Horner and helmert (#456)

Introducing the Horner polynomial evaluator also introduces the need for
very long +init:tag arguments (a n'th order 2D polynomium has
(n+1)(n+2)/2 coefficients, and n is typically in the range 5-10, i.e. up
to around 60 coefficients for each polynomium, and there are 4 polynomia
in a complete back/forward transformation set).

Hence, in this commit, along with the first part of the Horner code, the
code for reading +init files has been modified in a (for all practical
purposes) backwards compatible way, by making it possible to introduce
line continuations by escaping line breaks, i.e. preceding them with a
backslash.

An escaped line break works (as it would in TeX), by skipping all
following whitespace, including interspersed #-comments. This simple
extension makes it possible to create very long initialization elements
without losing track of the structure (cf. s45b.pol and pj_init_test.c
in the examples-directory for a demo).

The s45b.pol file was created by hand-editing the output of the software
doing the original constrained adjustment for the polynomial
coefficients. The simple adding of the “skip following whitespace and
comments” feature has made it possible to retain almost all metadata
from the source material.

This is considered very important, since 1) For the lack of a prior
common file format for geodetic polynomial coefficients, there is a good
chance that this will become THE standard, at least for the time being,
and 2) Without the metadata represented, it will be very hard for a
human to debug code involving a slightly misrepresented polynomium.

Due to the current architecture of the pj_init.c code (mostly around the
fill_buffer() function), it is next to impossible to implement the line
continuation functionality in full generality. Hence, it has been
necessary to limit this format extension to files smaller than 64 kB.

* Correction of spherical HEALpix test case

The first HEALpix test case in nad/testvarious is clearly intended to
invoke the spherical form of HEALpix.

It does, however, specify the spheroid using the +a=1 size parameter,
without specifying any shape parameter.

But since +no_defs is not specified either, a shape parameter is picked
up from the nad/proj_def.dat file (where ellps=WGS84 is given in the
<general> section).

It appears that this has not happened before I updated the pj_init code to support projection
pipelines (see below). I do, however, believe that the present behaviour is the correct one,
and rather than retrohacking the pj_init code, to (incorrectly, I
believe) reproduce the prior behaviour, I have corrected the test case
invocation in nad/testvarious to specify the spheroid using the +R=1
size parameter (which was already used in the following test case).

* Repair scaling of projections stomping on value of semimajor axis

* Workaround MSVC HUGE_VAL misimplementation.

The "return const err object" idiom (i.e.  const <type> err =
{HUGE_VAL,...}; ...  if (bad) return err) is problematic to implement
due to MSVC's misimplementation of HUGE_VAL as a non-const.

Hence, we need to run-time initialize these. In the pj_inv functions,
this was mistakenly done to the wrong object.

For pj_fwdobs/invobs and the remaining part of the obs-based API, this
is now worked around by providing functions returning a run time
HUGE_VAL initialized PJ_OBS or PJ_COO resp.

Obnoxious, but given MSVC's market penetration there is really not much
else we can do.

2 files changed, 418 insertions, 17 deletions

diff --git a/examples/pj_obs_api_test.c b/examples/pj_obs_api_test.c
index c75b4a21..bb792c62 100644
--- a/examples/pj_obs_api_test.c
+++ b/examples/pj_obs_api_test.c
@@ -44,8 +44,6 @@
 
 int pj_pipeline_selftest (void);
 
-
-
 int main (void) {
     PJ *P;
     PJ_OBS a, b;
@@ -71,7 +69,7 @@ int main (void) {
         return puts ("Oops"), 0;
 
     /* zero initialize everything, then set (longitude, latitude) to (12, 55) */
-    a = pj_obs_null;
+    a = pj_obs_null ();
     /* a.coo.lp: The coordinate part of a, interpreted as a classic LP pair */
     a.coo.lp.lam = TORAD(12);
     a.coo.lp.phi = TORAD(55);
@@ -100,13 +98,12 @@ int main (void) {
     dist = pj_xyz_dist (a.coo.xyz, b.coo.xyz);
     printf ("Roundtrip deviation, (nm): %15.9f\n", dist*1e9);
 
-
     /* Invalid projection */
     a = pj_trans (P, 42, a);
     if (a.coo.lpz.lam!=DBL_MAX)
         printf ("%15.9f %15.9f\n", a.coo.lpz.lam, a.coo.lpz.phi);
-    err = pj_error (P);
-    printf ("pj_error: %d\n", err);
+    err = pj_err_level (P, PJ_ERR_TELL);
+    printf ("pj_err_level: %d\n", err);
 
