mirror of https://github.com/zcash/halo2.git
Split choice table into two tables
This commit is contained in:
therealyingtong
parent
67c4790ce6
commit
c920bdf9a6
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@ -349,24 +349,27 @@ Input from previous operations:
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- $evens$ is defined as $\mathtt{spread}(2^{32} - 1)$
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- $evens$ is defined as $\mathtt{spread}(2^{32} - 1)$
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- $evens_0 = evens_1 = \mathtt{spread}(2^{16} - 1)$
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- $evens_0 = evens_1 = \mathtt{spread}(2^{16} - 1)$
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s_neg|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ |
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#### E ∧ F
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-----|----|-------------|-------------|-----------------------------|------------------------------------|------------------------------------|
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|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ |
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0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$ |$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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|----|-------------|-------------|-----------------------------|------------------------------------|------------------------------------|
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0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ |$\texttt{spread}(P_1^{odd})$ | |
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|0 |{0,1,2,3,4,5}|$P_0^{even}$ |$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$ |$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ |
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|1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ |$\texttt{spread}(P_1^{odd})$ | |
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0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | $evens_0$ | $evens_1$ |
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|0 |{0,1,2,3,4,5}|$P_1^{even}$ |$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ |
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1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$ |$\texttt{spread}(Q_0^{even})$|$\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ |
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|0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | |
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0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E^{lo})$ |$evens_1 - \mathtt{spread}(E^{hi})$ |
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0 | 1 |{0,1,2,3,4,5}|$Q_1^{even}$ |$\texttt{spread}(Q_1^{even})$|$\texttt{spread}(Q_1^{odd})$ | |
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#### ¬E ∧ G
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0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ |$\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ |
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s_ch_neg| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ |
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--------|-------------|-------------|-----------------------------|------------------------------------|------------------------------------|------------------------------------|
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0 |{0,1,2,3,4,5}|$Q_0^{even}$ |$\texttt{spread}(Q_0^{even})$|$\mathtt{spread}(E_{neg}^{lo})$ | $\mathtt{spread}(E_{neg}^{hi})$ | $\mathtt{spread}(E^{lo})$ |
