kicad/common/trigo.cpp

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/****************************/
/* Trigonometric functions. */
/****************************/
#include "fctsys.h"
#include "trigo.h"
/**
* Function TestSegmentHit
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* test for hit on line segment
* i.e. cursor within a given distance from segment
* @param aRefPoint = cursor (point to test) coords
* @param aStart is the first end-point of the line segment
* @param aEnd is the second end-point of the line segment
* @param aDist = maximum distance for hit
*/
bool TestSegmentHit( wxPoint aRefPoint, wxPoint aStart, wxPoint aEnd, int aDist )
{
// make coordinates relatives to aStart:
aEnd -= aStart;
aRefPoint -= aStart;
return DistanceTest( aDist, aEnd.x, aEnd.y, aRefPoint.x, aRefPoint.y );
}
/**
* Function DistanceTest
* Calculate the distance from mouse cursor to a line segment.
* Returns:
* False if distance > threshold
* True if distance <= threshold
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*/
bool DistanceTest( int seuil, int dx, int dy, int spot_cX, int spot_cY )
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{
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/* We can have 4 cases::
* horizontal segment
* vertical segment
* 45 degrees segment
* other slopes
*/
int cXrot, cYrot, segX, segY;
int pointX, pointY;
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segX = dx;
segY = dy;
pointX = spot_cX;
pointY = spot_cY;
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/*Recalculating coord for the segment is in 1st quadrant (coord >= 0)*/
if( segX < 0 ) /* set > 0 by symmetry about the Y axis */
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{
segX = -segX;
pointX = -pointX;
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}
if( segY < 0 ) /* set > 0 by symmetry about the X axis */
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{
segY = -segY;
pointY = -pointY;
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}
if( segY == 0 ) /* horizontal */
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{
if( abs( pointY ) <= seuil )
{
if( ( pointX >= 0 ) && ( pointX <= segX ) )
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return 1;
if( ( pointX < 0 ) && ( pointX >= -seuil ) )
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{
if( ( ( pointX * pointX ) + ( pointY * pointY ) )
<= ( seuil * seuil ) )
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return true;
}
if( ( pointX > segX ) && ( pointX <= ( segX + seuil ) ) )
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{
if( ( ( ( pointX - segX ) * ( pointX - segX ) )
+ ( pointY * pointY ) ) <= ( seuil * seuil ) )
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return true;
}
}
}
else if( segX == 0 ) /* vertical */
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{
if( abs( pointX ) <= seuil )
{
if( ( pointY >= 0 ) && ( pointY <= segY ) )
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return true;
if( ( pointY < 0 ) && ( pointY >= -seuil ) )
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{
if( ( ( pointY * pointY ) + ( pointX * pointX ) )
<= ( seuil * seuil ) )
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return true;
}
if( ( pointY > segY ) && ( pointY <= ( segY + seuil ) ) )
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{
if( ( ( ( pointY - segY ) * ( pointY - segY ) )
+ ( pointX * pointX ) ) <= ( seuil * seuil ) )
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return true;
}
}
}
else if( segX == segY ) /* 45 degrees */
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{
/* Rotate axes of 45 degrees. mouse was then
* Coord: x1 = x * y * cos45 + sin45
* y1 = y * cos45 - sin45 x *
* And the segment of track is horizontal.
* Coord recalculation of the mouse (sin45 = cos45 = .707 = 7 / 10
* Note: sin or cos45 = .707, and when recalculating coord
* dx45 and dy45, lect coeff .707 is neglected, dx and dy are
* actually 0707 times
* Too big. (security hole too small)
* Spot_cX, Y * must be by .707 * .707 = 0.5
