Issue N^{o} 4, 1997 
OPTIMIZATION OF THE GENERAL FORM MATRIX OPERATIONS FOR PENTIUM PRO PROCESSOR
Bruce Greer C., S.V. Kazakov, S.V. Sivolgin VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 310.
Multilevel optimization of matrix float operations for Pentium Pro processor is described using one BLAS library program as an example. The upper levels of optimization increase the efficiency of using cache memory. The lower optimization level takes into account specific features of a microprocessor architecture. Performance plots for different algorithms are given.

PRINCIPLES OF USING MMX TECHNOLOGY IN 3DR GRAPHIC LIBRARY G.I. Voronov, S.P. Perepelkin, S.I. Sapronov VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 1113.
The paper describes principles of the Intel product, 3DR grapfic library, optimization on the base of MMX technology for Pentium microprocessor. Works have been performed during the period of trial operation of new microprocessors. The programming was being performed on ? language using the compiler Proton. The work resulted in creation of the generalpurpose graphic library version functioning on Intel´s processors both with traditional command system and using MMX technology.

THE USE OF SMPBLAS LIBRARY FOR SOLVING BAND SYSTEMS E.V. Gvozdev, I.N. Orlov VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 1417.
The paper shows a feasibility of the parallel SMPBLAS library oriented to operations with dense matrices for solving band symmetric positive definite system A⋅x = b using Cholesky decomposition. The efficiency of such approach is estimated.

OPTIMIZATION OF FAST FOURIER TRANSFORMATION PROGRAM FOR PENTIUM AND PENTIUM PRO PROCESSORS G.I Voronov, G.A. Danilov, N.N. Degtyarenko, Aleksandr A. Kibkalo, V.F. Kuryakin, B.P. Shamraev VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 1827.
Implementation of the fast Fourier transformation (FFT) function family in SPL and RPL libraries is described. Estimates of complexity of most well known FFT computation algorithms are given which take into account specific features of implementation using Pentium and Pentiun Pro processors. General principles of FFT function family arrangement, implementations of different FFT algorithms and support operations, as well as areas of optimization for certain processors, including processors with MMX technology, are considered.

TEST SYSTEM ARRANGEMENT FOR SPL LIBRARY I.V. Aleksandrova, V.F. Kuryakin, I.E. Smirnov, Yu.G. Fedorova VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 2833.
The paper gives the description of the test system for SPLfunction library for digital signal processing. It is shown that this system provides powerful and flexible means to develop tests and control testings. The test system tools and its ideology are used to develop and maintain not only SPL, but RPLfunction library for primitive recognition and IPLfunction library for image processing as well.

VECTOR FUNCTION OPTIMIZATION OF COMPUTATIONS I.I. Zavarzin, V.F. Kuryakin, V.V. Lunev, D.M. Obuvalin, V.G. Ryzhikh VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 3438.
Using three functions 1/x, ln x, exp x as an example it is shown that Pentium and Pentium Pro type processor´s performance may be increased 2—3 times (as compared to hardware implementation), if a set of argument values is known beforehand. The proposed techniques are acceptable for optimization of these and other functions of a vector argument on any superscalar processor. These techniques do not cause the result accuracy decrease, moreover, the reduction in accuracy requirements is an additional reserve of increasing such function performancy.

FAST SHADING TECHNIQUES IN REALISTIC GRAPHICS F.A. Pletenev VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 3950.
New fast shading techniques are proposed which don´t yield to Phong shading technique in quality and are comparable with Gouraud technique in speed of operation information used in the proposed technique allows to take into account surface roughnesses without changes in surface element geometry. Significant speedup of shading techniques allows to use them in dynamic packages of realistic graphics. The simplicity of formulas in some of them permits hardware implementation in graphic chips“accelerators”.

ANTIALIASING ALGORITHM FOR IMAGE IMPROVEMENT V.V. Zmushko VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 5153.
Antialiasing algorithm for smoothing defects in images of 3D objects due to raster discreteness is described. The algorithm is based on approximate estimation of area of this object intersection with boundary pixels and averaging of the object color according to the estimate as well as on separate handling of each scanline for more complex objects. Noticeable improvement of image quality is gained with minimum loss of reproduction performance, about 1030%. The proposed algorithm has been verified using 3DR graphic library.

ABOUT ONE ALGORITHM OF ISOSURFACE DESIGNING IN 3D CARTESIAN SPACE V.V. Bashurov VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 5459.
The shortcut method of constructing isosurfaces in 3D Cartesian space on a regular grid is presented which uses quick algorithm of 8bit encoding of original grid nodes. Due to precalculated isosurface structure in each grid cell processor time spent for isosurface formation reduce in comparison with available techniques. The final isosurface is set by a number of triangles which vertices are specified both by their own coordinates of normal vector to the obtained surface.

PARALLELIZATION OF BLAS LIBRARY OF MAJOR LINEAR ALGEBRA OPERATIONS USING COMMON MEMORY V.V. Lunev, D.M. Obuvalin, I.N. Orlov, S.V. Sivolgin VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 6068.
The results of works on creation of highperfomance parallel BLAS library for systems with shared memory under OS Windows NT and UNIX are given. Parallel algorithms for this library programs are described and their efficiency for different processor numbers is estimated. The new formula for parallelization efficiency estimation is proposed.

THE PROJECT OF THE LIBRARY OF CLASSES FOR VIRTUAL WORLD CONSTRUCTION A.G. Subbotin VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 6974.
An approach to tool development for designing virtual reality systems is proposed which is based on modern objectoriented technology of analysis and designing. The following aspects are considered: simplicity of maintenance and use, scalability, an ability of porting to different operating systems and hardware platforms.

DISCRETE HARTLEY TRANSFORMATION AND ITS APPLICATION B.P. Sabanin VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 7584.
Discrete Hartley transformation and its fast algorithm implementation are considered. Twodimensional linear convolution is developed and being discussed as Hartley transformation application. Some test results and comparison with alternate convolution implementation on the base of fast Fourier transformation are given.

ON RELATIONSHIP BETWEEN A MATRIX DETERMINANT AND ITS MINORS A.A. Kibkalo VANT. Ser.: Mat. Mod. Fiz. Proc. 1997. No 4. P. 8587.
The theorem of relationship between a matrix determinant and its minors is proved. The obtained results may be used both for analytical studies and computation practice.

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