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1 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$\texttt{spread}(Q_1^{odd})$ | | $\mathtt{spread}(E^{hi})$ |
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0 |{0,1,2,3,4,5}|$Q_1^{even}$ |$\texttt{spread}(Q_1^{even})$|$\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | |
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0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | | | |
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Constraints:
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Constraints:
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- `s_ch` (choice): $LHS - RHS = 0$
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- `s_ch` (choice): $LHS - RHS = 0$
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- $LHS = a_3 \omega^{-1} + a_3 \omega + 2^{32}(a_4 \omega^{-1} + a_4 \omega)$
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- $LHS = a_3 \omega^{-1} + a_3 \omega + 2^{32}(a_4 \omega^{-1} + a_4 \omega)$
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- $RHS = a_2 \omega^{-1} + 2* a_2 + 2^{32}(a_2 \omega + 2* a_3)$
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- $RHS = a_2 \omega^{-1} + 2* a_2 + 2^{32}(a_2 \omega + 2* a_3)$
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- `s_neg` (negation):
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- `s_ch_neg` (negation): `s_ch` with an extra negation check
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- $a_3\omega^{-1} - a_3 - a_3\omega = 0$
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- $a_4\omega^{-1} - a_4 - a_4\omega = 0$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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- $\mathtt{spread}$ lookup on $(a_0, a_1, a_2)$
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- permutation between $(a_2, a_3)$
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- permutation between $(a_2, a_3)$
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@ -823,37 +826,37 @@ Constraints:
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#### Initial round:
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#### Initial round:
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sd_abcd|sd_efgh|ss0|ss1|s_maj|s_neg|s_ch| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ |
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sd_abcd|sd_efgh|ss0|ss1|s_maj|s_ch_neg|s_ch|s_a_new |s_e_new |s_h_prime| $a_0$ | $a_1$ | $a_2$ | $a_3$ | $a_4$ | $a_5$ | $a_6$ | $a_7$ | $a_8$ | $a_9$ |
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-------|-------|---|---|-----|-----|----|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|
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-------|-------|---|---|-----|--------|----|--------|--------|---------|-------------|------------|-----------------------------|-------------------------------------|-------------------------------------|----------------------------------------|------------------------------------|------------------------------------|------------------------------------|------------------------------------|
