////////////////////////////////////////////////////////////////////////////// // // // _ _ __ _ ____ // // __| | ___ __| | / _|| |_ |___ \ ___ // // / _` | / _ \ / _` || |_ | __| __) | / __| // // | (_| || (_) | | (_| || _|| |_ / __/ _| (__ // // \__,_| \___/_____\__,_||_| \__||_____|(_)\___| // // |_____| // // // ////////////////////////////////////////////////////////////////////////////// // // // Copyright (c) 2013 by S.F.T. Inc. - All rights reserved // // Use, copying, and distribution of this software may be licensed // // using a GPLv2, GPLv3, MIT, or BSD license, as appropriate. // // // // OR - if you prefer - just use/distribute it without ANY license. // // But I'd like some credit for it. A favorable mention is appreciated. // // // ////////////////////////////////////////////////////////////////////////////// #define _GNU_SOURCE #include #include #include #include #include #include #include //************************************************************************** // build command: cc -O3 -o do_dft2 do_dft2.c -lm -lpthread // // you can add '-D' directives as appropriate (such as '-DUSE_FAST_SINCOS') //************************************************************************** // approximate value of pi beyond precision of double #define _PI_ 3.1415926535897932384626433832795028841971693993751 #define MAX_HARMONIC 4096 //#define USE_FAST_SINCOS /* define this out to use the fast sin/cos instead of the 'libc' sin/cos */ //#define TEST_FAST_SINCOS /* define this to include the test '-!' for fast sin/cos */ #ifdef __gnu_linux__ #define HAS_SINCOS /* this should work for all GNU-LINUX implementations */ // NOTE: if this causes build problems, please let me know. #endif // __gnu_linux__ // NOTE: FreeBSD's libc does not have 'sincos', nor do any of the ports // for gcc, as far as I can tell. It's a GNU extension. #ifdef USE_FAST_SINCOS #define sin fast_sin #define cos fast_cos #define sincos fast_sincos double dDebugY = 0.0; int wDebugIndex = -1; void fast_sincos(double dTheta, double *pSin, double *pCos); double fast_cos(double); double fast_sin(double); #ifndef HAS_SINCOS #define HAS_SINCOS #endif // HAS_SINCOS static const float _SIN_VALUES_[]; static const float * const _COS_VALUES_; #endif // USE_FAST_SINCOS typedef struct _XY_ { double dX; double dY; } XY; typedef struct _MY_XY_ { XY *pData; int nItems; // # of items int nSize; //memory block size } MY_XY; typedef struct _WORK_UNIT_ { double *pdA, *pdB; XY *pData; int nVal; double dC, dX0, dXY; // for retest and for scaling X(Xnew = X * dXY + dX0, use 0.0 and 1.0 to leave X as - is) long lStart, lEnd; double dRval; // NOTE: cannot be 'passed in', initial value will be 0.0 volatile long lState; // initially zero, non - zero when thread has finished pthread_t idThread; // caller waits on this object; object must be free 'd by caller via pthread_detach // call pthread_join when finished to properly clean up and get err return } WORK_UNIT; WORK_UNIT *create_work_unit(double *pdA, double *pdB, double dC, XY * pData, int nVal, double dX0, double dXY, long lStart, long