Lightweight trigonometry doc (#1356)

* Doc units of trig functions

* "Very simple" yet I made a mistake

* sins returns in [-0x7FFF,0x7FFF] as the [-1,1] range

* Also `sys_math_atan.c`

* Remove `@param`s without descriptions

* Add note on Math_Atan2S/F arguments being unlike atan2

* "from (1,0) to (x,y)" -> "from vector ..."

* arg names -> `angle`

* Improve `@return` comment on atans

9 files changed, 99 insertions, 35 deletions

diff --git a/src/code/code_800FCE80.c b/src/code/code_800FCE80.c
index 500e2c01d..3d73123da 100644
--- a/src/code/code_800FCE80.c
+++ b/src/code/code_800FCE80.c
@@ -3,9 +3,13 @@
 
 s32 gUseAtanContFrac;
 
-f32 Math_FTanF(f32 x) {
-    f32 sin = sinf(x);
-    f32 cos = cosf(x);
+/**
+ * @param angle radians
+ * @return tan(angle)
+ */
+f32 Math_FTanF(f32 angle) {
+    f32 sin = sinf(angle);
+    f32 cos = cosf(angle);
 
     return sin / cos;
 }
@@ -42,7 +46,7 @@ f32 Math_FAtanTaylorQF(f32 x) {
     const f32* c = coeffs;
     f32 term;
 
-    while (1) {
+    while (true) {
         term = *c++ * exp;
         if (poly + term == poly) {
             break;
@@ -124,6 +128,9 @@ f32 Math_FAtanContFracF(f32 x) {
     }
 }
 
+/**
+ * @return arctan(x) in radians, in (-pi/2,pi/2) range
+ */
 f32 Math_FAtanF(f32 x) {
     if (!gUseAtanContFrac) {
         return Math_FAtanTaylorF(x);
@@ -132,6 +139,9 @@ f32 Math_FAtanF(f32 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) {
@@ -152,10 +162,16 @@ f32 Math_FAtan2F(f32 y, f32 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);
 }
diff --git a/src/code/sys_math.c b/src/code/sys_math.c
index 0a85d5cf6..f19719bb9 100644
--- a/src/code/sys_math.c
+++ b/src/code/sys_math.c
@@ -38,10 +38,18 @@ f32 Math_PowF(f32 base, s32 exp) {
     return ret;
 }
 
+/**
+ * @param angle radians
+ * @return sin(angle)
+ */
 f32 Math_SinF(f32 angle) {
     return sins((s16)(angle * (0x7FFF / M_PI))) * SHT_MINV;
 }
 
+/**
+ * @param angle radians
+ * @return cos(angle)
+ */
 f32 Math_CosF(f32 angle) {
     return coss((s16)(angle * (0x7FFF / M_PI))) * SHT_MINV;
 }
diff --git a/src/code/sys_math_atan.c b/src/code/sys_math_atan.c
index 4e346da4e..efbe8a205 100644
--- a/src/code/sys_math_atan.c
+++ b/src/code/sys_math_atan.c
@@ -1,6 +1,6 @@
 #include "global.h"
 
-static u16 sATan2Tbl[] = {
+static u16 sAtan2Tbl[] = {
     0x0000, 0x000A, 0x0014, 0x001F, 0x0029, 0x0033, 0x003D, 0x0047, 0x0051, 0x005C, 0x0066, 0x0070, 0x007A, 0x0084,
     0x008F, 0x0099, 0x00A3, 0x00AD, 0x00B7, 0x00C2, 0x00CC, 0x00D6, 0x00E0, 0x00EA, 0x00F4, 0x00FF, 0x0109, 0x0113,
     0x011D, 0x0127, 0x0131, 0x013C, 0x0146, 0x0150, 0x015A, 0x0164, 0x016F, 0x0179, 0x0183, 0x018D, 0x0197, 0x01A1,
@@ -77,24 +77,34 @@ static u16 sATan2Tbl[] = {
     0x1FF6, 0x1FFB, 0x2000,
 };
 
-u16 Math_GetAtan2Tbl(f32 x, f32 y) {
+/**
+ * @param y must be >= 0 and <= x
+ * @param x must be >= 0
+ * @return arctan(y/x) as binang, in [0,0x2000] range
+ */
+u16 Math_GetAtan2Tbl(f32 y, f32 x) {
     u16 ret;
 
-    if (y == 0.0f) {
-        ret = sATan2Tbl[0];
+    if (x == 0.0f) {
+        ret = sAtan2Tbl[0];
     } else {
-        s32 tblIdx = ((x / y) * 1024.0f) + 0.5f;
+        s32 tblIdx = ((y / x) * 1024.0f) + 0.5f;
 
