any reason why gamma function behave differently from other functions ? and why complex number results dust ?

[nycos62]

hello, while testing functions I ended on this :

math.config({
  number: "BigNumber", 
  precision: 509,
  relTol: 1e-300,
  absTol: 1e-300
});

math.evaluate('floor((1/3)^3)').toString()
//'0'

math.evaluate('gamma((1/3)^3)').toString()
gamma.js:89 Uncaught Error: Integer BigNumber expected
    at BigNumber (gamma.js:89:13)
    at gamma (typed-function.js:1465:22)
    at FunctionNode.js:184:24
    at Object.evaluate (Node.js:54:16)
    at Object.string (evaluate.js:44:36)
    at Object.evaluate (typed-function.js:1459:22)
    at <anonymous>:1:6

math.evaluate('(1/4)!').toString()
gamma.js:89 Uncaught Error: Integer BigNumber expected
    at BigNumber (gamma.js:89:13)
    at gamma (typed-function.js:1465:22)
    at BigNumber (factorial.js:44:14)
    at factorial (typed-function.js:1462:22)
    at e (OperatorNode.js:318:18)
    at Object.evaluate (Node.js:54:16)
    at Object.string (evaluate.js:44:36)
    at Object.evaluate (typed-function.js:1459:22)
    at <anonymous>:1:6

is there something missing in gamma function to behave like floor function ?

also bonus question : is this result for imaginary part is correct ?

math.config({
  number: "BigNumber", 
  precision: 509,
  relTol: 1e-300,
  absTol: 1e-300
});
math.evaluate('e^(i*pi)+1')
//s {re: 0, im: 1.2246467991473532e-16}
math.evaluate('e^(i*pi)+1==0')
//false
math.evaluate('re(e^(i*pi)+1)==0')
//true
math.evaluate('im(e^(i*pi)+1)')
//'0'
math.evaluate('im(e^(i*pi)+1)==0')
//Uncaught TypeError: Cannot implicitly convert a number with >15 significant digits to BigNumber (value: 1.2246467991473532e-16). Use function bignumber(x) to convert to BigNumber.
    at convert (typed.js:179:17)
    at Array.t (typed-function.js:1076:22)
    at r (typed-function.js:1030:43)
    at ae (typed-function.js:1448:27)
    at equal (typed-function.js:1476:24)
    at OperatorNode.js:324:18
    at Object.evaluate (Node.js:54:16)
    at Object.string (evaluate.js:44:36)
    at Object.evaluate (typed-function.js:1459:22)
    at <anonymous>:1:6
math.evaluate('[(1/(1+i))^2; re((1/(1+i))^2); im((1/(1+i))^2)]')
//s {re: 3.061616997868383e-17, im: -0.5}
[3.061616997868383e-17]
[-0.5]
//but should be [0-i/2,  0 , -0.5] correct ?

[josdejong]

The BigNumber implementations of gamma and factorial lack support for non-integer values.