Patent Application: US-79687085-A

Abstract:
this invention provides a computing device which calculates the total energy and total pairwise , central forces between selected pairs of interacting particles within a system . the device comprises a means for generating both a retrievable identifier for the spatial coordinates of a particle i and retrievable identifiers of the type of pairwise , central interaction between i and a second particle j ; a means for determining r 2 , the square of the radius vector between i and j ; a means for determining r , the square root of r 2 ; a means for calculating energy and force / r values for each ij pair ; means for determining the force on each particle ; and means for accumulating energy and force / r values for each ij particle pair .

Description:
the processor can functionally be broken into five units , as shown in fig2 : unit i : the neighbor list . this contains the addresses necessary to look up the coordinates of the individual atoms ; an ij bit which identifies an atom as an i or a j atom ; and a pair type , which indicates the type of pair a atom forms with the most recently accessed i atom . each clock cycle , these three atom oriented pieces of information are delivered to the other units . unit ii : the r squared calculation . this unit contains the coordinate memories , and the associated hardware to calculate unit iii : the r calculation . this unit performs a quadratic table look - up to obtain the value of r , given the value of r squared . unit iv : the energy and force / r tables . this unit contains the quadratically - interpolated tables used to look up the energy and the magnitude of the force / r between a j atom and the most recently considered i atom . the energy and the force / r sections are identical , and consist of weighted sums of two contributions : for the energy , the coefficient tables a , b , c , and d contain information relating to the products of the partial charges ( q 1 × q 2 ) on the atoms and information relating to the van der waals forces , as is well known . unit v : the energy and force accumulators . this unit contains sum accumulation memories which accumulate the total energies associated with a few selected classes of atoms and the total force components associated with each atom . the components are calculated by multiplying f / r by ( x i - x j ) to obtain f x etc . throughout the diagram , various delays , either labelled &# 34 ; delay &# 34 ; or &# 34 ; d &# 34 ;, have been indicated . these are either file register delays ( where the delays are long ) or shift register delays ( where the delays are short ). these delays guarantee the arrival of information pertaining to a given pair at the appropriate input to a unit in synch . the quadratic interlopers , shown schematically in fig3 are used to look up the values of the energy , the force / r , and the square root . the central memories , y 0 , y &# 39 ;, and y &# 34 ;, contain tables of the functional values , slopes , and 1 / 2 times the second derivatives of the desired function . the beginning of the appropriate table for a given pair type is stored in an offset memory . this offset is added to the high order bits of the incoming ( integer ) independent parameter , and the result is used to address the central memories . this value is represented by the letter x in the figure . the adders and multipliers form the combination where d consists of the low order bits of the independent parameter . it is understood that the notation dx represents delta x ; which is , for example , the output of the x - coordinate subtractor in fig2 . there are also two memories , max and min , which store the maximum and minimum addresses of the tables associate with any given pair type . if the generated address falls outside of this range , an &# 34 ; invalid bit &# 34 ; is set . the invention described herein is designed to be extremely flexible and will serve for any currently addressed problem in molecular mechanics . the flexibility arises from the fact that all function evaluations are done as table look - ups in which the functions and their first and second derivatives are stored in tables which represent a local quadratic fit for each function needed . since the tables are loaded from the host computer and can be changed to suit a given problem , new force fields can always be accommodated . in addition , the invention is designed to calculate only the force of each atom due to the pairwise interactions , leaving all other calculations to be done in a programmable array processor . the overall system , consisting of the device of this invention , the array processor , a host computer , mass storage , and communications and display hardware , will yield speeds roughly an order of magnitude greater than those available on cray - 1 - ls or cyber 205 for molecular mechanics calculations . on any general purpose computer , the most time intensive part of the calculation is the evaluation of the interaction energy and the vector forces on each atom . once the 3n component force vector is formed , a much smaller computation consists of updating the 3n coordinates of the atoms given the forces and total energy . to limit the size of the calculation , most investigators carrying out simulations or minimizations generate a list of atom - pairs which are close enough to each other to be included in the force and energy calculation . the size of these pair - lists or &# 34 ; neighbor &# 34 ; lists depend on the distance cutoff used in the force and energy calculations and may vary for different energy types . the pair - list must be regenerated as the atoms move and the number of interactions , or time steps , between the regenerations will depend on the number of neighbors we assume for each atom . the larger the pair - list , the less often it must be regenerated , and in operation the system will have to be optimized for each problem with respect to pair - list size . the overall hardware architecture of the present invention , which mirrors the software architecture