diff options
author | Franklin Wei <git@fwei.tk> | 2017-01-21 15:18:31 -0500 |
---|---|---|
committer | Franklin Wei <git@fwei.tk> | 2017-12-23 21:01:26 -0500 |
commit | a855d6202536ff28e5aae4f22a0f31d8f5b325d0 (patch) | |
tree | 8c75f224dd64ed360505afa8843d016b0d75000b /apps/plugins/sdl/src/video/e_pow.h | |
parent | 01c6dcf6c7b9bb1ad2fa0450f99bacc5f3d3e04b (diff) | |
download | rockbox-a855d6202536ff28e5aae4f22a0f31d8f5b325d0.tar.gz rockbox-a855d6202536ff28e5aae4f22a0f31d8f5b325d0.zip |
Port of Duke Nukem 3D
This ports Fabien Sanglard's Chocolate Duke to run on a version of SDL
for Rockbox.
Change-Id: I8f2c4c78af19de10c1633ed7bb7a997b43256dd9
Diffstat (limited to 'apps/plugins/sdl/src/video/e_pow.h')
-rw-r--r-- | apps/plugins/sdl/src/video/e_pow.h | 302 |
1 files changed, 302 insertions, 0 deletions
diff --git a/apps/plugins/sdl/src/video/e_pow.h b/apps/plugins/sdl/src/video/e_pow.h new file mode 100644 index 0000000000..0aa372a68f --- /dev/null +++ b/apps/plugins/sdl/src/video/e_pow.h | |||
@@ -0,0 +1,302 @@ | |||
1 | /* @(#)e_pow.c 5.1 93/09/24 */ | ||
2 | /* | ||
3 | * ==================================================== | ||
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | ||
5 | * | ||
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | ||
7 | * Permission to use, copy, modify, and distribute this | ||
8 | * software is freely granted, provided that this notice | ||
9 | * is preserved. | ||
10 | * ==================================================== | ||
11 | */ | ||
12 | |||
13 | #if defined(LIBM_SCCS) && !defined(lint) | ||
14 | static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; | ||
15 | #endif | ||
16 | |||
17 | /* __ieee754_pow(x,y) return x**y | ||
18 | * | ||
19 | * n | ||
20 | * Method: Let x = 2 * (1+f) | ||
21 | * 1. Compute and return log2(x) in two pieces: | ||
22 | * log2(x) = w1 + w2, | ||
23 | * where w1 has 53-24 = 29 bit trailing zeros. | ||
24 | * 2. Perform y*log2(x) = n+y' by simulating muti-precision | ||
25 | * arithmetic, where |y'|<=0.5. | ||
26 | * 3. Return x**y = 2**n*exp(y'*log2) | ||
27 | * | ||
28 | * Special cases: | ||
29 | * 1. (anything) ** 0 is 1 | ||
30 | * 2. (anything) ** 1 is itself | ||
31 | * 3. (anything) ** NAN is NAN | ||
32 | * 4. NAN ** (anything except 0) is NAN | ||
33 | * 5. +-(|x| > 1) ** +INF is +INF | ||
34 | * 6. +-(|x| > 1) ** -INF is +0 | ||
35 | * 7. +-(|x| < 1) ** +INF is +0 | ||
36 | * 8. +-(|x| < 1) ** -INF is +INF | ||
37 | * 9. +-1 ** +-INF is NAN | ||
38 | * 10. +0 ** (+anything except 0, NAN) is +0 | ||
39 | * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 | ||
40 | * 12. +0 ** (-anything except 0, NAN) is +INF | ||
41 | * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF | ||
42 | * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) | ||
43 | * 15. +INF ** (+anything except 0,NAN) is +INF | ||
44 | * 16. +INF ** (-anything except 0,NAN) is +0 | ||
45 | * 17. -INF ** (anything) = -0 ** (-anything) | ||
46 | * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) | ||
47 | * 19. (-anything except 0 and inf) ** (non-integer) is NAN | ||
48 | * | ||
49 | * Accuracy: | ||
50 | * pow(x,y) returns x**y nearly rounded. In particular | ||
51 | * pow(integer,integer) | ||
52 | * always returns the correct integer provided it is | ||
53 | * representable. | ||
54 | * | ||
55 | * Constants : | ||
56 | * The hexadecimal values are the intended ones for the following | ||
57 | * constants. The decimal values may be used, provided that the | ||
58 | * compiler will convert from decimal to binary accurately enough | ||
59 | * to produce the hexadecimal values shown. | ||
60 | */ | ||
61 | |||
62 | /*#include "math.h"*/ | ||
63 | #include "math_private.h" | ||
64 | |||
65 | #ifdef __STDC__ | ||
66 | static const double | ||
67 | #else | ||
68 | static double | ||
69 | #endif | ||
70 | bp[] = {1.0, 1.5,}, | ||
71 | dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ | ||
72 | dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ | ||
73 | /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ | ||
74 | L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ | ||
75 | L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ | ||
76 | L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ | ||
77 | L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ | ||