*/
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cXrot = (pointX + pointY) >> 1;
cYrot = (pointY - pointX) >> 1;
/* Recalculating coord of segment extremity, which will be vertical
* following the orientation of axes on the screen: dx45 = pointx
* (or pointy) and 1.414 is actually greater, and dy45 = 0
*/
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// * Threshold should be .707 to reflect the change in coeff dx, dy
seuil *= 7;
seuil /= 10;
if( abs( cYrot ) <= seuil ) /* ok on vertical axis */
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{
if( ( cXrot >= 0 ) && ( cXrot <= segX ) )
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return true;
/* Check extremes using the radius of a circle. */
if( ( cXrot < 0 ) && ( cXrot >= -seuil ) )
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{
if( ( ( cXrot * cXrot ) + ( cYrot * cYrot ) )
<= ( seuil * seuil ) )
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return true;
}
if( ( cXrot > segX ) && ( cXrot <= ( segX + seuil ) ) )
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{
if( ( ( ( cXrot - segX ) * ( cXrot - segX ) )
+ ( cYrot * cYrot ) ) <= ( seuil * seuil ) )
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return true;
}
}
}
else /* any orientation */
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{
/* There is a change of axis (rotation), so that the segment
* track is horizontal in the new reference
*/
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int angle;
angle = wxRound( ( atan2( (double) segY,
(double) segX ) * 1800.0 / M_PI ) );
cXrot = pointX;
cYrot = pointY;
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RotatePoint( &cXrot, &cYrot, angle ); /* Rotate the point to be tested */
RotatePoint( &segX, &segY, angle ); /* Rotate the segment */
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/* The track is horizontal, following the amendments to coordinate
* axis and, therefore segX = length of segment
*/
if( abs( cYrot ) <= seuil ) /* vertical axis */
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{
if( ( cXrot >= 0 ) && ( cXrot <= segX ) )
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return true;
if( ( cXrot < 0 ) && ( cXrot >= -seuil ) )
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{
if( ( ( cXrot * cXrot ) + ( cYrot * cYrot ) )
<= ( seuil * seuil ) )
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return true;
}
if( ( cXrot > segX ) && ( cXrot <= ( segX + seuil ) ) )
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{
if( ( ( ( cXrot - segX ) * ( cXrot - segX ) )
+ ( cYrot * cYrot ) ) <= ( seuil * seuil ) )
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return true;
}
}
}
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return false;
}
/* Return the arc tangent of 0.1 degrees coord vector dx, dy
* between -1800 and 1800
* Equivalent to atan2 (but faster for calculations if
* the angle is 0 to -1800, or + - 900
*/
int ArcTangente( int dy, int dx )
{
double fangle;
if( dy == 0 )
{
if( dx >= 0 )
return 0;
else
return -1800;
}
if( dx == 0 )
{
if( dy >= 0 )
return 900;
else
return -900;
}
if( dx == dy )
{
if( dx >= 0 )
return 450;
else
return -1800 + 450;
}
if( dx == -dy )
{
if( dx >= 0 )
return -450;
else
return 1800 - 450;
}
fangle = atan2( (double) dy, (double) dx ) / M_PI * 1800;
return wxRound( fangle );
}
/*
* Calculate the new point of coord coord pX, pY,
* for a rotation center 0, 0, and angle in (1 / 10 degree)
*/
void RotatePoint( int* pX, int* pY, int angle )
{
double fpx, fpy;
int tmp;
while( angle < 0 )
angle += 3600;
while( angle >= 3600 )
angle -= 3600;
if( angle == 0 )
return;
/* coord: xrot = y*sin + x*cos
* yrot = y*cos - x*sin
*/
if( angle == 900 ) /* sin = 1, cos = 0 */
{
tmp = *pX;
*pX = *pY;
*pY = -tmp;
}
else if( angle == 1800 ) /* sin = 0, cos = -1 */
{
*pX = -*pX;
*pY = -*pY;
}
else if( angle == 2700 ) /* sin = -1, cos = 0 */
{
tmp = *pX;
*pX = -*pY;
*pY = tmp;
}
else
{
fpx = ( *pY * fsinus[angle] ) + ( *pX * fcosinus[angle] );
fpy = ( *pY * fcosinus[angle] ) - ( *pX * fsinus[angle] );
