--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mupdf-source/thirdparty/tesseract/src/ccstruct/quadlsq.cpp	Mon Sep 15 11:43:07 2025 +0200
@@ -0,0 +1,144 @@
+/**********************************************************************
+ * File:        quadlsq.cpp  (Formerly qlsq.c)
+ * Description: Code for least squares approximation of quadratics.
+ * Author:      Ray Smith
+ *
+ * (C) Copyright 1993, Hewlett-Packard Ltd.
+ ** Licensed under the Apache License, Version 2.0 (the "License");
+ ** you may not use this file except in compliance with the License.
+ ** You may obtain a copy of the License at
+ ** http://www.apache.org/licenses/LICENSE-2.0
+ ** Unless required by applicable law or agreed to in writing, software
+ ** distributed under the License is distributed on an "AS IS" BASIS,
+ ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ ** See the License for the specific language governing permissions and
+ ** limitations under the License.
+ *
+ **********************************************************************/
+
+#include "quadlsq.h"
+
+#include "tprintf.h"
+
+#include <cmath>
+#include <cstdio>
+
+namespace tesseract {
+
+// Minimum variance in least squares before backing off to a lower degree.
+const long double kMinVariance = 1.0L / 1024;
+
+/**********************************************************************
+ * QLSQ::clear
+ *
+ * Function to initialize a QLSQ.
+ **********************************************************************/
+
+void QLSQ::clear() { // initialize
+  a = 0.0;
+  b = 0.0;
+  c = 0.0;
+  n = 0;      // No elements.
+  sigx = 0.0; // Zero accumulators.
+  sigy = 0.0;
+  sigxx = 0.0;
+  sigxy = 0.0;
+  sigyy = 0.0;
+  sigxxx = 0.0;
+  sigxxy = 0.0;
+  sigxxxx = 0.0;
+}
+
+/**********************************************************************
+ * QLSQ::add
+ *
+ * Add an element to the accumulator.
+ **********************************************************************/
+
+void QLSQ::add(double x, double y) {
+  n++;       // Count elements.
+  sigx += x; // Update accumulators.
+  sigy += y;
+  sigxx += x * x;
+  sigxy += x * y;
+  sigyy += y * y;
+  sigxxx += static_cast<long double>(x) * x * x;
+  sigxxy += static_cast<long double>(x) * x * y;
+  sigxxxx += static_cast<long double>(x) * x * x * x;
+}
+
+/**********************************************************************
+ * QLSQ::remove
+ *
+ * Delete an element from the accumulator.
+ **********************************************************************/
+
+void QLSQ::remove(double x, double y) {
+  if (n <= 0) {
+    tprintf("Can't remove an element from an empty QLSQ accumulator!\n");
+    return;
+  }
+  n--;       // Count elements.
+  sigx -= x; // Update accumulators.
+  sigy -= y;
+  sigxx -= x * x;
+  sigxy -= x * y;
+  sigyy -= y * y;
+  sigxxx -= static_cast<long double>(x) * x * x;
+  sigxxy -= static_cast<long double>(x) * x * y;
+  sigxxxx -= static_cast<long double>(x) * x * x * x;
+}
+
+/**********************************************************************
+ * QLSQ::fit
+ *
+ * Fit the given degree of polynomial and store the result.
+ * This creates a quadratic of the form axx + bx + c, but limited to
+ * the given degree.
+ **********************************************************************/
+
+void QLSQ::fit(int degree) {
+  long double x_variance =
+      static_cast<long double>(sigxx) * n - static_cast<long double>(sigx) * sigx;
+
+  // Note: for computational efficiency, we do not normalize the variance,
+  // covariance and cube variance here as they are in the same order in both
+  // nominators and denominators. However, we need be careful in value range
+  // check.
+  if (x_variance < kMinVariance * n * n || degree < 1 || n < 2) {
+    // We cannot calculate b reliably so forget a and b, and just work on c.
+    a = b = 0.0;
+    if (n >= 1 && degree >= 0) {
+      c = sigy / n;
+    } else {
+      c = 0.0;
+    }
+    return;
+  }
+  long double top96 = 0.0;    // Accurate top.
+  long double bottom96 = 0.0; // Accurate bottom.
+  long double cubevar = sigxxx * n - static_cast<long double>(sigxx) * sigx;
+  long double covariance =
+      static_cast<long double>(sigxy) * n - static_cast<long double>(sigx) * sigy;
+
+  if (n >= 4 && degree >= 2) {
+    top96 = cubevar * covariance;
+    top96 += x_variance * (static_cast<long double>(sigxx) * sigy - sigxxy * n);
+
+    bottom96 = cubevar * cubevar;
+    bottom96 -= x_variance * (sigxxxx * n - static_cast<long double>(sigxx) * sigxx);
+  }
+  if (bottom96 >= kMinVariance * n * n * n * n) {
+    // Denominators looking good
+    a = top96 / bottom96;
+    top96 = covariance - cubevar * a;
+    b = top96 / x_variance;
+  } else {
+    // Forget a, and concentrate on b.
+    a = 0.0;
+    b = covariance / x_variance;
+  }
+  c = (sigy - a * sigxx - b * sigx) / n;
+}
+
+} // namespace tesseract