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revolve.c
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revolve.c
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/* Wrapper to Andreas Griewank's REVOLVE. See the documentation following
mexFunction. */
#include <stdio.h>
#include <stdlib.h>
#include <mex.h>
/* #include "revolve.h" */
enum action { advance, takeshot, restore, firsturn, youturn, terminate, error};
double expense(int steps, int snaps);
int maxrange(int ss, int tt);
int adjustsize(int* steps, int* snaps, int* reps);
enum action revolve(int* check,int* capo,int* fine,int snaps,int* info);
/* [action check capo fine info] = revolve(check,capo,fine,snaps,info) */
void mexFunction(int nlhs, mxArray **plhs, int nrhs, const mxArray **prhs)
{
enum action whatodo;
char* saction = "terminate";
int check, capo, fine, steps, snaps, info;
if (nrhs != 5 || nlhs != 5)
mexErrMsgTxt("Usage: [action capo check fine info] = "
"revolve(check,capo,fine,snaps,info)");
check = (int) mxGetScalar(prhs[0]);
capo = (int) mxGetScalar(prhs[1]);
fine = (int) mxGetScalar(prhs[2]);
snaps = (int) mxGetScalar(prhs[3]);
info = (int) mxGetScalar(prhs[4]);
whatodo = revolve(&check, &capo, &fine, snaps, &info);
switch (whatodo) {
case advance: saction = "advance"; break;
case takeshot: saction = "takeshot"; break;
case firsturn: saction = "firsturn"; break;
case youturn: saction = "youturn"; break;
case restore: saction = "restore"; break;
case terminate: saction = "terminate"; break;
case error:
if (info == 14)
mexErrMsgTxt("REVOLVE: number of SNAPS exceeds CHECKUP, increase\n"
"constant CHECKUP and recompile.");
else {
char msg[128];
sprintf(msg, "REVOLVE: error = %d", info);
mexErrMsgTxt(msg);
}
break;
}
plhs[0] = mxCreateString(saction);
plhs[1] = mxCreateDoubleScalar((double) check);
plhs[2] = mxCreateDoubleScalar((double) capo);
plhs[3] = mxCreateDoubleScalar((double) fine);
plhs[4] = mxCreateDoubleScalar((double) info);
}
/* ----------------------------------------------------------------------------
* What follows was downloaded from TOMS. See the following documentation for
* further information and attribution.
*/
/* -----
* The function REVOLVE coded below is meant to be used as a *
* "controller" for running a time-dependent applications program *
* in the reverse mode with checkpointing described in the paper *
* "Achieving logarithmic Growth in temporal and spatial complexity *
* in reverse automatic differentiation", Optimization Methods and *
* Software, Vol.1 pp. 35-54. *
* A postscript source of that paper can be found in the ftp sites *
* info.mcs.anl.gov and nbtf02.math.tu-dresden.de. *
* Apart from REVOLVE this file contains five auxiliary routines *
* NUMFORW, EXPENSE, MAXRANGE, and ADJUST. *
* *
*--------------------------------------------------------------------*
* *
* To utilize REVOLVE the user must have procedures for *
* - Advancing the state of the modeled system to a certain time. *
* - Saving the current state onto a stack of snapshots. *
* - Restoring the the most recently saved snapshot and *
* restarting the forward simulation from there. *
* - Initializing the adjoints at the end of forward sweep. *
* - Performing one combined forward and adjoint step. *
* Through an encoding of its return value REVOLVE asks the *
* calling program to perform one of these 'actions', which we will *
* refer to as *
* *
* 'advance', 'takeshot', 'restore', 'firsturn' and 'youturn' .*
* There are two other return values, namely *
* 'terminate' and 'error' *
* which indicate a regular or faulty termination of the calls *
* to REVOLVE. *
* *
