diff --git a/sin.c b/sin.c
index 38b7191..1c65031 100644
--- a/sin.c
+++ b/sin.c
@@ -7,87 +7,94 @@
 #define x0 0.60725293500888125616944675250493
 #define y0 0
 static double atanlist[100] = {
-    0.78539816339744830961566084581988,0.46364760900080611621425623146121,
-    0.24497866312686415417208248121128,0.12435499454676143503135484916387,
-    0.062418809995957348473979112985505,0.031239833430268276253711744892491,
-    0.01562372862047683080280152125657,0.0078123410601011112964633918421993,
-    0.0039062301319669718276286653114244,0.0019531225164788186851214826250767,
-    0.00097656218955931943040343019971729,0.00048828121119489827546923962564485,
-    0.00024414062014936176401672294325966,0.00012207031189367020423905864611796,
-    0.000061035156174208775021662569173829,0.000030517578115526096861825953438536,
-    0.000015258789061315762107231935812698,7.6293945311019702633884823401051e-6,
-    3.814697265606496282923075616373e-6,1.9073486328101870353653693059172e-6,
-    9.5367431640596087942067068992311e-7,4.7683715820308885992758382144925e-7,
-    2.3841857910155798249094797721893e-7,1.1920928955078068531136849713792e-7,
-    5.9604644775390554413921062141789e-8,2.980232238769530367674013276771e-8,
-    1.4901161193847655147092516595963e-8,7.4505805969238279871365645744954e-9,
-    3.7252902984619140452670705718119e-9,1.8626451492309570290958838214765e-9,
-    9.3132257461547851535573547768456e-10,4.6566128730773925777884193471057e-10,
-    2.3283064365386962890204274183882e-10,1.1641532182693481445259909272985e-10,
-    5.8207660913467407226496761591232e-11,2.9103830456733703613273032698904e-11,
-    1.4551915228366851806639597837363e-11,7.2759576141834259033201841046704e-12,
-    3.6379788070917129516601402005838e-12,1.818989403545856475830076118823e-12,
-    9.0949470177292823791503881172787e-13,4.5474735088646411895751949990348e-13,
-    2.2737367544323205947875976170669e-13,1.1368683772161602973937988232271e-13,
-    5.6843418860808014869689941345026e-14,2.8421709430404007434844970695472e-14,
-    1.4210854715202003717422485350606e-14,7.1054273576010018587112426756617e-15,
-    3.5527136788005009293556213378757e-15,1.7763568394002504646778106689434e-15,
-    8.8817841970012523233890533447242e-16,4.440892098500626161694526672363e-16,
-    2.2204460492503130808472633361816e-16,1.1102230246251565404236316680908e-16,
-    5.5511151231257827021181583404541e-17,2.7755575615628913510590791702271e-17,
-    1.3877787807814456755295395851135e-17,6.9388939039072283776476979255676e-18,
-    3.4694469519536141888238489627838e-18,1.7347234759768070944119244813919e-18,
-    8.6736173798840354720596224069595e-19,4.3368086899420177360298112034798e-19,
-    2.1684043449710088680149056017399e-19,1.0842021724855044340074528008699e-19,
-    5.4210108624275221700372640043497e-20,2.7105054312137610850186320021749e-20,
-    1.3552527156068805425093160010874e-20,6.7762635780344027125465800054371e-21,
-    3.3881317890172013562732900027186e-21,1.6940658945086006781366450013593e-21,
-    8.4703294725430033906832250067964e-22,4.2351647362715016953416125033982e-22,
-    2.1175823681357508476708062516991e-22,1.0587911840678754238354031258496e-22,
-    5.2939559203393771191770156292478e-23,2.6469779601696885595885078146239e-23,
-    1.3234889800848442797942539073119e-23,6.6174449004242213989712695365597e-24,
-    3.3087224502121106994856347682799e-24,1.6543612251060553497428173841399e-24,
-    8.2718061255302767487140869206996e-25,4.1359030627651383743570434603498e-25,
-    2.0679515313825691871785217301749e-25,1.0339757656912845935892608650875e-25,
-    5.1698788284564229679463043254373e-26,2.5849394142282114839731521627186e-26,
-    1.2924697071141057419865760813593e-26,6.4623485355705287099328804067966e-27,
-    3.2311742677852643549664402033983e-27,1.6155871338926321774832201016991e-27,
-    8.0779356694631608874161005084957e-28,4.0389678347315804437080502542479e-28,
-    2.0194839173657902218540251271239e-28,1.009741958682895110927012563562e-28,
-    5.0487097934144755546350628178098e-29,2.5243548967072377773175314089049e-29,
-    1.2621774483536188886587657044525e-29,6.3108872417680944432938285222623e-30,
