From 15322f7f51b7787bde99c86b141c77879d9f239e Mon Sep 17 00:00:00 2001
From: Yiwu Chen <210at85@gmail.com>
Date: Mon, 17 Jun 2024 13:59:18 +0000
Subject: [PATCH] [stdlib] Improve `_horner_evaluate` docstring

- Small simplification to the function `_horner_evaluate`.
- Improve its docstring to match the argument names.
- Finish off removing `unroll` by cleaning up the imports.

Signed-off-by: Yiwu Chen <210at85@gmail.com>
---
 stdlib/src/math/polynomial.mojo | 21 ++++++++-------------
 1 file changed, 8 insertions(+), 13 deletions(-)

diff --git a/stdlib/src/math/polynomial.mojo b/stdlib/src/math/polynomial.mojo
index 2f4473c9f..1fc938e9f 100644
--- a/stdlib/src/math/polynomial.mojo
+++ b/stdlib/src/math/polynomial.mojo
@@ -21,7 +21,6 @@ from math.polynomial import polynomial_evaluate
 
 from collections import List
 
-from utils.loop import unroll
 
 # ===----------------------------------------------------------------------===#
 # polynomial_evaluate
@@ -64,11 +63,12 @@ fn _horner_evaluate[
 ](x: SIMD[dtype, simd_width]) -> SIMD[dtype, simd_width]:
     """Evaluates the polynomial using the passed in value and the specified
     coefficients using the Horner scheme. The Horner scheme evaluates the
-    polynomial as `horner(val, coeffs)` where val is a scalar and coeffs is a
-    list of coefficients [c0, c1, c2, ..., cn] by:
+    polynomial at point x as `horner(x, coeffs)` where x is a scalar and coeffs
+    is a list of coefficients [c0, c1, c2, ..., cn] by:
     ```
-    horner(val, coeffs) = c0 + val * (c1 + val * (c2 + val * (... + val * cn)))
-                = fma(val, horner(val, coeffs[1:]), c0)
+    horner(x, coeffs)
+        = c0 + x * (c1 + x * (c2 + x * (... + x * cn)))
+        = fma(x, horner(x, coeffs[1:]), coeffs[0])
     ```
 
     Parameters:
@@ -80,17 +80,12 @@ fn _horner_evaluate[
         x: The value to compute the polynomial with.
 
     Returns:
-        The polynomial evaluation results using the specified value and the
-        constant coefficients.
+        The polynomial specified by the coefficients evaluated at value x.
     """
-    alias num_coefficients = len(coefficients)
-    alias c_last = coefficients[num_coefficients - 1]
-    alias c_second_from_last = coefficients[num_coefficients - 2]
-
-    var result = x.fma(c_last, c_second_from_last)
+    var result = x.fma(coefficients[-1], coefficients[-2])
 
     @parameter
-    for i in reversed(range(num_coefficients - 2)):
+    for i in reversed(range(len(coefficients) - 2)):
         alias c = coefficients[i]
         result = result.fma(x, c)