lEnd, void *(*callback) (void *), int iThreadFlag) { WORK_UNIT *pRval = (WORK_UNIT *) malloc(sizeof(WORK_UNIT)); if(!pRval) { return NULL; } pRval->pdA = pdA; pRval->pdB = pdB; pRval->dC = dC; pRval->pData = pData; pRval->nVal = nVal; pRval->dX0 = dX0; pRval->dXY = dXY; pRval->lStart = lStart; pRval->lEnd = lEnd; pRval->dRval = 0.0; pRval->lState = 0; pRval->idThread = 0; // initially if(!iThreadFlag) // direct call, useful for first work unit(after spawning others) { // fprintf(stderr, "TEMPORARY: call direct\n"); // fflush(stderr); if(callback(pRval)) { free(pRval); return NULL; } return pRval; // so I can get the return info } // fprintf(stderr, "TEMPORARY: spawn thread\n"); // fflush(stderr); if(pthread_create(&(pRval->idThread), NULL, callback, (void *)pRval)) { if(pRval->idThread) { pthread_cancel(pRval->idThread); pRval->idThread = 0; } free(pRval); return NULL; } return pRval; } // determining # of cpus (workaround) #define THREAD_COUNT 16 static unsigned long long MyGetTick(void) { static unsigned long long iMyTick = 0; static unsigned long long lLastTickCount; static int iFirstTime = 1; struct timeval tv; long long lTick; gettimeofday(&tv, NULL); lTick = (long long)tv.tv_sec * (long long)1000000 + (long long)tv.tv_usec; if(iFirstTime) { lLastTickCount = lTick; iMyTick = lTick; iFirstTime = 0; } else { iMyTick += lTick - lLastTickCount; //TODO:improve this for wraparound? lLastTickCount = lTick; } return (iMyTick); } static void *thread_proc(void *pNothing) { volatile long *pMe = pNothing ? (volatile long *)pNothing : (volatile long *)&(pMe); volatile long long l1; unsigned long long lStart; int i1; usleep(1000); if(pNothing) { while(!*pMe) { usleep(100); } } lStart = MyGetTick(); for(i1 = 0; i1 < 1000000; i1++) { l1 += *pMe; } if(pNothing) { *((long *)pNothing) = MyGetTick() - lStart; return 0; } return (void *)(MyGetTick() - lStart); } int cpu_count0(void) { pthread_t thr[THREAD_COUNT] = {NULL}; static volatile long lResult[THREAD_COUNT] = {0}; long lResult0, lResultTTL; int i1; lResult0 = (long)thread_proc(0); usleep(1000); for(i1 = 0; i1 < THREAD_COUNT; i1++) { thr[i1] = NULL; //make sure if(pthread_create(&(thr[i1]), NULL, thread_proc, (void *)&(lResult[i1]))) { while(i1 >= 0) { if(thr[i1]) { pthread_cancel(thr[i1]); } i1--; } return -2; } } for(i1 = 0; i1 < THREAD_COUNT; i1++) { lResult[i1] = 1; } for(i1 = 0, lResultTTL = 0; i1 < THREAD_COUNT; i1++) { if(pthread_join(thr[i1], NULL)) { fprintf(stderr, "thread canceled\n"); pthread_cancel(thr[i1]); continue; } lResultTTL += lResult[i1]; } // printf("%ld %ld\n", lResultTTL, lResult0); lResultTTL += lResultTTL / 2; // for round-off, add 75 % lResultTTL /= (THREAD_COUNT * lResult0); // printf("Total CPU: %ld\n", lResultTTL); return (int)lResultTTL; } static int my_int_cmp(const void *p1, const void *p2) { int i1 = *((const int *)p1) - *((const int *)p2); return i1 > 0 ? 