From 3733383fafbb2f103b277521168ee46681df7cf4 Mon Sep 17 00:00:00 2001
From: upstream <upstream@localhost>
Date: Wed, 2 Sep 2026 04:47:48 +0200
Subject: [PATCH] Upstream tuneinsight/lattigo state of the touched files
 before 9e074460b4

---
 utils/bignum/eval.go | 51 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 utils/bignum/eval.go

diff --git a/utils/bignum/eval.go b/utils/bignum/eval.go
new file mode 100644
index 0000000..854bba5
--- /dev/null
+++ b/utils/bignum/eval.go
@@ -0,0 +1,51 @@
+package bignum
+
+import (
+	"math/big"
+)
+
+// MonomialEval evaluates y = sum x^i * poly[i].
+func MonomialEval(x *big.Float, poly []*big.Float) (y *big.Float) {
+	n := len(poly) - 1
+	y = new(big.Float).Set(poly[n-1])
+	for i := n - 2; i >= 0; i-- {
+		y.Mul(y, x)
+		y.Add(y, poly[i])
+	}
+	return
+}
+
+// ChebyshevEval evaluates y = sum Ti(x) * poly[i], where T0(x) = 1, T1(x) = (2x-a-b)/(b-a) and T{i+j}(x) = 2TiTj(x)- T|i-j|(x).
+func ChebyshevEval(x *big.Float, poly []*big.Float, inter Interval) (y *big.Float) {
+
+	precision := x.Prec()
+
+	two := NewFloat(2, precision)
+	var tmp, u = new(big.Float), new(big.Float)
+	var T, Tprev, Tnext = new(big.Float), new(big.Float), new(big.Float)
+
+	// u = (2*x - (a+b))/(b-a)
+	u.Set(x)
+	u.Mul(u, two)
+	u.Sub(u, &inter.A)
+	u.Sub(u, &inter.B)
+	tmp.Set(&inter.B)
+	tmp.Sub(tmp, &inter.A)
+	u.Quo(u, tmp)
+
+	Tprev.SetPrec(precision)
+	Tprev.SetFloat64(1)
+	T.Set(u)
+	y = new(big.Float).Set(poly[0])
+
+	for i := 1; i < len(poly); i++ {
+		y.Add(y, tmp.Mul(T, poly[i]))
+		Tnext.Mul(two, u)
+		Tnext.Mul(Tnext, T)
+		Tnext.Sub(Tnext, Tprev)
+		Tprev.Set(T)
+		T.Set(Tnext)
+	}
+
+	return
+}