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geographiclib_signtest.m
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geographiclib_signtest.m
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function geographiclib_signtest
%SIGN_TEST The test suite for the geographiclib package
%
% SIGN_TEST
%
% runs a variety of tests checking the treatment of +/-0 and +/-180
persistent octavep
if isempty(octavep)
octavep = exist('OCTAVE_VERSION', 'builtin') ~= 0;
end
n = 0;
i = checkAngRound(-eps/32, -eps/32);
if i, n=n+1; fprintf('AngRound(-eps/32) fail\n'); end
i = checkAngRound(-eps/64, -0.0 );
if i, n=n+1; fprintf('AngRound(-eps/64) fail\n'); end
i = checkAngRound(- 0.0 , -0.0 );
if i, n=n+1; fprintf('AngRound(- 0.0 ) fail\n'); end
i = checkAngRound( 0.0 , +0.0 );
if i, n=n+1; fprintf('AngRound( 0.0 ) fail\n'); end
i = checkAngRound( eps/64, +0.0 );
if i, n=n+1; fprintf('AngRound( eps/64) fail\n'); end
i = checkAngRound( eps/32, +eps/32);
if i, n=n+1; fprintf('AngRound( eps/32) fail\n'); end
i = checkAngRound((1-2*eps)/64, (1-2*eps)/64);
if i, n=n+1; fprintf('AngRound((1-2*eps)/64) fail\n'); end
i = checkAngRound((1-eps )/64, 1.0 /64);
if i, n=n+1; fprintf('AngRound((1-eps )/64) fail\n'); end
i = checkAngRound((1-eps/2)/64, 1.0 /64);
if i, n=n+1; fprintf('AngRound((1-eps/2)/64) fail\n'); end
i = checkAngRound((1-eps/4)/64, 1.0 /64);
if i, n=n+1; fprintf('AngRound((1-eps/4)/64) fail\n'); end
i = checkAngRound( 1.0 /64, 1.0 /64);
if i, n=n+1; fprintf('AngRound( 1.0 /64) fail\n'); end
i = checkAngRound((1+eps/2)/64, 1.0 /64);
if i, n=n+1; fprintf('AngRound((1+eps/2)/64) fail\n'); end
i = checkAngRound((1+eps )/64, 1.0 /64);
if i, n=n+1; fprintf('AngRound((1+eps )/64) fail\n'); end
i = checkAngRound((1+2*eps)/64, (1+2*eps)/64);
if i, n=n+1; fprintf('AngRound((1+2*eps)/64) fail\n'); end
i = checkAngRound((1-eps )/32, (1-eps )/32);
if i, n=n+1; fprintf('AngRound((1-eps )/32) fail\n'); end
i = checkAngRound((1-eps/2)/32, 1.0 /32);
if i, n=n+1; fprintf('AngRound((1-eps/2)/32) fail\n'); end
i = checkAngRound((1-eps/4)/32, 1.0 /32);
if i, n=n+1; fprintf('AngRound((1-eps/4)/32) fail\n'); end
i = checkAngRound( 1.0 /32, 1.0 /32);
if i, n=n+1; fprintf('AngRound( 1.0 /32) fail\n'); end
i = checkAngRound((1+eps/2)/32, 1.0 /32);
if i, n=n+1; fprintf('AngRound((1+eps/2)/32) fail\n'); end
i = checkAngRound((1+eps )/32, (1+eps )/32);
if i, n=n+1; fprintf('AngRound((1+eps )/32) fail\n'); end
i = checkAngRound((1-eps )/16, (1-eps )/16);
if i, n=n+1; fprintf('AngRound((1-eps )/16) fail\n'); end
i = checkAngRound((1-eps/2)/16, (1-eps/2)/16);
