diff options
| -rw-r--r-- | src/PJ_merc.c | 30 |
1 files changed, 29 insertions, 1 deletions
diff --git a/src/PJ_merc.c b/src/PJ_merc.c index a3e5e846..0bf98625 100644 --- a/src/PJ_merc.c +++ b/src/PJ_merc.c @@ -2,12 +2,40 @@ #include "proj_internal.h" #include "proj.h" #include "projects.h" +#include <float.h> PROJ_HEAD(merc, "Mercator") "\n\tCyl, Sph&Ell\n\tlat_ts="; PROJ_HEAD(webmerc, "Web Mercator / Pseudo Mercator") "\n\tCyl, Sph\n\t"; #define EPS10 1.e-10 +#if !defined(HAVE_C99_MATH) +#define HAVE_C99_MATH 0 +#endif + +#if HAVE_C99_MATH +#define log1px log1p +#else +static double log1px(double x) { + volatile double + y = 1 + x, + z = y - 1; + /* Here's the explanation for this magic: y = 1 + z, exactly, and z + * approx x, thus log(y)/z (which is nearly constant near z = 0) returns + * a good approximation to the true log(1 + x)/x. The multiplication x * + * (log(y)/z) introduces little additional error. */ + return z == 0 ? x : x * log(y) / z; +} +#endif + +static double logtanpfpim1(double x) { /* log(tan(x/2 + M_FORTPI)) */ + if (fabs(x) <= DBL_EPSILON) { + /* tan(M_FORTPI + .5 * x) can be approximated by 1.0 + x */ + return log1px(x); + } + return log(tan(M_FORTPI + .5 * x)); +} + static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */ XY xy = {0.0,0.0}; if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10) { @@ -27,7 +55,7 @@ static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */ return xy; } xy.x = P->k0 * lp.lam; - xy.y = P->k0 * log(tan(M_FORTPI + .5 * lp.phi)); + xy.y = P->k0 * logtanpfpim1(lp.phi); return xy; } |