*pX = wxRound( fpx );
*pY = wxRound( fpy );
}
}
/*
* Calculate the new point of coord coord pX, pY,
* for a rotation center cx, cy, and angle in (1 / 10 degree)
*/
void RotatePoint( int* pX, int* pY, int cx, int cy, int angle )
{
int ox, oy;
ox = *pX - cx;
oy = *pY - cy;
RotatePoint( &ox, &oy, angle );
*pX = ox + cx;
*pY = oy + cy;
}
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/*
* Calculates the new coord point point
* for a rotation angle in (1 / 10 degree)
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*/
void RotatePoint( wxPoint* point, int angle )
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{
int ox, oy;
ox = point->x;
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oy = point->y;
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RotatePoint( &ox, &oy, angle );
point->x = ox;
point->y = oy;
}
/*
* Calculates the new coord point point
* for a center rotation center and angle in (1 / 10 degree)
*/
void RotatePoint( wxPoint* point, const wxPoint& centre, int angle )
{
int ox, oy;
ox = point->x - centre.x;
oy = point->y - centre.y;
RotatePoint( &ox, &oy, angle );
point->x = ox + centre.x;
point->y = oy + centre.y;
}
void RotatePoint( double* pX, double* pY, double cx, double cy, int angle )
{
double ox, oy;
ox = *pX - cx;
oy = *pY - cy;
RotatePoint( &ox, &oy, angle );
*pX = ox + cx;
*pY = oy + cy;
}
void RotatePoint( double* pX, double* pY, int angle )
{
double tmp;
while( angle < 0 )
angle += 3600;
while( angle >= 3600 )
angle -= 3600;
if( angle == 0 )
return;
if( angle == 900 ) /* sin = 1, cos = 0 */
{
tmp = *pX;
*pX = *pY;
*pY = -tmp;
}
else if( angle == 1800 ) /* sin = 0, cos = -1 */
{
*pX = -*pX;
*pY = -*pY;
}
else if( angle == 2700 ) /* sin = -1, cos = 0 */
{
tmp = *pX;
*pX = -*pY;
*pY = tmp;
}
else
{
double fpx = (*pY * fsinus[angle]) + (*pX * fcosinus[angle]);
double fpy = (*pY * fcosinus[angle]) - (*pX * fsinus[angle]);
*pX = fpx;
*pY = fpy;
}
}
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double EuclideanNorm( wxPoint vector )
{
return sqrt( (double) vector.x * (double) vector.x + (double) vector.y * (double) vector.y );
}
wxPoint TwoPointVector( wxPoint startPoint, wxPoint endPoint )
{
return endPoint - startPoint;
}
double DistanceLinePoint( wxPoint linePointA, wxPoint linePointB, wxPoint referencePoint )
{
return fabs( (double) ( (linePointB.x - linePointA.x) * (linePointA.y - referencePoint.y) -
(linePointA.x - referencePoint.x ) * (linePointB.y - linePointA.y) )
/ EuclideanNorm( TwoPointVector( linePointA, linePointB ) ) );
}
bool HitTestPoints( wxPoint pointA, wxPoint pointB, double threshold )
{
wxPoint vectorAB = TwoPointVector( pointA, pointB );
double distance = EuclideanNorm( vectorAB );
return distance < threshold;
}
int CrossProduct( wxPoint vectorA, wxPoint vectorB )
{
return vectorA.x * vectorB.y - vectorA.y * vectorB.x;
}
double GetLineLength( const wxPoint& aPointA, const wxPoint& aPointB )
{
return sqrt( pow( (double) aPointA.x - (double) aPointB.x, 2 ) +
pow( (double) aPointA.y - (double) aPointB.y, 2 ) );
}
double fsinus[3600] =
{
0.0000000000, 0.0017453284, 0.0034906514, 0.0052359638,
0.0069812603, 0.0087265355, 0.0104717841, 0.0122170008, 0.0139621803,
0.0157073173, 0.0174524064, 0.0191974424, 0.0209424199, 0.0226873336,
0.0244321782, 0.0261769483, 0.0279216387, 0.0296662441, 0.0314107591,
0.0331551784, 0.0348994967, 0.0366437087, 0.0383878091, 0.0401317925,
0.0418756537, 0.0436193874, 0.0453629881, 0.0471064507, 0.0488497698,
0.0505929401, 0.0523359562, 0.0540788130, 0.0558215050, 0.0575640270,
0.0593063736, 0.0610485395, 0.0627905195, 0.0645323083, 0.0662739004,
0.0680152907, 0.0697564737, 0.0714974443, 0.0732381971, 0.0749787268,
0.0767190281, 0.0784590957, 0.0801989243, 0.0819385086, 0.0836778433,
0.0854169231, 0.0871557427, 0.0888942969, 0.0906325802, 0.0923705874,
0.0941083133, 0.0958457525, 0.0975828998, 0.0993197497, 0.1010562972,
0.1027925368, 0.1045284633, 0.1062640713, 0.1079993557, 0.1097343111,
0.1114689322, 0.1132032138, 0.1149371505, 0.1166707371, 0.1184039683,