if i, n=n+1; fprintf('AngRound((1-eps/2)/16) fail\n'); end
i = checkAngRound((1-eps/4)/16, 1.0 /16);
if i, n=n+1; fprintf('AngRound((1-eps/4)/16) fail\n'); end
i = checkAngRound( 1.0 /16, 1.0 /16);
if i, n=n+1; fprintf('AngRound( 1.0 /16) fail\n'); end
i = checkAngRound((1+eps/4)/16, 1.0 /16);
if i, n=n+1; fprintf('AngRound((1+eps/4)/16) fail\n'); end
i = checkAngRound((1+eps/2)/16, 1.0 /16);
if i, n=n+1; fprintf('AngRound((1+eps/2)/16) fail\n'); end
i = checkAngRound((1+eps )/16, (1+eps )/16);
if i, n=n+1; fprintf('AngRound((1+eps )/16) fail\n'); end
i = checkAngRound((1-eps )/ 8, (1-eps )/ 8);
if i, n=n+1; fprintf('AngRound((1-eps )/ 8) fail\n'); end
i = checkAngRound((1-eps/2)/ 8, (1-eps/2)/ 8);
if i, n=n+1; fprintf('AngRound((1-eps/2)/ 8) fail\n'); end
i = checkAngRound((1-eps/4)/ 8, 1.0 / 8);
if i, n=n+1; fprintf('AngRound((1-eps/4)/ 8) fail\n'); end
i = checkAngRound((1+eps/2)/ 8, 1.0 / 8);
if i, n=n+1; fprintf('AngRound((1+eps/2)/ 8) fail\n'); end
i = checkAngRound((1+eps )/ 8, (1+eps )/ 8);
if i, n=n+1; fprintf('AngRound((1+eps )/ 8) fail\n'); end
i = checkAngRound( 1-eps , 1-eps );
if i, n=n+1; fprintf('AngRound( 1-eps ) fail\n'); end
i = checkAngRound( 1-eps/2 , 1-eps/2 );
if i, n=n+1; fprintf('AngRound( 1-eps/2 ) fail\n'); end
i = checkAngRound( 1-eps/4 , 1 );
if i, n=n+1; fprintf('AngRound( 1-eps/4 ) fail\n'); end
i = checkAngRound( 1.0 , 1 );
if i, n=n+1; fprintf('AngRound( 1.0 ) fail\n'); end
i = checkAngRound( 1+eps/4 , 1 );
if i, n=n+1; fprintf('AngRound( 1+eps/4 ) fail\n'); end
i = checkAngRound( 1+eps/2 , 1 );
if i, n=n+1; fprintf('AngRound( 1+eps/2 ) fail\n'); end
i = checkAngRound( 1+eps , 1+ eps );
if i, n=n+1; fprintf('AngRound( 1+eps ) fail\n'); end
i = checkAngRound( 90.0-64*eps, 90-64*eps );
if i, n=n+1; fprintf('AngRound( 90.0-64*eps) fail\n'); end
i = checkAngRound( 90.0-32*eps, 90 );
if i, n=n+1; fprintf('AngRound( 90.0-32*eps) fail\n'); end
i = checkAngRound( 90.0 , 90 );
if i, n=n+1; fprintf('AngRound( 90.0 ) fail\n'); end
i = checksincosd(- inf, nan, nan);
if i, n=n+1; fprintf('sincosd(- inf) fail\n'); end
i = checksincosd(-810.0, -1.0, +0.0);
if i, n=n+1; fprintf('sincosd(-810.0) fail\n'); end
i = checksincosd(-720.0, -0.0, +1.0);
if i, n=n+1; fprintf('sincosd(-720.0) fail\n'); end
i = checksincosd(-630.0, +1.0, +0.0);
if i, n=n+1; fprintf('sincosd(-630.0) fail\n'); end
i = checksincosd(-540.0, -0.0, -1.0);
if i, n=n+1; fprintf('sincosd(-540.0) fail\n'); end
i = checksincosd(-450.0, -1.0, +0.0);
if i, n=n+1; fprintf('sincosd(-450.0) fail\n'); end
