Overview
This is a program that computes approximations to float -> float functions.
You give it a straight-line program in a certain form with some unspecified
constants, an interval, and a function giving, for each x in that interval,
the acceptable values for the function; it tries to fill in the blanks in your
straight-line program in order to get an acceptable approximation to the
function over the whole interval of interest.
Building
This program depends on QSopt_ex by Applegate, Cook, Dash, and
Espinoza.. This program also
depends on a complete and working installation of GMP.
Download and build QSopt_ex first in directory QSex090408, then run make.
Using
Hack main() to specify the straight-line program of interest, bounds on the
unspecified coefficients, and the interval. Hack get_bounds() to specify the
function and error bounds of interest. Then build and run the program.
The output
The output of this program is a mishmash of various kinds of status information.
A chunk that looks like this:
float c0 = 0x1.0ce86cp-4
float c1 = -0x1.81a69cp-4
float c2 = 0x1.07661ep-4
float c3 = 0x1.f6d1fp-8
float c4 = 0x1.c6cc72p-5
float c5 = 0x1.10f968p-3
float c6 = 0x1.55550ap-2
represents the current candidate list of coefficients.
A chunk that looks like this:
vector<float> testpoints = {0x1p-1,0x1.bf4876p-2,0x1.47d9bep-1,0x1.f0b3c2p-2,0x1.4e15b4p-1,0x1.2915f8p-1,0x1.36870ep-3,0x1.67b29ap-2,0x1.7bb93cp-1,0x1.762f4cp-1};
represents the current list of test points.
Lines that look like this:
0x1.7cp+10
0x1.a724p+16
0x1.3670a8p+22
0x1.a3342ep+24
0x1.1e7b58p+25
represent the current status of the diving search. Each line gives the number of floats for some coefficient that have not yet been proven infeasible.
At the end of execution, the program prints out 0, -1, or -2. 0 means
that the most recent candidate list of coefficients provably works. -1 means
that there are provably no coefficients that work. -2 means that the
heuristic gave up trying to solve the problem because a recursive search took too long.