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Diffstat (limited to 'third_party/jpeg-xl/lib/jxl/dct_scales.h')
| -rw-r--r-- | third_party/jpeg-xl/lib/jxl/dct_scales.h | 379 |
1 files changed, 379 insertions, 0 deletions
diff --git a/third_party/jpeg-xl/lib/jxl/dct_scales.h b/third_party/jpeg-xl/lib/jxl/dct_scales.h new file mode 100644 index 0000000000..23af03d60f --- /dev/null +++ b/third_party/jpeg-xl/lib/jxl/dct_scales.h @@ -0,0 +1,379 @@ +// Copyright (c) the JPEG XL Project Authors. All rights reserved. +// +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +#ifndef LIB_JXL_DCT_SCALES_H_ +#define LIB_JXL_DCT_SCALES_H_ + +// Scaling factors. + +#include <stddef.h> + +namespace jxl { + +static constexpr float kSqrt2 = 1.41421356237f; +static constexpr float kSqrt0_5 = 0.70710678118f; + +// For n != 0, the n-th basis function of a N-DCT, evaluated in pixel k, has a +// value of cos((k+1/2) n/(2N) pi). When downsampling by 2x, we average +// the values for pixel k and k+1 to get the value for pixel (k/2), thus we get +// +// [cos((k+1/2) n/N pi) + cos((k+3/2) n/N pi)]/2 = +// cos(n/(2N) pi) cos((k+1) n/N pi) = +// cos(n/(2N) pi) cos(((k/2)+1/2) n/(N/2) pi) +// +// which is exactly the same as the value of pixel k/2 of a N/2-sized DCT, +// except for the cos(n/(2N) pi) scaling factor (which does *not* +// depend on the pixel). Thus, when using the lower-frequency coefficients of a +// DCT-N to compute a DCT-(N/2), they should be scaled by this constant. Scaling +// factors for a DCT-(N/4) etc can then be obtained by successive +// multiplications. The structs below contain the above-mentioned scaling +// factors. +// +// Python code for the tables below: +// +// for i in range(N // 8): +// v = math.cos(i / (2 * N) * math.pi) +// v *= math.cos(i / (N) * math.pi) +// v *= math.cos(i / (N / 2) * math.pi) +// print(v, end=", ") + +template <size_t FROM, size_t TO> +struct DCTResampleScales; + +template <> +struct DCTResampleScales<8, 1> { + static constexpr float kScales[] = { + 1.000000000000000000, + }; +}; + +template <> +struct DCTResampleScales<16, 2> { + static constexpr float kScales[] = { + 1.000000000000000000, + 0.901764195028874394, + }; +}; + +template <> +struct DCTResampleScales<32, 4> { + static constexpr float kScales[] = { + 1.000000000000000000, + 0.974886821136879522, + 0.901764195028874394, + 0.787054918159101335, + }; +}; + +template <> +struct DCTResampleScales<64, 8> { + static constexpr float kScales[] = { + 1.0000000000000000, 0.9936866130906366, 0.9748868211368796, + 0.9440180941651672, 0.9017641950288744, 0.8490574973847023, + 0.7870549181591013, 0.7171081282466044, + }; +}; + +template <> +struct DCTResampleScales<128, 16> { + static constexpr float kScales[] = { + 1.0, + 0.9984194528776054, + 0.9936866130906366, + 0.9858278282666936, + 0.9748868211368796, + 0.9609244059440204, + 0.9440180941651672, + 0.9242615922757944, + 0.9017641950288744, + 0.8766500784429904, + 0.8490574973847023, + 0.8191378932865928, + 0.7870549181591013, + 0.7529833816270532, + 0.7171081282466044, + 0.6796228528314651, + }; +}; + +template <> +struct DCTResampleScales<256, 32> { + static constexpr float kScales[] = { + 1.0, + 0.9996047255830407, + 0.9984194528776054, + 0.9964458326264695, + 0.9936866130906366, + 0.9901456355893141, + 0.9858278282666936, + 0.9807391980963174, + 0.9748868211368796, + 0.9682788310563117, + 0.9609244059440204, + 0.9528337534340876, + 0.9440180941651672, + 0.9344896436056892, + 0.9242615922757944, + 0.913348084400198, + 0.9017641950288744, + 0.8895259056651056, + 0.8766500784429904, + 0.8631544288990163, + 0.8490574973847023, + 0.8343786191696513, + 0.8191378932865928, + 0.8033561501721485, + 0.7870549181591013, + 0.7702563888779096, + 0.7529833816270532, + 0.7352593067735488, + 0.7171081282466044, + 0.6985543251889097, + 0.6796228528314651, + 0.6603391026591464, + }; +}; + +// Inverses of the above. +template <> +struct DCTResampleScales<1, 8> { + static constexpr float kScales[] = { + 1.000000000000000000, + }; +}; + +template <> +struct DCTResampleScales<2, 