1 : (i1 < 0 ? -1 : 0); } int cpu_count(void) { int i1, i2[THREAD_COUNT]; for(i1 = 0; i1 < THREAD_COUNT; i1++) { i2[i1] = cpu_count0(); } qsort(i2, sizeof(i2[0]), THREAD_COUNT, my_int_cmp); return i2[THREAD_COUNT / 2]; } ///////////////////////////////////////////////////////////////////////////// // FUNCTION: dFourier // // on entry 'aVal' is array of XY, 'nVal' is # of entries in aVal, // nH is # harmonic (sin,cos) coefficients to generate [excluding '0'] // and 'dA' and 'dB' are the sin and cos arrays, and 'dC' is the 'C0' value. // and 'nWU' is the # of 'work units' (using pthreads) // // note: list must be sorted by X value, no duplicate X values // ///////////////////////////////////////////////////////////////////////////// void *dFourier_work(void *pV) { WORK_UNIT *pW = (WORK_UNIT *) pV; int i1, i2, i3; double dX, dY, dX0, dXY; XY *aVal; int nVal; double dRval, *dA, *dB; if(!pV) { return NULL; } dRval = 0; aVal = pW->pData; nVal = pW->nVal; dA = pW->pdA; dB = pW->pdB; dX0 = pW->dX0; dXY = pW->dXY; for(i1 = pW->lStart, i3 = pW->lEnd; i1 <= i3; i1++) { for(i2 = 0; i2 < nVal; i2++) { if(!i1) { dRval += aVal[i2].dY; // printf("temporary: item %d X=%g\n",i2, (double)(dX0 + aVal[i2].dX * dXY)); } else { double dS, dC, dXNew = i1 * (dX0 + aVal[i2].dX * dXY); #ifdef HAS_SINCOS // GNU linux and when I do 'fast sin/cos' sincos(dXNew, &dS, &dC); // NOTE: 'sincos' should be slightly faster than individual calls #else // HAS_SINCOS dS = sin(dXNew); dC = cos(dXNew); #endif // HAS_SINCOS dA[i1 - 1] += aVal[i2].dY * dC; dB[i1 - 1] += aVal[i2].dY * dS; } } } pW->dRval = dRval; pW->lState = 1; // to say I 'm done return 0; } void dFourier(XY * aVal, int nVal, int nH, double *dC, double *dA, double *dB, int nWU, int iAutoScale) { int i1, i2, iW; double dX, dY, dX0, dXY; WORK_UNIT *aW[THREAD_COUNT] = {0}; *dC = 0.0; // fprintf(stderr, "call to dFourier, %d work units\n", nWU); // fflush(stderr); // usleep(10000); // assume sorted list, calculate X0, XY for x = -PI to PI if(!iAutoScale) { dXY = 1.0; dX0 = 0.0; } else { dXY = 2.0 * _PI_ / (aVal[nVal - 1].dX + (aVal[nVal - 1].dX - aVal[0].dX) / (nVal - 1)); dX0 = -dXY * aVal[0].dX - _PI_; // derived from -_PI_ == dX0 + dXY * aVal[0].dX } if(nH < nWU) { nWU = nH; } if(nVal < 1024) { nWU = 1; } for(i1 = 0; i1 < nH; i1++) { dA[i1] = dB[i1] = 0.0; // zero this out } for(iW = 0, i1 = 0; iW < nWU; iW++) { i2 = (iW + 1) * nH / nWU; // next i1 if(i2 <= i1) { continue; // just in case } if(i2 >= nH || (iW == (nWU - 1))) { i2 = nH + 1; // to make sure I capture the last data point in the work unit } // fprintf(stderr, "temporary: work unit %d\n", iW); // fflush(stderr); aW[iW] = create_work_unit(dA, dB, 0.0, aVal, nVal, dX0, dXY, i1, i2 - 1, dFourier_work, iW < (nWU - 1) ? 1 : 0); i1 = i2; // "next" if(i2 >= nH) { break; // safety(for now) } } //now we must wait for all of the work units to complete for(iW = 0; iW < nWU; iW++) { if(!aW[iW]) { continue; } if(aW[iW]->idThread) { pthread_join(aW[iW]->idThread, NULL); // ignore any error for now // pthread_detach(&(aW[iW].idThread); *dC += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC' } else // not a thread, keep 'dC' return here also { *dC += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC' } free(aW[iW]); aW[iW] = NULL; // by convention } // fix