i = checksincosd(-360.0, -0.0, +1.0);
if i, n=n+1; fprintf('sincosd(-360.0) fail\n'); end
i = checksincosd(-270.0, +1.0, +0.0);
if i, n=n+1; fprintf('sincosd(-270.0) fail\n'); end
i = checksincosd(-180.0, -0.0, -1.0);
if i, n=n+1; fprintf('sincosd(-180.0) fail\n'); end
i = checksincosd(- 90.0, -1.0, +0.0);
if i, n=n+1; fprintf('sincosd(- 90.0) fail\n'); end
i = checksincosd(- 0.0, -0.0, +1.0);
if i, n=n+1; fprintf('sincosd(- 0.0) fail\n'); end
i = checksincosd(+ 0.0, +0.0, +1.0);
if i, n=n+1; fprintf('sincosd(+ 0.0) fail\n'); end
i = checksincosd(+ 90.0, +1.0, +0.0);
if i, n=n+1; fprintf('sincosd(+ 90.0) fail\n'); end
i = checksincosd(+180.0, +0.0, -1.0);
if i, n=n+1; fprintf('sincosd(+180.0) fail\n'); end
i = checksincosd(+270.0, -1.0, +0.0);
if i, n=n+1; fprintf('sincosd(+270.0) fail\n'); end
i = checksincosd(+360.0, +0.0, +1.0);
if i, n=n+1; fprintf('sincosd(+360.0) fail\n'); end
i = checksincosd(+450.0, +1.0, +0.0);
if i, n=n+1; fprintf('sincosd(+450.0) fail\n'); end
i = checksincosd(+540.0, +0.0, -1.0);
if i, n=n+1; fprintf('sincosd(+540.0) fail\n'); end
i = checksincosd(+630.0, -1.0, +0.0);
if i, n=n+1; fprintf('sincosd(+630.0) fail\n'); end
i = checksincosd(+720.0, +0.0, +1.0);
if i, n=n+1; fprintf('sincosd(+720.0) fail\n'); end
i = checksincosd(+810.0, +1.0, +0.0);
if i, n=n+1; fprintf('sincosd(+810.0) fail\n'); end
i = checksincosd(+ inf, nan, nan);
if i, n=n+1; fprintf('sincosd(+ inf) fail\n'); end
i = checksincosd( nan, nan, nan);
if i, n=n+1; fprintf('sincosd( nan) fail\n'); end
[s1, c1] = sincosdx(9);
[s2, c2] = sincosdx(81);
[s3, c3] = sincosdx(-123456789);
i = equiv(s1, c2) + equiv(s1, s3) + equiv(c1, s2) + equiv(c1, -c3);
if i, n=n+1; fprintf('sincosd accuracy fail\n'); end
i = checkatan2d(+0.0 , +0.0 , +0.0 );
if i, n=n+1; fprintf('atan2d(+0.0 , +0.0 ) fail\n'); end
if octavep
% MATLAB gets these wrong, but we don't care about the 0,0 pairs
i = checkatan2d(+0.0 , -0.0 , +180 );
if i, n=n+1; fprintf('atan2d(+0.0 , -0.0 ) fail\n'); end
i = checkatan2d(-0.0 , -0.0 , -180 );
if i, n=n+1; fprintf('atan2d(-0.0 , -0.0 ) fail\n'); end
i = checkatan2d(-0.0 , +0.0 , -0.0 );
if i, n=n+1; fprintf('atan2d(-0.0 , +0.0 ) fail\n'); end
end
i = checkatan2d(+0.0 , -1.0 , +180 );
if i, n=n+1; fprintf('atan2d(+0.0 , -1.0 ) fail\n'); end
i = checkatan2d(-0.0 , -1.0 , -180 );
if i, n=n+1; fprintf('atan2d(-0.0 , -1.0 ) fail\n'); end
i = checkatan2d(+0.0 , +1.0 , +0.0 );
if i, n=n+1; fprintf('atan2d(+0.0 , +1.0 ) fail\n'); end
i = checkatan2d(-0.0 , +1.0 , -0.0 );
if i, n=n+1; fprintf('atan2d(-0.0 , +1.0 ) fail\n'); end
