Function DCT

extern/toojpeg/toojpeg.cpp:206–249

forward DCT computation "in one dimension" (fast AAN algorithm by Arai, Agui and Nakajima: "A fast DCT-SQ scheme for images")

// forward DCT computation "in one dimension" (fast AAN algorithm by Arai, Agui and Nakajima: "A fast DCT-SQ scheme for images")
void DCT(float block[8*8], uint8_t stride) // stride must be 1 (=horizontal) or 8 (=vertical)
{
  const auto SqrtHalfSqrt = 1.306562965f; //    sqrt((2 + sqrt(2)) / 2) = cos(pi * 1 / 8) * sqrt(2)
  const auto InvSqrt      = 0.707106781f; // 1 / sqrt(2)                = cos(pi * 2 / 8)
  const auto HalfSqrtSqrt = 0.382683432f; //     sqrt(2 - sqrt(2)) / 2  = cos(pi * 3 / 8)
  const auto InvSqrtSqrt  = 0.541196100f; // 1 / sqrt(2 - sqrt(2))      = cos(pi * 3 / 8) * sqrt(2)

  // modify in-place
  auto& block0 = block[0         ];
  auto& block1 = block[1 * stride];
  auto& block2 = block[2 * stride];
  auto& block3 = block[3 * stride];
  auto& block4 = block[4 * stride];
  auto& block5 = block[5 * stride];
  auto& block6 = block[6 * stride];
  auto& block7 = block[7 * stride];

  // based on https://dev.w3.org/Amaya/libjpeg/jfdctflt.c , the original variable names can be found in my comments
  auto add07 = block0 + block7; auto sub07 = block0 - block7; // tmp0, tmp7
  auto add16 = block1 + block6; auto sub16 = block1 - block6; // tmp1, tmp6
  auto add25 = block2 + block5; auto sub25 = block2 - block5; // tmp2, tmp5
  auto add34 = block3 + block4; auto sub34 = block3 - block4; // tmp3, tmp4

  auto add0347 = add07 + add34; auto sub07_34 = add07 - add34; // tmp10, tmp13 ("even part" / "phase 2")
  auto add1256 = add16 + add25; auto sub16_25 = add16 - add25; // tmp11, tmp12

  block0 = add0347 + add1256; block4 = add0347 - add1256; // "phase 3"

  auto z1 = (sub16_25 + sub07_34) * InvSqrt; // all temporary z-variables kept their original names
  block2 = sub07_34 + z1; block6 = sub07_34 - z1; // "phase 5"

  auto sub23_45 = sub25 + sub34; // tmp10 ("odd part" / "phase 2")
  auto sub12_56 = sub16 + sub25; // tmp11
  auto sub01_67 = sub16 + sub07; // tmp12

  auto z5 = (sub23_45 - sub01_67) * HalfSqrtSqrt;
  auto z2 = sub23_45 * InvSqrtSqrt  + z5;
  auto z3 = sub12_56 * InvSqrt;
  auto z4 = sub01_67 * SqrtHalfSqrt + z5;
  auto z6 = sub07 + z3; // z11 ("phase 5")
  auto z7 = sub07 - z3; // z13
  block1 = z6 + z4; block7 = z6 - z4; // "phase 6"
  block5 = z7 + z2; block3 = z7 - z2;
}

// run DCT, quantize and write Huffman bit codes
int16_t encodeBlock(BitWriter& writer, float block[8][8], const float scaled[8*8], int16_t lastDC,