     /* Clean up */
     pj_free (P);
@@ -117,7 +114,7 @@ int main (void) {
         return puts ("Oops"), 0;
 
     /* zero initialize everything, then set (longitude, latitude, height) to (12, 55, 100) */
-    a = b = pj_obs_null;
+    a = b = pj_obs_null ();
     a.coo.lpz.lam = TORAD(12);
     a.coo.lpz.phi = TORAD(55);
     a.coo.lpz.z   = 100;
@@ -152,17 +149,18 @@ int main (void) {
 
                   P I P E L I N E   T E S T S
 
-    ****************************************************************************
-
-
     ***************************************************************************/
 
     /* forward-reverse geo->utm->geo */
-    P = pj_create ("+proj=pipeline +ellps=GRS80 +zone=32 +step +proj=utm +step +proj=utm +inv");
+    P = pj_create (
+            "+proj=pipeline +ellps=GRS80 +zone=32 +step "
+            "+proj=utm +step "
+            "+proj=utm +inv"
+        );
     if (0==P)
         return puts ("Oops"), 0;
     /* zero initialize everything, then set (longitude, latitude, height) to (12, 55, 100) */
-    a = b = pj_obs_null;
+    a = b = pj_obs_null ();
     a.coo.lpz.lam = TORAD(12);
     a.coo.lpz.phi = TORAD(55);
     a.coo.lpz.z   = 100;
@@ -180,12 +178,15 @@ int main (void) {
 
 
     /* And now the back-to-back situation utm->geo->utm */
-    P = pj_create ("+proj=pipeline +ellps=GRS80 +zone=32 +step +proj=utm +inv +step +proj=utm");
+    P = pj_create (
+        "+proj=pipeline +ellps=GRS80 +zone=32 +step "
+        "+proj=utm +inv +step "
+        "+proj=utm");
     if (0==P)
         return puts ("Oops"), 0;
 
     /* zero initialize everything, then set (easting, northing) to utm(12, 55) */
-    a = b = pj_obs_null;
+    a = b = pj_obs_null ();
     a.coo.xy = cph_utm32;
     printf ("PRE:   %15.9f %15.9f\n", a.coo.xy.x, a.coo.xy.y);
 
@@ -207,7 +208,7 @@ int main (void) {
         return puts ("Oops"), 0;
 
     /* zero initialize everything, then set (easting, northing) to utm(12, 55) */
-    a = b = pj_obs_null;
+    a = b = pj_obs_null ();
     a.coo.lpz.lam = TORAD(12);
     a.coo.lpz.phi = TORAD(55);
     printf ("PRE:   %15.9f %15.9f\n", TODEG(a.coo.lp.lam), TODEG(a.coo.lp.phi));
@@ -221,7 +222,6 @@ int main (void) {
     a = pj_trans (P, PJ_INV, b);
     printf ("INV:   %15.9f %15.9f\n", TODEG(a.coo.lp.lam), TODEG(a.coo.lp.phi));
 
-
     /* Geodesic distance between two points with angular 2D coordinates */
     a.coo.lp.lam = TORAD(12);
     a.coo.lp.phi = TORAD(60);
@@ -237,7 +237,6 @@ int main (void) {
     dist = pj_lp_dist (P, a.coo.lp, b.coo.lp);
     printf ("1 deg at Equator:   %15.9f\n", dist);
 
