Japanese Encoding Conversion Background
In JIS X 0208 a 94 by 94 map (kuten (区点)) is defined to encode Chinese characters (kanji), phonetic moras (kana) and other symbols. Along with this standard there are 3 different encodings that maintain 1-1 correspondences with the map, namely JIS, Shift_JIS and EUC. These encodings take 2 bytes for each character in the kuten map. The mappings are different that random characters may occur (mojibake) if the wrong encoding is used.
Conversion Algorithm
In the formulae below, kuten is an ordered pair of numbers \$(区,点)\$ where \$1\le 区,点\le94\$, and \$(a,b)\$ is an ordered pair of bytes where \$0\le a,b\le 255\$. The conversions between kuten and the 3 encodings are as follows:
$$\text{JIS}: (a,b)=(32+区,32+点)$$
$$\text{Shift_JIS}: (a,b)=\begin{cases}
\left(128+\left\lceil\frac{区}{2}\right\rceil+64\left\lfloor\frac{区}{63}\right\rfloor,63+点+\left\lfloor\frac{点}{64}\right\rfloor\right)&amp;\text{if }区\text{ is odd}\\
\left(128+\left\lceil\frac{区}{2}\right\rceil+64\left\lfloor\frac{区}{63}\right\rfloor,158+点\right)&amp;\text{if }区\text{ is even}
\end{cases}$$
$$\text{EUC}: (a,b)=(160+区,160+点)$$
Challenge
Write a program or function that, given a byte pair, the source encoding and the destination encoding, converts the byte pair from the source encoding to the destination encoding and outputs the result. You may assume that the input byte pair represents a valid codepoint in the source encoding.
The input and output formats are flexible and are accepted if reasonable. For example, you may receive or output the byte pair as a list, as two numbers or as a number, either in decimal or hexadecimal; you may also assign a number to each of the possible encodings and use them as the input format of the encodings.
Sample IO
The format used in the samples is SrcCodePoint, SrcEncoding, DstEncoding -&gt; DstCodePoint. Decimal is used here but hexadecimal is also acceptable. The Unicode character and its assigned kuten are for explanation.
(227, 129), Shift_JIS, EUC -&gt; (229, 225) (Kuten: 69-65; U+7E3A 縺)
(101, 98), JIS, Shift_JIS  -&gt; (227, 130) (Kuten: 69-66; U+7E67 繧)
(229, 227), EUC, JIS       -&gt; (101, 99)  (Kuten: 69-67; U+7E5D 繝)
(137, 126), Shift_JIS, JIS -&gt; (49, 95)   (Kuten: 17-63; U+5186 円)
(177, 224), EUC, Shift_JIS -&gt; (137, 128) (Kuten: 17-64; U+5712 園)
(49, 97), JIS, EUC         -&gt; (177, 225) (Kuten: 17-65; U+5830 堰)

See here (in Japanese) for the full table.
Winning condition
This is a code-golf challenge, so the shortest valid submission for each language wins. Standard loopholes are forbidden by default.
Ruby, 140 116 bytes

Takes code point as an array, and encodings are JIS, Shift_JIS, and EUC-JP, respectively.

Ruby supports converting between EUC-JP and SHIFT_JIS, so we math JIS encoding into EUC, perform the appropriate conversion, then math back the JIS encoding if that's the destination encoding.

-34 bytes by getting permission to take EUC input as EUC-JP.



-&gt;c,s,d{(c.map!{|e|e+=128};s="EUCJP")if s=~r=/^J/
c.pack('c*').encode(d[r]?"EUCJP":d,s).bytes.map{|e|e-=d[r]?128:0}}


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Explanation

-&gt;c,s,d{                                            # Function that takes 3 parameters
        (                           )if s=~r=/^J/   # If s is JIS: (starts with J)
                                                    #  (also store this regex for later)
         c.map!{|e|e+=128};                         # Add 128 to each codepoint
                           s="EUCJP"                # Change s to EUC-JP locale
  c.pack('c*')                                      # Pack codepoints into bytestring
    .encode(                                        # Encode the bytestring as follows:
                                                    #  Destination encoding is:
      d[r]?"EUCJP":d,                               #   If d is JIS, use EUC-JP instead
      s                                             #  Source encoding
    )
    .bytes                                          # Convert to bytes
    .map{|e|e-=d[r]?128:0}                          # If d is JIS, subtract 128
}


Pure Math Version, 164 162 bytes

Takes code points separately, and the encodings are integers: 0=JIS, 1=SHIFT_JIS, 2=EUC.

-2 bytes from Jonathan Allen.

-&gt;a,b,s,d,e=160{k,t=[[a-32,b-32],[a*2-1+b/158-(2+a/222)*128,b-63-b/128-b/158*94],[a-e,b-e]][s]
[[k+32,t+32],[128+k/2+k%2+k/63*64,158+t+t/64-k%2*95],[k+e,t+e]][d]}


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