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dericedmichaelni
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consistant math escaping
remove unneeded escapes for underscores within $$-quotes reduce tripe escapes to double escapes for literal underscores in $$-quotes Github: Closes #213
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ffv1.md

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@@ -274,7 +274,7 @@ The FFV1 bitstream contains one or more Quantization Table Sets. Each Quantizati
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SVGI:!---
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SVGI:![svg](quantizationtablesets.svg "quantization table sets")
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SVGI:!---
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SVGC:quantizationtablesets.svg=Q_{j}[k]=quant\\\_tables[i][j][k\\&255]
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SVGC:quantizationtablesets.svg=$$Q_{j}[k]=quant\\_tables[i][j][k\\&255]$$
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AART:Q_{j}[k] = quant_tables[i][j][k&255]
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In this formula, `i` is the Quantization Table Set index, `j` is the Quantized Table index, `k` the Quantized Sample Difference.
@@ -373,7 +373,7 @@ Instead of coding the n+1 bits of the Sample Difference with Huffman or Range co
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SVGI:!---
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SVGI:![svg](samplediff.svg "coding of the sample difference")
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SVGI:!---
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SVGC:samplediff.svg=$$coder\\\_input=[(sample\\\_difference+2^{bits-1})\\&(2^{bits}-1)]-2^{bits-1}$$
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SVGC:samplediff.svg=$$coder\\_input=[(sample\\_difference+2^{bits-1})\\&(2^{bits}-1)]-2^{bits-1}$$
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AART:coder_input = [(sample_difference + 2 ^ (bits - 1)) &
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AART: (2 ^ bits - 1)] - 2 ^ (bits - 1)
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Figure: Description of the coding of the Sample Difference in the bitstream. {#figureSampleDifference}
@@ -389,13 +389,13 @@ To encode binary digits efficiently a Range coder is used. `C(i)` is the i-th Co
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SVGI:!---
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SVGI:![svg](rangebinaryvalues1.svg "range binary values 1")
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SVGI:!---
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SVGC:rangebinaryvalues1.svg=$$r\_{i}=\\\\lfloor\\\\frac{R_{i}S_{i,C_{i}}}{2^{8}}\\\\rfloor$$
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SVGC:rangebinaryvalues1.svg=$$r_{i}=\\\\lfloor\\\\frac{R_{i}S_{i,C_{i}}}{2^{8}}\\\\rfloor$$
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AART:r_{i} = floor( ( R_{i} * S_{i,C_{i}} ) / 2 ^ 8 )
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SVGI:!---
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SVGI:![svg](rangebinaryvalues2.svg "range binary values 2")
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SVGI:!---
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SVGC:rangebinaryvalues2.svg=$$\\\\begin{array}{ccccccccc} S\_{i+1,C\_{i}}=zero\\_state\_{S\_{i,C\_{i}}} & \\\\wedge & l{}\_{i}=L\_{i} & \\\\wedge & t\_{i}=R\_{i}-r\_{i} & \\\\Longleftarrow & b\_{i}=0 & \\\\Longleftrightarrow & L\_{i}<R\_{i}-r\_{i} \\\\\\ S\_{i+1,C\_{i}}=one\_state\_{S\_{i,C\_{i}}} & \\\\wedge & l\_{i}=L\_{i}-R\_{i}+r\_{i} & \\\\wedge & t\_{i}=r\_{i} & \\\\Longleftarrow & b\_{i}=1 & \\\\Longleftrightarrow & L\_{i}\\\\geq R\_{i}-r\_{i} \\\\end{array}$$
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SVGC:rangebinaryvalues2.svg=$$\\\\begin{array}{ccccccccc} S_{i+1,C_{i}}=zero\\_state_{S_{i,C_{i}}} & \\\\wedge & l_{i}=L_{i} & \\\\wedge & t_{i}=R_{i}-r_{i} & \\\\Longleftarrow & b_{i}=0 & \\\\Longleftrightarrow & L_{i}<R_{i}-r_{i} \\\\\\ S_{i+1,C_{i}}=one\\_state_{S_{i,C_{i}}} & \\\\wedge & l_{i}=L_{i}-R_{i}+r_{i} & \\\\wedge & t_{i}=r_{i} & \\\\Longleftarrow & b_{i}=1 & \\\\Longleftrightarrow & L_{i}\\\\geq R_{i}-r_{i} \\\\end{array}$$
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AART:S_{i+1,C_{i}} = zero_state_{S_{i,C_{i}}} AND
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AART: l_i = L_i AND