16> { + static constexpr float kScales[] = { + 1.000000000000000000, + 1.108937353592731823, + }; +}; + +template <> +struct DCTResampleScales<4, 32> { + static constexpr float kScales[] = { + 1.000000000000000000, + 1.025760096781116015, + 1.108937353592731823, + 1.270559368765487251, + }; +}; + +template <> +struct DCTResampleScales<8, 64> { + static constexpr float kScales[] = { + 1.0000000000000000, 1.0063534990068217, 1.0257600967811158, + 1.0593017296817173, 1.1089373535927318, 1.1777765381970435, + 1.2705593687654873, 1.3944898413647777, + }; +}; + +template <> +struct DCTResampleScales<16, 128> { + static constexpr float kScales[] = { + 1.0, + 1.0015830492062623, + 1.0063534990068217, + 1.0143759095928793, + 1.0257600967811158, + 1.0406645869480142, + 1.0593017296817173, + 1.0819447744633812, + 1.1089373535927318, + 1.1407059950032632, + 1.1777765381970435, + 1.2207956782315876, + 1.2705593687654873, + 1.3280505578213306, + 1.3944898413647777, + 1.4714043176061107, + }; +}; + +template <> +struct DCTResampleScales<32, 256> { + static constexpr float kScales[] = { + 1.0, + 1.0003954307206069, + 1.0015830492062623, + 1.0035668445360069, + 1.0063534990068217, + 1.009952439375063, + 1.0143759095928793, + 1.0196390660647288, + 1.0257600967811158, + 1.0327603660498115, + 1.0406645869480142, + 1.049501024072585, + 1.0593017296817173, + 1.0701028169146336, + 1.0819447744633812, + 1.0948728278734026, + 1.1089373535927318, + 1.124194353004584, + 1.1407059950032632, + 1.158541237256391, + 1.1777765381970435, + 1.1984966740820495, + 1.2207956782315876, + 1.244777922949508, + 1.2705593687654873, + 1.2982690107339132, + 1.3280505578213306, + 1.3600643892400104, + 1.3944898413647777, + 1.4315278911623237, + 1.4714043176061107, + 1.5143734423314616, + }; +}; + +// Constants for DCT implementation. Generated by the following snippet: +// for i in range(N // 2): +// print(1.0 / (2 * math.cos((i + 0.5) * math.pi / N)), end=", ") +template <size_t N> +struct WcMultipliers; + +template <> +struct WcMultipliers<4> { + static constexpr float kMultipliers[] = { + 0.541196100146197, + 1.3065629648763764, + }; +}; + +template <> +struct WcMultipliers<8> { + static constexpr float kMultipliers[] = { + 0.5097955791041592, + 0.6013448869350453, + 0.8999762231364156, + 2.5629154477415055, + }; +}; + +template <> +struct WcMultipliers<16> { + static constexpr float kMultipliers[] = { + 0.5024192861881557, 0.5224986149396889, 0.5669440348163577, + 0.6468217833599901, 0.7881546234512502, 1.060677685990347, + 1.7224470982383342, 5.101148618689155, + }; +}; + +template <> +struct WcMultipliers<32> { + static constexpr float kMultipliers[] = { + 0.5006029982351963, 0.5054709598975436, 0.5154473099226246, + 0.5310425910897841, 0.5531038960344445, 0.5829349682061339, + 0.6225041230356648, 0.6748083414550057, 0.7445362710022986, + 0.8393496454155268, 0.9725682378619608, 1.1694399334328847, + 1.4841646163141662, 2.057781009953411, 3.407608418468719, + 10.190008123548033, + }; +}; +template <> +struct WcMultipliers<64> { + static constexpr float kMultipliers[] = { + 0.500150636020651, 0.5013584524464084, 0.5037887256810443, + 0.5074711720725553, 0.5124514794082247, 0.5187927131053328, + 0.52657731515427, 0.535909816907992, 0.5469204379855088, + 0.5597698129470802, 0.57465518403266, 0.5918185358574165, + 0.6115573478825099, 0.6342389366884031, 0.6603198078137061, + 0.6903721282002123, 0.7251205223771985, 0.7654941649730891, + 0.8127020908144905, 0.8683447152233481, 0.9345835970364075, + 1.0144082649970547, 1.1120716205797176, 1.233832737976571, + 1.3892939586328277, 1.5939722833856311, 1.8746759800084078, + 2.282050068005162, 2.924628428158216, 4.084611078129248, + 6.796750711673633, 20.373878167231453, + }; +}; +template <> +struct WcMultipliers<128> { + static constexpr float kMultipliers[] = { + 0.5000376519155477, 0.5003390374428216, 0.5009427176380873, + 0.5018505174842379, 0.5030651913013697, 0.5045904432216454, + 0.5064309549285542, 0.5085924210498143, 0.5110815927066812, + 0.5139063298475396, 0.5170756631334912, 