-
     pj_free (P);
     pj_pipeline_selftest ();
     return 0;
diff --git a/examples/s45b.pol b/examples/s45b.pol
new file mode 100644
index 00000000..9b70fbf7
--- /dev/null
+++ b/examples/s45b.pol
@@ -0,0 +1,402 @@
+################################################################################
+#
+#  Horner polynomial evaluation demo data
+#
+################################################################################
+#
+#  These are the polynomial coefficients used for transforming to and from
+#  the Danish legacy system s45b "System 45 Bornholm"
+#
+################################################################################
+
+<s45b>
+proj=pipeline
+
+step  init=./s45b.pol:s45b_tc32
+# step  init=./s45b.pol:tc32_utm32
+
+step  proj=utm inv   ellps=intl zone=32
+step  proj=cart      ellps=intl
+
+step  proj=helmert ellps=GRS80
+      x=-81.0703 y=-89.3603 z=-115.7526
+     rx=-484.88 ry=-24.36  rz=-413.21   s=-0.540645
+
+step  proj=cart inv ellps=GRS80
+step  proj=utm ellps=GRS80  zone=32
+
+
+
+
+################################################################################
+#
+#                          S 4 5 B    ->    T C 3 2
+#
+################################################################################
+<s45b_tc32>
+
+proj=horner
+ellps=intl
+range=500000
+
+fwd_origin=47022.563745,51779.260103
+inv_origin=878354.943082,6125305.175366
+deg=6
+
+
+# static  double     C_ttb[]
+# tc32_ed50 -> s45b
+# m_lim_gen:  0.153  red  = 0      OBS   = 1074
+# m = 1.51 cm my_loss =    +3  y_enp = +8.4
+# m = 1.53 cm mx_loss =    +4  x_enp = +8.4
+
+#  mht C_ttb er
+# fwd-inv ombyttet ifht original Poder/Engsager-kode
+# For at opnå at to fwd transform fører fra s45b->tc32->utm32 (->ETRS89)
+
+inv_v=\
+# Poly NORTH :: e-degree =  0  : n-degree =  6
+    5.1779004699e+04,\
+    9.9508320295e-01,\
+   -2.9453823207e-10,\
+    1.9995084102e-14,\
+   -1.4895751366e-18,\
+   -9.9734812211e-23,\
+    1.1194218845e-26,\
+
+# Poly NORTH :: e-degree =  1  : n-degree =  5
+   -8.4285679515e-02,\
+   -7.9623049286e-09,\
+   -3.7190046062e-14,\
+   -2.3324127411e-18,\
+   -1.1150449763e-22,\
+    2.8703154270e-27,\
+
+# Poly NORTH :: e-degree =  2  : n-degree =  4
+    8.7160434140e-10,\
+   -3.3634602927e-14,\
+   -5.5718245313e-18,\
+    6.2611750909e-23,\
+   -2.1011243838e-26,\
+
+# Poly NORTH :: e-degree =  3  : n-degree =  3
+    1.0905463989e-14,\
+   -4.3960034360e-18,\
+    3.6121595001e-22,\
+   -1.3493066011e-27,\
+
+# Poly NORTH :: e-degree =  4  : n-degree =  2
+   -1.3360171462e-18,\
+    1.0780850646e-22,\
+    4.5118286607e-26,\
+
+# Poly NORTH :: e-degree =  5  : n-degree =  1
+   -1.3718883973e-22,\
+    1.6263920750e-26,\
+
+# Poly NORTH :: e-degree =  6  : n-degree =  0
+   -5.1004217526e-27
+
+# tcy    6125305.175366
+
+inv_u=\
+# Poly EAST  :: n-degree =  0  : e-degree =  6
+    4.7022495967e+04,\
+   -9.9508282498e-01,\
+    3.2436283039e-09,\
+   -2.6276394334e-15,\
+    8.6318533291e-18,\
+   -3.8327518550e-23,\
+   -2.5704924282e-26,\
+
+# Poly EAST  :: n-degree =  1  : e-degree =  5
+   -8.4285975934e-02,\
+    5.7098765263e-10,\
+   -6.0863955939e-14,\
+    2.3608788740e-18,\
+    6.8899581969e-24,\
+   -1.1429511179e-26,\
+
+# Poly EAST  :: n-degree =  2  : e-degree =  4
