From 07e18043145f3d91c8ea7ec3ad41b3c905585277 Mon Sep 17 00:00:00 2001
From: Ethan Werner <mail@ethanwerner.com>
Date: Wed, 1 Jul 2026 09:42:39 +0400
Subject: initial commit: ts time series analysis library v0.1.0

- 354 financial and mathematical time-series indicators
- Uniform C11 API with consistent function signatures
- 349 passing tests with -Werror
- Static and shared library builds
- pkg-config integration
- Python bindings
- Fuzzing and sanitizer support
- Security hardening flags
---
 lib/ellint_2.c | 64 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 64 insertions(+)
 create mode 100644 lib/ellint_2.c

(limited to 'lib/ellint_2.c')

diff --git a/lib/ellint_2.c b/lib/ellint_2.c
new file mode 100644
index 0000000..59660cd
--- /dev/null
+++ b/lib/ellint_2.c
@@ -0,0 +1,64 @@
+// Complete Elliptic Integral of the Second Kind
+//
+// ellint_2 - E(m)
+//
+// E(m) = ∫₀^(π/2) √(1 - m*sin²(θ)) dθ, computed via AGM
+//
+// Inputs:    1 (parameter m)
+// Outputs:   1 (E(m))
+// Constants: 0
+
+#include <math.h>
+#include "ts.h"
+
+
+ts_parameter_t const ts_ellint_2_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 0, .params_size = 0 };
+
+uint_t ts_ellint_2_offset( ts_constant_t const *c )
+{
+	( void )c;
+	return ( 0 );
+}
+
+int ts_ellint_2(
+	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_2_p );
+	(void)c;
+    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] = 1.0;
+        }
+        else
+        {
+            fp_t a = 1.0;
+            fp_t b = sqrt(1.0 - m);
+            fp_t s = 0.0;
+            fp_t scale = 0.5;
+            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 c_new = (a - b) / 2.0;
+                s += scale * c_new * c_new;
+                a = a_new;
+                b = b_new;
+                scale *= 2.0;
+                if (c_new < 1e-15) break;
+            }
+            y[0][i] = (PI / (2.0 * a)) * (1.0 - s);
+        }
+    }
+	return 0;
+}
+
-- 
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