0.5205998663018917, + 0.524490540114724, 0.5287607092074876, 0.5334249333971333, + 0.538499435291984, 0.5440022463817783, 0.549953374183236, + 0.5563749934898856, 0.5632916653417023, 0.5707305880121454, + 0.5787218851348208, 0.5872989370937893, 0.5964987630244563, + 0.606362462272146, 0.6169357260050706, 0.6282694319707711, + 0.6404203382416639, 0.6534518953751283, 0.6674352009263413, + 0.6824501259764195, 0.6985866506472291, 0.7159464549705746, + 0.7346448236478627, 0.7548129391165311, 0.776600658233963, + 0.8001798956216941, 0.8257487738627852, 0.8535367510066064, + 0.8838110045596234, 0.9168844461846523, 0.9531258743921193, + 0.9929729612675466, 1.036949040910389, 1.0856850642580145, + 1.1399486751015042, 1.2006832557294167, 1.2690611716991191, + 1.346557628206286, 1.4350550884414341, 1.5369941008524954, + 1.6555965242641195, 1.7952052190778898, 1.961817848571166, + 2.163957818751979, 2.4141600002500763, 2.7316450287739396, + 3.147462191781909, 3.7152427383269746, 4.5362909369693565, + 5.827688377844654, 8.153848602466814, 13.58429025728446, + 40.744688103351834, + }; +}; + +template <> +struct WcMultipliers<256> { + static constexpr float kMultipliers[128] = { + 0.5000094125358878, 0.500084723455784, 0.5002354020255269, + 0.5004615618093246, 0.5007633734146156, 0.5011410648064231, + 0.5015949217281668, 0.502125288230386, 0.5027325673091954, + 0.5034172216566842, 0.5041797745258774, 0.5050208107132756, + 0.5059409776624396, 0.5069409866925212, 0.5080216143561264, + 0.509183703931388, 0.5104281670536573, 0.5117559854927805, + 0.5131682130825206, 0.5146659778093218, 0.516250484068288, + 0.5179230150949777, 0.5196849355823947, 0.5215376944933958, + 0.5234828280796439, 0.52552196311921, 0.5276568203859896, + 0.5298892183652453, 0.5322210772308335, 0.5346544231010253, + 0.537191392591309, 0.5398342376841637, 0.5425853309375497, + 0.545447171055775, 0.5484223888484947, 0.551513753605893, + 0.554724179920619, 0.5580567349898085, 0.5615146464335654, + 0.5651013106696203, 0.5688203018875696, 0.5726753816701664, + 0.5766705093136241, 0.5808098529038624, 0.5850978012111273, + 0.58953897647151, 0.5941382481306648, 0.5989007476325463, + 0.6038318843443582, 0.6089373627182432, 0.614223200800649, + 0.6196957502119484, 0.6253617177319102, 0.6312281886412079, + 0.6373026519855411, 0.6435930279473415, 0.6501076975307724, + 0.6568555347890955, 0.6638459418498757, 0.6710888870233562, + 0.6785949463131795, 0.6863753486870501, 0.6944420255086364, + 0.7028076645818034, 0.7114857693151208, 0.7204907235796304, + 0.7298378629074134, 0.7395435527641373, 0.749625274727372, + 0.7601017215162176, 0.7709929019493761, 0.7823202570613161, + 0.7941067887834509, 0.8063772028037925, 0.8191580674598145, + 0.83247799080191, 0.8463678182968619, 0.860860854031955, + 0.8759931087426972, 0.8918035785352535, 0.9083345588266809, + 0.9256319988042384, 0.9437459026371479, 0.962730784794803, + 0.9826461881778968, 1.0035572754078206, 1.0255355056139732, + 1.048659411496106, 1.0730154944316674, 1.0986992590905857, + 1.1258164135986009, 1.1544842669978943, 1.184833362908442, + 1.217009397314603, 1.2511754798461228, 1.287514812536712, + 1.326233878832723, 1.3675662599582539, 1.411777227500661, + 1.459169302866857, 1.5100890297227016, 1.5649352798258847, + 1.6241695131835794, 1.6883285509131505, 1.7580406092704062, + 1.8340456094306077, 1.9172211551275689, 2.0086161135167564, + 2.1094945286246385, 2.22139377701127, 2.346202662531156, + 2.486267909203593, 2.644541877144861, 2.824791402350551, + 3.0318994541759925, 3.2723115884254845, 3.5547153325075804, + 3.891107790700307, 4.298537526449054, 4.802076008665048, + 5.440166215091329, 6.274908408039339, 7.413566756422303, + 9.058751453879703, 11.644627325175037, 16.300023088031555, + 27.163977662448232, 81.48784219222516, + }; +}; + +// Apply the DCT algorithm-intrinsic constants to DCTResampleScale. +template <size_t FROM, size_t TO> +constexpr float DCTTotalResampleScale(size_t x) { + return DCTResampleScales<FROM, TO>::kScales[x]; +} + +} // namespace jxl + +#endif // LIB_JXL_DCT_SCALES_H_ |