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https://github.com/zeldaret/oot.git
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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
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Dragorn421
GitHub
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0283493db8
10 changed files with 104 additions and 40 deletions
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@ -1945,7 +1945,7 @@ s8 PadUtils_GetRelX(Input* input);
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s8 PadUtils_GetRelY(Input* input);
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void PadUtils_UpdateRelXY(Input* input);
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s32 PadSetup_Init(OSMesgQueue* mq, u8* outMask, OSContStatus* status);
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f32 Math_FTanF(f32 x);
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f32 Math_FTanF(f32 angle);
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f32 Math_FFloorF(f32 x);
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f32 Math_FCeilF(f32 x);
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f32 Math_FRoundF(f32 x);
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@ -2043,8 +2043,8 @@ s32 JpegDecoder_ParseNextSymbol(JpegHuffmanTable* hTable, s16* outCoeff, s8* out
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u16 JpegDecoder_ReadBits(u8 len);
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s32 osPfsFreeBlocks(OSPfs* pfs, s32* leftoverBytes);
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void guScale(Mtx* m, f32 x, f32 y, f32 z);
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f32 sinf(f32);
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s16 sins(u16);
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f32 sinf(f32 angle);
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s16 sins(u16 angle);
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OSTask* _VirtualToPhysicalTask(OSTask* intp);
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void osSpTaskLoad(OSTask* intp);
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void osSpTaskStartGo(OSTask* tp);
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@ -2108,8 +2108,8 @@ s32 osPfsDeleteFile(OSPfs* pfs, u16 companyCode, u32 gameCode, u8* gameName, u8*
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s32 __osPfsReleasePages(OSPfs* pfs, __OSInode* inode, u8 initialPage, u8 bank, __OSInodeUnit* finalPage);
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void guOrthoF(f32[4][4], f32, f32, f32, f32, f32, f32, f32);
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void guOrtho(Mtx*, f32, f32, f32, f32, f32, f32, f32);
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f32 cosf(f32);
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s16 coss(u16);
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f32 cosf(f32 angle);
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s16 coss(u16 angle);
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void osViSetEvent(OSMesgQueue* mq, OSMesg msg, u32 retraceCount);
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s32 osPfsIsPlug(OSMesgQueue* mq, u8* pattern);
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void __osPfsRequestData(u8 cmd);
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@ -3,9 +3,13 @@
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s32 gUseAtanContFrac;
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f32 Math_FTanF(f32 x) {
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f32 sin = sinf(x);
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f32 cos = cosf(x);
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/**
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* @param angle radians
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* @return tan(angle)
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*/
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f32 Math_FTanF(f32 angle) {
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f32 sin = sinf(angle);
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f32 cos = cosf(angle);
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return sin / cos;
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}
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@ -42,7 +46,7 @@ f32 Math_FAtanTaylorQF(f32 x) {
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const f32* c = coeffs;
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f32 term;
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while (1) {
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while (true) {
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term = *c++ * exp;
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if (poly + term == poly) {
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break;
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@ -124,6 +128,9 @@ f32 Math_FAtanContFracF(f32 x) {
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}
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}
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/**
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* @return arctan(x) in radians, in (-pi/2,pi/2) range
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*/
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f32 Math_FAtanF(f32 x) {
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if (!gUseAtanContFrac) {
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return Math_FAtanTaylorF(x);
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@ -132,6 +139,9 @@ f32 Math_FAtanF(f32 x) {
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}
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}
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/**
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* @return angle to (x,y) from vector (1,0) around (0,0) in radians, in (-pi,pi] range
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*/
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f32 Math_FAtan2F(f32 y, f32 x) {
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if (x == 0.0f) {
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if (y == 0.0f) {
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@ -152,10 +162,16 @@ f32 Math_FAtan2F(f32 y, f32 x) {
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}
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}
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/**
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* @return arcsin(x) in radians, in [-pi/2,pi/2] range
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*/
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f32 Math_FAsinF(f32 x) {
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return Math_FAtan2F(x, sqrtf(1.0f - SQ(x)));
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}
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/**
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* @return arccos(x) in radians, in [0,pi] range
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*/
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f32 Math_FAcosF(f32 x) {
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return M_PI / 2 - Math_FAsinF(x);
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}
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@ -38,10 +38,18 @@ f32 Math_PowF(f32 base, s32 exp) {
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return ret;
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}
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/**
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* @param angle radians
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* @return sin(angle)
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*/
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f32 Math_SinF(f32 angle) {
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return sins((s16)(angle * (0x7FFF / M_PI))) * SHT_MINV;
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}
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/**
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* @param angle radians
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* @return cos(angle)
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*/
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f32 Math_CosF(f32 angle) {
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return coss((s16)(angle * (0x7FFF / M_PI))) * SHT_MINV;