i = checkatan2d(-1.0 , +0.0 , -90 );
if i, n=n+1; fprintf('atan2d(-1.0 , +0.0 ) fail\n'); end
i = checkatan2d(-1.0 , -0.0 , -90 );
if i, n=n+1; fprintf('atan2d(-1.0 , -0.0 ) fail\n'); end
i = checkatan2d(+1.0 , +0.0 , +90 );
if i, n=n+1; fprintf('atan2d(+1.0 , +0.0 ) fail\n'); end
i = checkatan2d(+1.0 , -0.0 , +90 );
if i, n=n+1; fprintf('atan2d(+1.0 , -0.0 ) fail\n'); end
i = checkatan2d(+1.0 , -inf, +180 );
if i, n=n+1; fprintf('atan2d(+1.0 , -inf) fail\n'); end
i = checkatan2d(-1.0 , -inf, -180 );
if i, n=n+1; fprintf('atan2d(-1.0 , -inf) fail\n'); end
i = checkatan2d(+1.0 , +inf, +0.0 );
if i, n=n+1; fprintf('atan2d(+1.0 , +inf) fail\n'); end
i = checkatan2d(-1.0 , +inf, -0.0 );
if i, n=n+1; fprintf('atan2d(-1.0 , +inf) fail\n'); end
i = checkatan2d( +inf, +1.0 , +90 );
if i, n=n+1; fprintf('atan2d( +inf, +1.0 ) fail\n'); end
i = checkatan2d( +inf, -1.0 , +90 );
if i, n=n+1; fprintf('atan2d( +inf, -1.0 ) fail\n'); end
i = checkatan2d( -inf, +1.0 , -90 );
if i, n=n+1; fprintf('atan2d( -inf, +1.0 ) fail\n'); end
i = checkatan2d( -inf, -1.0 , -90 );
if i, n=n+1; fprintf('atan2d( -inf, -1.0 ) fail\n'); end
i = checkatan2d( +inf, -inf, +135 );
if i, n=n+1; fprintf('atan2d( +inf, -inf) fail\n'); end
i = checkatan2d( -inf, -inf, -135 );
if i, n=n+1; fprintf('atan2d( -inf, -inf) fail\n'); end
i = checkatan2d( +inf, +inf, +45 );
if i, n=n+1; fprintf('atan2d( +inf, +inf) fail\n'); end
i = checkatan2d( -inf, +inf, -45 );
if i, n=n+1; fprintf('atan2d( -inf, +inf) fail\n'); end
i = checkatan2d( nan, +1.0 , nan );
if i, n=n+1; fprintf('atan2d( nan, +1.0 ) fail\n'); end
i = checkatan2d(+1.0 , nan, nan );
if i, n=n+1; fprintf('atan2d(+1.0 , nan) fail\n'); end
s = 7e-16; i = equiv( atan2dx(s, -1), 180 - atan2dx(s, 1) );
if i, n=n+1; fprintf('atan2d accuracy fail\n'); end
i = checksum(+9.0, -9.0, +0.0 );
if i, n=n+1; fprintf('sum(+9.0, -9.0) fail\n'); end
i = checksum(-9.0, +9.0, +0.0 );
if i, n=n+1; fprintf('sum(-9.0, +9.0) fail\n'); end
i = checksum(-0.0, +0.0, +0.0 );
if i, n=n+1; fprintf('sum(-0.0, +0.0) fail\n'); end
i = checksum(+0.0, -0.0, +0.0 );
if i, n=n+1; fprintf('sum(+0.0, -0.0) fail\n'); end
i = checksum(-0.0, -0.0, -0.0 );
if i, n=n+1; fprintf('sum(-0.0, -0.0) fail\n'); end
i = checksum(+0.0, +0.0, +0.0 );
if i, n=n+1; fprintf('sum(+0.0, +0.0) fail\n'); end
i = checkAngNormalize(-900.0, -180 );
if i, n=n+1; fprintf('AngNormalize(-900.0) fail\n'); end
i = checkAngNormalize(-720.0, -0.0 );
if i, n=n+1; fprintf('AngNormalize(-720.0) fail\n'); end
i = checkAngNormalize(-540.0, -180 );
if i, n=n+1; fprintf('AngNormalize(-540.0) fail\n'); end
