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
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
|
/*
* Copyright (C) 2024 Niklas Haas
*
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* FFmpeg is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with FFmpeg; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "libavutil/csp.h"
#include "csputils.h"
#include "format.h"
void ff_sws_matrix3x3_mul(SwsMatrix3x3 *a, const SwsMatrix3x3 *b)
{
float a00 = a->m[0][0], a01 = a->m[0][1], a02 = a->m[0][2],
a10 = a->m[1][0], a11 = a->m[1][1], a12 = a->m[1][2],
a20 = a->m[2][0], a21 = a->m[2][1], a22 = a->m[2][2];
for (int i = 0; i < 3; i++) {
a->m[0][i] = a00 * b->m[0][i] + a01 * b->m[1][i] + a02 * b->m[2][i];
a->m[1][i] = a10 * b->m[0][i] + a11 * b->m[1][i] + a12 * b->m[2][i];
a->m[2][i] = a20 * b->m[0][i] + a21 * b->m[1][i] + a22 * b->m[2][i];
}
}
void ff_sws_matrix3x3_invert(SwsMatrix3x3 *mat)
{
double m00 = mat->m[0][0], m01 = mat->m[0][1], m02 = mat->m[0][2],
m10 = mat->m[1][0], m11 = mat->m[1][1], m12 = mat->m[1][2],
m20 = mat->m[2][0], m21 = mat->m[2][1], m22 = mat->m[2][2];
// calculate the adjoint
double a00 = (m11 * m22 - m21 * m12);
double a01 = -(m01 * m22 - m21 * m02);
double a02 = (m01 * m12 - m11 * m02);
double a10 = -(m10 * m22 - m20 * m12);
double a11 = (m00 * m22 - m20 * m02);
double a12 = -(m00 * m12 - m10 * m02);
double a20 = (m10 * m21 - m20 * m11);
double a21 = -(m00 * m21 - m20 * m01);
double a22 = (m00 * m11 - m10 * m01);
// calculate the determinant (as inverse == 1/det * adjoint,
// adjoint * m == identity * det, so this calculates the det)
double det = m00 * a00 + m10 * a01 + m20 * a02;
det = 1.0 / det;
mat->m[0][0] = det * a00;
mat->m[0][1] = det * a01;
mat->m[0][2] = det * a02;
mat->m[1][0] = det * a10;
mat->m[1][1] = det * a11;
mat->m[1][2] = det * a12;
mat->m[2][0] = det * a20;
mat->m[2][1] = det * a21;
mat->m[2][2] = det * a22;
}
void ff_sws_matrix3x3_apply(const SwsMatrix3x3 *mat, float vec[3])
{
float x = vec[0], y = vec[1], z = vec[2];
for (int i = 0; i < 3; i++)
vec[i] = mat->m[i][0] * x + mat->m[i][1] * y + mat->m[i][2] * z;
}
/* Recovers (X / Y) from a CIE xy value. */
static inline AVRational cie_X(AVCIExy xy)
{
return av_div_q(xy.x, xy.y);
}
/* Recovers (Z / Y) from a CIE xy value. */
static inline AVRational cie_Z(AVCIExy xy)
{
return av_div_q(av_sub_q(av_sub_q(av_make_q(1, 1), xy.x), xy.y), xy.y);
}
SwsMatrix3x3 ff_sws_rgb2xyz(const AVColorPrimariesDesc *desc)
{
SwsMatrix3x3 out = {{{0}}};
float S[3], X[3], Z[3], Xw, Zw;
X[0] = av_q2d(cie_X(desc->prim.r));
X[1] = av_q2d(cie_X(desc->prim.g));
X[2] = av_q2d(cie_X(desc->prim.b));
Z[0] = av_q2d(cie_Z(desc->prim.r));
Z[1] = av_q2d(cie_Z(desc->prim.g));
Z[2] = av_q2d(cie_Z(desc->prim.b));
Xw = av_q2d(cie_X(desc->wp));
Zw = av_q2d(cie_Z(desc->wp));
/* S = XYZ^-1 * W */
for (int i = 0; i < 3; i++) {
out.m[0][i] = X[i];
out.m[1][i] = 1.0f;
out.m[2][i] = Z[i];
}