up arrays and whatnot *dC /= nVal; // C0 must be half A[0] i.e Y = A[0] / 2 +[sum n = 1 - ?] An *cos(n * X) + Bn * sin(n * X) // see http : //en.wikipedia.org / wiki / Fourier_series for(i1 = 0; i1 < nH; i1++) { dA[i1] *= 2.0 / nVal; dB[i1] *= 2.0 / nVal; } } // FUNCTION:xy_comp - sort compare for 'XY' structure int xy_comp(const void *p1, const void *p2) { int iRval = ((XY *) p1)->dX - ((XY *) p2)->dX; if(iRval > 0) { return 1; } if(iRval < 0) { return -1; } return 0; } //FUNCTION:get_xy_data - file input of X and Y values(space delimiter) MY_XY get_xy_data(FILE * pIn) { char tbuf[512]; double dX, dY; MY_XY xyNULL = {NULL, 0, 0}, xy = {NULL, 0, 0}; while(fgets(tbuf, sizeof(tbuf), pIn)) { if(!xy.pData || xy.nItems * sizeof(xy.pData[0]) >= xy.nSize) { if(xy.nItems > 1024) { xy.nSize = (xy.nItems * 2) * sizeof(xy.pData[0]); } else { xy.nSize = 2048 * sizeof(xy.pData[0]); } if(xy.pData) { void *p1 = realloc(xy.pData, xy.nSize + 1); if(!p1) { free(xy.pData); return xyNULL; } xy.pData = (XY *) p1; } else { xy.pData = (XY *) malloc(xy.nSize); if(!xy.pData) { return xyNULL; } } } dX = dY = 0.0; sscanf(tbuf, "%lg %lg\n", &dX, &dY); // printf("TEMPORARY: data point %d %g %g %s\n", xy.nItems, dX, dY, tbuf); xy.pData[xy.nItems].dX = dX; xy.pData[xy.nItems].dY = dY; xy.nItems++; } // sort data by X qsort(xy.pData, xy.nItems, sizeof(xy.pData[0]), xy_comp); return xy; } void usage(void) { fprintf(stderr, " Copyright (c) 2013 by S.F.T. Inc. - All rights reserved\n" " Use, copying, and distribution of this software may be licensed\n" " using a GPLv2, GPLv3, MIT, or BSD license, as appropriate.\n" "\n" " OR - if you prefer - just use/distribute it without ANY license.\n" " But I'd like some credit for it. A favorable mention is appreciated.\n" "\n" "USAGE: do_dft -h\n" " do_dft [-a|-s m,n][-t nthrd][input_file [input_file [...]]]\n" "where 'input_file' is the name of a file containing rows of sorted X and Y\n" " values delimited by white-space and terminated with LF\n" " and '-a' indicates 'auto scale X' to 0-2pi\n" " and '-s' specifies a range of 'm to n'\n" " and '-t' indicates how many threads you want to use\n" " and '-h' instructs do_dft to print this information\n" " (if no file or '-h' specified, input is 'stdin')\n"); } // check_callback - offloads work for multiple threads to check data and calc std dev void *check_callback(void *pV) { WORK_UNIT *pW = (WORK_UNIT *) pV; int i1, i2, i3; double dX, dY, dX0, dXY, dC; XY *aVal; int nHarm; double dErr, *pdA, *pdB; if(!pV) { return 0; } dErr = 0.0; aVal = pW->pData; nHarm = pW->nVal; pdA = pW->pdA; pdB = pW->pdB; dC = pW->dC; dX0 = pW->dX0; dXY = pW->dXY; for(i1 = pW->lStart; i1 < pW->lEnd; i1++) { double dCheck = dC; for(i2 = 0; i2 < nHarm; i2++) { dCheck += pdA[i2] * cos((i2 + 1) * (aVal[i1].dX * dXY + dX0)) + pdB[i2] * sin((i2 + 1) * (aVal[i1].dX * dXY + dX0)); } // printf(" data point %d\t%g\t%g\t%g\n", i1, xy.pData[i1].dX, xy.pData[i1].dY, dCheck); dErr += (dCheck - aVal[i1].dY) * (dCheck - aVal[i1].dY); } pW->dRval = dErr; pW->lState = 1; return 0; } //////////////// // MAIN /////////////// int