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0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(E_0 d(7)) $ | $E_0 b(5)^{lo}$ | $\texttt{spread}(E_0 b(5)^{lo})$ | $E_0 b(5)^{hi}$ | $\texttt{spread}(E_0 b(5)^{hi}) $ | $E_0^{lo}$ | $\mathtt{spread}(E_0^{lo})$ | |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(E_0 d(7)) $ | $E_0 b(5)^{lo}$ | $\texttt{spread}(E_0 b(5)^{lo})$ | $E_0 b(5)^{hi}$ | $\texttt{spread}(E_0 b(5)^{hi}) $ | $E_0^{lo}$ | $\mathtt{spread}(E_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$E_0 c(14)$ |$\texttt{spread}(E_0 c(14))$ | $E_0 a(6)^{lo}$ | $\texttt{spread}(E_0 a(6)^{lo})$ | $E_0 a(6)^{hi}$ | $\texttt{spread}(E_0 a(6)^{hi}) $ | $E_0^{hi}$ | $\mathtt{spread}(E_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$E_0 c(14)$ |$\texttt{spread}(E_0 c(14))$ | $E_0 a(6)^{lo}$ | $\texttt{spread}(E_0 a(6)^{lo})$ | $E_0 a(6)^{hi}$ | $\texttt{spread}(E_0 a(6)^{hi}) $ | $E_0^{hi}$ | $\mathtt{spread}(E_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(E_0 b(5)^{lo})$ | $\texttt{spread}(E_0 b(5)^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(E_0 b(5)^{lo})$ | $\texttt{spread}(E_0 b(5)^{hi})$ | | | | | |
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0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | |
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0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(E_0 d(7))$ | $\texttt{spread}(E_0 c(14))$ | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(E_0 a(6)^{lo})$ | $\texttt{spread}(E_0 a(6)^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(E_0 a(6)^{lo})$ | $\texttt{spread}(E_0 a(6)^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(F_0 d(7)) $ | $F_0 b(5)^{lo}$ | $\texttt{spread}(F_0 b(5)^{lo})$ | $F_0 b(5)^{hi}$ | $\texttt{spread}(F_0 b(5)^{hi}) $ | $F_0^{lo}$ | $\mathtt{spread}(F_0^{lo})$ | |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$F_0 d(7)$ |$\texttt{spread}(F_0 d(7)) $ | $F_0 b(5)^{lo}$ | $\texttt{spread}(F_0 b(5)^{lo})$ | $F_0 b(5)^{hi}$ | $\texttt{spread}(F_0 b(5)^{hi}) $ | $F_0^{lo}$ | $\mathtt{spread}(F_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$F_0 c(14)$ |$\texttt{spread}(F_0 c(14))$ | $F_0 a(6)^{lo}$ | $\texttt{spread}(F_0 a(6)^{lo})$ | $F_0 a(6)^{hi}$ | $\texttt{spread}(F_0 a(6)^{hi}) $ | $F_0^{hi}$ | $\mathtt{spread}(F_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$F_0 c(14)$ |$\texttt{spread}(F_0 c(14))$ | $F_0 a(6)^{lo}$ | $\texttt{spread}(F_0 a(6)^{lo})$ | $F_0 a(6)^{hi}$ | $\texttt{spread}(F_0 a(6)^{hi}) $ | $F_0^{hi}$ | $\mathtt{spread}(F_0^{hi})$ | |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$G_0 d(7)$ |$\texttt{spread}(G_0 d(7)) $ | $G_0 b(5)^{lo}$ | $\texttt{spread}(G_0 b(5)^{lo})$ | $G_0 b(5)^{hi}$ | $\texttt{spread}(G_0 b(5)^{hi}) $ | $G_0^{lo}$ | $\mathtt{spread}(G_0^{lo})$ | |
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0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$G_0 d(7)$ |$\texttt{spread}(G_0 d(7)) $ | $G_0 b(5)^{lo}$ | $\texttt{spread}(G_0 b(5)^{lo})$ | $G_0 b(5)^{hi}$ | $\texttt{spread}(G_0 b(5)^{hi}) $ | $G_0^{lo}$ | $\mathtt{spread}(G_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$G_0 c(14)$ |$\texttt{spread}(G_0 c(14))$ | $G_0 a(6)^{lo}$ | $\texttt{spread}(G_0 a(6)^{lo})$ | $G_0 a(6)^{hi}$ | $\texttt{spread}(G_0 a(6)^{hi}) $ | $G_0^{hi}$ | $\mathtt{spread}(G_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$G_0 c(14)$ |$\texttt{spread}(G_0 c(14))$ | $G_0 a(6)^{lo}$ | $\texttt{spread}(G_0 a(6)^{lo})$ | $G_0 a(6)^{hi}$ | $\texttt{spread}(G_0 a(6)^{hi}) $ | $G_0^{hi}$ | $\mathtt{spread}(G_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | $\texttt{spread}(Q_0^{odd})$ | $K_0^{lo}$ | $H_0^{lo}$ | $\mathtt{spread}(H_0^{lo})$ | $W_0^{lo}$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_0^{even}$|$\texttt{spread}(P_0^{even})$| $\mathtt{spread}(E^{lo})$ | $\mathtt{spread}(E^{hi})$ | $Q_0^{odd}$ | $K_0^{lo}$ | $H_0^{lo}$ | $\mathtt{spread}(H_0^{lo})$ | $W_0^{lo}$ |
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0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $\mathtt{spread}(H_0^{hi})$ | $W_0^{hi}$ |
