Module: PureJPEG::DCT

Defined in:
lib/pure_jpeg/dct.rb

Overview

Integer-scaled DCT based on the IJG (Independent JPEG Group) reference implementation (jfdctint.c / jidctint.c). Uses the Arai-Agui-Nakajima factorization with 13-bit fixed-point constants.

All arithmetic is pure Integer (additions, shifts, multiplies) — no Float operations. This is ~3x faster than the matrix-multiply float DCT under YJIT and eliminates millions of Float object allocations during decode.

Constant Summary collapse

MATRIX =

Keep the float matrix available for reference / testing

Array.new(8) { |k|
  ck = k == 0 ? 0.5 / Math.sqrt(2.0) : 0.5
  Array.new(8) { |n|
    ck * Math.cos((2.0 * n + 1.0) * k * Math::PI / 16.0)
  }
}.freeze
MATRIX_FLAT = 
MATRIX.flatten.freeze
MATRIX_T_FLAT = 
Array.new(64) { |i| MATRIX_FLAT[(i % 8) * 8 + i / 8] }.freeze
CONST_BITS =

Fixed-point constants (13-bit precision) from IJG reference.

13
PASS1_BITS = 
2
FIX_0_298631336 = 
2446
FIX_0_390180644 = 
3196
FIX_0_541196100 = 
4433
FIX_0_765366865 = 
6270
FIX_0_899976223 = 
7373
FIX_1_175875602 = 
9633
FIX_1_501321110 = 
12299
FIX_1_847759065 = 
15137
FIX_1_961570560 = 
16069
FIX_2_053119869 = 
16819
FIX_2_562915447 = 
20995
FIX_3_072711026 = 
25172
CB = 
CONST_BITS
P1 = 
PASS1_BITS
CB_M_P1 =

11

CB - P1
CB_P_P1_P3 =

18

CB + P1 + 3
P1_P3 =

5

P1 + 3
CB2_P_P1 =

28 (unused, was for column even-multiplied path)

CB * 2 + P1

Class Method Summary collapse

Class Method Details

.forward!(data, _temp = nil, _out = nil) ⇒ Object

Forward 2D DCT (in-place). Input: 64-element array of level-shifted integers (-128..127). Output: DCT coefficients (integers). The ‘_temp` and `_out` parameters are accepted for API compatibility but ignored; computation is done in-place on `data`.



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# File 'lib/pure_jpeg/dct.rb', line 51

def self.forward!(data, _temp = nil, _out = nil)
  # Pass 1: process rows
  8.times do |row|
    i = row << 3
    d0 = data[i]; d1 = data[i+1]; d2 = data[i+2]; d3 = data[i+3]
    d4 = data[i+4]; d5 = data[i+5]; d6 = data[i+6]; d7 = data[i+7]

    tmp0 = d0 + d7; tmp7 = d0 - d7
    tmp1 = d1 + d6; tmp6 = d1 - d6
    tmp2 = d2 + d5; tmp5 = d2 - d5
    tmp3 = d3 + d4; tmp4 = d3 - d4

    # Even part
    tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3
    tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2

    data[i]   = (tmp10 + tmp11) << P1
    data[i+4] = (tmp10 - tmp11) << P1

    z1 = (tmp12 + tmp13) * FIX_0_541196100
    data[i+2] = (z1 + tmp13 * FIX_0_765366865 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[i+6] = (z1 - tmp12 * FIX_1_847759065 + (1 << (CB_M_P1 - 1))) >> CB_M_P1

    # Odd part
    z1 = tmp4 + tmp7; z2 = tmp5 + tmp6
    z3 = tmp4 + tmp6; z4 = tmp5 + tmp7
    z5 = (z3 + z4) * FIX_1_175875602

    tmp4 = tmp4 * FIX_0_298631336
    tmp5 = tmp5 * FIX_2_053119869
    tmp6 = tmp6 * FIX_3_072711026
    tmp7 = tmp7 * FIX_1_501321110
    z1 = z1 * -FIX_0_899976223
    z2 = z2 * -FIX_2_562915447
    z3 = z3 * -FIX_1_961570560 + z5
    z4 = z4 * -FIX_0_390180644 + z5

    data[i+7] = (tmp4 + z1 + z3 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[i+5] = (tmp5 + z2 + z4 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[i+3] = (tmp6 + z2 + z3 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[i+1] = (tmp7 + z1 + z4 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
  end

  # Pass 2: process columns
  8.times do |col|
    d0 = data[col]; d1 = data[col+8]; d2 = data[col+16]; d3 = data[col+24]
    d4 = data[col+32]; d5 = data[col+40]; d6 = data[col+48]; d7 = data[col+56]

    tmp0 = d0 + d7; tmp7 = d0 - d7
    tmp1 = d1 + d6; tmp6 = d1 - d6
    tmp2 = d2 + d5; tmp5 = d2 - d5
    tmp3 = d3 + d4; tmp4 = d3 - d4

    tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3
    tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2

    data[col]    = (tmp10 + tmp11 + (1 << (P1_P3 - 1))) >> P1_P3
    data[col+32] = (tmp10 - tmp11 + (1 << (P1_P3 - 1))) >> P1_P3

    z1 = (tmp12 + tmp13) * FIX_0_541196100
    data[col+16] = (z1 + tmp13 * FIX_0_765366865 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[col+48] = (z1 - tmp12 * FIX_1_847759065 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3

