EIP 101: big-int precompile #258
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because A implies B.
gavofyork
reviewed
Mar 14, 2017
| \begin{eqnarray} | ||
| \Xi_{\mathtt{ID}} &\equiv& \Xi_{\mathtt{PRE}} \quad \text{where:} \\ | ||
| g_r &=& 15 + 3\Big\lceil \dfrac{|I_\mathbf{d}|}{32} \Big\rceil\\ | ||
| \mathbf{o} &=& I_\mathbf{d} | ||
| \end{eqnarray} | ||
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| The fifth contract performs arbitrary-precision addition on non-negative integers. | ||
| The first word in the input specifies the number of bytes that the first non-negative integer $X$ occupies. | ||
| The result is represented in the smallest possible number of bytes. The first byte in the output is never zero. |
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...the first byte in the output, if it exists...
gavofyork
reviewed
Mar 14, 2017
| \Xi_{\mathtt{ADD}} &\equiv& \Xi_{\mathtt{PRE}} \quad \text{except:}\\ | ||
| \Xi_{\mathtt{ADD}}(\boldsymbol{\sigma}, g, I) &\equiv& (\varnothing, 0, A^0, ()) \quad \text{if} \quad |I_\mathbf{d}| - 32 < I_\mathbf{d}[0..31] \\ | ||
| g_r &=& G_{addsubbase} + G_{arithword} \Big\lceil \dfrac{|I_\mathbf{d}|}{32} \Big\rceil \\ | ||
| \mathbf{o} &=& (X + Y) \in \mathbb{B}_\ell \\ |
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use BE or something similar to define integer -> bytes.
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- the symbol
\ellis already taken - the number of bits should be
8 \ellnot\ell.
gavofyork
reviewed
Mar 14, 2017
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| \begin{eqnarray} | ||
| \Xi_{\mathtt{ADD}} &\equiv& \Xi_{\mathtt{PRE}} \quad \text{except:}\\ | ||
| \Xi_{\mathtt{ADD}}(\boldsymbol{\sigma}, g, I) &\equiv& (\varnothing, 0, A^0, ()) \quad \text{if} \quad |I_\mathbf{d}| - 32 < I_\mathbf{d}[0..31] \\ |
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formalise conversion bytes -> integer
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- Maybe
I_\mathbf{d}[0..31]can be assigned to a variable. - Or the common parsing logic should be factored out.
gavofyork
reviewed
Mar 14, 2017
| \end{cases} | ||
| \end{eqnarray} | ||
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| The ninth contract performs arbitrary-precision exponentiation under modulo. Here, $0 ^ 0$ is taken to be one. |
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mention how the arguments are encoded here.
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To be reopend on |
pirapira
commented
Mar 14, 2017
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| \begin{eqnarray} | ||
| \Xi_{\mathtt{SUB}} &\equiv& \Xi_{\mathtt{PRE}} \quad \text{except:}\\ | ||
| \Xi_{\mathtt{SUB}}(\boldsymbol{\sigma}, g, I) &\equiv& (\varnothing, 0, A^0, ()) \quad \text{if} \quad |I_\mathbf{d}| - 32 < I_\mathbf{d}[0..31] \\ |
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... if ...; ... if ...should go intobegin{cases} \end{cases}
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If merged, this would solve #235 as part of the Metropolis changes.
Merging this requires the community's consensus on ethereum/EIPs#101