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0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |{0,1,2,3,4,5}|$P_0^{odd}$ |$\texttt{spread}(P_0^{odd})$ | $\texttt{spread}(P_1^{odd})$ | $\Sigma_1(E_0)^{lo}$ | $\Sigma_1(E_0)^{hi}$ | $K_0^{hi}$ | $H_0^{hi}$ | $\mathtt{spread}(H_0^{hi})$ | $W_0^{hi}$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $\texttt{spread}(Q_1^{odd})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{even}$|$\texttt{spread}(P_1^{even})$| $\mathtt{spread}(F^{lo})$ | $\mathtt{spread}(F^{hi})$ | $Q_1^{odd}$ | $P_1^{odd}$ | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | $Hprime_0 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | $D_0^{lo}$ | $E_1^{lo}$ | $\mathtt{spread}(E_1^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$P_1^{odd}$ |$\texttt{spread}(P_1^{odd})$ | | | | $D_0^{lo}$ | $E_1^{lo}$ | $\mathtt{spread}(E_1^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_0^{lo})$ | $\mathtt{spread}(E_0^{hi})$ | | $D_0^{hi}$ | $E_1^{hi}$ | $\mathtt{spread}(E_1^{hi})$ | $E_1 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |{0,1,2,3,4,5}|$Q_0^{even}$|$\texttt{spread}(Q_0^{even})$| $\mathtt{spread}(E_{neg}^{lo})$ | $\mathtt{spread}(E_{neg}^{hi})$ | $\mathtt{spread}(E^{lo})$ | $D_0^{hi}$ | $E_1^{hi}$ | $\mathtt{spread}(E_1^{hi})$ | $E_1 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ |$evens_0 - \mathtt{spread}(E_0^{lo})$|$evens_1 - \mathtt{spread}(E_0^{hi})$| | | $D_0^{lo}$ | $\mathtt{spread}(D_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_0^{odd}$ |$\texttt{spread}(Q_0^{odd})$ | $\texttt{spread}(Q_1^{odd})$ | | $\mathtt{spread}(E^{hi})$ | | $D_0^{lo}$ | $\mathtt{spread}(D_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 1 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\texttt{spread}(Q_1^{odd})$ | | | | $D_0^{hi}$ | $\mathtt{spread}(D_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{even}$|$\texttt{spread}(Q_1^{even})$| $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | $D_0^{hi}$ | $\mathtt{spread}(D_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | $\mathtt{spread}(G^{lo})$ | $\mathtt{spread}(G^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$Q_1^{odd}$ |$\texttt{spread}(Q_1^{odd})$ | | | | | | | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$A_0 b(11)$ |$\texttt{spread}(A_0 b(11))$ | $A_0 c(9)^{lo}$ | $\texttt{spread}(A_0 c(9)^{lo})$ | $A_0 c(9)^{mid}$ | $\texttt{spread}(A_0 c(9)^{mid})$ | $A_0^{lo}$ | $\mathtt{spread}(A_0^{lo})$ | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$A_0 b(11)$ |$\texttt{spread}(A_0 b(11))$ | $A_0 c(9)^{lo}$ | $\texttt{spread}(A_0 c(9)^{lo})$ | $A_0 c(9)^{mid}$ | $\texttt{spread}(A_0 c(9)^{mid})$ | $A_0^{lo}$ | $\mathtt{spread}(A_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$A_0 d(10)$ |$\texttt{spread}(A_0 d(10))$ | $A_0 a(2)$ | $\texttt{spread}(A_0 a(2))$ | $A_0 c(9)^{hi}$ | $\texttt{spread}(A_0 c(9)^{hi})$ | $A_0^{hi}$ | $\mathtt{spread}(A_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$A_0 d(10)$ |$\texttt{spread}(A_0 d(10))$ | $A_0 a(2)$ | $\texttt{spread}(A_0 a(2))$ | $A_0 c(9)^{hi}$ | $\texttt{spread}(A_0 c(9)^{hi})$ | $A_0^{hi}$ | $\mathtt{spread}(A_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(c(9)^{lo})$ | $\texttt{spread}(c(9)^{mid})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{even}$|$\texttt{spread}(R_0^{even})$| $\texttt{spread}(c(9)^{lo})$ | $\texttt{spread}(c(9)^{mid})$ | | | | | |
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0 | 0 | 0 | 1 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | |
