From 9fa4e779ff50edc99566153d2de850f28eaddb7c Mon Sep 17 00:00:00 2001
From: Sergey Bugaev <bugaevc@gmail.com>
Date: Mon, 17 Jun 2019 16:44:47 +0300
Subject: [PATCH] LibM: Rewrite trigonometric functions.

This way they seem to actually work as expected ;)
---
 LibM/math.cpp | 39 +++++++++++++++++++++++----------------
 1 file changed, 23 insertions(+), 16 deletions(-)

diff --git a/LibM/math.cpp b/LibM/math.cpp
index 88fac357f8..070458a41a 100644
--- a/LibM/math.cpp
+++ b/LibM/math.cpp
@@ -12,27 +12,34 @@ double cos(double angle)
     return sin(angle + M_PI_2);
 }
 
-double ampsin(double angle)
+static double sin_helper(double a)
 {
-    double looped_angle = fmod(M_PI + angle, M_TAU);
-    double looped_angle_squared = looped_angle * looped_angle;
+    double a3 = a * a * a;
+    double a5 = a3 * a * a;
+    return a - a3 / 6.0 + a5 / 120.0;
+}
 
-    double quadratic_term;
-    if (looped_angle_squared > 0) {
-        quadratic_term = -looped_angle_squared;
-    } else {
-        quadratic_term = looped_angle_squared;
-    }
-
-    double linear_term = M_PI * looped_angle;
-
-    return quadratic_term * linear_term;
+static double cos_helper(double a)
+{
+    double a2 = a * a;
+    double a4 = a2 * a2;
+    return 1 - a2 / 2.0 + a4 / 24.0;
 }
 
 double sin(double angle)
 {
-    double vertical_scaling = M_PI_2 * M_PI_2;
-    return ampsin(angle) / vertical_scaling;
+    double a = fmod(angle, M_TAU);
+    if (a < 0)
+        a += M_TAU;
+    if (a <= M_PI_2 * 0.5)
+        return sin_helper(a);
+    if (a <= M_PI_2)
+        return cos_helper(M_PI_2 - a);
+    if (a <= M_PI_2 * 1.5)
+        return cos_helper(a - M_PI_2);
+    if (a <= M_PI)
+        return sin_helper(M_PI - a);
+    return -sin(angle - M_PI);
 }
 
 double pow(double x, double y)
@@ -55,7 +62,7 @@ double tanh(double)
 
 double tan(double angle)
 {
-    return ampsin(angle) / ampsin(M_PI_2 + angle);
+    return sin(angle) / cos(angle);
 }
 
 double sqrt(double)