-        if (tblIdx >= ARRAY_COUNT(sATan2Tbl)) {
-            ret = sATan2Tbl[0];
+        if (tblIdx >= ARRAY_COUNT(sAtan2Tbl)) {
+            ret = sAtan2Tbl[0];
         } else {
-            ret = sATan2Tbl[tblIdx];
+            ret = sAtan2Tbl[tblIdx];
         }
     }
 
     return ret;
 }
 
+/**
+ * @return angle to (x,y) from vector (1,0) around (0,0) as binang, in [-0x8000,0x7FFF] range
+ *
+ * @note The arguments are (x,y), which is different from atan2's (y,x)
+ */
 s16 Math_Atan2S(f32 x, f32 y) {
     s32 ret;
 
@@ -107,7 +117,7 @@ s16 Math_Atan2S(f32 x, f32 y) {
             }
         } else {
             if (-x < y) {
-                ret = Math_GetAtan2Tbl(-x, y) + 0x4000;
+                ret = 0x4000 + Math_GetAtan2Tbl(-x, y);
             } else {
                 ret = 0x8000 - Math_GetAtan2Tbl(y, -x);
             }
@@ -115,21 +125,27 @@ s16 Math_Atan2S(f32 x, f32 y) {
     } else {
         if (x < 0.0f) {
             if (-y <= -x) {
-                ret = Math_GetAtan2Tbl(-y, -x) + 0x8000;
+                ret = 0x8000 + Math_GetAtan2Tbl(-y, -x);
             } else {
                 ret = 0xC000 - Math_GetAtan2Tbl(-x, -y);
             }
         } else {
             if (x < -y) {
-                ret = Math_GetAtan2Tbl(x, -y) + 0xC000;
+                ret = 0xC000 + Math_GetAtan2Tbl(x, -y);
             } else {
                 ret = -Math_GetAtan2Tbl(-y, x);
             }
         }
     }
-    return ret;
+
+    return (s16)ret;
 }
 
+/**
+ * @return angle to (x,y) from vector (1,0) around (0,0) in radians, in [-pi,pi) range
+ *
+ * @note The arguments are (x,y), which is different from atan2's (y,x)
+ */
 f32 Math_Atan2F(f32 x, f32 y) {
     return BINANG_TO_RAD(Math_Atan2S(x, y));
 }
diff --git a/src/code/z_lib.c b/src/code/z_lib.c
index 3dd0030f0..ac5220ab0 100644
--- a/src/code/z_lib.c
+++ b/src/code/z_lib.c
@@ -23,10 +23,18 @@ void Lib_MemSet(u8* dest, size_t len, u8 val) {
     // clang-format on
 }
 
+/**
+ * @param angle binang
+ * @return cos(angle)
+ */
 f32 Math_CosS(s16 angle) {
     return coss(angle) * SHT_MINV;
 }
 
+/**
+ * @param angle binang
+ * @return sin(angle)
+ */
 f32 Math_SinS(s16 angle) {
     return sins(angle) * SHT_MINV;
 }
diff --git a/src/libultra/gu/cosf.c b/src/libultra/gu/cosf.c
index cae7159ea..639084093 100644
--- a/src/libultra/gu/cosf.c
+++ b/src/libultra/gu/cosf.c
@@ -14,7 +14,11 @@ static const du pilo = { 0x3E6110B4, 0x611A6263 };
 
 static const fu zero = { 0x00000000 };
 
-f32 cosf(f32 x) {
+/**
+ * @param angle radians
+ * @return cos(angle)
+ */
+f32 cosf(f32 angle) {
     f32 absx;
     f64 dx;
     f64 xSq;
@@ -22,13 +26,13 @@ f32 cosf(f32 x) {
     f64 dn;
     s32 n;
     f64 result;
-    s32 ix = *(s32*)&x;
+    s32 ix = *(s32*)&angle;
     s32 xpt = (ix >> 22);
 
     xpt &= 0x1FF;
 
     if (xpt < 0x136) {
-        absx = (x > 0) ? x : -x;
+        absx = (angle > 0) ? angle : -angle;
         dx = absx;
 
         dn = dx * rpi.d + 0.5;
@@ -51,7 +55,7 @@ f32 cosf(f32 x) {
         }
         return -(f32)result;
     }
-    if (x != x) {
+    if (angle != angle) {
         return __libm_qnan_f;
     }
 
diff --git a/src/libultra/gu/coss.c b/src/libultra/gu/coss.c
index 2dca0234b..0eb8b5e65 100644
--- a/src/libultra/gu/coss.c
+++ b/src/libultra/gu/coss.c
@@ -1,5 +1,9 @@
 #include "global.h"
 