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0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_0^{odd}$ |$\texttt{spread}(R_0^{odd})$ | $\texttt{spread}(R_1^{odd})$ | $\texttt{spread}(d(10))$ | $\texttt{spread}(b(11))$ | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(a(2))$ | $\texttt{spread}(c(9)^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{even}$|$\texttt{spread}(R_1^{even})$| $\texttt{spread}(a(2))$ | $\texttt{spread}(c(9)^{hi})$ | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$R_1^{odd}$ |$\texttt{spread}(R_1^{odd})$ | | | | | | | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$B_0 b(11)$ |$\texttt{spread}(B_0 b(11))$ | $B_0 c(9)^{lo}$ | $\texttt{spread}(B_0 c(9)^{lo})$ | $B_0 c(9)^{mid}$ | $\texttt{spread}(B_0 c(9)^{mid})$ | $B_0^{lo}$ | $\mathtt{spread}(B_0^{lo})$ | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$B_0 b(11)$ |$\texttt{spread}(B_0 b(11))$ | $B_0 c(9)^{lo}$ | $\texttt{spread}(B_0 c(9)^{lo})$ | $B_0 c(9)^{mid}$ | $\texttt{spread}(B_0 c(9)^{mid})$ | $B_0^{lo}$ | $\mathtt{spread}(B_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$B_0 d(10)$ |$\texttt{spread}(B_0 d(10))$ | $B_0 a(2)$ | $\texttt{spread}(B_0 a(2))$ | $B_0 c(9)^{hi}$ | $\texttt{spread}(B_0 c(9)^{hi})$ | $B_0^{hi}$ | $\mathtt{spread}(B_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$B_0 d(10)$ |$\texttt{spread}(B_0 d(10))$ | $B_0 a(2)$ | $\texttt{spread}(B_0 a(2))$ | $B_0 c(9)^{hi}$ | $\texttt{spread}(B_0 c(9)^{hi})$ | $B_0^{hi}$ | $\mathtt{spread}(B_0^{hi})$ | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$C_0 b(11)$ |$\texttt{spread}(C_0 b(11))$ | $C_0 c(9)^{lo}$ | $\texttt{spread}(C_0 c(9)^{lo})$ | $C_0 c(9)^{mid}$ | $\texttt{spread}(C_0 c(9)^{mid})$ | $C_0^{lo}$ | $\mathtt{spread}(C_0^{lo})$ | |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1,2} |$C_0 b(11)$ |$\texttt{spread}(C_0 b(11))$ | $C_0 c(9)^{lo}$ | $\texttt{spread}(C_0 c(9)^{lo})$ | $C_0 c(9)^{mid}$ | $\texttt{spread}(C_0 c(9)^{mid})$ | $C_0^{lo}$ | $\mathtt{spread}(C_0^{lo})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$C_0 d(10)$ |$\texttt{spread}(C_0 d(10))$ | $C_0 a(2)$ | $\texttt{spread}(C_0 a(2))$ | $C_0 c(9)^{hi}$ | $\texttt{spread}(C_0 c(9)^{hi})$ | $C_0^{hi}$ | $\mathtt{spread}(C_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | {0,1} |$C_0 d(10)$ |$\texttt{spread}(C_0 d(10))$ | $C_0 a(2)$ | $\texttt{spread}(C_0 a(2))$ | $C_0 c(9)^{hi}$ | $\texttt{spread}(C_0 c(9)^{hi})$ | $C_0^{hi}$ | $\mathtt{spread}(C_0^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{even}$|$\texttt{spread}(M_0^{even})$| | $\mathtt{spread}(A_0^{lo})$ | $\mathtt{spread}(A_0^{hi})$ | | $Hprime_0^{lo}$ | $Hprime_0^{hi}$ | |
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0 | 0 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | | $\Sigma_0(A_0)^{lo}$ | $A_1^{lo}$ | $\mathtt{spread}(A_1^{lo})$ | $A_1 carry$ |
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0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |{0,1,2,3,4,5}|$M_0^{odd}$ |$\texttt{spread}(M_0^{odd})$ | $\texttt{spread}(M_1^{odd})$ | $\mathtt{spread}(B_0^{lo})$ | $\mathtt{spread}(B_0^{hi})$ | $\Sigma_0(A_0)^{lo}$ | $A_1^{lo}$ | $\mathtt{spread}(A_1^{lo})$ | $A_1 carry$ |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\texttt{spread}(M_1^{odd})$ | $\Sigma_0(A_0)^{hi}$ | $A_1^{hi}$ | $\mathtt{spread}(A_1^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{even}$|$\texttt{spread}(M_1^{even})$| | $\mathtt{spread}(C_0^{lo})$ | $\mathtt{spread}(C_0^{hi})$ | $\Sigma_0(A_0)^{hi}$ | $A_1^{hi}$ | $\mathtt{spread}(A_1^{hi})$ | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | |
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0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |{0,1,2,3,4,5}|$M_1^{odd}$ |$\texttt{spread}(M_1^{odd})$ | | | | | | | |
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Reference in New Issue