#include #include #include "cordic.h" extern double frexp(), ldexp(), modf(); char Table0_index[80] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 }; double Table0_coeff[80] = { /* alpha[i] delta[i] */ /* -------------------- ------------------ */ 7.8539816339744830961566084581988E-01, /* ATAN( 2 ** -0 ) */ 4.6364760900080611621425623146122E-01, /* ATAN( 2 ** -1 ) */ 2.4497866312686415417208248121128E-01, /* ATAN( 2 ** -2 ) */ 1.2435499454676143503135484916387E-01, /* ATAN( 2 ** -3 ) */ 6.2418809995957348473979112985505E-02, /* ATAN( 2 ** -4 ) */ 3.1239833430268276253711744892491E-02, /* ATAN( 2 ** -5 ) */ 1.5623728620476830802801521256570E-02, /* ATAN( 2 ** -6 ) */ 7.8123410601011112964633918421993E-03, /* ATAN( 2 ** -7 ) */ 3.9062301319669718276286653114244E-03, /* ATAN( 2 ** -8 ) */ 1.9531225164788186851214826250767E-03, /* ATAN( 2 ** -9 ) */ 9.7656218955931943040343019971729E-04, /* ATAN( 2 ** -10 ) */ 4.8828121119489827546923962564485E-04, /* ATAN( 2 ** -11 ) */ 2.4414062014936176401672294325966E-04, /* ATAN( 2 ** -12 ) */ 1.2207031189367020423905864611796E-04, /* ATAN( 2 ** -13 ) */ 6.1035156174208775021662569173829E-05, /* ATAN( 2 ** -14 ) */ 3.0517578115526096861825953438536E-05, /* ATAN( 2 ** -15 ) */ 1.5258789061315762107231935812698E-05, /* ATAN( 2 ** -16 ) */ 7.6293945311019702633884823401051E-06, /* ATAN( 2 ** -17 ) */ 3.8146972656064962829230756163730E-06, /* ATAN( 2 ** -18 ) */ 1.9073486328101870353653693059172E-06, /* ATAN( 2 ** -19 ) */ 9.5367431640596087942067068992311E-07, /* ATAN( 2 ** -20 ) */ 4.7683715820308885992758382144925E-07, /* ATAN( 2 ** -21 ) */ 2.3841857910155798249094797721893E-07, /* ATAN( 2 ** -22 ) */ 1.1920928955078068531136849713792E-07, /* ATAN( 2 ** -23 ) */ 5.9604644775390554413921062141789E-08, /* ATAN( 2 ** -24 ) */ 2.9802322387695303676740132767710E-08, /* ATAN( 2 ** -25 ) */ 1.4901161193847655147092516595963E-08, /* ATAN( 2 ** -26 ) */ 7.4505805969238279871365645744954E-09, /* ATAN( 2 ** -27 ) */ 3.7252902984619140452670705718119E-09, /* ATAN( 2 ** -28 ) */ 1.8626451492309570290958838214765E-09, /* ATAN( 2 ** -29 ) */ 9.3132257461547851535573547768456E-10, /* ATAN( 2 ** -30 ) */ 4.6566128730773925777884193471057E-10, /* ATAN( 2 ** -31 ) */ 2.3283064365386962890204274183882E-10, /* ATAN( 2 ** -32 ) */ 1.1641532182693481445259909272985E-10, /* ATAN( 2 ** -33 ) */ 5.8207660913467407226496761591232E-11, /* ATAN( 2 ** -34 ) */ 2.9103830456733703613273032698904E-11, /* ATAN( 2 ** -35 ) */ 1.4551915228366851806639597837363E-11, /* ATAN( 2 ** -36 ) */ 7.2759576141834259033201841046704E-12, /* ATAN( 2 ** -37 ) */ 3.6379788070917129516601402005838E-12, /* ATAN( 2 ** -38 ) */ 1.8189894035458564758300761188230E-12, /* ATAN( 2 ** -39 ) */ 9.0949470177292823791503881172787E-13, /* ATAN( 2 ** -40 ) */ 4.5474735088646411895751949990348E-13, /* ATAN( 2 ** -41 ) */ 2.2737367544323205947875976170669E-13, /* ATAN( 2 ** -42 ) */ 1.1368683772161602973937988232271E-13, /* ATAN( 2 ** -43 ) */ 5.6843418860808014869689941345026E-14, /* ATAN( 2 ** -44 ) */ 2.8421709430404007434844970695472E-14, /* ATAN( 2 ** -45 ) */ 1.4210854715202003717422485350606E-14, /* ATAN( 2 ** -46 ) */ 7.1054273576010018587112426756617E-15, /* ATAN( 2 ** -47 ) */ 3.5527136788005009293556213378757E-15, /* ATAN( 2 ** -48 ) */ 1.7763568394002504646778106689434E-15, /* ATAN( 2 ** -49 ) */ 8.8817841970012523233890533447242E-16, /* ATAN( 2 ** -50 ) */ 4.4408920985006261616945266723630E-16, /* ATAN( 2 ** -51 ) */ 2.2204460492503130808472633361816E-16, /* ATAN( 2 ** -52 ) */ 1.1102230246251565404236316680908E-16, /* ATAN( 2 ** -53 ) */ 5.5511151231257827021181583404541E-17, /* ATAN( 2 ** -54 ) */ 2.7755575615628913510590791702271E-17, /* ATAN( 2 ** -55 ) */ 1.3877787807814456755295395851135E-17, /* ATAN( 2 ** -56 ) */ 6.9388939039072283776476979255676E-18, /* ATAN( 2 ** -57 ) */ 3.4694469519536141888238489627838E-18, /* ATAN( 2 ** -58 ) */ 1.7347234759768070944119244813919E-18, /* ATAN( 2 ** -59 ) */ 8.6736173798840354720596224069595E-19, /* ATAN( 2 ** -60 ) */ 4.3368086899420177360298112034798E-19, /* ATAN( 2 ** -61 ) */ 2.1684043449710088680149056017399E-19, /* ATAN( 2 ** -62 ) */ 1.0842021724855044340074528008699E-19, /* ATAN( 2 ** -63 ) */ 5.4210108624275221700372640043497E-20, /* ATAN( 2 ** -64 ) */ 2.7105054312137610850186320021749E-20, /* ATAN( 2 ** -65 ) */ 1.3552527156068805425093160010874E-20, /* ATAN( 2 ** -66 ) */ 6.7762635780344027125465800054371E-21, /* ATAN( 2 ** -67 ) */ 3.3881317890172013562732900027186E-21, /* ATAN( 2 ** -68 ) */ 1.6940658945086006781366450013593E-21, /* ATAN( 2 ** -69 ) */ 8.4703294725430033906832250067964E-22, /* ATAN( 2 ** -70 ) */ 4.2351647362715016953416125033982E-22, /* ATAN( 2 ** -71 ) */ 2.1175823681357508476708062516991E-22, /* ATAN( 2 ** -72 ) */ 1.0587911840678754238354031258496E-22, /* ATAN( 2 ** -73 ) */ 5.2939559203393771191770156292478E-23, /* ATAN( 2 ** -74 ) */ 2.6469779601696885595885078146239E-23, /* ATAN( 2 ** -75 ) */ 1.3234889800848442797942539073119E-23, /* ATAN( 2 ** -76 ) */ 6.6174449004242213989712695365597E-24, /* ATAN( 2 ** -77 ) */ 3.3087224502121106994856347682799E-24, /* ATAN( 2 ** -78 ) */ 1.6543612251060553497428173841399E-24 /* ATAN( 2 ** -79 ) */ }; CORDIC_Table CORDIC_Table0[1] = { 60, /* Table Size */ 1, /* m = 1 */ 1.6467602581210656483660512222823E+00, /* value */ Table0_index, /* indexes */ Table0_coeff /* Coefficients */ }; char Table1_index[80] = { 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77 }; double Table1_coeff[80] = { 0.0000000000000000000000000000000E+00, /* EMPTY */ 5.4930614433405484569762261846126E-01, /* ATANH( 2 ** -1 ) */ 2.5541281188299534160275704815183E-01, /* ATANH( 2 ** -2 ) */ 1.2565721414045303884256886520094E-01, /* ATANH( 2 ** -3 ) */ 6.2581571477003007126765023862207E-02, /* ATANH( 2 ** -4 ) */ 3.1260178490666994764012245172648E-02, /* ATANH( 2 ** -5 ) */ 1.5626271752052211379201778751638E-02, /* ATANH( 2 ** -6 ) */ 7.8126589515404209103234712760400E-03, /* ATANH( 2 ** -7 ) */ 3.9062698683968260531275633697076E-03, /* ATANH( 2 ** -8 ) */ 1.9531274835325499986507708868542E-03, /* ATANH( 2 ** -9 ) */ 9.7656281044103584096445002988456E-04, /* ATANH( 2 ** -10 ) */ 4.8828128880511282676100662627039E-04, /* ATANH( 2 ** -11 ) */ 2.4414062985063858292797225210244E-04, /* ATANH( 2 ** -12 ) */ 1.2207031310632980660296307873708E-04, /* ATANH( 2 ** -13 ) */ 6.1035156325791225317150609727698E-05, /* ATANH( 2 ** -14 ) */ 3.0517578134473903148761958402142E-05, /* ATANH( 2 ** -15 ) */ 1.5258789063684237893098936432131E-05, /* ATANH( 2 ** -16 ) */ 7.6293945313980297366218574175503E-06, /* ATANH( 2 ** -17 ) */ 3.8146972656435037170772475010538E-06, /* ATANH( 2 ** -18 ) */ 1.9073486328148129646346407914542E-06, /* ATANH( 2 ** -19 ) */ 9.5367431640653912057932962562050E-07, /* ATANH( 2 ** -20 ) */ 4.7683715820316114007241618841150E-07, /* ATANH( 2 ** -21 ) */ 2.3841857910156701750905202231884E-07, /* ATANH( 2 ** -22 ) */ 1.1920928955078181468863150284763E-07, /* ATANH( 2 ** -23 ) */ 5.9604644775390695586078937857760E-08, /* ATANH( 2 ** -24 ) */ 2.9802322387695321323259867232276E-08, /* ATANH( 2 ** -25 ) */ 1.4901161193847657352907483404036E-08, /* ATANH( 2 ** -26 ) */ 7.4505805969238282628634354255046E-09, /* ATANH( 2 ** -27 ) */ 3.7252902984619140797329292355951E-09, /* ATANH( 2 ** -28 ) */ 1.8626451492309570334041161664864E-09, /* ATANH( 2 ** -29 ) */ 9.3132257461547851589426452156312E-10, /* ATANH( 2 ** -30 ) */ 4.6566128730773925784615806524241E-10, /* ATANH( 2 ** -31 ) */ 2.3283064365386962891045725815824E-10, /* ATANH( 2 ** -32 ) */ 1.1641532182693481445365090726996E-10, /* ATANH( 2 ** -33 ) */ 5.8207660913467407226628238408757E-11, /* ATANH( 2 ** -34 ) */ 2.9103830456733703613289467301095E-11, /* ATANH( 2 ** -35 ) */ 