0.1201368388, 0.1218693434, 0.1236014767, 0.1253332336, 0.1270646086,
0.1287955966, 0.1305261922, 0.1322563903, 0.1339861854, 0.1357155724,
0.1374445460, 0.1391731010, 0.1409012319, 0.1426289337, 0.1443562010,
0.1460830286, 0.1478094111, 0.1495353434, 0.1512608202, 0.1529858363,
0.1547103863, 0.1564344650, 0.1581580673, 0.1598811877, 0.1616038211,
0.1633259622, 0.1650476059, 0.1667687467, 0.1684893796, 0.1702094992,
0.1719291003, 0.1736481777, 0.1753667261, 0.1770847403, 0.1788022151,
0.1805191453, 0.1822355255, 0.1839513506, 0.1856666154, 0.1873813146,
0.1890954430, 0.1908089954, 0.1925219665, 0.1942343512, 0.1959461442,
0.1976573404, 0.1993679344, 0.2010779211, 0.2027872954, 0.2044960518,
0.2062041854, 0.2079116908, 0.2096185629, 0.2113247965, 0.2130303863,
0.2147353272, 0.2164396139, 0.2181432414, 0.2198462044, 0.2215484976,
0.2232501160, 0.2249510543, 0.2266513074, 0.2283508701, 0.2300497372,
0.2317479035, 0.2334453639, 0.2351421131, 0.2368381461, 0.2385334576,
0.2402280425, 0.2419218956, 0.2436150118, 0.2453073859, 0.2469990127,
0.2486898872, 0.2503800041, 0.2520693582, 0.2537579446, 0.2554457579,
0.2571327932, 0.2588190451, 0.2605045086, 0.2621891786, 0.2638730500,
0.2655561175, 0.2672383761, 0.2689198206, 0.2706004460, 0.2722802470,
0.2739592187, 0.2756373558, 0.2773146533, 0.2789911060, 0.2806667089,
0.2823414568, 0.2840153447, 0.2856883674, 0.2873605198, 0.2890317969,
0.2907021936, 0.2923717047, 0.2940403252, 0.2957080500, 0.2973748741,
0.2990407923, 0.3007057995, 0.3023698908, 0.3040330609, 0.3056953050,
0.3073566178, 0.3090169944, 0.3106764296, 0.3123349185, 0.3139924560,
0.3156490369, 0.3173046564, 0.3189593093, 0.3206129906, 0.3222656952,
0.3239174182, 0.3255681545, 0.3272178990, 0.3288666467, 0.3305143927,
0.3321611319, 0.3338068592, 0.3354515698, 0.3370952584, 0.3387379202,
0.3403795502, 0.3420201433, 0.3436596946, 0.3452981990, 0.3469356516,
0.3485720473, 0.3502073813, 0.3518416484, 0.3534748438, 0.3551069624,
0.3567379993, 0.3583679495, 0.3599968081, 0.3616245701, 0.3632512305,
0.3648767843, 0.3665012267, 0.3681245527, 0.3697467573, 0.3713678356,
0.3729877826, 0.3746065934, 0.3762242631, 0.3778407868, 0.3794561595,
0.3810703764, 0.3826834324, 0.3842953227, 0.3859060423, 0.3875155865,
0.3891239501, 0.3907311285, 0.3923371166, 0.3939419096, 0.3955455026,
0.3971478906, 0.3987490689, 0.4003490326, 0.4019477767, 0.4035452964,
0.4051415868, 0.4067366431, 0.4083304604, 0.4099230338, 0.4115143586,
0.4131044298, 0.4146932427, 0.4162807923, 0.4178670738, 0.4194520824,
0.4210358134, 0.4226182617, 0.4241994227, 0.4257792916, 0.4273578634,
0.4289351334, 0.4305110968, 0.4320857488, 0.4336590846, 0.4352310994,
0.4368017884, 0.4383711468, 0.4399391699, 0.4415058528, 0.4430711908,
0.4446351792, 0.4461978131, 0.4477590878, 0.4493189986, 0.4508775407,
0.4524347093, 0.4539904997, 0.4555449072, 0.4570979271, 0.4586495545,
0.4601997848, 0.4617486132, 0.4632960351, 0.4648420457, 0.4663866403,
0.4679298143, 0.4694715628, 0.4710118812, 0.4725507649, 0.4740882090,
0.4756242091, 0.4771587603, 0.4786918579, 0.4802234974, 0.4817536741,
0.4832823833, 0.4848096202, 0.4863353804, 0.4878596591, 0.4893824517,
0.4909037536, 0.4924235601, 0.4939418666, 0.4954586684, 0.4969739610,
0.4984877398, 0.5000000000, 0.5015107372, 0.5030199466, 0.5045276238,
0.5060337641, 0.5075383630, 0.5090414158, 0.5105429179, 0.5120428649,
0.5135412521, 0.5150380749, 0.5165333289, 0.5180270094, 0.5195191119,
0.5210096318, 0.5224985647, 0.5239859060, 0.5254716511, 0.5269557955,
0.5284383347, 0.5299192642, 0.5313985795, 0.5328762761, 0.5343523494,
0.5358267950, 0.5372996083, 0.5387707850, 0.5402403205, 0.5417082103,
0.5431744500, 0.5446390350, 0.5461019610, 0.5475632235, 0.5490228180,
0.5504807401, 0.5519369853, 0.5533915492, 0.5548444274, 0.5562956155,
0.5577451090, 0.5591929035, 0.5606389946, 0.5620833779, 0.5635260489,
0.5649670034, 0.5664062369, 0.5678437451, 0.5692795234, 0.5707135677,
0.5721458734, 0.5735764364, 0.5750052520, 0.5764323162, 0.5778576244,
0.5792811723, 0.5807029557, 0.5821229702, 0.5835412114, 0.5849576750,