+/**
+ * @param angle binang
+ * @return cos(angle)*0x7FFF
+ */
 s16 coss(u16 angle) {
     return sins(angle + 0x4000);
 }
diff --git a/src/libultra/gu/sinf.c b/src/libultra/gu/sinf.c
index bb7f58e72..49929e843 100644
--- a/src/libultra/gu/sinf.c
+++ b/src/libultra/gu/sinf.c
@@ -14,20 +14,24 @@ static const du pilo = { 0x3E6110B4, 0x611A6263 };
 
 static const fu zero = { 0x00000000 };
 
-f32 sinf(f32 x) {
+/**
+ * @param angle radians
+ * @return sin(angle)
+ */
+f32 sinf(f32 angle) {
     f64 dx;
     f64 xSq;
     f64 polyApprox;
     f64 dn;
     s32 n;
     f64 result;
-    s32 ix = *(s32*)&x;
+    s32 ix = *(s32*)&angle;
     s32 xpt = (ix >> 22);
 
     xpt &= 0x1FF;
 
     if (xpt < 0xFF) {
-        dx = x;
+        dx = angle;
 
         if (xpt >= 0xE6) {
             xSq = SQ(dx);
@@ -35,11 +39,11 @@ f32 sinf(f32 x) {
             result = dx + (dx * xSq) * polyApprox;
             return (f32)result;
         }
-        return x;
+        return angle;
     }
 
     if (xpt < 0x136) {
-        dx = x;
+        dx = angle;
         dn = dx * rpi.d;
         n = ROUND(dn);
         dn = n;
@@ -57,7 +61,7 @@ f32 sinf(f32 x) {
         return -(f32)result;
     }
 
-    if (x != x) {
+    if (angle != angle) {
         return __libm_qnan_f;
     }
     return zero.f;
diff --git a/src/libultra/gu/sins.c b/src/libultra/gu/sins.c
index b6c2d229a..636b76bd6 100644
--- a/src/libultra/gu/sins.c
+++ b/src/libultra/gu/sins.c
@@ -2,18 +2,22 @@
 
 #include "sintable.inc.c"
 
-s16 sins(u16 x) {
+/**
+ * @param angle binang
+ * @return sin(angle)*0x7FFF
+ */
+s16 sins(u16 angle) {
     s16 value;
 
-    x >>= 4;
+    angle >>= 4;
 
-    if (x & 0x400) {
-        value = sintable[0x3FF - (x & 0x3FF)];
+    if (angle & 0x400) {
+        value = sintable[0x3FF - (angle & 0x3FF)];
     } else {
-        value = sintable[x & 0x3FF];
+        value = sintable[angle & 0x3FF];
     }
 
-    if (x & 0x800) {
+    if (angle & 0x800) {
         return -value;
     } else {
         return value;
diff --git a/src/overlays/actors/ovl_Boss_Ganon/z_boss_ganon.c b/src/overlays/actors/ovl_Boss_Ganon/z_boss_ganon.c
index 79e1999f3..3fb7bc7c2 100644
--- a/src/overlays/actors/ovl_Boss_Ganon/z_boss_ganon.c
+++ b/src/overlays/actors/ovl_Boss_Ganon/z_boss_ganon.c
@@ -618,7 +618,7 @@ void BossGanon_IntroCutscene(BossGanon* this, PlayState* play) {
             this->csCamEye.z = 300.0f;
 
             this->csCamAt.x = 0.0f;
-            this->unk_704 = 1.2566371f;
+            this->unk_704 = 2 * M_PI / 5;
             FALLTHROUGH;
         case 3:
             this->envLightMode = 0;
@@ -3178,8 +3178,8 @@ void BossGanon_Update(Actor* thisx, PlayState* play2) {
         this->unk_278.y = this->unk_2EC[0].y + 50.0f + 30.0f;
         this->unk_278.z = this->unk_2EC[0].z;
 
-        xOffset = (sinf(i * 1.2566371f) * 600.0f);
-        zOffset = (cosf(i * 1.2566371f) * 600.0f);
+        xOffset = (sinf(i * (2 * M_PI / 5)) * 600.0f);
+        zOffset = (cosf(i * (2 * M_PI / 5)) * 600.0f);
 
         // 5 or 6 light balls that go into the charge. not the same as the ones that he throws
         Actor_SpawnAsChild(&play->actorCtx, &this->actor, play, ACTOR_BOSS_GANON, this->unk_1FC.x + xOffset,