* The action 'firsturn' includes a 'youturn', in that it requires *
* -advancing through the last time-step with recording *
* of intermediates *
* -initializing the adjoint values (possibly after *
* performing some IO) *
* -reversing the last time step using the record just written *
* The action 'firsturn' is obtained when the difference FINE-CAPO *
* has been reduced to 1 for the first time. *
* *
*--------------------------------------------------------------------*
* *
* The calling sequence is *
* *
* REVOLVE(CHECK,CAPO,FINE,SNAPS,INFO) *
* *
* with the return value being one of the actions to be taken. The *
* calling parameters are all integers with the following meaning *
* *
* CHECK number of checkpoint being written or retrieved *
* CAPO beginning of subrange currently being processed *
* FINE end of subrange currently being processed *
* SNAPS upper bound on number of checkpoints taken *
* INFO determines how much information will be printed *
* and contains information about an error occured *
* *
* Since REVOLVE involves only a few integer operations its *
* run-time is truly negligible within any nontrivial application. *
* *
* The parameter SNAPS is selected by the user (possibly with the *
* help of the routines EXPENSE and ADJUST described below ) and *
* remains unchanged throughout. *
* *
* The pair (CAPO,FINE) always represents the initial and final *
* state of the subsequence of time steps currently being traversed *
* backwards. *
* *
* The conditions *
* CHECK >= -1 and CAPO <= FINE *
* are necessary and sufficient for a regular response of REVOLVE. *
* If either condition is violated the value 'error' is returned. *
* *
* The first call to REVOLVE must be with CHECK=-1 so that *
* appropriate initializations can be performed internally. *
* *
* When CHECK =-1 and CAPO = FINE then 'terminate' is returned as *
* action value. This combination necessarily arises after a *
* sufficiently large number of calls to REVOLVE, which depends *
* only on the initial difference FINE-CAPO. *
* *
* The last parameter INFO determines how much information about *
* the actions performed will be printed. When INFO =0 no *
* information is sent to standard output. When INFO > 0 REVOLVE *
* produces an output that contains a prediction of the number of *
* forward steps and of the factor by which the execution will slow *
* down. When an error occurs, the return value of INFO contains *
* information about the reason: *
* *
* INFO = 10: number of checkpoints stored exceeds CHECKUP, *
* increase constant CHECKUP and recompile *
* INFO = 11: number of checkpoints stored exceeds SNAPS, ensure *
* SNAPS greater than 0 and increase initial FINE *
* INFO = 12: error occurs in NUMFORW *
* INFO = 13: enhancement of FINE, SNAPS checkpoints stored, *
* SNAPS must be increased *
* INFO = 14: number of SNAPS exceeds CHECKUP, increase constant *
* CHECKUP and recompile *
* INFO = 15: number of REPS exceeds REPSUP, increase constant *
* REPSUP and recompile *
* *
*--------------------------------------------------------------------*
* *
* Some further explanations and motivations: *
* *
* There is an implicit bound on CHECK through the dimensioning of *
* the integer array CH[CHEKUP] with CHECKUP = 64 being the default.*
* If anybody wants to have that even larger he must change the *
* source. Also for the variable REPS an upper bound REPSUP is *
* defined. The default value equals 64. If during a call to *
* TREEVERSE a (CHECKUP+1)-st checkpoint would normally be called *
* for then control is returned after an appropriate error message. *
* When the calculated REPS exceeds REPSUP also an error message *