0.5863723567, 0.5877852523, 0.5891963574, 0.5906056676, 0.5920131788,
0.5934188866, 0.5948227868, 0.5962248750, 0.5976251470, 0.5990235985,
0.6004202253, 0.6018150232, 0.6032079877, 0.6045991149, 0.6059884003,
0.6073758397, 0.6087614290, 0.6101451639, 0.6115270402, 0.6129070537,
0.6142852001, 0.6156614753, 0.6170358751, 0.6184083954, 0.6197790318,
0.6211477803, 0.6225146366, 0.6238795967, 0.6252426563, 0.6266038114,
0.6279630576, 0.6293203910, 0.6306758074, 0.6320293027, 0.6333808726,
0.6347305132, 0.6360782203, 0.6374239897, 0.6387678175, 0.6401096995,
0.6414496316, 0.6427876097, 0.6441236298, 0.6454576877, 0.6467897795,
0.6481199011, 0.6494480483, 0.6507742173, 0.6520984038, 0.6534206040,
0.6547408137, 0.6560590290, 0.6573752458, 0.6586894601, 0.6600016680,
0.6613118653, 0.6626200482, 0.6639262127, 0.6652303547, 0.6665324702,
0.6678325555, 0.6691306064, 0.6704266190, 0.6717205893, 0.6730125135,
0.6743023876, 0.6755902076, 0.6768759697, 0.6781596699, 0.6794413043,
0.6807208690, 0.6819983601, 0.6832737737, 0.6845471059, 0.6858183529,
0.6870875108, 0.6883545757, 0.6896195437, 0.6908824111, 0.6921431739,
0.6934018283, 0.6946583705, 0.6959127966, 0.6971651029, 0.6984152854,
0.6996633405, 0.7009092643, 0.7021530530, 0.7033947028, 0.7046342100,
0.7058715707, 0.7071067812, 0.7083398377, 0.7095707365, 0.7107994739,
0.7120260460, 0.7132504492, 0.7144726796, 0.7156927337, 0.7169106077,
0.7181262978, 0.7193398003, 0.7205511117, 0.7217602281, 0.7229671459,
0.7241718614, 0.7253743710, 0.7265746710, 0.7277727577, 0.7289686274,
0.7301622766, 0.7313537016, 0.7325428988, 0.7337298645, 0.7349145951,
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-0.2605045086, -0.2588190451, -0.2571327932, -0.2554457579,-0.2537579446,
-0.2520693582, -0.2503800041, -0.2486898872, -0.2469990127,-0.2453073859,
-0.2436150118, -0.2419218956, -0.2402280425, -0.2385334576,-0.2368381461,
-0.2351421131, -0.2334453639, -0.2317479035, -0.2300497372,-0.2283508701,
-0.2266513074, -0.2249510543, -0.2232501160, -0.2215484976,-0.2198462044,
-0.2181432414, -0.2164396139, -0.2147353272, -0.2130303863,-0.2113247965,
-0.2096185629, -0.2079116908, -0.2062041854, -0.2044960518,-0.2027872954,
-0.2010779211, -0.1993679344, -0.1976573404, -0.1959461442,-0.1942343512,
-0.1925219665, -0.1908089954, -0.1890954430, -0.1873813146,-0.1856666154,
-0.1839513506, -0.1822355255, -0.1805191453, -0.1788022151,-0.1770847403,
-0.1753667261, -0.1736481777, -0.1719291003, -0.1702094992,-0.1684893796,
-0.1667687467, -0.1650476059, -0.1633259622, -0.1616038211,-0.1598811877,
-0.1581580673, -0.1564344650, -0.1547103863, -0.1529858363,-0.1512608202,
-0.1495353434, -0.1478094111, -0.1460830286, -0.1443562010,-0.1426289337,
-0.1409012319, -0.1391731010, -0.1374445460, -0.1357155724,-0.1339861854,
-0.1322563903, -0.1305261922, -0.1287955966, -0.1270646086,-0.1253332336,
-0.1236014767, -0.1218693434, -0.1201368388, -0.1184039683,-0.1166707371,
-0.1149371505, -0.1132032138, -0.1114689322, -0.1097343111,-0.1079993557,
-0.1062640713, -0.1045284633, -0.1027925368, -0.1010562972,-0.0993197497,
-0.0975828998, -0.0958457525, -0.0941083133, -0.0923705874,-0.0906325802,
-0.0888942969, -0.0871557427, -0.0854169231, -0.0836778433,-0.0819385086,
-0.0801989243, -0.0784590957, -0.0767190281, -0.0749787268,-0.0732381971,
-0.0714974443, -0.0697564737, -0.0680152907, -0.0662739004,-0.0645323083,
-0.0627905195, -0.0610485395, -0.0593063736, -0.0575640270,-0.0558215050,
-0.0540788130, -0.0523359562, -0.0505929401, -0.0488497698,-0.0471064507,
-0.0453629881, -0.0436193874, -0.0418756537, -0.0401317925,-0.0383878091,
-0.0366437087, -0.0348994967, -0.0331551784, -0.0314107591,-0.0296662441,
-0.0279216387, -0.0261769483, -0.0244321782, -0.0226873336,-0.0209424199,
-0.0191974424, -0.0174524064, -0.0157073173, -0.0139621803,-0.0122170008,
-0.0104717841, -0.0087265355, -0.0069812603, -0.0052359638,-0.0034906514,
-0.0017453284
};
double fcosinus[3600] =
{
1.0000000000, 0.9999984769, 0.9999939077, 0.9999862922,
0.9999756307, 0.9999619231, 0.9999451694, 0.9999253697, 0.9999025240,