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}
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@ -1,6 +1,6 @@
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#include "global.h"
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static u16 sATan2Tbl[] = {
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static u16 sAtan2Tbl[] = {
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0x0000, 0x000A, 0x0014, 0x001F, 0x0029, 0x0033, 0x003D, 0x0047, 0x0051, 0x005C, 0x0066, 0x0070, 0x007A, 0x0084,
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0x008F, 0x0099, 0x00A3, 0x00AD, 0x00B7, 0x00C2, 0x00CC, 0x00D6, 0x00E0, 0x00EA, 0x00F4, 0x00FF, 0x0109, 0x0113,
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0x011D, 0x0127, 0x0131, 0x013C, 0x0146, 0x0150, 0x015A, 0x0164, 0x016F, 0x0179, 0x0183, 0x018D, 0x0197, 0x01A1,
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@ -77,24 +77,34 @@ static u16 sATan2Tbl[] = {
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0x1FF6, 0x1FFB, 0x2000,
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};
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u16 Math_GetAtan2Tbl(f32 x, f32 y) {
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/**
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* @param y must be >= 0 and <= x
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* @param x must be >= 0
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* @return arctan(y/x) as binang, in [0,0x2000] range
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*/
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u16 Math_GetAtan2Tbl(f32 y, f32 x) {
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u16 ret;
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if (y == 0.0f) {
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ret = sATan2Tbl[0];
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if (x == 0.0f) {
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ret = sAtan2Tbl[0];
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} else {
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s32 tblIdx = ((x / y) * 1024.0f) + 0.5f;
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s32 tblIdx = ((y / x) * 1024.0f) + 0.5f;
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if (tblIdx >= ARRAY_COUNT(sATan2Tbl)) {
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ret = sATan2Tbl[0];
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if (tblIdx >= ARRAY_COUNT(sAtan2Tbl)) {
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ret = sAtan2Tbl[0];
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} else {
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ret = sATan2Tbl[tblIdx];
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ret = sAtan2Tbl[tblIdx];
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}
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}
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return ret;
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}
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/**
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* @return angle to (x,y) from vector (1,0) around (0,0) as binang, in [-0x8000,0x7FFF] range
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*
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* @note The arguments are (x,y), which is different from atan2's (y,x)
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*/
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s16 Math_Atan2S(f32 x, f32 y) {
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s32 ret;
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@ -107,7 +117,7 @@ s16 Math_Atan2S(f32 x, f32 y) {
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}
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} else {
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if (-x < y) {
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ret = Math_GetAtan2Tbl(-x, y) + 0x4000;
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ret = 0x4000 + Math_GetAtan2Tbl(-x, y);
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} else {
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ret = 0x8000 - Math_GetAtan2Tbl(y, -x);
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}
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@ -115,21 +125,27 @@ s16 Math_Atan2S(f32 x, f32 y) {
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} else {
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if (x < 0.0f) {
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if (-y <= -x) {
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ret = Math_GetAtan2Tbl(-y, -x) + 0x8000;
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ret = 0x8000 + Math_GetAtan2Tbl(-y, -x);
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} else {
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ret = 0xC000 - Math_GetAtan2Tbl(-x, -y);
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}
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} else {
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if (x < -y) {
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ret = Math_GetAtan2Tbl(x, -y) + 0xC000;
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ret = 0xC000 + Math_GetAtan2Tbl(x, -y);
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} else {
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ret = -Math_GetAtan2Tbl(-y, x);
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}
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}
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}
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return ret;
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return (s16)ret;
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}
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/**
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* @return angle to (x,y) from vector (1,0) around (0,0) in radians, in [-pi,pi) range
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*
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* @note The arguments are (x,y), which is different from atan2's (y,x)
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*/
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f32 Math_Atan2F(f32 x, f32 y) {
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return BINANG_TO_RAD(Math_Atan2S(x, y));
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}
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@ -23,10 +23,18 @@ void Lib_MemSet(u8* dest, size_t len, u8 val) {
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// clang-format on
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}
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/**
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* @param angle binang
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* @return cos(angle)
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*/
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f32 Math_CosS(s16 angle) {
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return coss(angle) * SHT_MINV;
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}
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/**
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* @param angle binang
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* @return sin(angle)
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*/
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f32 Math_SinS(s16 angle) {
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return sins(angle) * SHT_MINV;
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}
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@ -14,7 +14,11 @@ static const du pilo = { 0x3E6110B4, 0x611A6263 };
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static const fu zero = { 0x00000000 };
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f32 cosf(f32 x) {
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/**
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* @param angle radians
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* @return cos(angle)
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*/
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f32 cosf(f32 angle) {
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f32 absx;
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f64 dx;
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f64 xSq;
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@ -22,13 +26,13 @@ f32 cosf(f32 x) {