ff_sws_matrix3x3_invert(&out);
for (int i = 0; i < 3; i++)
S[i] = out.m[i][0] * Xw + out.m[i][1] + out.m[i][2] * Zw;
/* M = [Sc * XYZc] */
for (int i = 0; i < 3; i++) {
out.m[0][i] = S[i] * X[i];
out.m[1][i] = S[i];
out.m[2][i] = S[i] * Z[i];
}
return out;
}
SwsMatrix3x3 ff_sws_xyz2rgb(const AVColorPrimariesDesc *prim)
{
SwsMatrix3x3 out = ff_sws_rgb2xyz(prim);
ff_sws_matrix3x3_invert(&out);
return out;
}
/* Matrix used in CAT16, a revised one-step linear transform method */
static const SwsMatrix3x3 m_cat16 = {{
{ 0.401288f, 0.650173f, -0.051461f },
{ -0.250268f, 1.204414f, 0.045854f },
{ -0.002079f, 0.048952f, 0.953127f },
}};
static const SwsMatrix3x3 m_cat16_inv = {{
{ 1.862068f, -1.011255f, 0.149187f },
{ 0.387527f, 0.621447f, -0.008974f },
{ -0.015841f, -0.034123f, 1.049964f },
}};
// M := M * XYZd<-XYZs
static void apply_chromatic_adaptation(AVWhitepointCoefficients src,
AVWhitepointCoefficients dst,
SwsMatrix3x3 *mat)
{
SwsMatrix3x3 tmp = {0};
float C[3][2];
const float srcX = av_q2d(cie_X(src)),
srcZ = av_q2d(cie_Z(src)),
dstX = av_q2d(cie_X(dst)),
dstZ = av_q2d(cie_Z(dst));
if (ff_cie_xy_equal(src, dst))
return;
// Linear "von Kries" method, adapted from CIECAM16
// http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html
for (int i = 0; i < 3; i++) {
// source cone
C[i][0] = m_cat16.m[i][0] * srcX
+ m_cat16.m[i][1] * 1
+ m_cat16.m[i][2] * srcZ,
// dest cone
C[i][1] = m_cat16.m[i][0] * dstX
+ m_cat16.m[i][1] * 1
+ m_cat16.m[i][2] * dstZ;
}
// tmp := I * [Cd/Cs] * Ma
for (int i = 0; i < 3; i++)
tmp.m[i][i] = C[i][1] / C[i][0];
ff_sws_matrix3x3_mul(&tmp, &m_cat16);
// M := M * Ma^-1 * tmp
ff_sws_matrix3x3_mul(mat, &m_cat16_inv);
ff_sws_matrix3x3_mul(mat, &tmp);
}
SwsMatrix3x3 ff_sws_get_adaptation(const AVPrimaryCoefficients *prim,
AVWhitepointCoefficients from,
AVWhitepointCoefficients to)
{
SwsMatrix3x3 rgb2xyz, xyz2rgb;
const AVColorPrimariesDesc csp = {
.prim = *prim,
.wp = from,
};
rgb2xyz = ff_sws_rgb2xyz(&csp);
xyz2rgb = ff_sws_xyz2rgb(&csp);
apply_chromatic_adaptation(from, to, &xyz2rgb);
ff_sws_matrix3x3_mul(&xyz2rgb, &rgb2xyz);
return xyz2rgb;
}
static const AVWhitepointCoefficients d65 = {
.x = {3127, 10000},
.y = {3290, 10000}
};
static const SwsMatrix3x3 hpe = {{ /* HPE XYZ->LMS (D65) method */
{ 0.40024f, 0.70760f, -0.08081f },
{ -0.22630f, 1.16532f, 0.04570f },
{ 0.00000f, 0.00000f, 0.91822f },
}};
SwsMatrix3x3 ff_sws_ipt_rgb2lms(const AVColorPrimariesDesc *prim)
{
const float c = 0.04f; // 4% crosstalk
SwsMatrix3x3 rgb2xyz;
SwsMatrix3x3 m = {{
{ 1 - 2*c, c, c },
{ c, 1 - 2*c, c },
{ c, c, 1 - 2*c },
}};
ff_sws_matrix3x3_mul(&m, &hpe);
// Apply chromatic adaptation to D65 if the input white point differs
apply_chromatic_adaptation(prim->wp, d65, &m);
rgb2xyz = ff_sws_rgb2xyz(prim);
ff_sws_matrix3x3_mul(&m, &rgb2xyz);
return m;
}
SwsMatrix3x3 ff_sws_ipt_lms2rgb(const AVColorPrimariesDesc *prim)
{
SwsMatrix3x3 rgb2lms = ff_sws_ipt_rgb2lms(prim);