i = checkAngNormalize(-360.0, -0.0 );
if i, n=n+1; fprintf('AngNormalize(-360.0) fail\n'); end
i = checkAngNormalize(-180.0, -180 );
if i, n=n+1; fprintf('AngNormalize(-180.0) fail\n'); end
i = checkAngNormalize( -0.0, -0.0 );
if i, n=n+1; fprintf('AngNormalize( -0.0) fail\n'); end
i = checkAngNormalize( +0.0, +0.0 );
if i, n=n+1; fprintf('AngNormalize( +0.0) fail\n'); end
i = checkAngNormalize( 180.0, +180 );
if i, n=n+1; fprintf('AngNormalize( 180.0) fail\n'); end
i = checkAngNormalize( 360.0, +0.0 );
if i, n=n+1; fprintf('AngNormalize( 360.0) fail\n'); end
i = checkAngNormalize( 540.0, +180 );
if i, n=n+1; fprintf('AngNormalize( 540.0) fail\n'); end
i = checkAngNormalize( 720.0, +0.0 );
if i, n=n+1; fprintf('AngNormalize( 720.0) fail\n'); end
i = checkAngNormalize( 900.0, +180 );
if i, n=n+1; fprintf('AngNormalize( 900.0) fail\n'); end
i = checkAngDiff(+ 0.0, + 0.0, +0.0 );
if i, n=n+1; fprintf('AngDiff(+ 0.0, + 0.0) fail\n'); end
i = checkAngDiff(+ 0.0, - 0.0, -0.0 );
if i, n=n+1; fprintf('AngDiff(+ 0.0, - 0.0) fail\n'); end
i = checkAngDiff(- 0.0, + 0.0, +0.0 );
if i, n=n+1; fprintf('AngDiff(- 0.0, + 0.0) fail\n'); end
i = checkAngDiff(- 0.0, - 0.0, +0.0 );
if i, n=n+1; fprintf('AngDiff(- 0.0, - 0.0) fail\n'); end
i = checkAngDiff(+ 5.0, +365.0, +0.0 );
if i, n=n+1; fprintf('AngDiff(+ 5.0, +365.0) fail\n'); end
i = checkAngDiff(+365.0, + 5.0, -0.0 );
if i, n=n+1; fprintf('AngDiff(+365.0, + 5.0) fail\n'); end
i = checkAngDiff(+ 5.0, +185.0, +180.0 );
if i, n=n+1; fprintf('AngDiff(+ 5.0, +185.0) fail\n'); end
i = checkAngDiff(+185.0, + 5.0, -180.0 );
if i, n=n+1; fprintf('AngDiff(+185.0, + 5.0) fail\n'); end
i = checkAngDiff( +eps , +180.0, +180.0 );
if i, n=n+1; fprintf('AngDiff( +eps , +180.0) fail\n'); end
i = checkAngDiff( -eps , +180.0, -180.0 );
if i, n=n+1; fprintf('AngDiff( -eps , +180.0) fail\n'); end
i = checkAngDiff( +eps , -180.0, +180.0 );
if i, n=n+1; fprintf('AngDiff( +eps , -180.0) fail\n'); end
i = checkAngDiff( -eps , -180.0, -180.0 );
if i, n=n+1; fprintf('AngDiff( -eps , -180.0) fail\n'); end
x = 138 + 128 * eps; y = -164;
i = equiv(AngDiff(x, y), 58 - 128 * eps);
if i, n=n+1; fprintf('AngDiff accuracy fail\n'); end
% azimuth of geodesic line with points on equator determined by signs of
% latitude
% lat1 lat2 azi1/2
C = [ +0, -0, 180;
-0, +0, 0 ];
[~, azi1, azi2] = geoddistance(C(:,1), 0, C(:,2), 0);
i = equiv(azi1, C(:,3)) + equiv(azi2, C(:,3));
if i, n=n+1; fprintf('coincident points on equator fail\n'); end
% Does the nearly antipodal equatorial solution go north or south?
