] nint([ ])[g] Dimensionless Dimensionless sin( [radians] ) Any Dimensionless sinh( [ ] ) Any Dimensionless sqrt( [a] ) [a]^0.5 step( [ ] ) [h] Any Dimensionless tan( [radians] )[i] Any Dimensionless tanh( [ ] ) Any Dimensionless [a] atan does not determine the quadrant of the result, but atan2 does. [b] The value of the first dimensionless operand n, also referred to as the order of the Bessel function, must be an integer (n=0, 1, 2, ....). The second argument is a dimensionless real number. [c] The int() function truncates the dimensionless argument to its integer part. Examples: int(1) = 1 int(2.5) = 2 int(-3.1) = -3 int(-4.8) = -4 The int() function requires a dimensionless argument but will not report an error if the argument of the function has a dimension of radians or degrees. [d] ln(x) is valid as an alias for loge(x) [e] log(x) is valid as an alias for log10(x) [f] mod(x, y) returns the remainder on dividing x by y; the function is not defined for y = 0. [g] The nint function requires a dimensionless argument and is defined as: int(x + 0.5) if x = 0 int(x - 0.5) if x 0 See the implementation of int( ) function in the table above. Examples: nint(2.6) = 3 nint(2.5) = 3 nint(2.4) = 2 nint(1) = 1