78 | L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ | ||
79 | L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ | ||
80 | P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | ||
81 | P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | ||
82 | P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | ||
83 | P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | ||
84 | P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ | ||
85 | lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | ||
86 | lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ | ||
87 | lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ | ||
88 | ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ | ||
89 | cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ | ||
90 | cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ | ||
91 | cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ | ||
92 | ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ | ||
93 | ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ | ||
94 | ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ | ||
95 | |||
96 | #ifdef __STDC__ | ||
97 | double __ieee754_pow(double x, double y) | ||
98 | #else | ||
99 | double __ieee754_pow(x,y) | ||
100 | double x, y; | ||
101 | #endif | ||
102 | { | ||
103 | double z,ax,z_h,z_l,p_h,p_l; | ||
104 | double y1,t1,t2,r,s,t,u,v,w; | ||
105 | int32_t i,j,k,yisint,n; | ||
106 | int32_t hx,hy,ix,iy; | ||
107 | u_int32_t lx,ly; | ||
108 | |||
109 | EXTRACT_WORDS(hx,lx,x); | ||
110 | EXTRACT_WORDS(hy,ly,y); | ||
111 | ix = hx&0x7fffffff; iy = hy&0x7fffffff; | ||
112 | |||
113 | /* y==zero: x**0 = 1 */ | ||
114 | if((iy|ly)==0) return one; | ||
115 | |||
116 | /* +-NaN return x+y */ | ||
117 | if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || | ||
118 | iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) | ||
119 | return x+y; | ||
120 | |||
121 | /* determine if y is an odd int when x < 0 | ||
122 | * yisint = 0 ... y is not an integer | ||
123 | * yisint = 1 ... y is an odd int | ||
124 | * yisint = 2 ... y is an even int | ||
125 | */ | ||
126 | yisint = 0; | ||
127 | if(hx<0) { | ||
128 | if(iy>=0x43400000) yisint = 2; /* even integer y */ | ||
129 | else if(iy>=0x3ff00000) { | ||
130 | k = (iy>>20)-0x3ff; /* exponent */ | ||
131 | if(k>20) { | ||
132 | j = ly>>(52-k); | ||
133 | if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); | ||
134 | } else if(ly==0) { | ||
135 | j = iy>>(20-k); | ||
136 | if((j<<(20-k))==iy) yisint = 2-(j&1); | ||
137 | } | ||
138 | } | ||
139 | } | ||
140 | |||
141 | /* special value of y */ | ||
142 | if(ly==0) { | ||
143 | if (iy==0x7ff00000) { /* y is +-inf */ | ||
144 | if(((ix-0x3ff00000)|lx)==0) | ||
145 | return y - y; /* inf**+-1 is NaN */ | ||
146 | else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ | ||
147 | return (hy>=0)? y: zero; | ||
148 | else /* (|x|<1)**-,+inf = inf,0 */ | ||
149 | return (hy<0)?-y: zero; | ||
150 | } | ||
151 | if(iy==0x3ff00000) { /* y is +-1 */ | ||
152 | if(hy<0) return one/x; else return x; | ||
153 | } | ||
154 | if(hy==0x40000000) return x*x; /* y is 2 */ | ||
155 | if(hy==0x3fe00000) { /* y is 0.5 */ | ||
156 | if(hx>=0) /* x >= +0 */ | ||
157 | return __ieee754_sqrt(x); | ||
158 | } | ||
159 | } | ||
160 | |||
161 | ax = x < 0 ? -x : x; /*fabs(x);*/ | ||
162 | /* special value of x */ | ||
163 | if(lx==0) { | ||
164 | if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ | ||
165 | z = ax; /*x is +-0,+-inf,+-1*/ | ||
166 | if(hy<0) z = one/z; /* z = (1/|x|) */ | ||
167 | if(hx<0) { | ||
168 | if(((ix-0x3ff00000)|yisint)==0) { | ||
169 | z = (z-z)/(z-z); /* (-1)**non-int is NaN */ | ||
170 | } else if(yisint==1) | ||
171 | z = -z; /* (x<0)**odd = -(|x|**odd) */ | ||
172 | } | ||
173 | return z; | ||
174 | } | ||
175 | } | ||
176 | |||
177 | /* (x<0)**(non-int) is NaN */ | ||
178 | if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); | ||
179 | |||
180 | /* |y| is huge */ | ||
181 | if(iy>0x41e00000) { /* if |y| > 2**31 */ | ||
182 | if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ | ||
183 | if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; | ||
184 | if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; | ||
185 | } | ||
186 | /* over/underflow if x is not close to one */ | ||