% lat1 lat2 azi1 azi2
C = [ +0, +0, 56, 124;
-0, -0, 124, 56];
[~, azi1, azi2] = geoddistance(C(:,1), 0, C(:,2), 179.5);
i = assertEquals(azi1, C(:,3), 1) + assertEquals(azi2, C(:,4), 1);
if i, n=n+1; fprintf('nearly antipodal points on equator fail\n'); end
% How does the exact antipodal equatorial path go N/S + E/W
% lat1 lat2 lon2 azi1 azi2
C = [ +0, +0, +180, +0, +180;
-0, -0, +180, +180, +0;
+0, +0, -180, -0, -180;
-0, -0, -180, -180, -0 ];
[~, azi1, azi2] = geoddistance(C(:,1), 0, C(:,2), C(:,3));
i = equiv(azi1, C(:,4)) + equiv(azi2, C(:,5));
if i, n=n+1; fprintf('antipodal points on equator fail\n'); end
% Antipodal points on the equator with prolate ellipsoid
% lon2 azi1/2
C = [+180, +90;
-180, -90];
[~, azi1, azi2] = geoddistance(0, 0, 0, C(:,1), [6.4e6, flat2ecc(-1/300)]);
i = equiv(azi1, C(:,2)) + equiv(azi2, C(:,2));
if i, n=n+1; fprintf('`antipodal points on equator, prolate, fail\n'); end
% azimuths = +/-0 and +/-180 for the direct problem
% azi1, lon2, azi2
C = [ +0, +180, +180;
-0, -180, -180;
+180, +180, +0;
-180, -180, -0 ];
[~, lon2, azi2] = geodreckon(0, 0, 15e6, C(:,1), 2);
i = equiv(lon2, C(:,2)) + equiv(azi2, C(:,3));
if i, n=n+1; fprintf('geodreckon azi1 = +/-0 +/-180, fail\n'); end
% lat = +/-0 in utmups_fwd
% lat y northp
C = [ +0, 0, 1;
-0, 10e6, 0 ];
[x, y, zone, northp] = utmups_fwd(C(:,1), 3);
i = equiv(y, C(:,2)) + equiv(northp, C(:,3));
if i, n=n+1; fprintf('utmups_fwd lat = +/-0, fail\n'); end
mgrs = mgrs_fwd(x, y, zone, northp, 2);
i = ~strcmp(mgrs{1,1}, '31NEA0000') + ~strcmp(mgrs{2,1}, '31MEV0099');
if i, n=n+1; fprintf('mgrs_fwd lat = +/-0, fail\n'); end
assert(n == 0);
end
function n = assertEquals(x, y, d)
n = abs(x - y) <= d;
n = sum(~n(:));
end
function n = equiv(x, y)
n = (isnan(x) & isnan(y)) | (x == y & signbitx(x) == signbitx(y));
n = sum(~n(:));
end
function n = checkAngRound(x, y)
z = AngRound(x);
n = equiv(z, y);
end
function n = checksincosd(x, s, c)
[ss, cc] = sincosdx(x);
n = equiv(ss, s) + equiv(cc, c);
end
function n = checkatan2d(y, x, a)
aa = atan2dx(y, x);
n = equiv(aa, a);
end
function n = checksum(x, y, s)
ss = sumx(x, y);
n = equiv(ss, s);
end
function n = checkAngNormalize(x, y)
z = AngNormalize(x);
n = equiv(z, y);
end
function n = checkAngDiff(x, y, d)
dd = AngDiff(x, y);
n = equiv(dd, d);
end
%!test geographiclib_signtest