/*
Fast?Fourier/Cosine/Sine?Transform
????dimension???:one
????data?length?:power?of?2
????decimation??:frequency
????radix???????:split-radix
????data????????:inplace
????table???????:not?use
functions
????cdft:?Complex?Discrete?Fourier?Transform
????rdft:?Real?Discrete?Fourier?Transform
????ddct:?Discrete?Cosine?Transform
????ddst:?Discrete?Sine?Transform
????dfct:?Cosine?Transform?of?RDFT?（Real?Symmetric?DFT）
????dfst:?Sine?Transform?of?RDFT?（Real?Anti-symmetric?DFT）
function?prototypes
????void?cdft（int?int?double?*）;
????void?rdft（int?int?double?*）;
????void?ddct（int?int?double?*）;
????void?ddst（int?int?double?*）;
????void?dfct（int?double?*）;
????void?dfst（int?double?*）;


--------?Complex?DFT?（Discrete?Fourier?Transform）?--------
????[definition]
????????
????????????X[k]?=?sum_j=0^n-1?x[j]*exp（2*pi*i*j*k/n）?0<=k????????
????????????X[k]?=?sum_j=0^n-1?x[j]*exp（-2*pi*i*j*k/n）?0<=k????????（notes:?sum_j=0^n-1?is?a?summation?from?j=0?to?n-1）
????[usage]
????????
????????????cdft（2*n?1?a）;
????????
????????????cdft（2*n?-1?a）;
????[parameters]
????????2*n????????????:data?length?（int）
????????????????????????n?>=?1?n?=?power?of?2
????????a[0...2*n-1]???:input/output?data?（double?*）
????????????????????????input?data
????????????????????????????a[2*j]?=?Re（x[j]）?
????????????????????????????a[2*j+1]?=?Im（x[j]）?0<=j????????????????????????output?data
????????????????????????????a[2*k]?=?Re（X[k]）?
????????????????????????????a[2*k+1]?=?Im（X[k]）?0<=k????[remark]
????????Inverse?of?
????????????cdft（2*n?-1?a）;
????????is?
????????????cdft（2*n?1?a）;
????????????for?（j?=?0;?j?<=?2?*?n?-?1;?j++）?{
????????????????a[j]?*=?1.0?/?n;
????????????}
????????.


--------?Real?DFT?/?Inverse?of?Real?DFT?--------
????[definition]
?????????RDFT
????????????R[k]?=?sum_j=0^n-1?a[j]*cos（2*pi*j*k/n）?0<=k<=n/2
????????????I[k]?=?sum_j=0^n-1?a[j]*sin（2*pi*j*k/n）?0?????????IRDFT?（excluding?scale）
????????????a[k]?=?（R[0]?+?R[n/2]*cos（pi*k））/2?+?
???????????????????sum_j=1^n/2-1?R[j]*cos（2*pi*j*k/n）?+?
???????????????????sum_j=1^n/2-1?I[j]*sin（2*pi*j*k/n）?0<=k????[usage]
????????
????????????rdft（n?1?a）;
????????
????????????rdft（n?-1?a）;
????[parameters]
????????n??????????????:data?length?（int）
????????????????????????n?>=?2?n?=?power?of?2
????????a[0...n-1]?????:input/output?data?（double?*）
????????????????????????
????????????????????????????output?data
????????????????????????????????a[2*k]?=?R[k]?0<=k????????????????????????????????a[2*k+1]?=?I[k]?0????????????????????????????????a[1]?=?R[n/2]
????????????????????????
????????????????????????????input?data
????????????????????????????????a[2*j]?=?R[j]?0<=j????????????????????????????????a[2*j+1]?=?I[j]?0????????????????????????????????a[1]?=?R[n/2]
????[remark]
????????Inverse?of?
????????????rdft（n?1?a）;
????????is?
????????????rdft（n?-1?a）;
????????????for?（j?=