ff_sws_matrix3x3_invert(&rgb2lms);
return rgb2lms;
}
/* Test the sign of 'p' relative to the line 'ab' (barycentric coordinates) */
static int test_point_line(AVCIExy p, AVCIExy a, AVCIExy b)
{
return av_cmp_q(av_mul_q(av_sub_q(p.x, b.x), av_sub_q(a.y, b.y)),
av_mul_q(av_sub_q(a.x, b.x), av_sub_q(p.y, b.y)));
}
/* Test if a point is entirely inside a gamut */
static float test_point_gamut(const AVCIExy point,
const AVPrimaryCoefficients *prim)
{
int d1 = test_point_line(point, prim->r, prim->g),
d2 = test_point_line(point, prim->g, prim->b),
d3 = test_point_line(point, prim->b, prim->r);
bool has_neg = d1 < 0 || d2 < 0 || d3 < 0,
has_pos = d1 > 0 || d2 > 0 || d3 > 0;
return !(has_neg && has_pos);
}
bool ff_prim_superset(const AVPrimaryCoefficients *a, const AVPrimaryCoefficients *b)
{
return test_point_gamut(b->r, a) &&
test_point_gamut(b->g, a) &&
test_point_gamut(b->b, a);
}
const float ff_pq_eotf_lut[PQ_LUT_SIZE+1] = {
0.0000000e+00f, 4.0422718e-05f, 1.3111372e-04f, 2.6236826e-04f, 4.3151495e-04f, 6.3746885e-04f, 8.7982383e-04f, 1.1585362e-03f,
1.4737819e-03f, 1.8258818e-03f, 2.2152586e-03f, 2.6424098e-03f, 3.1078907e-03f, 3.6123021e-03f, 4.1562821e-03f, 4.7405001e-03f,
5.3656521e-03f, 6.0324583e-03f, 6.7416568e-03f, 7.4940095e-03f, 8.2902897e-03f, 9.1312924e-03f, 1.0017822e-02f, 1.0950702e-02f,
1.1930764e-02f, 1.2958861e-02f, 1.4035847e-02f, 1.5162600e-02f, 1.6340000e-02f, 1.7568948e-02f, 1.8850346e-02f, 2.0185119e-02f,
2.1574192e-02f, 2.3018509e-02f, 2.4519029e-02f, 2.6076704e-02f, 2.7692516e-02f, 2.9367449e-02f, 3.1102509e-02f, 3.2898690e-02f,
3.4757019e-02f, 3.6678526e-02f, 3.8664261e-02f, 4.0715262e-02f, 4.2832601e-02f, 4.5017354e-02f, 4.7270617e-02f, 4.9593473e-02f,
5.1987040e-02f, 5.4452441e-02f, 5.6990819e-02f, 5.9603301e-02f, 6.2291055e-02f, 6.5055251e-02f, 6.7897080e-02f, 7.0817717e-02f,
7.3818379e-02f, 7.6900283e-02f, 8.0064675e-02f, 8.3312774e-02f, 8.6645849e-02f, 9.0065169e-02f, 9.3572031e-02f, 9.7167704e-02f,
1.0085351e-01f, 1.0463077e-01f, 1.0850082e-01f, 1.1246501e-01f, 1.1652473e-01f, 1.2068130e-01f, 1.2493614e-01f, 1.2929066e-01f,
1.3374626e-01f, 1.3830439e-01f, 1.4296648e-01f, 1.4773401e-01f, 1.5260848e-01f, 1.5759132e-01f, 1.6268405e-01f, 1.6788821e-01f,
1.7320534e-01f, 1.7863697e-01f, 1.8418467e-01f, 1.8985004e-01f, 1.9563470e-01f, 2.0154019e-01f, 2.0756818e-01f, 2.1372031e-01f,
2.1999824e-01f, 2.2640365e-01f, 2.3293824e-01f, 2.3960372e-01f, 2.4640186e-01f, 2.5333431e-01f, 2.6040288e-01f, 2.6760935e-01f,
2.7495552e-01f, 2.8244319e-01f, 2.9007421e-01f, 2.9785041e-01f, 3.0577373e-01f, 3.1384594e-01f, 3.2206899e-01f, 3.3044481e-01f,
3.3897533e-01f, 3.4766253e-01f, 3.5650838e-01f, 3.6551487e-01f, 3.7468409e-01f, 3.8401794e-01f, 3.9351855e-01f, 4.0318799e-01f,
4.1302836e-01f, 4.2304177e-01f, 4.3323036e-01f, 4.4359629e-01f, 4.5414181e-01f, 4.6486897e-01f, 4.7578006e-01f, 4.8687732e-01f,
