1 /*
2 Copyright (c) 2010, Warmux Team
3
4 Large parts of the code are from the fixed point library of Markus Trenkwalder
5 Copyright (c) 2007, Markus Trenkwalder
6
7 Portions taken from the Vicent 3D rendering library
8 Copyright (c) 2004, David Blythe, Hans Martin Will
9
10 All rights reserved.
11
12 Redistribution and use in source and binary forms, with or without
13 modification, are permitted provided that the following conditions are met:
14
15 * Redistributions of source code must retain the above copyright notice,
16 this list of conditions and the following disclaimer.
17
18 * Redistributions in binary form must reproduce the above copyright notice,
19 this list of conditions and the following disclaimer in the documentation
20 and/or other materials provided with the distribution.
21
22 * Neither the name of the library's copyright owner nor the names of its
23 contributors may be used to endorse or promote products derived from this
24 software without specific prior written permission.
25
26 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
27 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
28 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
29 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
30 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
31 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
32 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
33 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
34 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
35 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
36 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
37 */
38
39 #include <stdio.h>
40 #include "fixed_func.h"
41
42 namespace fp {
43
44 static const int32_t FIX16_2PI = float2fix<16>(2*M_PI);
45 static const int32_t FIX16_HALF_PI = float2fix<16>(0.5*M_PI);
46 static const int32_t FIX16_R2PI = float2fix<16>(1/(2*M_PI));
47
48 static const uint16_t sin_tab[] = {
49 #include "fixsintab.h"
50 };
51
52 static const int32_t asin_tab[] = {
53 #include "fixasintab.h"
54 };
55
56 static const uint16_t atan_tab[] = {
57 #include "fixatantab.h"
58 };
59
60
fixcos16(fint_t a)61 fint_t fixcos16(fint_t a)
62 {
63 fint_t v;
64 /* reduce to [0,1) */
65 while (a < 0) a += FIX16_2PI;
66 a = fixmul<16>(a, FIX16_R2PI);
67 a += 0x4000;
68
69 /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
70 a >>= 4;
71
72 v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
73 v = fixmul<16>(v, 1 << 16);
74 return (a & 0x800) ? -v : v;
75 }
76
fixsin16(fint_t a)77 fint_t fixsin16(fint_t a)
78 {
79 fint_t v;
80
81 /* reduce to [0,1) */
82 while (a < 0) a += FIX16_2PI;
83 a = fixmul<16>(a, FIX16_R2PI);
84
85 /* now in the range [0, 0xffff], reduce to [0, 0xfff] */
86 a >>= 4;
87
88 v = (a & 0x400) ? sin_tab[0x3ff - (a & 0x3ff)] : sin_tab[a & 0x3ff];
89 v = fixmul<16>(v, 1 << 16);
90 return (a & 0x800) ? -v : v;
91 }
92
fixacos16(fint_t a)93 fint_t fixacos16(fint_t a)
94 {
95 return FIX16_HALF_PI - fixasin16(a);
96 }
97
fixasin16(fint_t a)98 fint_t fixasin16(fint_t a)
99 {
100 if (a > 0) {
101 if (a >= 0x10000)
102 a = 0x10000;
103 return asin_tab[a];;
104 } else {
105 if (a <= -0x10000)
106 a = -0x10000;
107 return -asin_tab[-a];
108 }
109 }
110
fixatan16(fint_t a)111 fint_t fixatan16(fint_t a)
112 {
113 if (a > 0) {
114 if (a <= 0x10000) {
115 return atan_tab[a];
116 } else {
117 return FIX16_HALF_PI - atan_tab[fixinv<16>(a)];;
118 }
119 } else {
120 if (a >= -0x10000) {
121 return - atan_tab[-a];
122 } else {
123 return -FIX16_HALF_PI + atan_tab[-fixinv<16>(a)];
124 }
125 }
126 }
127
fixrsqrt16(fint_t a)128 fint_t fixrsqrt16(fint_t a)
129 {
130 fint_t x;
131
132 static const uint16_t rsq_tab[] = { /* domain 0.5 .. 1.0-1/16 */
133 0xb504, 0xaaaa, 0xa1e8, 0x9a5f, 0x93cd, 0x8e00, 0x88d6, 0x8432,
134 };
135
136 fint_t i, exp;
137 if (a == 0) return 0x7fffffff;
138 if (a == (1<<16)) return a;
139
140 exp = detail::CountLeadingZeros(a);
141 x = rsq_tab[(a>>(28-exp))&0x7]<<1;
142
143 exp -= 16;
144 if (exp <= 0)
145 x >>= -exp>>1;
146 else
147 x <<= (exp>>1)+(exp&1);
148 if (exp&1) x = fixmul<16>(x, rsq_tab[0]);
149
150
151 /* newton-raphson */
152 /* x = x/2*(3-(a*x)*x) */
153 i = 0;
154 do {
155 x = fixmul<16>((x>>1),((1<<16)*3 - fixmul<16>(fixmul<16>(a,x),x)));
156 } while(++i < 3);
157
158 return x;
159 }
160
fast_div16(fint_t a,fint_t b)161 static inline fint_t fast_div16(fint_t a, fint_t b)
162 {
163 if ((b >> 24) && (b >> 24) + 1) {
164 return fixmul<16>(a >> 8, fixinv<16>(b >> 8));
165 } else {
166 return fixmul<16>(a, fixinv<16>(b));
167 }
168 }
169
fixsqrt16(fint_t a)170 fint_t fixsqrt16(fint_t a)
171 {
172 if (a < 1<<7) {
173 return 0;
174 }
175
176 #if 0
177 static fint_t max = 0;
178 if (max < a) {
179 printf("max: %"PRIi64"\n", a);
180 max = a;
181 }
182 #endif
183
184 fint_t s = (a + (1<<16)) >> 1;
185 /* 14 iterations to find exact value for max 948015267840 */
186 for (int i = 0; i < 14; i++) {
187 s = (s + (a<<16) / s) >> 1;
188 }
189 return s;
190 }
191
fixsqrt16_approx(fint_t a)192 fint_t fixsqrt16_approx(fint_t a)
193 {
194 if (a < 1<<7) {
195 return 0;
196 }
197
198 #if 0
199 static fint_t max = 0;
200 if (max < a) {
201 printf("max: %"PRIi64"\n", a);
202 max = a;
203 }
204 #endif
205
206 fint_t s = (a + (1<<16)) >> 1;
207 /* 6 iterations to find exact value for max 34668544 */
208 for (int i = 0; i < 6; i++) {
209 s = (s + (a<<16) / s) >> 1;
210 }
211 return s;
212 }
213
214 } // end namespace fp
215