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AART: t_i = R_i - r_i <==
@@ -411,13 +411,13 @@ AART: L_i >= R_i - r_i
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SVGI:!---
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SVGI:![svg](rangebinaryvalues3.svg "range binary values 3")
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SVGI:!---
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SVGC:rangebinaryvalues3.svg=$$\\\\begin{array}{ccc}S\_{i+1,k}=S\_{i,k} & \\\\Longleftarrow & C\_{i} \\\\neq k\\\\end{array}$$
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SVGC:rangebinaryvalues3.svg=$$\\\\begin{array}{ccc}S_{i+1,k}=S_{i,k} & \\\\Longleftarrow & C_{i} \\\\neq k\\\\end{array}$$
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AART:S_{i+1,k} = S_{i,k} <== C_i != k
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SVGI:!---
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SVGI:![svg](rangebinaryvalues4.svg "range binary values 4")
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SVGI:!---
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SVGC:rangebinaryvalues4.svg=$$\\\\begin{array}{ccccccc} R\_{i+1}=2^{8}t\_{i} & \\\\wedge & L\_{i+1}=2^{8}l\_{i}+B\_{j\_{i}} & \\\\wedge & j\_{i+1}=j\_{i}+1 & \\\\Longleftarrow & t\_{i}<2^{8}\\\\\\ R\_{i+1}=t\_{i} & \\\\wedge & L\_{i+1}=l\_{i} & \\\\wedge & j\_{i+1}=j\_{i} & \\\\Longleftarrow & t\_{i}\\\\geq2^{8}\\\\end{array}$$
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SVGC:rangebinaryvalues4.svg=$$\\\\begin{array}{ccccccc} R_{i+1}=2^{8}t_{i} & \\\\wedge & L_{i+1}=2^{8}l_{i}+B_{j_{i}} & \\\\wedge & j_{i+1}=j_{i}+1 & \\\\Longleftarrow & t_{i}<2^{8}\\\\\\ R_{i+1}=t_{i} & \\\\wedge & L_{i+1}=l_{i} & \\\\wedge & j_{i+1}=j_{i} & \\\\Longleftarrow & t_{i}\\\\geq2^{8}\\\\end{array}$$
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AART:R_{i+1} = 2 ^ 8 * t_{i} AND
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AART:L_{i+1} = 2 ^ 8 * l_{i} + B_{j_{i}} AND
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AART:j_{i+1} = j_{i} + 1 <==
@@ -509,14 +509,14 @@ At keyframes all Range coder state variables are set to their initial state.
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SVGI:!---
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SVGI:![svg](statetransitiontable1.svg "state transition table 1")
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SVGI:!---
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SVGC:statetransitiontable1.svg=$$one\\\_state\_{i}=default\\\_state\\\_transition\_{i}+state\\\_transition\\\_delta\_{i}$$
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SVGC:statetransitiontable1.svg=$$one\\_state_{i}=default\\_state\\_transition_{i}+state\\_transition\\_delta_{i}$$
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AART:one_state_{i} =
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AART: default_state_transition_{i} + state_transition_delta_{i}
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SVGI:!---
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SVGI:![svg](statetransitiontable2.svg "state transition table 2")
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SVGI:!---
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SVGC:statetransitiontable2.svg=$$zero\\\_state\_{i}=256-one\\\_state\_{256-i}$$
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SVGC:statetransitiontable2.svg=$$zero\\_state_{i}=256-one\\_state_{256-i}$$
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AART:zero_state_{i} = 256 - one_state_{256-i}
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#### default\_state\_transition
@@ -1080,7 +1080,7 @@ Inferred to be 0 if not present.
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SVGI:!---
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SVGI:![svg](initialstatedelta1.svg "initial state delta 1")
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SVGI:!---
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SVGC:initialstatedelta1.svg=$$pred = j ? initial\\_states[ i ][j - 1][ k ] : 128$$
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SVGC:initialstatedelta1.svg=pred = j ? initial\_states[ i ][j - 1][ k ] : 128
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AART:pred = j ? initial_states[ i ][j - 1][ k ] : 128
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SVGI:!---

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