zkevm-docs/8-arithmetic.markdown

@@ -71,6 +71,7 @@ operand* 用来存放算术中的参数值，如 a+b=c+overflow 指令中的 a,b
   - c hi + carry hi \* 2^128 = a hi + b hi + carry lo
 
 - Sub_Lt_Gt (a+b=c+overflow\*2^256) (可以使用 select struct)
+
   - 如果是 0 行，则 cnt_prev=1,cnt_prev_prev=0
   - carry hi is bool
   - carry lo is bool
@@ -79,8 +80,38 @@ operand* 用来存放算术中的参数值，如 a+b=c+overflow 指令中的 a,b
   - if tag is sub 有 c_lo = u16 sum(rotation cur),c_hi = u16 sum(rotation prev) and carry_hi iszero
   - if tag is lt 则有 carry_hi iszero
   - if tag is gt 则有 carry_hi 1
-- Div_Mod
-- Mul
+
+- Div_Mod (a\*b+c=d 同时约束 c 小于 b)
+
+  - define t_lo=operand3_0*operand1_0+(operand3_0*operand1_1+operand3_1*operand1_0)*2^64
+  - define t_hi=(operand3_0*operand1_2+operand3_1*operand1_1+operand3_2*operand1_0)+(operand3_0*operand1_3+operand3_1*operand1_2+operand3_2*operand1_1+operand3_3*operand1_0)*2^64
+  - 如果是 0 行，约束 num_row is 8,并且约束 cnt 自增的有效性
+  - a_lo = u16 sum(rotation cur)
+  - a_hi = u16 sum(rotation -1)
+  - b_lo = u16 sum(rotation -2)
+  - b_hi = u16 sum(rotation -3)
+  - c_lo = u16 sum(rotation -4)
+  - c_hi = u16 sum(rotation -5)
+  - d_lo = u16 sum(rotation -6)
+  - d_hi = u16 sum(rotation -7)
+  - (t_lo+operand2_3+operand2_2*2^64-car_lo*2^128) - (operand0_3+operand0_2\*2^64)
+  - (t_hi+operand2_0+operand2_1*2^64+car_lo-car_hi*2^128) - (operand0_1+operand0_0\*2^64)
+  - 约束 c lt d
+
+- Mul(需要 6 行对 a,b,c lookup ) 其中 operand0 是 a,operand1 是 b
+
+  - define t_lo=operand0_0*operand1_0+(operand0_0*operand1_1+operand0_1*operand1_0)*2^64
+  - define t_hi=(operand0_0*operand1_2+operand0_1*operand1_1+operand0_2*operand1_0)+(operand0_0*operand1_3+operand0_1*operand1_2+operand0_2*operand1_1+operand0_3*operand1_0)*2^64
+  - 如果是 0 行，约束 num_row is 6,并且约束 cnt 自增的有效性
+  - a_lo = u16 sum(rotation cur)
+  - a_hi = u16 sum(rotation -1)
+  - b_lo = u16 sum(rotation -2)
+  - b_hi = u16 sum(rotation -3)
+  - c_lo = u16 sum(rotation -4)
+  - c_hi = u16 sum(rotation -5)
+  - （t_lo-car_lo*2^128） -（operand2_3+operand2_2*2^64）
+  - （t_hi+car_lo-car_hi*2^128）- （operand2_1+operand2_0*2^64）
+
 - Slt_Sgt
 - Sdiv_Smod
 - Addmod