Merge pull request #1919 from rouault/backport_fix_for_1906

[Backport 6.3] fixes for #1906 (test failures on i386)

4 files changed, 15 insertions, 5 deletions

diff --git a/src/conversions/cart.cpp b/src/conversions/cart.cpp
index a7817443..537fc29f 100644
--- a/src/conversions/cart.cpp
+++ b/src/conversions/cart.cpp
@@ -165,8 +165,9 @@ static PJ_LPZ geodetic (PJ_XYZ cart,  PJ *P) {
     if( fabs(lpz.phi) > M_HALFPI ) {
         // this happen on non-sphere ellipsoid when x,y,z is very close to 0
         // there is no single solution to the cart->geodetic conversion in
-        // that case, so arbitrarily pickup phi = 0.
-        lpz.phi = 0;
+        // that case, clamp to -90/90 deg and avoid a discontinuous boundary
+        // near the poles
+        lpz.phi = copysign(M_HALFPI, lpz.phi);
     }
     lpz.lam  =  atan2 (cart.y, cart.x);
     N        =  normal_radius_of_curvature (P->a, P->es, lpz.phi);
diff --git a/src/projections/laea.cpp b/src/projections/laea.cpp
index a1e4bf8f..3d135864 100644
--- a/src/projections/laea.cpp
+++ b/src/projections/laea.cpp
@@ -44,7 +44,8 @@ static PJ_XY laea_e_forward (PJ_LP lp, PJ *P) {          /* Ellipsoidal, forward
 
     if (Q->mode == OBLIQ || Q->mode == EQUIT) {
         sinb = q / Q->qp;
-        cosb = sqrt(1. - sinb * sinb);
+        const double cosb2 = 1. - sinb * sinb;
+        cosb = cosb2 > 0 ? sqrt(cosb2) : 0;
     }
 
     switch (Q->mode) {
diff --git a/src/projections/robin.cpp b/src/projections/robin.cpp
index 2e36106a..5a3b081c 100644
--- a/src/projections/robin.cpp
+++ b/src/projections/robin.cpp
@@ -84,7 +84,7 @@ static PJ_XY robin_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forwar
     (void) P;
 
     dphi = fabs(lp.phi);
-    i = isnan(lp.phi) ? -1 : lround(floor(dphi * C1));
+    i = isnan(lp.phi) ? -1 : lround(floor(dphi * C1 + 1e-15));
     if( i < 0 ){
         proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
         return xy;
diff --git a/src/projections/vandg.cpp b/src/projections/vandg.cpp
index 7d485aff..e7cbbdb6 100644
--- a/src/projections/vandg.cpp
+++ b/src/projections/vandg.cpp
@@ -39,6 +39,14 @@ static PJ_XY vandg_s_forward (PJ_LP lp, PJ *P) {           /* Spheroidal, forwar
         g2 = g * g;
         p2 = g * (2. / p2 - 1.);
         p2 = p2 * p2;
+        {
+            // Force floating-point computations done on 80 bit on
+            // i386 to go back to 64 bit. This is to avoid the test failures
+            // of https://github.com/OSGeo/PROJ/issues/1906#issuecomment-583168348
+            // The choice of p2 is completely arbitrary.
+            volatile double p2_tmp = p2;
+            p2 = p2_tmp;
+        }
         xy.x = g - p2; g = p2 + al2;
         xy.x = M_PI * (al * xy.x + sqrt(al2 * xy.x * xy.x - g * (g2 - p2))) / g;
         if (lp.lam < 0.) xy.x = -xy.x;
@@ -81,7 +89,7 @@ static PJ_LP vandg_s_inverse (PJ_XY xy, PJ *P) {           /* Spheroidal, invers
     m = 2. * sqrt(-THIRD * al);
     d = C2_27 * c2 * c2 * c2 + (c0 * c0 - THIRD * c2 * c1) / c3;
     const double al_mul_m = al * m;
-    if( al_mul_m == 0 ) {
+    if( fabs(al_mul_m) < 1e-16 ) {
         proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
         return proj_coord_error().lp;
     }