init: add sin.c
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commit
c8874275c3
137
sin.c
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137
sin.c
Normal file
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#include <stdio.h>
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#include <time.h>
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#include <math.h>
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#define PI 3.14159265358979323846264338327950288419716939937
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#define x0 0.60725293500888125616944675250493
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#define y0 0
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static double atanlist[100] = {
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0.78539816339744830961566084581988,0.46364760900080611621425623146121,
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0.24497866312686415417208248121128,0.12435499454676143503135484916387,
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0.062418809995957348473979112985505,0.031239833430268276253711744892491,
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0.01562372862047683080280152125657,0.0078123410601011112964633918421993,
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0.0039062301319669718276286653114244,0.0019531225164788186851214826250767,
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0.00097656218955931943040343019971729,0.00048828121119489827546923962564485,
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0.00024414062014936176401672294325966,0.00012207031189367020423905864611796,
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0.000061035156174208775021662569173829,0.000030517578115526096861825953438536,
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0.000015258789061315762107231935812698,7.6293945311019702633884823401051e-6,
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3.814697265606496282923075616373e-6,1.9073486328101870353653693059172e-6,
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9.5367431640596087942067068992311e-7,4.7683715820308885992758382144925e-7,
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2.3841857910155798249094797721893e-7,1.1920928955078068531136849713792e-7,
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5.9604644775390554413921062141789e-8,2.980232238769530367674013276771e-8,
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1.4901161193847655147092516595963e-8,7.4505805969238279871365645744954e-9,
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3.7252902984619140452670705718119e-9,1.8626451492309570290958838214765e-9,
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9.3132257461547851535573547768456e-10,4.6566128730773925777884193471057e-10,
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2.3283064365386962890204274183882e-10,1.1641532182693481445259909272985e-10,
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5.8207660913467407226496761591232e-11,2.9103830456733703613273032698904e-11,
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1.4551915228366851806639597837363e-11,7.2759576141834259033201841046704e-12,
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3.6379788070917129516601402005838e-12,1.818989403545856475830076118823e-12,
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9.0949470177292823791503881172787e-13,4.5474735088646411895751949990348e-13,
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2.2737367544323205947875976170669e-13,1.1368683772161602973937988232271e-13,
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5.6843418860808014869689941345026e-14,2.8421709430404007434844970695472e-14,
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1.4210854715202003717422485350606e-14,7.1054273576010018587112426756617e-15,
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3.5527136788005009293556213378757e-15,1.7763568394002504646778106689434e-15,
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8.8817841970012523233890533447242e-16,4.440892098500626161694526672363e-16,
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2.2204460492503130808472633361816e-16,1.1102230246251565404236316680908e-16,
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5.5511151231257827021181583404541e-17,2.7755575615628913510590791702271e-17,
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1.3877787807814456755295395851135e-17,6.9388939039072283776476979255676e-18,
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3.4694469519536141888238489627838e-18,1.7347234759768070944119244813919e-18,
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8.6736173798840354720596224069595e-19,4.3368086899420177360298112034798e-19,
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2.1684043449710088680149056017399e-19,1.0842021724855044340074528008699e-19,
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5.4210108624275221700372640043497e-20,2.7105054312137610850186320021749e-20,
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1.3552527156068805425093160010874e-20,6.7762635780344027125465800054371e-21,
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3.3881317890172013562732900027186e-21,1.6940658945086006781366450013593e-21,
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8.4703294725430033906832250067964e-22,4.2351647362715016953416125033982e-22,
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2.1175823681357508476708062516991e-22,1.0587911840678754238354031258496e-22,
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5.2939559203393771191770156292478e-23,2.6469779601696885595885078146239e-23,
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1.3234889800848442797942539073119e-23,6.6174449004242213989712695365597e-24,
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3.3087224502121106994856347682799e-24,1.6543612251060553497428173841399e-24,
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8.2718061255302767487140869206996e-25,4.1359030627651383743570434603498e-25,
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2.0679515313825691871785217301749e-25,1.0339757656912845935892608650875e-25,
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5.1698788284564229679463043254373e-26,2.5849394142282114839731521627186e-26,
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1.2924697071141057419865760813593e-26,6.4623485355705287099328804067966e-27,
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3.2311742677852643549664402033983e-27,1.6155871338926321774832201016991e-27,
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8.0779356694631608874161005084957e-28,4.0389678347315804437080502542479e-28,
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2.0194839173657902218540251271239e-28,1.009741958682895110927012563562e-28,
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5.0487097934144755546350628178098e-29,2.5243548967072377773175314089049e-29,
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1.2621774483536188886587657044525e-29,6.3108872417680944432938285222623e-30,
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3.1554436208840472216469142611311e-30,1.5777218104420236108234571305656e-30
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};
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int trig(double theta, double *xy, double *dxy){
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int i = 0;
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double t = 1.0; //t=2^-i
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int d = 0;
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double alpha = theta;
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double dnorm = 1.0;
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xy[0] = x0;
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xy[1] = y0;
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while(i<100 && dnorm>1e-32){
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d = alpha>0?1:(alpha<0?-1:0);
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dxy[0] = -d*xy[1]*t;
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dxy[1] = d*xy[0]*t;
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dnorm = dxy[0]*dxy[0] + dxy[1]*dxy[1];
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xy[0] += dxy[0];
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xy[1] += dxy[1];
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alpha -= d*atanlist[i];
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i++;
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t/=2.0;
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}
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return i;
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}
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double sin1(double theta, int *it, double *dsin){
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if(theta < 0) return -sin1(theta, it, dsin);
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if(theta > 2*PI) return sin1(theta - 2*PI, it, dsin);
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if(theta > PI) return -sin1(theta - PI, it, dsin);
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if(theta > PI/2) return sin1(PI - theta, it, dsin);
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double xy[2];
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double dxy[2];
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*it = trig(theta, xy, dxy);
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*dsin = dxy[1];
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return xy[1];
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}
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double sin2(double theta, int *it, double *dsin){
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if(theta < 0) return -sin2(theta, it, dsin);
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if(theta > 2*PI) return sin2(theta - 2*PI, it, dsin);
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if(theta > PI) return -sin2(theta - PI, it, dsin);
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if(theta > PI/2) return sin2(PI - theta, it, dsin);
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double result = 0;
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double term=theta;
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int i = 0;
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while (i<100 && fabs(term)>1e-16){
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result += term;
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i += 1;
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term *= -1;
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term /= 2*i;
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term /= (2*i+1);
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term *= theta*theta;
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}
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*it = i;
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*dsin = term;
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return result;
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}
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int main(){
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int it;
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double theta = 1.0;
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double sin,dsin;
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clock_t start, end;
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start = clock();
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for (int i=0; i<10000; i++) sin = sin1(theta, &it, &dsin);
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end = clock();
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printf("sin1(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end-start)/CLOCKS_PER_SEC);
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start = clock();
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for (int i=0; i<10000; i++) sin = sin2(theta, &it, &dsin);
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end = clock();
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printf("sin2(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end-start)/CLOCKS_PER_SEC);
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return 0;
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}
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