+   -4.6079778412e-09,\
+    1.5072604543e-14,\
+    5.4063862378e-18,\
+    1.2591327827e-22,\
+    7.9336388691e-27,\
+
+# Poly EAST  :: n-degree =  3  : e-degree =  3
+   -2.9479268638e-14,\
+    1.7090049434e-18,\
+    2.8413337985e-22,\
+   -3.3577391552e-27,\
+
+# Poly EAST  :: n-degree =  4  : e-degree =  2
+    3.0434879273e-18,\
+   -1.8081673510e-22,\
+   -2.3651419850e-26,\
+
+# Poly EAST  :: n-degree =  5  : e-degree =  1
+    9.2060044804e-23,\
+    3.7807953325e-27,\
+
+# Poly EAST  :: n-degree =  6  : e-degree =  0
+   -4.9415665221e-27
+
+# tcx     878354.943082
+
+
+# static  double      C_btt[]
+# s45b -> tc32_ed50
+# m_lim_gen:  0.154  red  = 0      OBS   = 1074
+# m = 1.50 cm my_loss =    +3  y_enp = +8.5
+# m = 1.54 cm mx_loss =    +4  x_enp = +8.3
+
+fwd_v=\
+# Poly NORTH :: e-degree =  0  : n-degree =  6
+    6.1253054245e+06,\
+    9.9778251908e-01,\
+   -7.7346152025e-10,\
+   -2.5359789369e-14,\
+    1.5614918228e-18,\
+    9.8091134295e-23,\
+   -1.1092581145e-26,\
+
+# Poly NORTH :: e-degree =  1  : n-degree =  5
+   -8.4514352088e-02,\
+   -7.9847579284e-09,\
+   -2.6865560962e-14,\
+   -2.0731372756e-18,\
+   -1.3660341123e-22,\
+    1.1244836340e-26,\
+
+# Poly NORTH :: e-degree =  2  : n-degree =  4
+    8.0551988135e-11,\
+    3.6661500679e-14,\
+    5.4247705403e-18,\
+    8.4494604807e-23,\
+    1.3334858516e-26,\
+
+# Poly NORTH :: e-degree =  3  : n-degree =  3
+    8.3889821184e-15,\
+   -4.8124202237e-18,\
+    2.9088188830e-22,\
+   -2.0129874264e-26,\
+
+# Poly NORTH :: e-degree =  4  : n-degree =  2
+   2.4716463766e-18,\
+  -2.1717177513e-22,\
+  -3.2828537638e-26,\
+
+# Poly NORTH :: e-degree =  5  : n-degree =  1
+  -1.2080655753e-22,\
+   2.5050435391e-26,\
+
+# Poly NORTH :: e-degree =  6  : n-degree =  0
+   1.1383483826e-27
+
+# tcy      51779.260103,
+
+fwd_u=\
+# Poly EAST  :: n-degree =  0  : e-degree =  6
+    8.7835485387e+05,\
+   -9.9778289691e-01,\
+    3.2537215213e-09,\
+    6.9217640616e-15,\
+    8.6268883840e-18,\
+    4.6748156909e-23,\
+   -2.6492402009e-26,\
+
+# Poly EAST  :: n-degree =  1  : e-degree =  5
+   -8.4514648771e-02,\
+    1.4399520180e-09,\
+   -6.0423329711e-14,\
+    6.9816167332e-20,\
+    6.7729233542e-23,\
+   -5.3308251880e-27,\
+
+# Poly EAST  :: n-degree =  2  : e-degree =  4
+   -4.5697800099e-09,\
+   -1.5194038814e-14,\
+    5.1112653016e-18,\
+   -2.0307532869e-22,\
+    1.0374125432e-26,\
+
+# Poly EAST  :: n-degree =  3  : e-degree =  3
+   -2.8983003841e-14,\
+   -1.6414425785e-18,\
+    1.7874983379e-22,\
+    1.5492164174e-26,\
+
+# Poly EAST  :: n-degree =  4  : e-degree =  2
+    2.7919197366e-18,\
+    1.9218613279e-22,\
+   -2.1007264634e-26,\
+
+# Poly EAST  :: n-degree =  5  : e-degree =  1
+    1.0032412389e-22,\
+   -5.9007997846e-27,\
+
+# Poly EAST  :: n-degree =  6  : e-degree =  0
+    -4.4410970979e-27
+
+# tcx      47022.563745
+
+
+
+
+
+################################################################################
+#
+#                        T C 3 2    ->    U T M 3 2
+#
+################################################################################
+
+<tc32_utm32>
+
+proj=horner
+ellps=intl
+range=500000
+
+
+fwd_origin=877605.269066,6125810.306769
