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#include "libc64/math64.h"
#include "z_math.h"
#if !PLATFORM_N64
s32 gUseAtanContFrac;
#endif
/**
* @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);
}
#if PLATFORM_N64
f64 Math_FAbs(f64 x) {
return x < 0.0 ? -x : x;
}
f32 Math_FAbsF(f32 x) {
return x < 0.0f ? -x : x;
}
#endif
f32 Math_FRoundF(f32 x) {
return roundf(x);
}
f32 Math_FTruncF(f32 x) {
return truncf(x);
}
f32 Math_FNearbyIntF(f32 x) {
return nearbyintf(x);
}
#if !PLATFORM_N64
/* 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;
}
}
#endif
/* Arctangent approximation using a continued fraction */
f32 Math_FAtanContFracF(f32 x) {
s32 sector;
f32 z;
f32 conv;
f32 sq;
s32 i;
#if PLATFORM_N64
if (x > 1.0f) {
sector = 1;
x = 1.0f / x;
} else if (x < -1.0f) {
sector = -1;
x = 1.0f / x;
} else {
sector = 0;
}
#else
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;
}
#endif
sq = SQ(x);
conv = 0.0f;
#if PLATFORM_N64
z = 24.0f;
i = 24;
#else
z = 8.0f;
i = 8;
#endif
while (i != 0) {
conv = SQ(z) * sq / (2.0f * z + 1.0f + conv);
z -= 1.0f;
i--;
}
#if PLATFORM_N64
if (sector > 0) {
return M_PI / 2 - (x / (1.0f + conv));
} else if (sector < 0) {
return -M_PI / 2 - (x / (1.0f + conv));
} else {
return x / (1.0f + conv);
}
#else
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;
}
#endif
}
#if !PLATFORM_N64
/**
* @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);
}
}
#endif
/**
* @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 PLATFORM_N64
if (y == 0.0f && x == 0.0f) {
return 0.0f;
}
if (x == 0.0f) {
if (y < 0.0f) {
return -M_PI / 2;
} else {
return M_PI / 2;
}
} else if (x < 0.0f) {
if (y < 0.0f) {
return -(M_PI - Math_FAtanContFracF(fabs(y / x)));
} else {
return M_PI - Math_FAtanContFracF(fabs(y / x));
}
} else { // x > 0.0f
return Math_FAtanContFracF(y / x);
}
#else
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 { // x < 0.0f
if (y < 0.0f) {
return Math_FAtanF(y / x) - M_PI;
} else {
return M_PI - Math_FAtanF(-(y / x));
}
}
#endif
}
/**
* @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);
}
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