4.9816302e-01f, 5.0963944e-01f, 5.2130889e-01f, 5.3317369e-01f, 5.4523628e-01f, 5.5749886e-01f, 5.6996391e-01f, 5.8263384e-01f,
5.9551111e-01f, 6.0859816e-01f, 6.2189750e-01f, 6.3541162e-01f, 6.4914307e-01f, 6.6309439e-01f, 6.7726819e-01f, 6.9166705e-01f,
7.0629384e-01f, 7.2115077e-01f, 7.3624074e-01f, 7.5156646e-01f, 7.6713065e-01f, 7.8293608e-01f, 7.9898553e-01f, 8.1528181e-01f,
8.3182776e-01f, 8.4862623e-01f, 8.6568012e-01f, 8.8299235e-01f, 9.0056585e-01f, 9.1840360e-01f, 9.3650860e-01f, 9.5488388e-01f,
9.7353277e-01f, 9.9245779e-01f, 1.0116623e+00f, 1.0311496e+00f, 1.0509226e+00f, 1.0709847e+00f, 1.0913391e+00f, 1.1119889e+00f,
1.1329376e+00f, 1.1541885e+00f, 1.1757448e+00f, 1.1976100e+00f, 1.2197875e+00f, 1.2422807e+00f, 1.2650931e+00f, 1.2882282e+00f,
1.3116900e+00f, 1.3354812e+00f, 1.3596059e+00f, 1.3840676e+00f, 1.4088701e+00f, 1.4340170e+00f, 1.4595121e+00f, 1.4853593e+00f,
1.5115622e+00f, 1.5381247e+00f, 1.5650507e+00f, 1.5923442e+00f, 1.6200090e+00f, 1.6480492e+00f, 1.6764688e+00f, 1.7052718e+00f,
1.7344629e+00f, 1.7640451e+00f, 1.7940233e+00f, 1.8244015e+00f, 1.8551840e+00f, 1.8863752e+00f, 1.9179792e+00f, 1.9500006e+00f,
1.9824437e+00f, 2.0153130e+00f, 2.0486129e+00f, 2.0823479e+00f, 2.1165227e+00f, 2.1511419e+00f, 2.1862101e+00f, 2.2217319e+00f,
2.2577128e+00f, 2.2941563e+00f, 2.3310679e+00f, 2.3684523e+00f, 2.4063146e+00f, 2.4446597e+00f, 2.4834925e+00f, 2.5228182e+00f,
2.5626417e+00f, 2.6029683e+00f, 2.6438031e+00f, 2.6851514e+00f, 2.7270184e+00f, 2.7694094e+00f, 2.8123299e+00f, 2.8557852e+00f,
2.8997815e+00f, 2.9443230e+00f, 2.9894159e+00f, 3.0350657e+00f, 3.0812783e+00f, 3.1280593e+00f, 3.1754144e+00f, 3.2233495e+00f,
3.2718705e+00f, 3.3209833e+00f, 3.3706938e+00f, 3.4210082e+00f, 3.4719324e+00f, 3.5234727e+00f, 3.5756351e+00f, 3.6284261e+00f,
3.6818526e+00f, 3.7359195e+00f, 3.7906340e+00f, 3.8460024e+00f, 3.9020315e+00f, 3.9587277e+00f, 4.0160977e+00f, 4.0741483e+00f,
4.1328861e+00f, 4.1923181e+00f, 4.2524511e+00f, 4.3132921e+00f, 4.3748480e+00f, 4.4371260e+00f, 4.5001332e+00f, 4.5638768e+00f,
4.6283650e+00f, 4.6936032e+00f, 4.7595999e+00f, 4.8263624e+00f, 4.8938982e+00f, 4.9622151e+00f, 5.0313205e+00f, 5.1012223e+00f,
5.1719283e+00f, 5.2434463e+00f, 5.3157843e+00f, 5.3889502e+00f, 5.4629521e+00f, 5.5377982e+00f, 5.6134968e+00f, 5.6900560e+00f,
5.7674843e+00f, 5.8457900e+00f, 5.9249818e+00f, 6.0050682e+00f, 6.0860578e+00f, 6.1679595e+00f, 6.2507819e+00f, 6.3345341e+00f,
6.4192275e+00f, 6.5048661e+00f, 6.5914616e+00f, 6.6790231e+00f, 6.7675600e+00f, 6.8570816e+00f, 6.9475975e+00f, 7.0391171e+00f,
7.1316500e+00f, 7.2252060e+00f, 7.3197948e+00f, 7.4154264e+00f, 7.5121107e+00f, 7.6098577e+00f, 7.7086777e+00f, 7.8085807e+00f,
7.9095772e+00f, 8.0116775e+00f, 8.1148922e+00f, 8.2192318e+00f, 8.3247071e+00f, 8.4313287e+00f, 8.5391076e+00f, 8.6480548e+00f,
8.7581812e+00f, 8.8694982e+00f, 8.9820168e+00f, 9.0957485e+00f, 9.2107048e+00f, 9.3268971e+00f, 9.4443372e+00f, 9.5630368e+00f,