187 | if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; | ||
188 | if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; | ||
189 | /* now |1-x| is tiny <= 2**-20, suffice to compute | ||
190 | log(x) by x-x^2/2+x^3/3-x^4/4 */ | ||
191 | t = x-1; /* t has 20 trailing zeros */ | ||
192 | w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); | ||
193 | u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ | ||
194 | v = t*ivln2_l-w*ivln2; | ||
195 | t1 = u+v; | ||
196 | SET_LOW_WORD(t1,0); | ||
197 | t2 = v-(t1-u); | ||
198 | } else { | ||
199 | double s2,s_h,s_l,t_h,t_l; | ||
200 | n = 0; | ||
201 | /* take care subnormal number */ | ||
202 | if(ix<0x00100000) | ||
203 | {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } | ||
204 | n += ((ix)>>20)-0x3ff; | ||
205 | j = ix&0x000fffff; | ||
206 | /* determine interval */ | ||
207 | ix = j|0x3ff00000; /* normalize ix */ | ||
208 | if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ | ||
209 | else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ | ||
210 | else {k=0;n+=1;ix -= 0x00100000;} | ||
211 | SET_HIGH_WORD(ax,ix); | ||
212 | |||
213 | /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ | ||
214 | u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ | ||
215 | v = one/(ax+bp[k]); | ||
216 | s = u*v; | ||
217 | s_h = s; | ||
218 | SET_LOW_WORD(s_h,0); | ||
219 | /* t_h=ax+bp[k] High */ | ||
220 | t_h = zero; | ||
221 | SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); | ||
222 | t_l = ax - (t_h-bp[k]); | ||
223 | s_l = v*((u-s_h*t_h)-s_h*t_l); | ||
224 | /* compute log(ax) */ | ||
225 | s2 = s*s; | ||
226 | r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); | ||
227 | r += s_l*(s_h+s); | ||
228 | s2 = s_h*s_h; | ||
229 | t_h = 3.0+s2+r; | ||
230 | SET_LOW_WORD(t_h,0); | ||
231 | t_l = r-((t_h-3.0)-s2); | ||
232 | /* u+v = s*(1+...) */ | ||
233 | u = s_h*t_h; | ||
234 | v = s_l*t_h+t_l*s; | ||
235 | /* 2/(3log2)*(s+...) */ | ||
236 | p_h = u+v; | ||
237 | SET_LOW_WORD(p_h,0); | ||
238 | p_l = v-(p_h-u); | ||
239 | z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | ||
240 | z_l = cp_l*p_h+p_l*cp+dp_l[k]; | ||
241 | /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | ||
242 | t = (double)n; | ||
243 | t1 = (((z_h+z_l)+dp_h[k])+t); | ||
244 | SET_LOW_WORD(t1,0); | ||
245 | t2 = z_l-(((t1-t)-dp_h[k])-z_h); | ||
246 | } | ||
247 | |||
248 | s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | ||
249 | if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) | ||
250 | s = -one;/* (-ve)**(odd int) */ | ||
251 | |||
252 | /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | ||
253 | y1 = y; | ||
254 | SET_LOW_WORD(y1,0); | ||
255 | p_l = (y-y1)*t1+y*t2; | ||
256 | p_h = y1*t1; | ||
257 | z = p_l+p_h; | ||
258 | EXTRACT_WORDS(j,i,z); | ||
259 | if (j>=0x40900000) { /* z >= 1024 */ | ||
260 | if(((j-0x40900000)|i)!=0) /* if z > 1024 */ | ||
261 | return s*huge*huge; /* overflow */ | ||
262 | else { | ||
263 | if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ | ||
264 | } | ||
265 | } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ | ||
266 | if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ | ||
267 | return s*tiny*tiny; /* underflow */ | ||
268 | else { | ||
269 | if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | ||
270 | } | ||
271 | } | ||
272 | /* | ||
273 | * compute 2**(p_h+p_l) | ||
274 | */ | ||
275 | i = j&0x7fffffff; | ||
276 | k = (i>>20)-0x3ff; | ||
277 | n = 0; | ||
278 | if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ | ||
279 | n = j+(0x00100000>>(k+1)); | ||
280 | k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ | ||
281 | t = zero; | ||
282 | SET_HIGH_WORD(t,n&~(0x000fffff>>k)); | ||
283 | n = ((n&0x000fffff)|0x00100000)>>(20-k); | ||
284 | if(j<0) n = -n; | ||
285 | p_h -= t; | ||
286 | } | ||
287 | t = p_l+p_h; | ||
288 | SET_LOW_WORD(t,0); | ||
289 | u = t*lg2_h; | ||
290 | v = (p_l-(t-p_h))*lg2+t*lg2_l; | ||
291 | z = u+v; | ||
292 | w = v-(z-u); | ||
293 | t = z*z; | ||
294 | t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | ||
295 | r = (z*t1)/(t1-two)-(w+z*w); | ||
296 | z = one-(r-z); | ||
297 | GET_HIGH_WORD(j,z); | ||
298 | j += (n<<20); | ||
299 | if((j>>20)<=0) z = SDL_NAME(scalbn)(z,n); /* subnormal output */ | ||
300 | else SET_HIGH_WORD(z,j); | ||
301 | return s*z; | ||
302 | } | ||