0.9998766325, 0.9998476952, 0.9998157121, 0.9997806835, 0.9997426093,
0.9997014898, 0.9996573250, 0.9996101150, 0.9995598601, 0.9995065604,
0.9994502159, 0.9993908270, 0.9993283938, 0.9992629164, 0.9991943951,
0.9991228301, 0.9990482216, 0.9989705698, 0.9988898750, 0.9988061373,
0.9987193572, 0.9986295348, 0.9985366703, 0.9984407642, 0.9983418166,
0.9982398279, 0.9981347984, 0.9980267284, 0.9979156183, 0.9978014683,
0.9976842788, 0.9975640503, 0.9974407829, 0.9973144772, 0.9971851335,
0.9970527522, 0.9969173337, 0.9967788785, 0.9966373868, 0.9964928592,
0.9963452962, 0.9961946981, 0.9960410654, 0.9958843986, 0.9957246982,
0.9955619646, 0.9953961984, 0.9952274000, 0.9950555700, 0.9948807088,
0.9947028171, 0.9945218954, 0.9943379441, 0.9941509640, 0.9939609555,
0.9937679192, 0.9935718557, 0.9933727656, 0.9931706495, 0.9929655081,
0.9927573419, 0.9925461516, 0.9923319379, 0.9921147013, 0.9918944426,
0.9916711624, 0.9914448614, 0.9912155403, 0.9909831997, 0.9907478405,
0.9905094632, 0.9902680687, 0.9900236577, 0.9897762309, 0.9895257891,
0.9892723330, 0.9890158634, 0.9887563810, 0.9884938868, 0.9882283814,
0.9879598658, 0.9876883406, 0.9874138068, 0.9871362651, 0.9868557164,
0.9865721616, 0.9862856015, 0.9859960371, 0.9857034691, 0.9854078985,
0.9851093262, 0.9848077530, 0.9845031800, 0.9841956080, 0.9838850379,
0.9835714708, 0.9832549076, 0.9829353491, 0.9826127965, 0.9822872507,
0.9819587127, 0.9816271834, 0.9812926640, 0.9809551553, 0.9806146585,
0.9802711746, 0.9799247046, 0.9795752496, 0.9792228106, 0.9788673888,
0.9785089851, 0.9781476007, 0.9777832368, 0.9774158943, 0.9770455744,
0.9766722783, 0.9762960071, 0.9759167619, 0.9755345439, 0.9751493543,
0.9747611942, 0.9743700648, 0.9739759673, 0.9735789029, 0.9731788728,
0.9727758782, 0.9723699204, 0.9719610006, 0.9715491200, 0.9711342799,
0.9707164816, 0.9702957263, 0.9698720153, 0.9694453499, 0.9690157314,
0.9685831611, 0.9681476404, 0.9677091705, 0.9672677528, 0.9668233886,
0.9663760793, 0.9659258263, 0.9654726309, 0.9650164945, 0.9645574185,
0.9640954042, 0.9636304532, 0.9631625668, 0.9626917464, 0.9622179935,
0.9617413095, 0.9612616959, 0.9607791542, 0.9602936857, 0.9598052920,
0.9593139745, 0.9588197349, 0.9583225745, 0.9578224948, 0.9573194975,
0.9568135841, 0.9563047560, 0.9557930148, 0.9552783621, 0.9547607995,
0.9542403285, 0.9537169507, 0.9531906678, 0.9526614813, 0.9521293927,
0.9515944039, 0.9510565163, 0.9505157316, 0.9499720515, 0.9494254776,
0.9488760116, 0.9483236552, 0.9477684100, 0.9472102777, 0.9466492601,
0.9460853588, 0.9455185756, 0.9449489122, 0.9443763702, 0.9438009516,
0.9432226579, 0.9426414911, 0.9420574528, 0.9414705448, 0.9408807690,
0.9402881270, 0.9396926208, 0.9390942521, 0.9384930228, 0.9378889346,
0.9372819895, 0.9366721892, 0.9360595357, 0.9354440308, 0.9348256764,
0.9342044743, 0.9335804265, 0.9329535348, 0.9323238012, 0.9316912276,
0.9310558159, 0.9304175680, 0.9297764859, 0.9291325715, 0.9284858269,
0.9278362539, 0.9271838546, 0.9265286309, 0.9258705848, 0.9252097184,
0.9245460336, 0.9238795325, 0.9232102171, 0.9225380895, 0.9218631516,
0.9211854056, 0.9205048535, 0.9198214973, 0.9191353393, 0.9184463813,
0.9177546257, 0.9170600744, 0.9163627296, 0.9156625933, 0.9149596678,
0.9142539552, 0.9135454576, 0.9128341772, 0.9121201162, 0.9114032766,
0.9106836608, 0.9099612709, 0.9092361090, 0.9085081775, 0.9077774785,
0.9070440143, 0.9063077870, 0.9055687990, 0.9048270525, 0.9040825497,
0.9033352929, 0.9025852843, 0.9018325264, 0.9010770213, 0.9003187714,
0.8995577790, 0.8987940463, 0.8980275758, 0.8972583697, 0.8964864304,
0.8957117602, 0.8949343616, 0.8941542368, 0.8933713883, 0.8925858185,
0.8917975296, 0.8910065242, 0.8902128046, 0.8894163733, 0.8886172327,
0.8878153851, 0.8870108332, 0.8862035792, 0.8853936258, 0.8845809752,
0.8837656301, 0.8829475929, 0.8821268660, 0.8813034521, 0.8804773535,
0.8796485729, 0.8788171127, 0.8779829754, 0.8771461637, 0.8763066800,
0.8754645270, 0.8746197071, 0.8737722230, 0.8729220773, 0.8720692724,