main(int argc, char *argv[]) { double dC, dXY, dX0, *pdA = NULL, *pdB = NULL, dErr; int i1, i2, iW; FILE *pIn = stdin; int nHarm, nThread = 0; WORK_UNIT *aW[THREAD_COUNT]; double dScale1 = 0.0, dScale2 = 0.0; int bDoScale = 0; double dXFactor, dXOffset; char tbuf[256]; while(argc > 1) { const char *p1 = argv[1]; char *p2; if(*p1 != '-') { break; } p1++; #if defined(TEST_FAST_SINCOS) && defined(USE_FAST_SINCOS) #undef sin /* I need the original versions for this section */ #undef cos /* so I must un-define them, then re-define them */ #define SINCOS_ACCURACY 0.000001 if(*p1 == '!') { // this is a special switch that allows self-testing the fast sin/cos functions double d1, dS, dC; int i2 = 0; for(i1=0, d1=-2.0 * _PI_ - 0.1; d1 < 2.0 * _PI_ + 0.1; d1 += 0.00001, i1+=4) { fast_sincos(d1, &dS, &dC); if(fabs(cos(d1) - dC) > SINCOS_ACCURACY) { fprintf(stderr, "cos(%0.3f) delta = %0.7f wIndex=%d y=%0.6f\n", d1, fabs(cos(d1) - dC), wDebugIndex, dDebugY); } else { i2++; } if(fabs(sin(d1) - dS) > SINCOS_ACCURACY) { fprintf(stderr, "sin(%0.3f) delta = %0.7f wIndex=%d y=%0.6f\n", d1, fabs(sin(d1) - dS), wDebugIndex, dDebugY); } else { i2++; } if(fabs(cos(d1) - fast_cos(d1)) > SINCOS_ACCURACY) { fprintf(stderr, "cos(%0.3f) delta = %0.7f wIndex=%d y=%0.6f\n", d1, fabs(cos(d1) - fast_cos(d1)), wDebugIndex, dDebugY); } else { i2++; } if(fabs(sin(d1) - fast_sin(d1)) > SINCOS_ACCURACY) { fprintf(stderr, "sin(%0.3f) delta = %0.7f wIndex=%d y=%0.6f\n", d1, fabs(sin(d1) - fast_sin(d1)), wDebugIndex, dDebugY); } else { i2++; } } fprintf(stderr, "Tested %d values, %d in spec\n", i1, i2); return 0; } #define sin fast_sin #define cos fast_cos #endif // USE_FAST_SINCOS, TEST_FAST_SINCOS if(!*p1) { usage(); return -1; } while(*p1) { if(*p1 == 'h') { usage(); if(p1[1] || argc > 2) { return -1; } else { return 0; } } else if(*p1 == 'a') // autoscale { bDoScale = -1; } else if(*p1 == 's') // set scale { bDoScale = 1; p1++; if(!*p1) { argc--; argv++; if(argc < 2) { usage(); return -1; } p1 = argv[1]; } p2 = tbuf; while(*p1 && *p1 != ',') { *(p2++) = *(p1++); } *p2 = 0; dScale1 = atof(tbuf); if(*p1 != ',' || !p1[1]) { usage(); return -1; } p1++; p2 = tbuf; while(*p1 && *p1 != ',') { *(p2++) = *(p1++); } *p2 = 0; dScale2 = atof(tbuf); break; //the parsing stops here for this term } else if(*p1 == 't') // # of threads { p1++; if(*p1) { nThread = atoi(p1); } else { argc--; argv++; if(argc < 2) { usage(); return -1; } nThread = atoi(argv[1]); } if(nThread <= 0) { usage(); return -2; } break; // the parsing stops here for this term } // TODO: other options, like cycle count maybe ? else { usage(); return -2; // unknown option } p1++; } argc--; // in anticipation of other options, this is the loop counter for it argv++; } if(!nThread) { nThread = cpu_count(); //fprintf(stderr, "TEMPORARY: %d threads\n"); } while(argc > 1 || pIn == stdin) { MY_XY xy; if(argc > 1) { pIn = fopen(argv[1], "r"); if(!pIn) { argv++; argc--; continue; } printf("FILE: %s\n", argv[1]); argv++; argc--; } xy = get_xy_data(pIn); fclose(pIn); pIn = NULL; if(!xy.pData || !xy.nItems) { continue; } if(bDoScale > 0) { if(xy.pData[xy.nItems - 1].dX > xy.pData[0].dX) { //assume data is sorted dXFactor = ((dScale2 - dScale1) // the delta scale(normally - pi to pi for autoscale) / (xy.pData[xy.nItems - 1].dX - xy.pData[0].dX)) // the delta X * (double)(xy.nItems - 1) / (double)(xy.nItems); // last data point represents "not quite 2 * pi" dXOffset = dScale1 - xy.pData[0].dX * dXFactor; for(i1 = 0; i1 < xy.nItems; i1++) { xy.pData[i1].dX = xy.pData[i1].dX * dXFactor + dXOffset; } } fprintf(stderr, "TEMPORARY: scaling factors: m=%g b=%g\n", dXFactor, dXOffset); } else if(bDoScale < 0) { fprintf(stderr, "TEMPORARY: autoscale -PI to PI\n"); } nHarm = xy.nItems / 2 > MAX_HARMONIC ? MAX_HARMONIC : xy.nItems / 2; if(xy.nItems < 2 || nHarm < 1) { continue; } pdA = (double *)malloc(sizeof(*pdA) * (nHarm + 1) * 2); if(!pdA) { fprintf(stderr, "out of memory for work buffers\n"); return -3; } pdB = pdA + nHarm + 1; dFourier(xy.pData, xy.nItems, nHarm, &dC, pdA, pdB, nThread, bDoScale < 0 ? 1 : 0); printf("harm #\t magnitude\t phase (deg)\t offset (C0)=%g\n", dC); for(i1 = 0; i1 < nHarm; i1++) { printf(" %3d\t" // "%7g\t%7g\t" "%15.6f\t%15.6f\n", i1 + 1, //dA[i1], //dB[i1], sqrt(pdA[i1] * pdA[i1] + pdB[i1] * pdB[i1]), atan2(pdB[i1], pdA[i1]) * 180 / _PI_ + 180); // NOTE: atan result for cosine will be - 180, sin - 90 // because the analysis is - PI to PI // adding 180 will give you 0, 90 } // figure out relative error (i.e. std deviation) and report it // if() TODO - make this optional // { dXY = 2.0 * _PI_ / (xy.pData[xy.nItems - 1].dX + (xy.pData[xy.nItems - 1].dX - xy.pData[0].dX) / (xy.nItems - 1)); dX0 = -dXY * xy.pData[0].dX - _PI_; // derived from -_PI_ == dX0 + dXY * aVal[0].dX for(i1 = 0, iW = 0; iW < nThread; iW++) { i2 = (iW + 1) * xy.nItems / nThread; if(i2 > xy.nItems) { i2 = xy.nItems; } aW[iW] = create_work_unit(pdA, pdB, dC, xy.pData, nHarm, dX0, dXY, i1, i2 - 1, check_callback, iW < (nThread - 1)); if(!aW[iW]) { fprintf(stderr, "threading error on data check\n"); return -3; } i1 = i2; // next group } for(iW = 0, dErr = 0.0; iW < nThread; iW++) { if(!aW[iW]) { continue; } if(aW[iW]->idThread) { pthread_join(aW[iW]->idThread, NULL); // ignore any error for now //pthread_detach(&(aW[iW].idThread); dErr += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC' } else // not a thread, keep 'dC' return here also { dErr += aW[iW]->dRval; // returned C0 value(when applicable) adds into 'dC' } free(aW[iW]); aW[iW] = NULL; // by convention } printf("relative accuracy: %g\n", sqrt(dErr / xy.nItems)); // } if(xy.pData) { free(xy.pData); } if(pdA) { free(pdA); } } return 0; } #ifdef USE_FAST_SINCOS // FAST SIN/COS UTILITIES - you can use these as you see fit, by the way (no license restrictions) // These really are trivial, though, so it's no big deal. Just has a sin/cos table. // What makes it faster is a) float precision, b) table lookup, c) shared calcs for 'fast_sincos' // And the precision tester, if you compile it in, shows that it's a match within 6 digits of precision // so there should be no problem using it, though your results