Experiment: remove global.h dependency from sys_math, sys_math3d, z_lib (#1956)

* split sys_math, sys_math3d, z_lib from global.h

* suggestions

* forgot this

* more math stuff

* nit fix

* re-add ichain.h

* resolve tharo's comments

1 files changed, 177 insertions, 0 deletions

diff --git a/src/code/fp_math.c b/src/code/fp_math.c
new file mode 100644
index 000000000..c429b83e2
--- /dev/null
+++ b/src/code/fp_math.c
@@ -0,0 +1,177 @@
+#include "z64math.h"
+#include "macros.h"
+
+s32 gUseAtanContFrac;
+
+/**
+ * @param angle radians
+ * @return tan(angle)
+ */
+f32 Math_FTanF(f32 angle) {
+    f32 sin = sinf(angle);
+    f32 cos = cosf(angle);
+
+    return sin / cos;
+}
+
+f32 Math_FFloorF(f32 x) {
+    return floorf(x);
+}
+
+f32 Math_FCeilF(f32 x) {
+    return ceilf(x);
+}
+
+f32 Math_FRoundF(f32 x) {
+    return roundf(x);
+}
+
+f32 Math_FTruncF(f32 x) {
+    return truncf(x);
+}
+
+f32 Math_FNearbyIntF(f32 x) {
+    return nearbyintf(x);
+}
+
+/* Arctangent approximation using a Taylor series (one quadrant) */
+f32 Math_FAtanTaylorQF(f32 x) {
+    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;
+
+    while (true) {
+        term = *c++ * exp;
+        if (poly + term == poly) {
+            break;
+        }
+        poly += term;
+        exp *= sq;
+    }
+
+    return poly;
+}
+
+/* Ditto for two quadrants */
+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 {
+        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 */
+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;
+    }
+
+    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;
+    }
+}
+
+/**
+ * @return arctan(x) in radians, in (-pi/2,pi/2) range
+ */
+f32 Math_FAtanF(f32 x) {
+    if (!gUseAtanContFrac) {
+        return Math_FAtanTaylorF(x);
+    } else {
+        return Math_FAtanContFracF(x);
+    }
+}
+
+/**
+ * @return angle to (x,y) from vector (1,0) around (0,0) in radians, in (-pi,pi] range
+ */
+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));
+    }
+}
+
+/**
+ * @return arcsin(x) in radians, in [-pi/2,pi/2] range
+ */
+f32 Math_FAsinF(f32 x) {
+    return Math_FAtan2F(x, sqrtf(1.0f - SQ(x)));
+}
+
+/**
+ * @return arccos(x) in radians, in [0,pi] range
+ */
+f32 Math_FAcosF(f32 x) {
+    return M_PI / 2 - Math_FAsinF(x);
+}