-    3.1554436208840472216469142611311e-30,1.5777218104420236108234571305656e-30
+    0.78539816339744830961566084581988, 0.46364760900080611621425623146121,
+    0.24497866312686415417208248121128, 0.12435499454676143503135484916387,
+    0.062418809995957348473979112985505, 0.031239833430268276253711744892491,
+    0.01562372862047683080280152125657, 0.0078123410601011112964633918421993,
+    0.0039062301319669718276286653114244, 0.0019531225164788186851214826250767,
+    0.00097656218955931943040343019971729, 0.00048828121119489827546923962564485,
+    0.00024414062014936176401672294325966, 0.00012207031189367020423905864611796,
+    0.000061035156174208775021662569173829, 0.000030517578115526096861825953438536,
+    0.000015258789061315762107231935812698, 7.6293945311019702633884823401051e-6,
+    3.814697265606496282923075616373e-6, 1.9073486328101870353653693059172e-6,
+    9.5367431640596087942067068992311e-7, 4.7683715820308885992758382144925e-7,
+    2.3841857910155798249094797721893e-7, 1.1920928955078068531136849713792e-7,
+    5.9604644775390554413921062141789e-8, 2.980232238769530367674013276771e-8,
+    1.4901161193847655147092516595963e-8, 7.4505805969238279871365645744954e-9,
+    3.7252902984619140452670705718119e-9, 1.8626451492309570290958838214765e-9,
+    9.3132257461547851535573547768456e-10, 4.6566128730773925777884193471057e-10,
+    2.3283064365386962890204274183882e-10, 1.1641532182693481445259909272985e-10,
+    5.8207660913467407226496761591232e-11, 2.9103830456733703613273032698904e-11,
+    1.4551915228366851806639597837363e-11, 7.2759576141834259033201841046704e-12,
+    3.6379788070917129516601402005838e-12, 1.818989403545856475830076118823e-12,
+    9.0949470177292823791503881172787e-13, 4.5474735088646411895751949990348e-13,
+    2.2737367544323205947875976170669e-13, 1.1368683772161602973937988232271e-13,
+    5.6843418860808014869689941345026e-14, 2.8421709430404007434844970695472e-14,
+    1.4210854715202003717422485350606e-14, 7.1054273576010018587112426756617e-15,
+    3.5527136788005009293556213378757e-15, 1.7763568394002504646778106689434e-15,
+    8.8817841970012523233890533447242e-16, 4.440892098500626161694526672363e-16,
+    2.2204460492503130808472633361816e-16, 1.1102230246251565404236316680908e-16,
+    5.5511151231257827021181583404541e-17, 2.7755575615628913510590791702271e-17,
+    1.3877787807814456755295395851135e-17, 6.9388939039072283776476979255676e-18,
+    3.4694469519536141888238489627838e-18, 1.7347234759768070944119244813919e-18,
+    8.6736173798840354720596224069595e-19, 4.3368086899420177360298112034798e-19,
+    2.1684043449710088680149056017399e-19, 1.0842021724855044340074528008699e-19,
+    5.4210108624275221700372640043497e-20, 2.7105054312137610850186320021749e-20,
+    1.3552527156068805425093160010874e-20, 6.7762635780344027125465800054371e-21,
+    3.3881317890172013562732900027186e-21, 1.6940658945086006781366450013593e-21,
+    8.4703294725430033906832250067964e-22, 4.2351647362715016953416125033982e-22,
+    2.1175823681357508476708062516991e-22, 1.0587911840678754238354031258496e-22,
+    5.2939559203393771191770156292478e-23, 2.6469779601696885595885078146239e-23,
+    1.3234889800848442797942539073119e-23, 6.6174449004242213989712695365597e-24,
+    3.3087224502121106994856347682799e-24, 1.6543612251060553497428173841399e-24,
+    8.2718061255302767487140869206996e-25, 4.1359030627651383743570434603498e-25,
+    2.0679515313825691871785217301749e-25, 1.0339757656912845935892608650875e-25,
+    5.1698788284564229679463043254373e-26, 2.5849394142282114839731521627186e-26,
+    1.2924697071141057419865760813593e-26, 6.4623485355705287099328804067966e-27,
+    3.2311742677852643549664402033983e-27, 1.6155871338926321774832201016991e-27,
+    8.0779356694631608874161005084957e-28, 4.0389678347315804437080502542479e-28,
+    2.0194839173657902218540251271239e-28, 1.009741958682895110927012563562e-28,
+    5.0487097934144755546350628178098e-29, 2.5243548967072377773175314089049e-29,
+    1.2621774483536188886587657044525e-29, 6.3108872417680944432938285222623e-30,
+    3.1554436208840472216469142611311e-30, 1.5777218104420236108234571305656e-30
 };
 