+inv_origin=877605.760036,6125811.281773
+
+
+# tc32_ed50 -> utm32_ed50 : Bornholm
+
+deg=4
+
+# ttu_n and ttu_e are based on static double C_ttu_b[]
+# m_lim_gen:  0.086  red  = 0      OBS   =    852
+# m = 1.38 cm my_loss =    +2  y_enp = +10.5
+# m = 1.44 cm mx_loss =    +2  x_enp = +10.4
+# static  double ttu_n[]
+
+fwd_v=\
+# Poly NORTH :: e-degree =  0  : n-degree =  0..4
+    6.1258112678e+06,\
+    9.9999971567e-01,\
+    1.5372750011e-10,\
+    5.9300860915e-15,\
+    2.2609497633e-19,\
+
+# Poly NORTH :: e-degree =  1  : n-degree =  0..3
+    4.3188227445e-05,\
+    2.8225130416e-10,\
+    7.8740007114e-16,\
+   -1.7453997279e-19,\
+
+# Poly NORTH :: e-degree =  2  : n-degree =  0..2
+    1.6877465415e-10,\
+   -1.1234649773e-14,\
+   -1.7042333358e-18,\
+
+# Poly NORTH :: e-degree =  3  : n-degree =  0..1
+   -7.9303467953e-15,\
+   -5.2906832535e-19,\
+
+# Poly NORTH :: e-degree =  4  : n-degree =  0
+    3.9984284847e-19
+
+# tcy    6125810.306769
+
+
+
+# static  double ttu_e[]
+fwd_u=\
+# Poly EAST  :: n-degree =  0  : e-degree =  0..4
+    8.7760574982e+05,\
+    9.9999752475e-01,\
+    2.8817299305e-10,\
+    5.5641310680e-15,\
+   -1.5544700949e-18,\
+
+# Poly EAST  :: n-degree =  1  : e-degree =  3
+   -4.1357045890e-05,\
+    4.2106213519e-11,\
+    2.8525551629e-14,\
+   -1.9107771273e-18,\
+
+# Poly EAST  :: n-degree =  2  : e-degree =  2
+    3.3615590093e-10,\
+    2.4380247154e-14,\
+   -2.0241230315e-18,\
+
+# Poly EAST  :: n-degree =  3  : e-degree =  1
+    1.2429019719e-15,\
+    5.3886155968e-19,\
+
+# Poly EAST  :: n-degree =  4  : e-degree =  0
+   -1.0167505000e-18
+
+# tcx     877605.760036
+
+
+# utt_n and utt_e are based on static  double C_utt_b[]
+# utm32_ed50 -> tc32_ed50 : Bornholm
+# m_lim_gen:  0.086  red  = 0      OBS   =    852
+# m = 1.38 cm my_loss =    +2  y_enp = +10.8
+# m = 1.44 cm mx_loss =    +2  x_enp = +10.7
+# static  double utt_n[]
+
+inv_v=\
+# Poly NORTH :: e-degree =  0  : n-degree =  4
+    6.1258103208e+06,\
+    1.0000002826e+00,\
+   -1.5372762184e-10,\
+   -5.9304261011e-15,\
+   -2.2612705361e-19,\
+
+# Poly NORTH :: e-degree =  1  : n-degree =  3
+   -4.3188331419e-05,\
+   -2.8225549995e-10,\
+   -7.8529116371e-16,\
+    1.7476576773e-19,\
+
+# Poly NORTH :: e-degree =  2  : n-degree =  2
+   -1.6875687989e-10,\
+    1.1236475299e-14,\
+    1.7042518057e-18,\
+
+# Poly NORTH :: e-degree =  3  : n-degree =  1
+    7.9300735257e-15,\
+    5.2881862699e-19,\
+
+# Poly NORTH :: e-degree =  4  : n-degree =  0
+   -3.9990736798e-19
+
+# tcy    6125811.281773
+
+
+
+
+# static  double utt_e[]
+inv_u=\
+# Poly EAST  :: n-degree =  0  : e-degree =  0..4
+    8.7760527928e+05,\
+    1.0000024735e+00,\
+   -2.8817540032e-10,\
+   -5.5627059451e-15,\
+    1.5543637570e-18,\
+
+# Poly EAST  :: n-degree =  1  : e-degree =  0..3
+    4.1357152105e-05,\
+   -4.2114813612e-11,\
+   -2.8523713454e-14,\
+    1.9109017837e-18,\
+
+# Poly EAST  :: n-degree =  2  : e-degree =  0..2
+   -3.3616407783e-10,\
+   -2.4382678126e-14,\
+    2.0245020199e-18,\
+
+# Poly EAST  :: n-degree =  3  : e-degree =  0..1
+   -1.2441377565e-15,\
+   -5.3885232238e-19,\
+
+# Poly EAST  :: n-degree =  4  : e-degree =  0
+    1.0167203661e-18
+
+# tcx     877605.760036
+
+<>