1 files changed, 191 insertions, 0 deletions
diff --git a/src/boot/O2/math64.c b/src/boot/O2/math64.c
new file mode 100644
index 000000000..cb77bed50
--- /dev/null
+++ b/src/boot/O2/math64.c
@@ -0,0 +1,191 @@
+/**
+ * MathF library
+ * Contains tangent function, wrappers for a number of the handwritten functions in fp, and a suite of arctangents
+ */
+#include "global.h"
+#include "fixed_point.h"
+
+s32 gUseAtanContFrac;
+
+/**
+ * Tangent function computed using libultra sinf and cosf
+ */
+f32 Math_FTanF(f32 x) {
+    return sinf(x) / cosf(x);
+}
+
+// Unused
+f32 Math_FFloorF(f32 x) {
+    return floorf(x);
+}
+
+// Unused
+f32 Math_FCeilF(f32 x) {
+    return ceilf(x);
+}
+
+// Unused
+f32 Math_FRoundF(f32 x) {
+    return roundf(x);
+}
+
+// Unused
+f32 Math_FTruncF(f32 x) {
+    return truncf(x);
+}
+
+f32 Math_FNearbyIntF(f32 x) {
+    return nearbyintf(x);
+}
+
+/**
+ * Arctangent approximation using a Maclaurin series [https://mathworld.wolfram.com/MaclaurinSeries.html]
+ * (one quadrant, i.e. |x| < 1)
+ */
+f32 Math_FAtanTaylorQF(f32 x) {
+    // Coefficients of Maclaurin series of arctangent
+    static const f32 coeffs[] = {
+        -1.0f / 3, +1.0f / 5, -1.0f / 7, +1.0f / 9, -1.0f / 11, +1.0f / 13, -1.0f / 15, +1.0f / 17, 0.0f,
+    };
+
+    f32 poly = x;
+    f32 sq = SQ(x);
+    f32 exp = x * sq;
+    const f32* c = coeffs;
+    f32 term;
+
+    // Calculate the series until adding more terms does not change the float
+    while (true) {
+        term = *c++ * exp;
+        if (poly + term == poly) {
+            break;
+        }
+        poly += term;
+        exp *= sq;
+    }
+
+    return poly;
+}
+
+/**
+ * Extends previous arctangent function to the rest of the real numbers.
+ * Uses the formulae arctan(x) = pi/2 - arctan(1/x)
+ * and arctan(x) = pi/4 - arctan( (1-x)/(1+x) )
+ * to extend the range in which the series computed by Math_FAtanTaylorQF is a good approximation
+ */
+f32 Math_FAtanTaylorF(f32 x) {
+    f32 t;
+    f32 q;
+
+    if (x > 0.0f) {
+        t = x;
+    } else if (x < 0.0f) {
+        t = -x;
+    } else if (x == 0.0f) {
+        return 0.0f;
+    } else {
+        return qNaN0x10000;
+    }
+
+    if (t <= M_SQRT2 - 1.0f) {
+        return Math_FAtanTaylorQF(x);
+    }
+
+    if (t >= M_SQRT2 + 1.0f) {
+        q = M_PI / 2 - Math_FAtanTaylorQF(1.0f / t);
+    } else { // in the interval (\sqrt{2} - 1, \sqrt{2} + 1)
+        q = M_PI / 4 - Math_FAtanTaylorQF((1.0f - t) / (1.0f + t));
+    }
+
+    if (x > 0.0f) {
+        return q;
+    } else {
+        return -q;
+    }
+}
+
+/**
+ * Arctangent approximation using a continued fraction
+ * Cf. https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction#The_series_2F1_2 ,
+ * https://dlmf.nist.gov/4.25#E4
+ */
+f32 Math_FAtanContFracF(f32 x) {
+    s32 sector;
+    f32 z;
+    f32 conv;
+    f32 sq;
+    s32 i;
+
+    if (x >= -1.0f && x <= 1.0f) {
+        sector = 0;
+    } else if (x > 1.0f) {
+        sector = 1;
+        x = 1.0f / x;
+    } else if (x < -1.0f) {
+        sector = -1;
+        x = 1.0f / x;
+    } else {
+        return qNaN0x10000;
+    }
+
+    // Builds the continued fraction from the innermost fraction out
+    sq = SQ(x);
+    conv = 0.0f;
+    z = 8.0f;
+    for (i = 8; i != 0; i--) {
+        conv = SQ(z) * sq / (2.0f * z + 1.0f + conv);
+        z -= 1.0f;
+    }
+    conv = x / (1.0f + conv);
+
+    if (sector == 0) {
+        return conv;
+    } else if (sector > 0) {
+        return M_PI / 2 - conv;
+    } else {
+        return -M_PI / 2 - conv;
+    }
+}
+
+/**
+ * Single-argument arctangent, only used by the two-argument function.
+ * Nothing else sets the bss variable gUseAtanContFrac, so the Maclaurin series is always used
+ */
+f32 Math_FAtanF(f32 x) {
+    if (!gUseAtanContFrac) {
+        return Math_FAtanTaylorF(x);
+    } else {
+        return Math_FAtanContFracF(x);
+    }
+}
+
+/**
+ * Main two-argument arctangent function
+ */
+f32 Math_FAtan2F(f32 y, f32 x) {
+    if (x == 0.0f) {
+        if (y == 0.0f) {
+            return 0.0f;
+        } else if (y > 0.0f) {
+            return M_PI / 2;
+        } else if (y < 0.0f) {
+            return -M_PI / 2;
+        } else {
+            return qNaN0x10000;
+        }
+    } else if (x >= 0.0f) {
+        return Math_FAtanF(y / x);
+    } else if (y < 0.0f) {
+        return Math_FAtanF(y / x) - M_PI;
+    } else {
+        return M_PI - Math_FAtanF(-(y / x));
+    }
+}
+
+f32 Math_FAsinF(f32 x) {
+    return Math_FAtan2F(x, sqrtf(1.0f - SQ(x)));
+}
+
+f32 Math_FAcosF(f32 x) {
+    return M_PI / 2 - Math_FAsinF(x);
+}