* occurs. *
* During the forward sweep the user is free to change the last *
* three parameters from call to call, except that FINE may never *
* be less than the current value of CAPO. This may be useful when *
* the total number of time STEPS to be taken is not a priori *
* known. The choice FINE=CAPO+1 initiates the reverse sweep, which *
* happens automatically if is left constant as CAPO is eventually *
* moved up to it. Once the first reverse or restore action has *
* been taken only the last two parameters should be changed. *
* *
*--------------------------------------------------------------------*
* *
* The necessary number of forward steps without recording is *
* calculated by the function *
* *
* NUMFORW(STEPS,SNAPS) *
* *
* STEPS denotes the total number of time steps, i.e. FINE-CAPO *
* during the first call of REVOLVE. When SNAPS is less than 1 an *
* error message will be given and -1 is returned as value. *
* *
*--------------------------------------------------------------------*
* *
* To choose an appropriated value of SNAPS the function *
* *
* EXPENSE(STEPS,SNAPS) *
* *
* estimates the run-time factor incurred by REVOLVE for a *
* particular value of SNAPS. The ratio NUMFORW(STEPS,SNAPS)/STEPS *
* is returned. This ratio corresponds to the run-time factor of *
* the execution relative to the run-time of one forward time step. *
* *
*--------------------------------------------------------------------*
* *
* The auxiliary function *
* *
* MAXRANGE(SNAPS,REPS) *
* *
* returns the integer (SNAPS+REPS)!/(SNAPS!REPS!) provided *
* SNAPS >=0, REPS >= 0. Otherwise there will be appropriate error *
* messages and the value -1 will be returned. If the binomial *
* expression is not representable as a signed 4 byte integer, *
* greater than 2^31-1, this maximal value is returned and a *
* warning message printed. *
* *
*--------------------------------------------------------------------*
* *
* Furthermore, the function *
* *
* ADJUST(STEPS) *
* *
* is provided. It can be used to determine a value of SNAPS so *
* that the increase in spatial complexity equals approximately the *
* increase in temporal complexity. For that ADJUST computes a *
* return value satisfying SNAPS ~= log_4 (STEPS) because of the *
* theory developed in the paper mentioned above. *
* *
*--------------------------------------------------------------------*/
/*#define checkup 64
#define repsup 64 */
#define checkup 1024
#define repsup 256
#define MAXINT 2147483647
struct
{
int advances;
int takeshots;
int commands;
} numbers;
/* ************************************************************************* */
int numforw(int steps, int snaps)
{
int reps, range, num;
if (snaps < 1)
{
printf(" error occurs in numforw: snaps < 1\n");
return -1;
}
if (snaps > checkup)
{
printf(" number of snaps=%d exceeds checkup \n",snaps);
printf(" redefine 'checkup' \n");
return -1;
}
reps = 0;
range = 1;
while(range < steps)
{
reps += 1;
range = range*(reps + snaps)/reps;
}
if (reps > repsup)
{
printf(" number of reps=%d exceeds repsup \n",reps);
printf(" redefine 'repsup' \n");
return -1;
}
num = reps * steps - range*reps/(snaps+1);
return num;
}
/* ************************************************************************* */
double expense(int steps, int snaps)
{
double ratio;
if (snaps < 1)
{
printf(" error occurs in expense: snaps < 0\n");
return -1;
}
if (steps < 1)
{
printf(" error occurs in expense: steps < 0\n");
return -1;
}
ratio = ((double) numforw(steps,snaps));
if (ratio == -1)
return -1;
ratio = ratio/steps;
return ratio;
}