9.6830115e+00f, 9.8042658e+00f, 9.9268155e+00f, 1.0050673e+01f, 1.0175850e+01f, 1.0302359e+01f, 1.0430213e+01f, 1.0559425e+01f,
1.0690006e+01f, 1.0821970e+01f, 1.0955331e+01f, 1.1090100e+01f, 1.1226290e+01f, 1.1363917e+01f, 1.1502992e+01f, 1.1643529e+01f,
1.1785542e+01f, 1.1929044e+01f, 1.2074050e+01f, 1.2220573e+01f, 1.2368628e+01f, 1.2518229e+01f, 1.2669390e+01f, 1.2822125e+01f,
1.2976449e+01f, 1.3132377e+01f, 1.3289925e+01f, 1.3449105e+01f, 1.3609935e+01f, 1.3772429e+01f, 1.3936602e+01f, 1.4102470e+01f,
1.4270054e+01f, 1.4439360e+01f, 1.4610407e+01f, 1.4783214e+01f, 1.4957794e+01f, 1.5134166e+01f, 1.5312345e+01f, 1.5492348e+01f,
1.5674192e+01f, 1.5857894e+01f, 1.6043471e+01f, 1.6230939e+01f, 1.6420317e+01f, 1.6611622e+01f, 1.6804871e+01f, 1.7000083e+01f,
1.7197275e+01f, 1.7396465e+01f, 1.7597672e+01f, 1.7800914e+01f, 1.8006210e+01f, 1.8213578e+01f, 1.8423038e+01f, 1.8634608e+01f,
1.8848308e+01f, 1.9064157e+01f, 1.9282175e+01f, 1.9502381e+01f, 1.9724796e+01f, 1.9949439e+01f, 2.0176331e+01f, 2.0405492e+01f,
2.0636950e+01f, 2.0870711e+01f, 2.1106805e+01f, 2.1345250e+01f, 2.1586071e+01f, 2.1829286e+01f, 2.2074919e+01f, 2.2322992e+01f,
2.2573525e+01f, 2.2826542e+01f, 2.3082066e+01f, 2.3340118e+01f, 2.3600721e+01f, 2.3863900e+01f, 2.4129676e+01f, 2.4398074e+01f,
2.4669117e+01f, 2.4942828e+01f, 2.5219233e+01f, 2.5498355e+01f, 2.5780219e+01f, 2.6064849e+01f, 2.6352271e+01f, 2.6642509e+01f,
2.6935589e+01f, 2.7231536e+01f, 2.7530377e+01f, 2.7832137e+01f, 2.8136843e+01f, 2.8444520e+01f, 2.8755196e+01f, 2.9068898e+01f,
2.9385662e+01f, 2.9705496e+01f, 3.0028439e+01f, 3.0354517e+01f, 3.0683758e+01f, 3.1016192e+01f, 3.1351846e+01f, 3.1690750e+01f,
3.2032932e+01f, 3.2378422e+01f, 3.2727250e+01f, 3.3079445e+01f, 3.3435038e+01f, 3.3794058e+01f, 3.4156537e+01f, 3.4522505e+01f,
3.4891993e+01f, 3.5265034e+01f, 3.5641658e+01f, 3.6021897e+01f, 3.6405785e+01f, 3.6793353e+01f, 3.7184634e+01f, 3.7579661e+01f,
3.7978468e+01f, 3.8381088e+01f, 3.8787555e+01f, 3.9197904e+01f, 3.9612169e+01f, 4.0030385e+01f, 4.0452587e+01f, 4.0878810e+01f,
4.1309104e+01f, 4.1743478e+01f, 4.2181981e+01f, 4.2624651e+01f, 4.3071525e+01f, 4.3522639e+01f, 4.3978031e+01f, 4.4437739e+01f,
4.4901803e+01f, 4.5370259e+01f, 4.5843148e+01f, 4.6320508e+01f, 4.6802379e+01f, 4.7288801e+01f, 4.7779815e+01f, 4.8275461e+01f,
4.8775780e+01f, 4.9280813e+01f, 4.9790603e+01f, 5.0305191e+01f, 5.0824620e+01f, 5.1348933e+01f, 5.1878172e+01f, 5.2412382e+01f,
5.2951607e+01f, 5.3495890e+01f, 5.4045276e+01f, 5.4599811e+01f, 5.5159540e+01f, 5.5724510e+01f, 5.6294765e+01f, 5.6870353e+01f,
5.7451339e+01f, 5.8037735e+01f, 5.8629606e+01f, 5.9227001e+01f, 5.9829968e+01f, 6.0438557e+01f, 6.1052818e+01f, 6.1672799e+01f,
6.2298552e+01f, 6.2930128e+01f, 6.3567578e+01f, 6.4210953e+01f, 6.4860306e+01f, 6.5515690e+01f, 6.6177157e+01f, 6.6844762e+01f,