-int trig(double theta, double *xy, double *dxy){
+int trig(double theta, double *xy, double *dxy)
+{
     int i = 0;
-    double t = 1.0; //t=2^-i
+    double t = 1.0; // t=2^-i
     int d = 0;
     double alpha = theta;
     double dnorm = 1.0;
 
     xy[0] = x0;
     xy[1] = y0;
-    while(i<100 && dnorm>1e-32){
-        d = alpha>0?1:(alpha<0?-1:0);
-	dxy[0] = -d*xy[1]*t;
-	dxy[1] = d*xy[0]*t;
-	dnorm = dxy[0]*dxy[0] + dxy[1]*dxy[1];
-	xy[0] += dxy[0];
-	xy[1] += dxy[1];
-	alpha -= d*atanlist[i];
-	i++;
-	t/=2.0;
+    while (i < 100 && dnorm > 1e-32)
+    {
+        d = alpha > 0 ? 1 : (alpha < 0 ? -1 : 0);
+        dxy[0] = -d * xy[1] * t;
+        dxy[1] = d * xy[0] * t;
+        dnorm = dxy[0] * dxy[0] + dxy[1] * dxy[1];
+        xy[0] += dxy[0];
+        xy[1] += dxy[1];
+        alpha -= d * atanlist[i];
+        i++;
+        t /= 2.0;
     }
     return i;
 }
 
-double sin1(double theta, int *it, double *dsin){
-    if(theta < 0) return -sin1(theta, it, dsin);
-    if(theta > 2*PI) return sin1(theta - 2*PI, it, dsin);
-    if(theta > PI) return -sin1(theta - PI, it, dsin);
-    if(theta > PI/2) return sin1(PI - theta, it, dsin);
-	
+double sin1(double theta, int *it, double *dsin)
+{
+    if (theta < 0)
+        return -sin1(theta, it, dsin);
+    if (theta > 2 * PI)
+        return sin1(theta - 2 * PI, it, dsin);
+    if (theta > PI)
+        return -sin1(theta - PI, it, dsin);
+    if (theta > PI / 2)
+        return sin1(PI - theta, it, dsin);
+
     double xy[2];
     double dxy[2];
 
@@ -96,42 +103,52 @@ double sin1(double theta, int *it, double *dsin){
     return xy[1];
 }
 
-double sin2(double theta, int *it, double *dsin){
-    if(theta < 0) return -sin2(theta, it, dsin);
-    if(theta > 2*PI) return sin2(theta - 2*PI, it, dsin);
-    if(theta > PI) return -sin2(theta - PI, it, dsin);
-    if(theta > PI/2) return sin2(PI - theta, it, dsin);
+double sin2(double theta, int *it, double *dsin)
+{
+    if (theta < 0)
+        return -sin2(theta, it, dsin);
+    if (theta > 2 * PI)
+        return sin2(theta - 2 * PI, it, dsin);
+    if (theta > PI)
+        return -sin2(theta - PI, it, dsin);
+    if (theta > PI / 2)
+        return sin2(PI - theta, it, dsin);
 
     double result = 0;
-    double term=theta;
+    double term = theta;
     int i = 0;
-    while (i<100 && fabs(term)>1e-16){
+    while (i < 100 && fabs(term) > 1e-16)
+    {
         result += term;
-	i += 1;
-	term *= -1;
-	term /= 2*i;
-	term /= (2*i+1);
-	term *= theta*theta;
+        i += 1;
+        term *= -1;
+        term /= 2 * i;
+        term /= (2 * i + 1);
+        term *= theta * theta;
     }
     *it = i;
     *dsin = term;
     return result;
 }
 
-int main(){
+int main()
+{
     int it;
     double theta = 1.0;
-    double sin,dsin;
+    double sin, dsin;
     clock_t start, end;
 
     start = clock();
-    for (int i=0; i<10000; i++) sin = sin1(theta, &it, &dsin);
+    for (int i = 0; i < 10000; i++)
+        sin = sin1(theta, &it, &dsin);
     end = clock();
-    printf("sin1(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end-start)/CLOCKS_PER_SEC);
-    
+    printf("sin1(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end - start) / CLOCKS_PER_SEC);
+
     start = clock();
-    for (int i=0; i<10000; i++) sin = sin2(theta, &it, &dsin);
+    for (int i = 0; i < 10000; i++)
+        sin = sin2(theta, &it, &dsin);
     end = clock();
-    printf("sin2(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end-start)/CLOCKS_PER_SEC);
+    printf("sin2(%.16g) = %.16g, it = %d, dsin=%.16g, took %.16g s.\n", theta, sin, it, dsin, (double)(end - start) / CLOCKS_PER_SEC);
+
     return 0;
 }