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f64 dn;
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s32 n;
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f64 result;
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s32 ix = *(s32*)&x;
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s32 ix = *(s32*)∠
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s32 xpt = (ix >> 22);
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xpt &= 0x1FF;
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if (xpt < 0x136) {
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absx = (x > 0) ? x : -x;
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absx = (angle > 0) ? angle : -angle;
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dx = absx;
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dn = dx * rpi.d + 0.5;
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@ -51,7 +55,7 @@ f32 cosf(f32 x) {
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}
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return -(f32)result;
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}
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if (x != x) {
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if (angle != angle) {
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return __libm_qnan_f;
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}
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@ -1,5 +1,9 @@
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#include "global.h"
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/**
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* @param angle binang
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* @return cos(angle)*0x7FFF
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*/
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s16 coss(u16 angle) {
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return sins(angle + 0x4000);
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}
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@ -14,20 +14,24 @@ static const du pilo = { 0x3E6110B4, 0x611A6263 };
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static const fu zero = { 0x00000000 };
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f32 sinf(f32 x) {
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/**
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* @param angle radians
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* @return sin(angle)
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*/
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f32 sinf(f32 angle) {
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f64 dx;
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f64 xSq;
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f64 polyApprox;
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f64 dn;
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s32 n;
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f64 result;
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s32 ix = *(s32*)&x;
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s32 ix = *(s32*)∠
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s32 xpt = (ix >> 22);
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xpt &= 0x1FF;
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if (xpt < 0xFF) {
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dx = x;
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dx = angle;
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if (xpt >= 0xE6) {
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xSq = SQ(dx);
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@ -35,11 +39,11 @@ f32 sinf(f32 x) {
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result = dx + (dx * xSq) * polyApprox;
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return (f32)result;
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}
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return x;
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return angle;
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}
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if (xpt < 0x136) {
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dx = x;
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dx = angle;
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dn = dx * rpi.d;
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n = ROUND(dn);
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dn = n;
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@ -57,7 +61,7 @@ f32 sinf(f32 x) {
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return -(f32)result;
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}
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if (x != x) {
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if (angle != angle) {
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return __libm_qnan_f;
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}
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return zero.f;
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@ -2,18 +2,22 @@
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#include "sintable.inc.c"
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s16 sins(u16 x) {
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/**
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* @param angle binang
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* @return sin(angle)*0x7FFF
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*/
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s16 sins(u16 angle) {
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s16 value;
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x >>= 4;
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angle >>= 4;
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if (x & 0x400) {
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value = sintable[0x3FF - (x & 0x3FF)];
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if (angle & 0x400) {
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value = sintable[0x3FF - (angle & 0x3FF)];
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} else {
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value = sintable[x & 0x3FF];
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value = sintable[angle & 0x3FF];
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}
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if (x & 0x800) {
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if (angle & 0x800) {
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return -value;
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} else {
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return value;
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@ -618,7 +618,7 @@ void BossGanon_IntroCutscene(BossGanon* this, PlayState* play) {
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this->csCamEye.z = 300.0f;
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this->csCamAt.x = 0.0f;
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this->unk_704 = 1.2566371f;
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this->unk_704 = 2 * M_PI / 5;
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FALLTHROUGH;
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case 3:
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this->envLightMode = 0;
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@ -3178,8 +3178,8 @@ void BossGanon_Update(Actor* thisx, PlayState* play2) {
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this->unk_278.y = this->unk_2EC[0].y + 50.0f + 30.0f;
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this->unk_278.z = this->unk_2EC[0].z;
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xOffset = (sinf(i * 1.2566371f) * 600.0f);
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zOffset = (cosf(i * 1.2566371f) * 600.0f);
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xOffset = (sinf(i * (2 * M_PI / 5)) * 600.0f);
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zOffset = (cosf(i * (2 * M_PI / 5)) * 600.0f);
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// 5 or 6 light balls that go into the charge. not the same as the ones that he throws
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Actor_SpawnAsChild(&play->actorCtx, &this->actor, play, ACTOR_BOSS_GANON, this->unk_1FC.x + xOffset,
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