LibM: Fixed sin() precision (#726)

The old implementation of sin() had a very unacceptable amount of
error that was causing a lot of texture perspective issues in Quake.
This has been remedied through the use of the hardware `fsin`
x87 instruction. As has been noted in #246, this instruction is both
very slow, and can become wildly inaccurate for more precise values,
however the current implementation made an incorrect assumption about
applications "will end up writing their own implemtnation anyways",
which is not the case for Quake in Software mode, which relies heavily
on a correct `sin()` and `cos()` function for `R_ScanEdges()`.

Realistically, we should be using something like the CORDIC algorithm
(https://en.wikipedia.org/wiki/CORDIC) or `Taylor Expansion`, however
for now these provides a somewhat accurate result that allows Quake to
run without any texture or geometry issues.

Libraries/LibM/math.cpp

@@ -32,6 +32,7 @@ template<size_t value>
 constexpr size_t product_odd() { return value * product_odd<value - 2>(); }
 
 extern "C" {
+
 double trunc(double x)
 {
     return (int64_t)x;
@@ -42,27 +43,19 @@ double cos(double angle)
     return sin(angle + M_PI_2);
 }
 
-double ampsin(double angle)
-{
-    double looped_angle = fmod(M_PI + angle, M_TAU) - M_PI;
-    double looped_angle_squared = looped_angle * looped_angle;
-
-    double quadratic_term;
-    if (looped_angle > 0) {
-        quadratic_term = -looped_angle_squared;
-    } else {
-        quadratic_term = looped_angle_squared;
-    }
-
-    double linear_term = M_PI * looped_angle;
-
-    return quadratic_term + linear_term;
-}
-
+// This can also be done with a taylor expansion, but for
+// now this works pretty well (and doesn't mess anything up
+// in quake in particular, which is very Floating-Point precision
+// heavy)
 double sin(double angle)
 {
-    double vertical_scaling = M_PI_2 * M_PI_2;
-    return ampsin(angle) / vertical_scaling;
+    double ret = 0.0;
+    __asm__(
+        "fsin"
+        : "=t"(ret)
+        : "0"(angle));
+
+    return ret;
 }
 
 double pow(double x, double y)
@@ -291,5 +284,4 @@ float ceilf(float value)
     }
     return as_int + 1;
 }
-
 }