1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
/**
* 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"
extern f32 func_80086C70(f32 x);
extern f32 func_80086CA8(f32 x);
extern f32 func_80086D50(f32 x);
extern f32 func_80086CE0(f32 x);
extern f32 func_80086D18(f32 x);
s32 gUseAtanContFrac;
/**
* Tangent function computed using libultra sinf and cosf
*/
// Math_FTanF
f32 func_80086760(f32 x) {
return sinf(x) / cosf(x);
}
// Unused
// Math_FFloorF
f32 func_80086794(f32 x) {
return func_80086C70(x);
}
// Unused
// Math_FCeilF
f32 func_800867B4(f32 x) {
return func_80086CA8(x);
}
// Unused
// Math_FRoundF
f32 func_800867D4(f32 x) {
return func_80086D50(x);
}
// Unused
// Math_FTruncF
f32 func_800867F4(f32 x) {
return func_80086CE0(x);
}
// Math_FNearbyIntF
f32 func_80086814(f32 x) {
return func_80086D18(x);
}
/**
* Arctangent approximation using a Maclaurin series [https://mathworld.wolfram.com/MaclaurinSeries.html]
* (one quadrant, i.e. |x| < 1)
*/
// Math_FAtanTaylorQF
f32 func_80086834(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 func_80086834 is a good approximation
*/
// Math_FAtanTaylorF
f32 func_80086880(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 func_80086834(x);
}
if (t >= M_SQRT2 + 1.0f) {
q = M_PI / 2 - func_80086834(1.0f / t);
} else { // in the interval (\sqrt{2} - 1, \sqrt{2} + 1)
q = M_PI / 4 - func_80086834((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
*/
// Math_FAtanContFracF
f32 func_800869A4(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;
}
}
// Math_FAtanF
/**
* 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 func_80086AF0(f32 x) {
if (!gUseAtanContFrac) {
return func_80086880(x);
} else {
return func_800869A4(x);
}
}
// Math_FAtan2F
/**
* Main two-argument arctangent function
*/
f32 func_80086B30(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 func_80086AF0(y / x);
} else if (y < 0.0f) {
return func_80086AF0(y / x) - M_PI;
} else {
return M_PI - func_80086AF0(-(y / x));
}
}
// Math_FAsinF
f32 func_80086C18(f32 x) {
return func_80086B30(x, sqrtf(1.0f - SQ(x)));
}
// Math_FAcosF
f32 func_80086C48(f32 x) {
return M_PI / 2 - func_80086C18(x);
}
|