described above , is shown in fig1 . there are two central modules , one of which is home built and the other of which is a commercially available array processor . the home built module , the device of this invention , calculates the total energy and vector force on each atom due to pairwise forces only . the commercial array processor calculates those forces involving 3 or 4 atoms ( torsional terms , angle bending terms , cross terms ), and uses these results combined with those from the device of this invention to update the coordinates to a new molecular conformation . roughly 95 % of the time spent in a calculation on a conventional computer is spent evaluating the pairwise forces ; as such , this device has been designed to give speeds roughly ten times greater than those available on supercomputers of the cray - ls class . by concentrating on the pairwise forces , only those portions of the inner loop which are the most time intensive and stable are frozen in hardware . the implementation of the coordinate update in a programmable array processor allows flexibility in tailoring the integration or minimization technique to a specific problem . the overall schematic of this device is shown in fig2 . the architecture adopted is a parallel , synchronous pipeline . each element in the machine is a multiplier , an adder , or a table look - up . most arithmetic is done in 32 bit floating point , and is accomplished by utilizing commercially available 32 bit floating point chips recently introduced by the weitek corporation . accumulation of forces and energies is done to higher bit precision , and the pipeline cycle time is 100ns . each clock cycle , an entry corresponding to an atom is etched from a pair list memory . the structure of the pair - list is such that every i atom entry ( slow moving index of a j pair ) is followed by all j i atom entries ( fast moving index ) in the list . each entry ( 32 bit total ) consists of a coordinate address , used to look up the coordinates of that atom ; a pair type ( j atoms only ), which identifies the type of interaction which that j atom forms with the most recent i atom ; and an ij bit , which identifies the atom as an i or j atom . the coordinate addresses are fed simultaneously to three coordinate memories ( x , y , and z ). these coordinates are passed to one of the inputs of three subtractors . if the atom is an i atom , nothing happens except that an empty cycle is generated . if the atom is a j atom , the subtraction is done to form delta - x , delta - y , and delta - z . these are squared and summed to form delta - r , squared , which is used as input to a table look - up to obtain the value of an interpolation function , which in the present invention is a square root table yielding r . this r , along with the pairtype which describes what kind of pair of atoms this ij pair is , is then used to look up the value of the energy and the value of f / r . the cartesian components of the force vector are obtained by multiplying f / r by delta - x , delta - y , and delta - z , and the total energy and the force vector memories are updated . in order to limit the total size of memory , the energy and the value of f / r are both calculated as a sum of two contributions , i . e . as e = a ( pt )* ea ( pt , r ) + b ( pt )* eb ( pt , r ), where pt is the pair type and r is the scalar distance between the atoms comprising the pair . since all function evaluations , including the square root , are handled by table lookups , this device is memory intensive . more specifically , as shown in fig2 the coefficient tables and interpolated tables are accessed or addressed by the pair - type ( pt ) information acting as retrievable identifiers , so that the proper coefficient corresponding to the particular pair - type under scrutiny is read out from the table . overall , there are about 5 - 10 mbytes of memory distributed , throughout the system when it is equipped to handle 16 , 000 atoms and 1 , 000 , 000 interacting pairs . note that if all hydrogens are included in the calculations , 16 , 000 atoms might require of the order of 1 . 5 million interacting pairs . the system has been designed so that additional pair list memory can be added at any time . each of the table look - ups is done by quadratic interpolation , as shown in fig3 . in each bin , the value of the function , the first derivative , and half of the second derivative are stored . the incoming value of the independent variable is scaled , integerized , and split into high and low order bits . the high order bits are added to an offset which is looked up as a function of the pair type and which gives the starting address of the table associated with that pair type . this sum is used to fetch the value , slope , and half of the second derivative from the tables , and these are used to compute : the energy and force calculator described above has been designed to evaluate pairwise , central forces between objects in three dimensional space only . in the empirical hamiltonian which is usually manipulated in molecular mechanics calculations , there are additional terms associated with bond angle bending , torsional excursions , and out - of - plane excursions which are not pairwise and central . the angle bending terms have been centralized by placing a non - hooks law spring between atoms 1 and 3 in a 1 - 2 - 3 atom triplet which maps out the angular dependence normally used . this introduces a maximum error of 10 % at 10 kt . the torsional terms can be handled in one of two ways : first , by positioning a point in space away from the 1 - 2 - 3 - 4 quadruplet using atoms 1 , 2 and 3 and rigid springs and subsequently dropping a non - hooks law spring to mimic the torsional potential for excursions of the 4th atom ; and second , by calculating these torsional contributions in the array processor which would otherwise be idle during the time the force and energy accumulator is working . the length of the pipe is several hundred cycles , since each weitek chip is 9 cycles deep internally . this effectively limits