0.8712138111, 0.8703556959, 0.8694949295, 0.8686315144, 0.8677654534,
0.8668967489, 0.8660254038, 0.8651514206, 0.8642748020, 0.8633955506,
0.8625136692, 0.8616291604, 0.8607420270, 0.8598522716, 0.8589598969,
0.8580649057, 0.8571673007, 0.8562670846, 0.8553642602, 0.8544588301,
0.8535507973, 0.8526401644, 0.8517269341, 0.8508111094, 0.8498926930,
0.8489716876, 0.8480480962, 0.8471219214, 0.8461931661, 0.8452618332,
0.8443279255, 0.8433914458, 0.8424523970, 0.8415107819, 0.8405666035,
0.8396198645, 0.8386705679, 0.8377187166, 0.8367643135, 0.8358073614,
0.8348478633, 0.8338858221, 0.8329212407, 0.8319541221, 0.8309844693,
0.8300122851, 0.8290375726, 0.8280603346, 0.8270805743, 0.8260982945,
0.8251134983, 0.8241261886, 0.8231363685, 0.8221440410, 0.8211492091,
0.8201518759, 0.8191520443, 0.8181497174, 0.8171448983, 0.8161375901,
0.8151277957, 0.8141155184, 0.8131007610, 0.8120835269, 0.8110638190,
0.8100416404, 0.8090169944, 0.8079898839, 0.8069603121, 0.8059282822,
0.8048937974, 0.8038568606, 0.8028174752, 0.8017756442, 0.8007313709,
0.7996846585, 0.7986355100, 0.7975839288, 0.7965299180, 0.7954734809,
0.7944146205, 0.7933533403, 0.7922896434, 0.7912235330, 0.7901550124,
0.7890840848, 0.7880107536, 0.7869350220, 0.7858568932, 0.7847763705,
0.7836934573, 0.7826081569, 0.7815204724, 0.7804304073, 0.7793379649,
0.7782431485, 0.7771459615, 0.7760464071, 0.7749444887, 0.7738402097,
0.7727335735, 0.7716245834, 0.7705132428, 0.7693995550, 0.7682835236,
0.7671651518, 0.7660444431, 0.7649214009, 0.7637960286, 0.7626683297,
0.7615383075, 0.7604059656, 0.7592713073, 0.7581343362, 0.7569950557,
0.7558534692, 0.7547095802, 0.7535633923, 0.7524149089, 0.7512641335,
0.7501110696, 0.7489557208, 0.7477980905, 0.7466381823, 0.7454759997,
0.7443115462, 0.7431448255, 0.7419758410, 0.7408045963, 0.7396310950,
0.7384553406, 0.7372773368, 0.7360970871, 0.7349145951, 0.7337298645,
0.7325428988, 0.7313537016, 0.7301622766, 0.7289686274, 0.7277727577,
0.7265746710, 0.7253743710, 0.7241718614, 0.7229671459, 0.7217602281,
0.7205511117, 0.7193398003, 0.7181262978, 0.7169106077, 0.7156927337,
0.7144726796, 0.7132504492, 0.7120260460, 0.7107994739, 0.7095707365,
0.7083398377, 0.7071067812, 0.7058715707, 0.7046342100, 0.7033947028,
0.7021530530, 0.7009092643, 0.6996633405, 0.6984152854, 0.6971651029,
0.6959127966, 0.6946583705, 0.6934018283, 0.6921431739, 0.6908824111,
0.6896195437, 0.6883545757, 0.6870875108, 0.6858183529, 0.6845471059,
0.6832737737, 0.6819983601, 0.6807208690, 0.6794413043, 0.6781596699,
0.6768759697, 0.6755902076, 0.6743023876, 0.6730125135, 0.6717205893,
0.6704266190, 0.6691306064, 0.6678325555, 0.6665324702, 0.6652303547,
0.6639262127, 0.6626200482, 0.6613118653, 0.6600016680, 0.6586894601,
0.6573752458, 0.6560590290, 0.6547408137, 0.6534206040, 0.6520984038,
0.6507742173, 0.6494480483, 0.6481199011, 0.6467897795, 0.6454576877,
0.6441236298, 0.6427876097, 0.6414496316, 0.6401096995, 0.6387678175,
0.6374239897, 0.6360782203, 0.6347305132, 0.6333808726, 0.6320293027,
0.6306758074, 0.6293203910, 0.6279630576, 0.6266038114, 0.6252426563,
0.6238795967, 0.6225146366, 0.6211477803, 0.6197790318, 0.6184083954,
0.6170358751, 0.6156614753, 0.6142852001, 0.6129070537, 0.6115270402,
0.6101451639, 0.6087614290, 0.6073758397, 0.6059884003, 0.6045991149,
0.6032079877, 0.6018150232, 0.6004202253, 0.5990235985, 0.5976251470,
0.5962248750, 0.5948227868, 0.5934188866, 0.5920131788, 0.5906056676,
0.5891963574, 0.5877852523, 0.5863723567, 0.5849576750, 0.5835412114,
0.5821229702, 0.5807029557, 0.5792811723, 0.5778576244, 0.5764323162,
0.5750052520, 0.5735764364, 0.5721458734, 0.5707135677, 0.5692795234,
0.5678437451, 0.5664062369, 0.5649670034, 0.5635260489, 0.5620833779,
0.5606389946, 0.5591929035, 0.5577451090, 0.5562956155, 0.5548444274,
0.5533915492, 0.5519369853, 0.5504807401, 0.5490228180, 0.5475632235,
0.5461019610, 0.5446390350, 0.5431744500, 0.5417082103, 0.5402403205,
0.5387707850, 0.5372996083, 0.5358267950, 0.5343523494, 0.5328762761,
0.5313985795, 0.5299192642, 0.5284383347, 0.5269557955, 0.5254716511,