1.4551915228366851806641652162637E-11, /* ATANH( 2 ** -36 ) */ 7.2759576141834259033200557093408E-12, /* ATANH( 2 ** -37 ) */ 3.6379788070917129516601241511676E-12, /* ATANH( 2 ** -38 ) */ 1.8189894035458564758300741126460E-12, /* ATANH( 2 ** -39 ) */ 9.0949470177292823791503856095574E-13, /* ATANH( 2 ** -40 ) */ 4.5474735088646411895751946855697E-13, /* ATANH( 2 ** -41 ) */ 2.2737367544323205947875975778837E-13, /* ATANH( 2 ** -42 ) */ 1.1368683772161602973937988183292E-13, /* ATANH( 2 ** -43 ) */ 5.6843418860808014869689941283803E-14, /* ATANH( 2 ** -44 ) */ 2.8421709430404007434844970687819E-14, /* ATANH( 2 ** -45 ) */ 1.4210854715202003717422485349649E-14, /* ATANH( 2 ** -46 ) */ 7.1054273576010018587112426755421E-15, /* ATANH( 2 ** -47 ) */ 3.5527136788005009293556213378607E-15, /* ATANH( 2 ** -48 ) */ 1.7763568394002504646778106689416E-15, /* ATANH( 2 ** -49 ) */ 8.8817841970012523233890533447219E-16, /* ATANH( 2 ** -50 ) */ 4.4408920985006261616945266723627E-16, /* ATANH( 2 ** -51 ) */ 2.2204460492503130808472633361816E-16, /* ATANH( 2 ** -52 ) */ 1.1102230246251565404236316680908E-16, /* ATANH( 2 ** -53 ) */ 5.5511151231257827021181583404541E-17, /* ATANH( 2 ** -54 ) */ 2.7755575615628912740218813947376E-17, /* ATANH( 2 ** -55 ) */ 1.3877787807814456562702401412412E-17, /* ATANH( 2 ** -56 ) */ 6.9388939039072283294994493158867E-18, /* ATANH( 2 ** -57 ) */ 3.4694469519536141767867868103636E-18, /* ATANH( 2 ** -58 ) */ 1.7347234759768070914026589432869E-18, /* ATANH( 2 ** -59 ) */ 8.6736173798840354645364585616969E-19, /* ATANH( 2 ** -60 ) */ 4.3368086899420177341490202421641E-19, /* ATANH( 2 ** -61 ) */ 2.1684043449710088675447078614110E-19, /* ATANH( 2 ** -62 ) */ 1.0842021724855044338899033657877E-19, /* ATANH( 2 ** -63 ) */ 5.4210108624275221697433904166441E-20, /* ATANH( 2 ** -64 ) */ 2.7105054312137610849451636052485E-20, /* ATANH( 2 ** -65 ) */ 1.3552527156068805424909489018558E-20, /* ATANH( 2 ** -66 ) */ 6.7762635780344027125006622573581E-21, /* ATANH( 2 ** -67 ) */ 3.3881317890172013562618105656988E-21, /* ATANH( 2 ** -68 ) */ 1.6940658945086006781337751421043E-21, /* ATANH( 2 ** -69 ) */ 8.4703294725430033906760503586591E-22, /* ATANH( 2 ** -70 ) */ 4.2351647362715016953398188413639E-22, /* ATANH( 2 ** -71 ) */ 2.1175823681357508476703578361905E-22, /* ATANH( 2 ** -72 ) */ 1.0587911840678754238352910219724E-22, /* ATANH( 2 ** -73 ) */ 5.2939559203393771191767353695549E-23, /* ATANH( 2 ** -74 ) */ 2.6469779601696885595884377497007E-23, /* ATANH( 2 ** -75 ) */ 1.3234889800848442797942363910811E-23, /* ATANH( 2 ** -76 ) */ 6.6174449004242213989712257459827E-24, /* ATANH( 