the minimum size the problem which is worth running of on this device , since a problem involving several hundred pairs would incur an effective overhead of a factor of two . however , this overhead is insignificant for typical problems involving proteins or dna , since the number of pairs for these problems is typically two orders of magnitude greater than the length of the pipe . for any problem , once the pipe is full , a pair is evaluated every 100ns . this speed can be compared to that which is available on several general purpose machines ; on a vax 780 with a floating point accelerator , a pair can be evaluated every 150 μs using assembler code . on a cyber 205 , a benchmark provided by osguthorpe et al ( osguthorpe , d . g ., p . dauber - osguthorpe , kitson , d ., wolff , j . and hagler , a . t ., a state of the art calculation of a biological system using a cyber 205 supercomputer ), achieves the evaluation of a pair every 600ns but only if there is no pair list and all pairs are evaluated . on a star st100 array processor , it is possible to evaluate a pair every 1 - 2 μs using microcoded routines with a pair - list . the device of this invention has been designed around the idea of easy maintainability . all tables are connected to a slow bus ( q bus ) and can be down loaded either from the host vax or through a resident motorola 68010 microprocessor . the system is designed so that a single step mode is available for debugging , with selected pipeline registers readable from the slow bus . the hardware is being implemented in 6 layer dec boards ( 13 &# 34 ;× 18 &# 34 ;), with interboard connections implemented through the back plane and via ribbon cable . there are approximately 20 different board types . the array processor chosen to complement this device is the star st100 . the star st100 is presently the fastest commercially available array processor , with a theoretical rating of 100 mflop . one feature of this machine which is crucial to this application is its ability to communicate with this device at a high rate , along with its ability to overlap communications and calculations . a crucial performance number for the array processor is the time required to evaluate a torsional couplet and resolve the forces into cartesian components on each of the four atoms . this involves four square roots or divides , along with about 35 multiplies or adds . the st100 is capable of evaluating a torsional couplet as a pipelined routine in 1 . 6 us , which is roughly ten times faster than its nearest presently available competitor . it is sufficiently fast to allow evaluation of torsional and angle bending terms during the time this device is evaluating the non - bonded pairwise central terms for most systems of biological interest . another crucial task assigned to the array processor is the updating of the pair - list . the pair - list is separated into two different parts containing fixed and variable pairs . the fixed pairs reflect the chemical connectivity of the atoms and thus do not change as the positions of the atoms move during the calculations . the variable pair - list is the one which is recalculated in the array processor after a number of iterations of the coordinate updates . the fixed pairlist is calculated once in the host and only changed by it if the connectivity changes . the structure of the star st100 permits rapid generation of the variable pair - list . although the details of the algorithm are flexible and change as , for example , boundary conditions change , a pair of atoms can be considered and accepted a lying within as cutoff in 3 equivalent cycles ( 3 pairs in 9 cycles ; each cycle in the st100 is 40 ns ). the speed of this device as measured in megaflops / sec ( m flops ) is simple to determine . the weitek computing chips perform one floating point operation every clock cycle ( 100ns ); that is , they operate at the rate of 10 m flops each . there are about sixty weitek chips in fastrun ; thus , it operates at a speed of 600 m flops once the pipe is full . note that , as discussed above , it takes several hundred cycles to fill the pipe . for a typical problem involving protein and solvent , this represents an overhead of about one percent . there is also an overhead associated with the introduction of each i atom into the pipe , since this generates an empty cycle . since each i atom is followed in practice by 50 to 100 ] atoms ( depending on the cutoff used ), this represents a one to two percent overhead to the operation of the device of this invention . the total fraction of running time ( i . e ., duty - cycle for this device ) varies depending on what algorithm is being used in the star to update the coordinates . however , it would be above 70 % for molecular dynamics using verlet integration , conjugate gradient energy minimization , and most monte carlo schemes . there are several ways in which future systems using a similar architecture can be made faster . the most obvious is to use faster calculating chips along with faster memory , and this will certainly happen as the technology develops . in addition , one can consider ways in which some aspects of the calculations can be done in parallel without duplicating all of the memories . however , at this time , it is not obvious that it would be practical to install more than four memory shared parallel pipes with the present architecture . thus , one can see ways of getting to several gigaflops in computing speed but much faster systems would probably require a very high order of parallelism in a very different architecture . an orthogonal future development might involve the installation of 64 bit multipliers and adders as they become cost competitive at 100 ns speeds . there are applications which would gain significantly by this increase in precision . the development of a 64 bit machine , while not trivial since all pathways and memories double in size , is feasible and would be strongly aided by the prior development of a 32 bit / 64 bit hybrid ; 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