6.7518558e+01f, 6.8198599e+01f, 6.8884942e+01f, 6.9577641e+01f, 7.0276752e+01f, 7.0982332e+01f, 7.1694438e+01f, 7.2413127e+01f,
7.3138457e+01f, 7.3870486e+01f, 7.4609273e+01f, 7.5354878e+01f, 7.6107361e+01f, 7.6866782e+01f, 7.7633203e+01f, 7.8406684e+01f,
7.9187312e+01f, 7.9975101e+01f, 8.0770139e+01f, 8.1572490e+01f, 8.2382216e+01f, 8.3199385e+01f, 8.4024059e+01f, 8.4856307e+01f,
8.5696193e+01f, 8.6543786e+01f, 8.7399153e+01f, 8.8262362e+01f, 8.9133482e+01f, 9.0012582e+01f, 9.0899733e+01f, 9.1795005e+01f,
9.2698470e+01f, 9.3610199e+01f, 9.4530265e+01f, 9.5458741e+01f, 9.6395701e+01f, 9.7341219e+01f, 9.8295370e+01f, 9.9258231e+01f,
1.0022988e+02f, 1.0121039e+02f, 1.0219984e+02f, 1.0319830e+02f, 1.0420587e+02f, 1.0522261e+02f, 1.0624862e+02f, 1.0728396e+02f,
1.0832872e+02f, 1.0938299e+02f, 1.1044684e+02f, 1.1152036e+02f, 1.1260365e+02f, 1.1369677e+02f, 1.1479982e+02f, 1.1591288e+02f,
1.1703605e+02f, 1.1816941e+02f, 1.1931305e+02f, 1.2046706e+02f, 1.2163153e+02f, 1.2280656e+02f, 1.2399223e+02f, 1.2518864e+02f,
1.2639596e+02f, 1.2761413e+02f, 1.2884333e+02f, 1.3008365e+02f, 1.3133519e+02f, 1.3259804e+02f, 1.3387231e+02f, 1.3515809e+02f,
1.3645549e+02f, 1.3776461e+02f, 1.3908555e+02f, 1.4041841e+02f, 1.4176331e+02f, 1.4312034e+02f, 1.4448961e+02f, 1.4587123e+02f,
1.4726530e+02f, 1.4867194e+02f, 1.5009126e+02f, 1.5152336e+02f, 1.5296837e+02f, 1.5442638e+02f, 1.5589753e+02f, 1.5738191e+02f,
1.5887965e+02f, 1.6039087e+02f, 1.6191567e+02f, 1.6345419e+02f, 1.6500655e+02f, 1.6657285e+02f, 1.6815323e+02f, 1.6974781e+02f,
1.7135672e+02f, 1.7298007e+02f, 1.7461800e+02f, 1.7627063e+02f, 1.7793810e+02f, 1.7962053e+02f, 1.8131805e+02f, 1.8303080e+02f,
1.8475891e+02f, 1.8650252e+02f, 1.8826176e+02f, 1.9003676e+02f, 1.9182767e+02f, 1.9363463e+02f, 1.9545777e+02f, 1.9729724e+02f,
1.9915319e+02f, 2.0102575e+02f, 2.0291507e+02f, 2.0482131e+02f, 2.0674460e+02f, 2.0868510e+02f, 2.1064296e+02f, 2.1261833e+02f,
2.1461136e+02f, 2.1662222e+02f, 2.1865105e+02f, 2.2069802e+02f, 2.2276328e+02f, 2.2484700e+02f, 2.2694934e+02f, 2.2907045e+02f,
2.3121064e+02f, 2.3336982e+02f, 2.3554827e+02f, 2.3774618e+02f, 2.3996370e+02f, 2.4220102e+02f, 2.4445831e+02f, 2.4673574e+02f,
2.4903349e+02f, 2.5135174e+02f, 2.5369067e+02f, 2.5605046e+02f, 2.5843129e+02f, 2.6083336e+02f, 2.6325684e+02f, 2.6570192e+02f,
2.6816880e+02f, 2.7065767e+02f, 2.7316872e+02f, 2.7570215e+02f, 2.7825815e+02f, 2.8083692e+02f, 2.8343867e+02f, 2.8606359e+02f,
2.8871189e+02f, 2.9138378e+02f, 2.9407946e+02f, 2.9679914e+02f, 2.9954304e+02f, 3.0231137e+02f, 3.0510434e+02f, 3.0792217e+02f,
3.1076508e+02f, 3.1363330e+02f, 3.1652704e+02f, 3.1944653e+02f, 3.2239199e+02f, 3.2536367e+02f, 3.2836178e+02f, 3.3138657e+02f,
3.3443826e+02f, 3.3751710e+02f, 3.4062333e+02f, 3.4375718e+02f, 3.4691890e+02f, 3.5010874e+02f, 3.5332694e+02f, 3.5657377e+02f,
3.5984946e+02f, 3.6315428e+02f, 3.6648848e+02f, 3.6985233e+02f, 3.7324608e+02f, 3.7667000e+02f, 3.8012436e+02f, 3.8360942e+02f,
