From c59b28926f4562174eb2e39b87e018f0fe09b139 Mon Sep 17 00:00:00 2001
From: Rokas Puzonas <rokas.puz@gmail.com>
Date: Mon, 16 Jun 2025 23:04:33 +0300
Subject: [PATCH] implement horners rule

---
 src/math_func_checker.c | 44 ++++++++++++++++++++++++++++++++++-------
 1 file changed, 37 insertions(+), 7 deletions(-)

diff --git a/src/math_func_checker.c b/src/math_func_checker.c
index 155dda6..7bbac04 100644
--- a/src/math_func_checker.c
+++ b/src/math_func_checker.c
@@ -154,6 +154,23 @@ static f64 sin_using_taylor(f64 input, f64 *coeffs, size_t coeffs_len)
     return result;
 }
 
+static f64 sin_using_taylor_horner(f64 input, f64 *coeffs, size_t coeffs_len)
+{
+    f64 input_sqr = input * input;
+
+    f64 result = coeffs[coeffs_len - 1];
+    for (size_t j = 1; j < coeffs_len; j++) {
+        size_t i = coeffs_len - j - 1;
+
+        result *= input_sqr;
+        result += coeffs[i];
+    }
+
+    result *= input;
+
+    return result;
+}
+
 static void tester_record_result(struct tester *tester, f64 input, f64 my_output, f64 reference_output)
 {
     f64 error = reference_output - my_output;
@@ -182,19 +199,32 @@ static void test_taylor_series(u64 samples, f64 *coeffs, size_t coeffs_len)
     create_taylor_series_coeffs(coeffs, coeffs_len);
 
     struct tester tester = { };
+    struct tester tester_horner = { };
+
     for (int j = 0; j < samples; j++) {
-        f64 input = lerp((f64)j / samples, -M_PI, M_PI);
+        f64 input = lerp((f64)j / samples, 0, M_PI/2);
         tester_record_result(&tester, input, sin_using_taylor(input, coeffs, coeffs_len), sin(input));
+        tester_record_result(&tester_horner, input, sin_using_taylor_horner(input, coeffs, coeffs_len), sin(input));
     }
 
-    char name[64] = { 0 };
-    snprintf(name, sizeof(name), "taylor %zu", coeffs_len);
-    tester_show_result(&tester, name);
+    {
+        char name[64] = { 0 };
+        snprintf(name, sizeof(name), "taylor   %zu", coeffs_len);
+        tester_show_result(&tester, name);
+    }
+
+    {
+        char name[64] = { 0 };
+        snprintf(name, sizeof(name), "taylor h %zu", coeffs_len);
+        tester_show_result(&tester_horner, name);
+    }
+
+    printf("            diff               %.16f\n", tester.max_error - tester_horner.max_error);
 }
 
 int main()
 {
-    uint64_t samples = 10000;
+    uint64_t samples = 100000;
     struct math_spec specs[] = {
         {
             .name = "sin",
@@ -267,8 +297,8 @@ int main()
         tester_show_result(&tester, spec.name);
     }
 
-    f64 taylor_coeffs[41];
-    for (int i = 3; i < ARRAY_LEN(taylor_coeffs); i++) {
+    f64 taylor_coeffs[10];
+    for (int i = 1; i < ARRAY_LEN(taylor_coeffs); i++) {
         test_taylor_series(samples, taylor_coeffs, i);
     }