0.5239859060, 0.5224985647, 0.5210096318, 0.5195191119, 0.5180270094,
0.5165333289, 0.5150380749, 0.5135412521, 0.5120428649, 0.5105429179,
0.5090414158, 0.5075383630, 0.5060337641, 0.5045276238, 0.5030199466,
0.5015107372, 0.5000000000, 0.4984877398, 0.4969739610, 0.4954586684,
0.4939418666, 0.4924235601, 0.4909037536, 0.4893824517, 0.4878596591,
0.4863353804, 0.4848096202, 0.4832823833, 0.4817536741, 0.4802234974,
0.4786918579, 0.4771587603, 0.4756242091, 0.4740882090, 0.4725507649,
0.4710118812, 0.4694715628, 0.4679298143, 0.4663866403, 0.4648420457,
0.4632960351, 0.4617486132, 0.4601997848, 0.4586495545, 0.4570979271,
0.4555449072, 0.4539904997, 0.4524347093, 0.4508775407, 0.4493189986,
0.4477590878, 0.4461978131, 0.4446351792, 0.4430711908, 0.4415058528,
0.4399391699, 0.4383711468, 0.4368017884, 0.4352310994, 0.4336590846,
0.4320857488, 0.4305110968, 0.4289351334, 0.4273578634, 0.4257792916,
0.4241994227, 0.4226182617, 0.4210358134, 0.4194520824, 0.4178670738,
0.4162807923, 0.4146932427, 0.4131044298, 0.4115143586, 0.4099230338,
0.4083304604, 0.4067366431, 0.4051415868, 0.4035452964, 0.4019477767,
0.4003490326, 0.3987490689, 0.3971478906, 0.3955455026, 0.3939419096,
0.3923371166, 0.3907311285, 0.3891239501, 0.3875155865, 0.3859060423,
0.3842953227, 0.3826834324, 0.3810703764, 0.3794561595, 0.3778407868,
0.3762242631, 0.3746065934, 0.3729877826, 0.3713678356, 0.3697467573,
0.3681245527, 0.3665012267, 0.3648767843, 0.3632512305, 0.3616245701,
0.3599968081, 0.3583679495, 0.3567379993, 0.3551069624, 0.3534748438,
0.3518416484, 0.3502073813, 0.3485720473, 0.3469356516, 0.3452981990,
0.3436596946, 0.3420201433, 0.3403795502, 0.3387379202, 0.3370952584,
0.3354515698, 0.3338068592, 0.3321611319, 0.3305143927, 0.3288666467,
0.3272178990, 0.3255681545, 0.3239174182, 0.3222656952, 0.3206129906,
0.3189593093, 0.3173046564, 0.3156490369, 0.3139924560, 0.3123349185,
0.3106764296, 0.3090169944, 0.3073566178, 0.3056953050, 0.3040330609,
0.3023698908, 0.3007057995, 0.2990407923, 0.2973748741, 0.2957080500,
0.2940403252, 0.2923717047, 0.2907021936, 0.2890317969, 0.2873605198,
0.2856883674, 0.2840153447, 0.2823414568, 0.2806667089, 0.2789911060,
0.2773146533, 0.2756373558, 0.2739592187, 0.2722802470, 0.2706004460,
0.2689198206, 0.2672383761, 0.2655561175, 0.2638730500, 0.2621891786,
0.2605045086, 0.2588190451, 0.2571327932, 0.2554457579, 0.2537579446,
0.2520693582, 0.2503800041, 0.2486898872, 0.2469990127, 0.2453073859,
0.2436150118, 0.2419218956, 0.2402280425, 0.2385334576, 0.2368381461,
0.2351421131, 0.2334453639, 0.2317479035, 0.2300497372, 0.2283508701,
0.2266513074, 0.2249510543, 0.2232501160, 0.2215484976, 0.2198462044,
0.2181432414, 0.2164396139, 0.2147353272, 0.2130303863, 0.2113247965,
0.2096185629, 0.2079116908, 0.2062041854, 0.2044960518, 0.2027872954,
0.2010779211, 0.1993679344, 0.1976573404, 0.1959461442, 0.1942343512,
0.1925219665, 0.1908089954, 0.1890954430, 0.1873813146, 0.1856666154,
0.1839513506, 0.1822355255, 0.1805191453, 0.1788022151, 0.1770847403,
0.1753667261, 0.1736481777, 0.1719291003, 0.1702094992, 0.1684893796,
0.1667687467, 0.1650476059, 0.1633259622, 0.1616038211, 0.1598811877,
0.1581580673, 0.1564344650, 0.1547103863, 0.1529858363, 0.1512608202,
0.1495353434, 0.1478094111, 0.1460830286, 0.1443562010, 0.1426289337,
0.1409012319, 0.1391731010, 0.1374445460, 0.1357155724, 0.1339861854,
0.1322563903, 0.1305261922, 0.1287955966, 0.1270646086, 0.1253332336,
0.1236014767, 0.1218693434, 0.1201368388, 0.1184039683, 0.1166707371,
0.1149371505, 0.1132032138, 0.1114689322, 0.1097343111, 0.1079993557,
0.1062640713, 0.1045284633, 0.1027925368, 0.1010562972, 0.0993197497,
0.0975828998, 0.0958457525, 0.0941083133, 0.0923705874, 0.0906325802,
0.0888942969, 0.0871557427, 0.0854169231, 0.0836778433, 0.0819385086,
0.0801989243, 0.0784590957, 0.0767190281, 0.0749787268, 0.0732381971,
0.0714974443, 0.0697564737, 0.0680152907, 0.0662739004, 0.0645323083,
0.0627905195, 0.0610485395, 0.0593063736, 0.0575640270, 0.0558215050,
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