Collect custom C99 math functions in proj_math.h

We are relying more and more on C99 math functions. On C89 systems where
those functions are not available our own custom versions of those
functions are used instead. So far these has been spread across the code
base. This commit gathers them in the same file and introduces the
proj_math.h header. The build system checks for C99 math functions. If
not found the proj_math.h header make sure that C99 functions are
defined as their pj_ equivalent.

Ideally proj_math.h is included instead of math.h. This removes the need
for any checks against HAVE_C99_MATH in the code making it easier to
read.

For this commit the functions hypot, log1p and asinh has been taken care
of.

1 files changed, 66 insertions, 0 deletions

diff --git a/src/pj_math.c b/src/pj_math.c
new file mode 100644
index 00000000..d5242636
--- /dev/null
+++ b/src/pj_math.c
@@ -0,0 +1,66 @@
+/******************************************************************************
+ * Project:  PROJ
+ * Purpose:  Make C99 math functions available on C89 systems
+ * Author:   Kristian Evers
+ *
+ ******************************************************************************
+ * Copyright (c) 2018, Kristian Evers
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ *****************************************************************************/
+
+#include "proj_math.h"
+
+#if !(defined(HAVE_C99_MATH) && HAVE_C99_MATH)
+
+/* Compute hypotenuse */
+double pj_hypot(double x, double y) {
+    x = fabs(x);
+    y = fabs(y);
+    if ( x < y ) {
+        x /= y;
+        return ( y * sqrt( 1. + x * x ) );
+    } else {
+        y /= (x != 0.0 ? x : 1.0);
+        return ( x * sqrt( 1. + y * y ) );
+    }
+}
+
+/* Compute log(1+x) accurately */
+double pj_log1p(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;
+}
+
+/* Compute asinh(x) accurately */
+double pj_asinh(double x) {
+    double y = fabs(x); /* Enforce odd parity */
+    y = log1p(y * (1 + y/(hypot(1.0, y) + 1)));
+    return x > 0 ? y : (x < 0 ? -y : x);
+}
+
+#endif /* !(defined(HAVE_C99_MATH) && HAVE_C99_MATH) */
+
+