fastermath
========

A library of math functions targeted at 32-bit and 64-bit x86 Linux systems.

The purpose of this library is to provide faster drop in replacements for
selected functions of the standard math library 'libm'. These functions
are written so they can be more optimized by compilers and all special
case tests for increased consistency and accuracy have been removed.
They are based on the corresponding implementations from the Cephes math
library by Stephen L. Moshier. The code has been simplified perusing
internal compiler facilities wherever possible and assuming little
endian IEEE-754 single and double precision math.

Installation
============

This package is x86 and Linux specific and  makes heavy use of advanced
features of the GNU compiler toolchain and thus requires a somewhat recent
GNU C compiler (tested with 4.4.x to 4.7.x) or a compatible Intel compiler
(tested with 13.0.x).

To compile simply type "make <configuration>". This will read a configuration
file in the directory config/ and will create an object directory for it and
compile all binaries in it. The config file naming convention is:
<bitness>-<fpmode>-<compiler>.inc
If you type "make" without any target will list all availalable configurations
that are compatible with the current platform. Typing "make all" will try to
compile all of them.

Compilation should produce two libraries (libfastermath.so & libfastermath.a),
two utility programs (genspline & tester) and a shared object (fastermath.so)
in the configuration specific object directory.

If the CPPFLAGS contains the flag -DLIBM_ALIAS the libraries contain entries
which alias the internal functions directly to the lib counterparts.

Usage
=====

The library contains math functions that are mostly equivalent with their
counterparts in libm. They have the same name, but the string 'fm_' prepended.
So renaming the functions calls, e.g. log(), with the library version, i.e.
fm_log() will call this library instead of libm. The fastermath.so shared
object would redirect function calls from the libm version to the fastermath
variant when the shared object is activated using LD_PRELOAD.

How it works
============

The normal math functions contain a lot of tests for over- and underflow 
and go through a lot of pains to handle borderline cases and maximize
accuracy. The functions in the fastermath library skip those, since in
most cases, those are not needed, but const a significant amount CPU
time. Similarly, the streamlined code can be optimized better by compilers.
In the case of logarithms, it has been found that using a cubic spline
interpolation is significantly faster than using the usual rational 
function expansion from math libraries like cephes or glibc.

How fast is it?
===============

That depends on the compiler, the code and the CPU. Speedup on 64-bit CPUs
is usually higher, speedup on Intel CPUs is often higher than on AMD CPUs.
Exponentials are 1.5-3 times faster, logarithms 2-4 times faster.
When you have well vectorizing code (like the tester in this package), the
Intel compiler can vectorize the loops and then use the short vector math
library (SVML), which can handle multiple function calls concurrently and
achieve much higher speedup.