2 ** -77 ) */ 3.3087224502121106994856238206356E-24, /* ATANH( 2 ** -78 ) */ 1.6543612251060553497428146472289E-24, /* ATANH( 2 ** -79 ) */ }; CORDIC_Table CORDIC_Table1[1] = { 60, /* Table Size */ -1, /* m = -1 */ 8.28159360960215359E-01, /* K value */ Table1_index, /* indexes */ Table1_coeff /* Coefficients */ }; void CORDIC_rotate0(method, tbl, x1, y1, z1) int method; CORDIC_Table *tbl; double *x1, *y1, *z1; { int i, idx; double xn, yn, zn; double x0, y0, z0; int ix, iy, iw; x0 = *x1; y0 = *y1; z0 = *z1; if (method == 0) { for (i = 0; i < tbl->size; i++) { idx = tbl->index[i]; xn = frexp(x0, &ix); xn = ldexp(xn, ix - idx); yn = frexp(y0, &iy); yn = ldexp(yn, iy - idx); if ((x0 >= 0.0 && y0 >= 0.0) || (x0 <= 0.0 && y0 <= 0.0)) { x0 += yn; y0 -= xn; z0 += tbl->coeff[idx]; } else { x0 -= yn; y0 += xn; z0 -= tbl->coeff[idx]; } } } else { for (i = 0; i < tbl->size; i++) { idx = tbl->index[i]; xn = frexp(x0, &ix); xn = ldexp(xn, ix - idx); yn = frexp(y0, &iy); yn = ldexp(yn, iy - idx); if (z0 < 0.0) { x0 += yn; y0 -= xn; z0 += tbl->coeff[idx]; } else { x0 -= yn; y0 += xn; z0 -= tbl->coeff[idx]; } } } *x1 = x0; *y1 = y0; *z1 = z0; } void CORDIC_rotate1(method, tbl, x1, y1, z1) int method; CORDIC_Table *tbl; double *x1, *y1, *z1; { int i, idx; double xn, yn, zn; double x0, y0, z0; int ix, iy, iw; x0 = *x1; y0 = *y1; z0 = *z1; if (method == 0) { for (i = 0; i < tbl->size; i++) { idx = tbl->index[i]; xn = frexp(x0, &ix); xn = ldexp(xn, ix - idx); yn = frexp(y0, &iy); yn = ldexp(yn, iy - idx); if ((x0 >= 0.0 && y0 >= 0.0) || (x0 <= 0.0 && y0 <= 0.0)) { x0 -= yn; y0 -= xn; z0 += tbl->coeff[idx]; } else { x0 += yn; y0 += xn; z0 -= tbl->coeff[idx]; } } } else { for (i = 0; i < tbl->size; i++) { idx = tbl->index[i]; xn = frexp(x0, &ix); xn = ldexp(xn, ix - idx); yn = frexp(y0, &iy); yn = ldexp(yn, iy - idx); if (z0 < 0.0) { x0 -= yn; y0 -= xn; z0 += tbl->coeff[idx]; } else { x0 += yn; y0 += xn; z0 -= tbl->coeff[idx]; } } } *x1 = x0; *y1 = y0; *z1 = z0; } #if 0 main() { double x, y, z; x = 1.0; y = 1.0; z = 0.0; CORDIC_rotate0(0, CORDIC_Table0, &x, &y, &z); printf("Method = %d (x = %g) (y = %g) (z = %g)\n", 0, x, y, z); x = -1.0; y = 1.0; z = 0.0; CORDIC_rotate0(1, CORDIC_Table0, &x, &y, &z); printf("Method = %d (x = %g) (y = %g) (z = %g)\n", 1, x, y, z); x = 1.5; y = -1.0; z = 0.0; CORDIC_rotate1(0, CORDIC_Table1, &x, &y, &z); printf("Method = %d (x = %g) (y = %g) (z = %g)\n", 0, x, y, z); x = -1.0; y = -1.0; z = 0.5; CORDIC_rotate1(1, CORDIC_Table1, &x, &y, &z); printf("Method = %d (x = %g) (y = %g) (z = %g)\n", 1, x, y, z); } #endif