3.8712547e+02f, 3.9067276e+02f, 3.9425159e+02f, 3.9786223e+02f, 4.0150496e+02f, 4.0518006e+02f, 4.0888783e+02f, 4.1262855e+02f,
4.1640274e+02f, 4.2021025e+02f, 4.2405159e+02f, 4.2792707e+02f, 4.3183699e+02f, 4.3578166e+02f, 4.3976138e+02f, 4.4377647e+02f,
4.4782724e+02f, 4.5191401e+02f, 4.5603709e+02f, 4.6019681e+02f, 4.6439350e+02f, 4.6862749e+02f, 4.7289910e+02f, 4.7720867e+02f,
4.8155654e+02f, 4.8594305e+02f, 4.9036854e+02f, 4.9483336e+02f, 4.9933787e+02f, 5.0388240e+02f, 5.0846733e+02f, 5.1309301e+02f,
5.1775981e+02f, 5.2246808e+02f, 5.2721821e+02f, 5.3201056e+02f, 5.3684551e+02f, 5.4172344e+02f, 5.4664473e+02f, 5.5160978e+02f,
5.5661897e+02f, 5.6167269e+02f, 5.6677135e+02f, 5.7191535e+02f, 5.7710508e+02f, 5.8234097e+02f, 5.8762342e+02f, 5.9295285e+02f,
5.9832968e+02f, 6.0375433e+02f, 6.0922723e+02f, 6.1474882e+02f, 6.2031952e+02f, 6.2593979e+02f, 6.3161006e+02f, 6.3733078e+02f,
6.4310241e+02f, 6.4892540e+02f, 6.5480021e+02f, 6.6072730e+02f, 6.6670715e+02f, 6.7274023e+02f, 6.7882702e+02f, 6.8496800e+02f,
6.9116365e+02f, 6.9741447e+02f, 7.0372096e+02f, 7.1008361e+02f, 7.1650293e+02f, 7.2297942e+02f, 7.2951361e+02f, 7.3610602e+02f,
7.4275756e+02f, 7.4946797e+02f, 7.5623818e+02f, 7.6306873e+02f, 7.6996016e+02f, 7.7691302e+02f, 7.8392787e+02f, 7.9100526e+02f,
7.9814576e+02f, 8.0534993e+02f, 8.1261837e+02f, 8.1995163e+02f, 8.2735032e+02f, 8.3481501e+02f, 8.4234632e+02f, 8.4994483e+02f,
8.5761116e+02f, 8.6534592e+02f, 8.7314974e+02f, 8.8102323e+02f, 8.8896702e+02f, 8.9698176e+02f, 9.0506809e+02f, 9.1322665e+02f,
9.2145810e+02f, 9.2976310e+02f, 9.3814232e+02f, 9.4659643e+02f, 9.5512612e+02f, 9.6373206e+02f, 9.7241496e+02f, 9.8117550e+02f,
9.9001441e+02f, 9.9893238e+02f, 1.0079301e+03f, 1.0170084e+03f, 1.0261679e+03f, 1.0354094e+03f, 1.0447337e+03f, 1.0541414e+03f,
1.0636334e+03f, 1.0732104e+03f, 1.0828731e+03f, 1.0926225e+03f, 1.1024592e+03f, 1.1123841e+03f, 1.1223979e+03f, 1.1325016e+03f,
1.1426958e+03f, 1.1529814e+03f, 1.1633594e+03f, 1.1738304e+03f, 1.1843954e+03f, 1.1950552e+03f, 1.2058107e+03f, 1.2166627e+03f,
1.2276122e+03f, 1.2386601e+03f, 1.2498072e+03f, 1.2610544e+03f, 1.2724027e+03f, 1.2838531e+03f, 1.2954063e+03f, 1.3070635e+03f,
1.3188262e+03f, 1.3306940e+03f, 1.3426686e+03f, 1.3547509e+03f, 1.3669420e+03f, 1.3792428e+03f, 1.3916544e+03f, 1.4041778e+03f,
1.4168140e+03f, 1.4295640e+03f, 1.4424289e+03f, 1.4554098e+03f, 1.4685078e+03f, 1.4817238e+03f, 1.4950591e+03f, 1.5085147e+03f,
1.5220916e+03f, 1.5357912e+03f, 1.5496144e+03f, 1.5635624e+03f, 1.5776364e+03f, 1.5918375e+03f, 1.6061670e+03f, 1.6206260e+03f,
1.6352156e+03f, 1.6499372e+03f, 1.6647920e+03f, 1.6797811e+03f, 1.6949059e+03f, 1.7101676e+03f, 1.7255674e+03f, 1.7411067e+03f,
1.7567867e+03f, 1.7726087e+03f, 1.7885742e+03f, 1.8046844e+03f, 1.8209406e+03f, 1.8373443e+03f, 1.8538967e+03f, 1.8705994e+03f,
1.8874536e+03f, 1.9044608e+03f, 1.9216225e+03f, 1.9389401e+03f, 1.9564150e+03f, 1.9740486e+03f, 1.9918426e+03f, 2.0097984e+03f,
