1 files changed, 65 insertions, 0 deletions
diff --git a/lib/ellint_1.c b/lib/ellint_1.c
new file mode 100644
index 0000000..8e0bab7
--- /dev/null
+++ b/lib/ellint_1.c
@@ -0,0 +1,65 @@
+// Complete Elliptic Integral of the First Kind
+//
+// ellint_1 - K(m)
+//
+// K(m) = ∫₀^(π/2) dθ / √(1 - m*sin²(θ)), computed via AGM
+//
+// Inputs:    1 (parameter m)
+// Outputs:   1 (K(m))
+// Constants: 0
+
+#include <math.h>
+#include "ts.h"
+
+
+ts_parameter_t const ts_ellint_1_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };
+
+uint_t ts_ellint_1_offset( ts_constant_t const *c )
+{
+	( void )c;
+	return ( 0 );
+}
+
+int ts_ellint_1(
+	fp_t * const *y, uint_t y_n,
+	fp_t const * const *x, uint_t x_n,
+	uint_t n, ts_constant_t const *c
+)
+{
+	TS_PROLOGUE( ts_ellint_1_p );
+	(void)c;
+    /* Complete elliptic integral of the first kind K(m) */
+    for (uint_t i = 0; i < n; ++i)
+    {
+        fp_t m = x[0][i];
+        if (m <= 0.0)
+        {
+            y[0][i] = PI / 2.0;
+        }
+        else if (m >= 1.0)
+        {
+            y[0][i] = INFINITY;
+        }
+        else
+        {
+            /* Arithmetic-geometric mean method */
+            fp_t a = 1.0;
+            fp_t b = sqrt(1.0 - m);
+            fp_t cn = (a - b) / 2.0;
+            for (uint_t j = 0; j < 30; ++j)
+            {
+                fp_t a_new = (a + b) / 2.0;
+                fp_t b_new = sqrt(a * b);
+                fp_t cn_new = (a_new - b_new) / 2.0;
+                a = a_new;
+                b = b_new;
+                cn = cn_new;
+                if (cn / a < 1e-15) break;
+            }
+            y[0][i] = PI / (2.0 * a);
+        }
+    }
+	return 0;
+}
+
+