    z1 = tmp4 + tmp7; z2 = tmp5 + tmp6
    z3 = tmp4 + tmp6; z4 = tmp5 + tmp7
    z5 = (z3 + z4) * FIX_1_175875602

    tmp4 = tmp4 * FIX_0_298631336
    tmp5 = tmp5 * FIX_2_053119869
    tmp6 = tmp6 * FIX_3_072711026
    tmp7 = tmp7 * FIX_1_501321110
    z1 = z1 * -FIX_0_899976223
    z2 = z2 * -FIX_2_562915447
    z3 = z3 * -FIX_1_961570560 + z5
    z4 = z4 * -FIX_0_390180644 + z5

    data[col+56] = (tmp4 + z1 + z3 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[col+40] = (tmp5 + z2 + z4 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[col+24] = (tmp6 + z2 + z3 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[col+8]  = (tmp7 + z1 + z4 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
  end

  data
end

.inverse!(data, _temp = nil, _out = nil) ⇒ Object

Inverse 2D DCT (in-place). Input: dequantized DCT coefficients (integers). Output: spatial-domain values (integers) that still need +128 level shift.



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# File 'lib/pure_jpeg/dct.rb', line 138

def self.inverse!(data, _temp = nil, _out = nil)
  # Pass 1: process columns
  8.times do |col|
    d0 = data[col]; d2 = data[col+16]; d4 = data[col+32]; d6 = data[col+48]
    d1 = data[col+8]; d3 = data[col+24]; d5 = data[col+40]; d7 = data[col+56]

    # Even part
    z1 = (d2 + d6) * FIX_0_541196100
    tmp2 = z1 - d6 * FIX_1_847759065
    tmp3 = z1 + d2 * FIX_0_765366865

    tmp0 = (d0 + d4) << CB
    tmp1 = (d0 - d4) << CB

    tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3
    tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2

    # Odd part
    tmp0 = d7; tmp1 = d5; tmp2 = d3; tmp3 = d1
    z1 = tmp0 + tmp3; z2 = tmp1 + tmp2
    z3 = tmp0 + tmp2; z4 = tmp1 + tmp3
    z5 = (z3 + z4) * FIX_1_175875602

    tmp0 = tmp0 * FIX_0_298631336
    tmp1 = tmp1 * FIX_2_053119869
    tmp2 = tmp2 * FIX_3_072711026
    tmp3 = tmp3 * FIX_1_501321110
    z1 = z1 * -FIX_0_899976223
    z2 = z2 * -FIX_2_562915447
    z3 = z3 * -FIX_1_961570560 + z5
    z4 = z4 * -FIX_0_390180644 + z5

    tmp0 += z1 + z3; tmp1 += z2 + z4
    tmp2 += z2 + z3; tmp3 += z1 + z4

    data[col]    = (tmp10 + tmp3 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+56] = (tmp10 - tmp3 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+8]  = (tmp11 + tmp2 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+48] = (tmp11 - tmp2 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+16] = (tmp12 + tmp1 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+40] = (tmp12 - tmp1 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+24] = (tmp13 + tmp0 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
    data[col+32] = (tmp13 - tmp0 + (1 << (CB_M_P1 - 1))) >> CB_M_P1
  end

  # Pass 2: process rows
  8.times do |row|
    i = row << 3
    d0 = data[i]; d2 = data[i+2]; d4 = data[i+4]; d6 = data[i+6]
    d1 = data[i+1]; d3 = data[i+3]; d5 = data[i+5]; d7 = data[i+7]

    # Even part
    z1 = (d2 + d6) * FIX_0_541196100
    tmp2 = z1 - d6 * FIX_1_847759065
    tmp3 = z1 + d2 * FIX_0_765366865

    tmp0 = (d0 + d4) << CB
    tmp1 = (d0 - d4) << CB

    tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3
    tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2

    # Odd part
    tmp0 = d7; tmp1 = d5; tmp2 = d3; tmp3 = d1
    z1 = tmp0 + tmp3; z2 = tmp1 + tmp2
    z3 = tmp0 + tmp2; z4 = tmp1 + tmp3
    z5 = (z3 + z4) * FIX_1_175875602

    tmp0 = tmp0 * FIX_0_298631336
    tmp1 = tmp1 * FIX_2_053119869
    tmp2 = tmp2 * FIX_3_072711026
    tmp3 = tmp3 * FIX_1_501321110
    z1 = z1 * -FIX_0_899976223
    z2 = z2 * -FIX_2_562915447
    z3 = z3 * -FIX_1_961570560 + z5
    z4 = z4 * -FIX_0_390180644 + z5

    tmp0 += z1 + z3; tmp1 += z2 + z4
    tmp2 += z2 + z3; tmp3 += z1 + z4

    data[i]   = (tmp10 + tmp3 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+7] = (tmp10 - tmp3 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+1] = (tmp11 + tmp2 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+6] = (tmp11 - tmp2 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+2] = (tmp12 + tmp1 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+5] = (tmp12 - tmp1 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+3] = (tmp13 + tmp0 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
    data[i+4] = (tmp13 - tmp0 + (1 << (CB_P_P1_P3 - 1))) >> CB_P_P1_P3
  end

  data
end