may differ slightly. double make_valid_sincos_range(double dTheta) { float x0; x0 = (float)dTheta; if(x0<(float)-(3 * _PI_) || x0>(float)(3 * _PI_)) { x0 -= ( floorf(x0 * (float)(1 / (2 * _PI_))) ) * (float)(2.0 * _PI_); } /* optimized, hopefully, to minimize multiplications! */ if(x0<(float)-_PI_) { x0+= (float)(2 * _PI_); /* ensure it's between -pi & pi */ } if(x0>(float)_PI_) { x0-= (float)(2 * _PI_); /* ensure it's between -pi & pi */ } return(x0); } void fast_sincos(double dTheta, double *pSin, double *pCos) { unsigned int wIndex; float x0, y; x0 = make_valid_sincos_range(dTheta); /* x is between -pi and pi */ y = (float)5000.0 + x0 * (float)(5000.0 / _PI_); /* convert to an 'index' value... */ wIndex = (unsigned int)floorf(y); y -= (float)wIndex; /* this gives us the index and the 'interpolate' value... */ dDebugY = y; wDebugIndex = wIndex; if(y == 0.0) // possible { *pCos = _COS_VALUES_[wIndex]; *pSin = _SIN_VALUES_[wIndex]; } else /* not an 'even' value - interpolate between two entries */ { *pCos = _COS_VALUES_[wIndex] + (_COS_VALUES_[wIndex + 1] - _COS_VALUES_[wIndex]) * y; *pSin = _SIN_VALUES_[wIndex] + (_SIN_VALUES_[wIndex + 1] - _SIN_VALUES_[wIndex]) * y; } } double fast_cos(double dTheta) { unsigned int wIndex; float x0, y; x0 = make_valid_sincos_range(dTheta); /* x is between -pi and pi */ y = (float)5000.0 + x0 * (float)(5000.0 / _PI_); /* convert to an 'index' value... */ wIndex = (unsigned int)floorf(y); y -= (float)wIndex; /* this gives us the index and the 'interpolate' value... */ if(!y) { return(_COS_VALUES_[wIndex]); } else /* not an 'even' value - interpolate between two entries */ { return(_COS_VALUES_[wIndex] + (_COS_VALUES_[wIndex + 1] - _COS_VALUES_[wIndex]) * y); } } double fast_sin(double dTheta) { unsigned int wIndex; float x0, y; x0 = make_valid_sincos_range(dTheta); /* x is between -pi and pi */ y = (float)5000.0 + x0 * (float)(5000.0 / _PI_); /* convert to an 'index' value... */ wIndex = (unsigned int)floorf(y); y -= (float)wIndex; /* this gives us the index and the 'interpolate' value... */ if(!y) { return(_SIN_VALUES_[wIndex]); } else /* not an 'even' value - interpolate between two entries */ { return(_SIN_VALUES_[wIndex] + (_SIN_VALUES_[wIndex + 1] - _SIN_VALUES_[wIndex]) * y); } } static const float _SIN_VALUES_[12501]= { 0.00000000,-0.00062831,-0.00125663,-0.00188495,-0.00251327, -0.00314158,-0.00376990,-0.00439821,-0.00502652,-0.00565483, -0.00628314,-0.00691144,-0.00753975,-0.00816804,-0.00879634, -0.00942463,-0.01005292,-0.01068121,-0.01130949,-0.01193776, -0.01256603,-0.01319430,-0.01382256,-0.01445082,-0.01507907, -0.01570731,-0.01633555,-0.01696378,-0.01759201,-0.01822022, 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-0.99992104,-0.99992874,-0.99993604,-0.99994295,-0.99994946, -0.99995558,-0.99996131,-0.99996664,-0.99997157,-0.99997611, -0.99998026,-0.99998401,-0.99998736,-0.99999032,-0.99999289, -0.99999506,-0.99999684,-0.99999822,-0.99999921,-0.99999980, -1.00000000 // extra element }; static const float * const _COS_VALUES_ = &(_SIN_VALUES_[2500]); #endif // USE_FAST_SINCOS