// 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];

}

Unexecuted instantiation: float jxl::DCTTotalResampleScale<8ul, 1ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<16ul, 2ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<32ul, 4ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<64ul, 8ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<128ul, 16ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<256ul, 32ul>(unsigned long)

float jxl::DCTTotalResampleScale<2ul, 16ul>(unsigned long)

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constexpr float DCTTotalResampleScale(size_t x) {

374

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  return DCTResampleScales<FROM, TO>::kScales[x];

375

282k

}

float jxl::DCTTotalResampleScale<1ul, 8ul>(unsigned long)

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constexpr float DCTTotalResampleScale(size_t x) {

374

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  return DCTResampleScales<FROM, TO>::kScales[x];

375

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}

float jxl::DCTTotalResampleScale<4ul, 32ul>(unsigned long)

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constexpr float DCTTotalResampleScale(size_t x) {

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  return DCTResampleScales<FROM, TO>::kScales[x];

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}

Unexecuted instantiation: float jxl::DCTTotalResampleScale<8ul, 64ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<16ul, 128ul>(unsigned long)

Unexecuted instantiation: float jxl::DCTTotalResampleScale<32ul, 256ul>(unsigned long)

}  // namespace jxl

#endif  // LIB_JXL_DCT_SCALES_H_