Fixed error message. Imported libsharp

external/sharp/libfftpack/README

@@ -0,0 +1,34 @@
+ls_fft description:
+
+This package is intended to calculate one-dimensional real or complex FFTs
+with high accuracy and good efficiency even for lengths containing large
+prime factors.
+The code is written in C, but a Fortran wrapper exists as well.
+
+Before any FFT is executed, a plan must be generated for it. Plan creation
+is designed to be fast, so that there is no significant overhead if the
+plan is only used once or a few times.
+
+The main component of the code is based on Paul N. Swarztrauber's FFTPACK in the
+double precision incarnation by Hugh C. Pumphrey
+(http://www.netlib.org/fftpack/dp.tgz).
+
+I replaced the iterative sine and cosine calculations in radfg() and radbg()
+by an exact calculation, which slightly improves the transform accuracy for
+real FFTs with lengths containing large prime factors.
+
+Since FFTPACK becomes quite slow for FFT lengths with large prime factors
+(in the worst case of prime lengths it reaches O(n*n) complexity), I
+implemented Bluestein's algorithm, which computes a FFT of length n by
+several FFTs of length n2>=2*n-1 and a convolution. Since n2 can be chosen
+to be highly composite, this algorithm is more efficient if n has large
+prime factors. The longer FFTs themselves are then computed using the FFTPACK
+routines.
+Bluestein's algorithm was implemented according to the description at
+http://en.wikipedia.org/wiki/Bluestein's_FFT_algorithm.
+
+Thread-safety:
+All routines can be called concurrently; all information needed by ls_fft
+is stored in the plan variable. However, using the same plan variable on
+multiple threads simultaneously is not supported and will lead to data
+corruption.