/*************************************************************************
?*??Compilation:??javac?MyMath.java
?*??Execution:????java?MyMath?z
?*
?*??Implements?a?number?of?mathematical?functions:?absolute?value
?*??square?root?exponential?error?function?and?the?cumulative
?*??Gaussian?distribution.?Also?produces?random?Gaussians.
?*??The?first?three?are?for?illustration?only?since?they?are
?*??already?in?the?standard?Math?library.
?*??
?*??The?test?client?reads?in?a?command?line?inputs?z?and?prints?out
?*??erf（z）?and?Phi（z）?to?7?significant?digits?where
?*
?*??????????????erf（z）?=?2?/?sqrt（pi）?*?integral（exp（-t*t）?t?=?0..z）?
?*??????????????Phi（z）?=?normal?cdf
?*
?*
?*??%?java?MyMath?1.0
?*??abs（1.0）?=?1.0
?*??exp（1.0）?=?2.7182818284590455
?*??cosh（1.0）?=?1.543080634815244
?*??sqrt（1.0）?=?1.0
?*??erf（1.0）?=?0.8427007877600067?????????//?actual?=?0.84270079294971486934
?*??Phi（1.0）?=?0.8413447386043253?????????//?actual?=?0.8413447460

?*
?*??%?java?MyMath?-1.0
?*??abs（-1.0）?=?1.0
?*??exp（-1.0）?=?0.36787944117144245
?*??cosh（-1.0）?=?1.543080634815244
?*??sqrt（-1.0）?=?NaN
?*??erf（-1.0）?=?-0.8427007877600068
?*??Phi（-1.0）?=?0.15865526139567465
?*
?*??%?java?MyMath?3.0
?*??abs（3.0）?=?3.0
?*??exp（3.0）?=?20.08553692318766
?*??cosh（3.0）?=?10.067661995777765
?*??sqrt（3.0）?=?1.7320508075688772
?*??erf（3.0）?=?0.9999779095015785?????????//?actual?=?0.99997790950300141456
?*??Phi（3.0）?=?0.9986501019267444
?*?
?*??%?java?MyMath?30
?*??abs（30.0）?=?30.0
?*??exp（30.0）?=?1.0686474581524467E13
?*??cosh（30.0）?=?5.343237290762231E12
?*??sqrt（30.0）?=?5.477225575051661
?*??erf（30.0）?=?1.0
?*??Phi（30.0）?=?1.0
?*
?*??%?java?MyMath?-30
?*??abs（-30.0）?=?30.0
?*??exp（-30.0）?=?9.357622968840171E-14
?*??cosh（-30.0）?=?5.343237290762231E12
?*??sqrt（-30.0）?=?NaN
?*??erf（-30.0）?=?-1.0
?*??Phi（-30.0）?=?0.0
?*
?*??%?java?MyMath?1E-20
?*??abs（1.0E-20）??=?1.0E-20
?*??exp（1.0E-20）??=?1.0
?*??cosh（1.0E-20）?=?1.0
?*??sqrt（1.0E-20）?=?9.999999999999999E-11
?*??erf（1.0E-20）??=?-3.0000000483809686E-8?????//?true?anser?1.13E-20
?*??Phi（1.0E-20）??=?0.49999998499999976


?*
?*??Reference:?Chebyshev?fitting?formula?for?erf（z）?from
?*??Numerical?Recipes?6.2
?*
?*************************************************************************/

package?com;


public?class?MyMath?{

????//?absolute?value
????public?static?double?abs（double?x）?{
????????if??????（x?==?0.0）?return??x;????//?for?-0?and?+0
????????else?if?（x?>??0.0）?return??x;
????????else???????????????return?-x;
????}

????//?exponentiation?-?special?case?for?negative?input?improves?accuracy
????public?static?double?exp（double?x）?{
????????double?term?=?1.0;
????????double?sum??=?1.0;
????????for?（int?N?=?1;?sum?!=?sum?+?term;?N++）?{
????????????term?=?term?*?Math.abs（x）?/?N;
????????????sum??=?sum?+?term;
????????}
????????if?（x?>=?0）?return?sum;
????????else????????return?1.0?/?sum;
????}

????//?calculate?square?root?using?Newton‘s?m