/* ************************************************************************* */
int maxrange(int ss, int tt)
{
int i, ires;
double res = 1.0;
if((tt<0) || (ss<0))
{
printf("error in MAXRANGE: negative parameter");
return -1;
}
for(i=1; i<= tt; i++)
{
res *= (ss + i);
res /= i;
if (res > MAXINT)
{
ires=MAXINT;
printf("warning from MAXRANGE: returned maximal integer %d\n",ires);
return ires;
}
}
ires = res;
return ires;
}
/* ************************************************************************* */
int adjust(int steps)
{
int snaps, s, reps;
snaps = 1;
reps = 1;
s = 0;
while( maxrange(snaps+s, reps+s) > steps )
s--;
while( maxrange(snaps+s, reps+s) < steps )
s++;
snaps += s;
reps += s ;
s = -1;
while( maxrange(snaps,reps) >= steps )
{
if (snaps > reps)
{
snaps -= 1;
s = 0;
}
else
{
reps -= 1;
s = 1;
}
}
if ( s == 0 )
snaps += 1 ;
if ( s == 1 )
reps += 1;
return snaps;
}
/* ************************************************************************* */
enum action revolve(int* check,int* capo,int* fine,int snaps,int* info)
{
static int turn, reps, range, ch[checkup], oldsnaps, oldfine;
int ds, oldcapo, num, bino1, bino2, bino3, bino4, bino5;
/* (*capo,*fine) is the time range currently under consideration */
/* ch[j] is the number of the state that is stored in checkpoint j */
numbers.commands += 1;
if ((*check < -1) || (*capo > *fine))
return error;
if ((*check == -1) && (*capo < *fine))
{
if (*check == -1)
turn = 0; /* initialization of turn counter */
*ch = *capo-1;
}
switch(*fine-*capo)
{
case 0: /* reduce capo to previous checkpoint, unless done */
if(*check == -1 || *capo==*ch )
{
*check -= 1;
if (*info > 0)
{
printf(" \n advances: %5d",numbers.advances);
printf(" \n takeshots: %4d",numbers.takeshots);
printf(" \n commands: %5d \n",numbers.commands);
}
return terminate;
}
else
{
*capo = ch[*check];
oldfine = *fine;
return restore;
}
case 1: /* (possibly first) combined forward/reverse step */
*fine -= 1;
if(*check >= 0 && ch[*check] == *capo)
*check -= 1;
if(turn == 0)
{
turn = 1;
oldfine = *fine;
return firsturn;
}
else
{
oldfine = *fine;
return youturn;
}
default:
if(*check == -1 || ch[*check] != *capo)
{
*check += 1 ;
if(*check >= checkup)
{
*info = 10;
return error;
}
if(*check+1 > snaps)
{
*info = 11;
return error;
}
ch[*check] = *capo;
if (*check == 0)
{
numbers.advances = 0;
numbers.takeshots = 0;
numbers.commands = 1;
oldsnaps = snaps;
if (snaps > checkup)
{
*info = 14;
return error;
}
if (*info > 0)
{
num = numforw(*fine-*capo,snaps);
if (num == -1)
{
*info = 12;
return error;
}
printf(" prediction of needed forward steps: %8d => \n",num);
printf(" slowdown factor: %8.4f \n\n",((double) num)/(*fine-*capo));
}
}
numbers.takeshots += 1;
oldfine = *fine;
return takeshot;
}
else
{
if ((oldfine < *fine) && (snaps == *check+1))
{
*info = 13;
return error;
}
oldcapo = *capo;
ds = snaps - *check;
if (ds < 1)
{
*info = 11;
return error;
}
reps = 0;
range = 1;
while(range < *fine - *capo)
{
reps += 1;
range = range*(reps + ds)/reps;
}
if (reps > repsup)
{
*info = 15;
return error;
}
if (snaps != oldsnaps)
{
if (snaps > checkup)
{
*info = 14;
return error;
}
}
bino1 = range*reps/(ds+reps);
bino2 = (ds > 1) ? bino1*ds/(ds+reps-1) : 1;
if (ds == 1)
bino3 = 0;
else
bino3 = (ds > 2) ? bino2*(ds-1)/(ds+reps-2) : 1;
bino4 = bino2*(reps-1)/ds;
if (ds < 3)
bino5 = 0;
else
bino5 = (ds > 3) ? bino3*(ds-2)/reps : 1;
if (*fine-*capo <= bino1 + bino3)
*capo = *capo+bino4;
else
{
if (*fine-*capo >= range - bino5)
*capo = *capo + bino1;
else
*capo = *fine-bino2-bino3;
}
if (*capo == oldcapo)
*capo = oldcapo+1;
numbers.advances = numbers.advances + *capo - oldcapo;
oldfine = *fine;
return advance;
}
}
free(ch);
}