2.0279175e+03f, 2.0462014e+03f, 2.0646517e+03f, 2.0832699e+03f, 2.1020577e+03f, 2.1210165e+03f, 2.1401481e+03f, 2.1594540e+03f,
2.1789359e+03f, 2.1985954e+03f, 2.2184342e+03f, 2.2384540e+03f, 2.2586565e+03f, 2.2790434e+03f, 2.2996165e+03f, 2.3203774e+03f,
2.3413293e+03f, 2.3624714e+03f, 2.3838068e+03f, 2.4053372e+03f, 2.4270646e+03f, 2.4489908e+03f, 2.4711177e+03f, 2.4934471e+03f,
2.5159811e+03f, 2.5387214e+03f, 2.5616702e+03f, 2.5848293e+03f, 2.6082007e+03f, 2.6317866e+03f, 2.6555888e+03f, 2.6796095e+03f,
2.7038507e+03f, 2.7283145e+03f, 2.7530031e+03f, 2.7779186e+03f, 2.8030631e+03f, 2.8284388e+03f, 2.8540479e+03f, 2.8798927e+03f,
2.9059754e+03f, 2.9322983e+03f, 2.9588635e+03f, 2.9856736e+03f, 3.0127308e+03f, 3.0400374e+03f, 3.0675959e+03f, 3.0954086e+03f,
3.1234780e+03f, 3.1518066e+03f, 3.1803969e+03f, 3.2092512e+03f, 3.2383723e+03f, 3.2677625e+03f, 3.2974246e+03f, 3.3273611e+03f,
3.3575747e+03f, 3.3880680e+03f, 3.4188437e+03f, 3.4499045e+03f, 3.4812533e+03f, 3.5128926e+03f, 3.5448255e+03f, 3.5770546e+03f,
3.6095828e+03f, 3.6424131e+03f, 3.6755483e+03f, 3.7089914e+03f, 3.7427454e+03f, 3.7768132e+03f, 3.8111979e+03f, 3.8459027e+03f,
3.8809304e+03f, 3.9162844e+03f, 3.9519678e+03f, 3.9879837e+03f, 4.0243354e+03f, 4.0610261e+03f, 4.0980592e+03f, 4.1354380e+03f,
4.1731681e+03f, 4.2112483e+03f, 4.2496844e+03f, 4.2884798e+03f, 4.3276381e+03f, 4.3671627e+03f, 4.4070572e+03f, 4.4473253e+03f,
4.4879706e+03f, 4.5289968e+03f, 4.5704076e+03f, 4.6122068e+03f, 4.6543981e+03f, 4.6969854e+03f, 4.7399727e+03f, 4.7833637e+03f,
4.8271625e+03f, 4.8713731e+03f, 4.9159995e+03f, 4.9610458e+03f, 5.0065162e+03f, 5.0524147e+03f, 5.0987457e+03f, 5.1455133e+03f,
5.1927219e+03f, 5.2403759e+03f, 5.2884795e+03f, 5.3370373e+03f, 5.3860537e+03f, 5.4355333e+03f, 5.4854807e+03f, 5.5359004e+03f,
5.5867972e+03f, 5.6381757e+03f, 5.6900408e+03f, 5.7423972e+03f, 5.7952499e+03f, 5.8486037e+03f, 5.9024637e+03f, 5.9568349e+03f,
6.0117223e+03f, 6.0671311e+03f, 6.1230664e+03f, 6.1795336e+03f, 6.2365379e+03f, 6.2940847e+03f, 6.3521793e+03f, 6.4108273e+03f,
6.4700342e+03f, 6.5298056e+03f, 6.5901471e+03f, 6.6510643e+03f, 6.7125632e+03f, 6.7746495e+03f, 6.8373290e+03f, 6.9006078e+03f,
6.9644918e+03f, 7.0289872e+03f, 7.0941001e+03f, 7.1598366e+03f, 7.2262031e+03f, 7.2932059e+03f, 7.3608513e+03f, 7.4291460e+03f,
7.4981006e+03f, 7.5677134e+03f, 7.6379952e+03f, 7.7089527e+03f, 7.7805929e+03f, 7.8529226e+03f, 7.9259489e+03f, 7.9996786e+03f,
8.0741191e+03f, 8.1492774e+03f, 8.2251609e+03f, 8.3017769e+03f, 8.3791329e+03f, 8.4572364e+03f, 8.5360950e+03f, 8.6157163e+03f,
8.6961082e+03f, 8.7772786e+03f, 8.8592352e+03f, 8.9419862e+03f, 9.0255397e+03f, 9.1099038e+03f, 9.1950869e+03f, 9.2810973e+03f,
9.3679435e+03f, 9.4556340e+03f, 9.5441776e+03f, 9.6335829e+03f, 9.7238588e+03f, 9.8150143e+03f, 9.9070583e+03f, 1.0000000e+04f,
1e4f, /* extra padding to avoid out of bounds access */
};
|
