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Copyright (C) 2014 Martin Kretschmar <mail@martin-kretschmar.de>

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If your software doesn’t run repeatedly for minutes, then you should
never try to optimize it! C resp.C++ is fastest.
(https://days2011.scala-lang.org/sites/days2011/files/ws3-1-Hundt.pdf),
C++ and Go are statically compiled, both Java and Scala run on the JVM.

Benchmark Time [sec] Factor
C++ Opt 23 1.0x
C++ Dbg 197 8.6x
Java 64-bit 134 5.8x
Java 32-bit 290 12.6x
Java 32-bit GC* 106 4.6x
Java 32-bit SPEC GC 89 3.7x
Scala 82 3.6x
Scala low-level* 67 2.9x
Scala low-level GC* 58 2.5x
Go 6g 161 7.0x
Go Pro* 126 5.5x

Fortran is the oldest programming language of the world. But for fast
high quality numerical computations its still the number one. The language
C has only exactly one sin(double x) function, while Fortran has 7
sin(REAL, DOUBLE, REAL*16, COMPLEX, DOUBLE COMPLEX
DOUBLE COMPLEX COMPLEX*32).

It must be noted  that the a mathematical co-processor as built-in since
the Intel 486 also must do his job somehow which can be really slow.
This is also true for embedded processors. So your code should use the
sin() function calls only in places where you really need them.

The code examples from the (http://en.wikipedia.org/wiki/Numerical_Recipes)
are meant to illustrate. The NAG Libraries are commercial, the LAPACK
(http://www.netlib.org/lapack) and BLAS(http://www.netlib.org/blas) are free.

The fastest free FFT is FFTW (http://en.wikipedia.org/wiki/FFTW). E. Prince
writes in his book, that before the FFT computer centers ran mostly fourier
calculations.

Although not mentioning Numerical Recipes by name, Whaley et al.[7]
demonstrate that LAPACK with a highly optimized BLAS library can
be an order of magnitude faster (or more) than textbook-style triply
nested-loop linear-algebra routines similar to the code in Numerical
Recipes. As another example, Frigo and Johnson[8] point out that the fast
Fourier transform (FFT) code in highly optimized programs on modern
computer architectures is 5–40 times faster than the example in Numerical
Recipes.

In C all function values are passed by value and all functions like
fprintf ( FILE *, …) have no fixed number of arguments and can be
called recursively. To achieve this the parameters values have to be
pushed on the stack, the function be called and the stack manually
cleaned up afterwards.

C also introduced a clean and simple pointer concept. A pointer p is a
normal variable like an int, and should be initialized with a NULL. With
the syntax (*p) the pointer is used to access the memory. If p is a char
pointer, then exactly one byte will be accessed. p++ points to the next
sensible object. For a FILE pointer the address is p+sizeof(FILE). a[I]
is a shortcut for *(a+i) ] is a commutative shortcut for *(i+a) ] is a
shortcut for i[a].

In Fortran all function values are passed by reference which are pointers
resp. addresses of the variables. So a Fortran function can modify all of
its variables its called with.