Expression 16: "M" left parenthesis, "a" , "b" , right parenthesis equals "F" left parenthesis, "a" "b" , right parenthesisMa,b=Fab
16
Expression 17: "M" left parenthesis, floor left parenthesis, "x" , right parenthesis , "B" , right parenthesis "I" left parenthesis, "x" , right parenthesisMfloorx,BIx
17
standard method
Hide this folder from students.
18
Expression 19: "M" Subscript, 1 , Baseline left parenthesis, "a" , "b" , right parenthesis equals floor left parenthesis, StartFraction, "F" left parenthesis, left parenthesis, "a" plus "b" , right parenthesis squared minus left parenthesis, "a" squared plus "b" squared , right parenthesis , right parenthesis Over 2 , EndFraction , right parenthesisM1a,b=floorFa+b2−a2+b22
19
Expression 20: "M" Subscript, 1 , Baseline left parenthesis, floor left parenthesis, "x" , right parenthesis , "B" , right parenthesis "I" left parenthesis, "x" , right parenthesisM1floorx,BIx
20
fancy method
Hide this folder from students.
21
quotient when divided by √(N/4) (bit shift and mask much simpler)
22
Expression 23: "Q" left parenthesis, "x" , right parenthesis equals floor left parenthesis, StartFraction, "x" Over StartRoot, StartNestedFraction, "N" NestedOver 4 , EndNestedFraction , EndRoot , EndFraction , right parenthesis plus left brace, "x" less than 0 : StartRoot, 4 "N" , EndRoot , 0 , right braceQx=floorxN4+x<0:4N,0
23
Expression 24: "Q" left parenthesis, floor left parenthesis, "x" , right parenthesis , right parenthesis "I" left parenthesis, "x" , right parenthesisQfloorxIx
24
remainder when divided by √(N/4) (bit mask much simpler)
25
Expression 26: "R" left parenthesis, "x" , right parenthesis equals "T" left parenthesis, "x" plus left brace, "x" less than 0 : StartFraction, "N" Over 2 , EndFraction , 0 , right brace , StartRoot, StartFraction, "N" Over 4 , EndFraction , EndRoot , right parenthesisRx=Tx+x<0:N2,0,N4
26
Expression 27: "R" left parenthesis, floor left parenthesis, "x" , right parenthesis , right parenthesis "I" left parenthesis, "x" , right parenthesisRfloorxIx
27
Expression 28: "M" Subscript, 2 , Baseline left parenthesis, "a" , "b" , right parenthesis equals "F" left parenthesis, "Q" left parenthesis, "a" , right parenthesis "Q" left parenthesis, "b" , right parenthesis StartFraction, "N" Over 4 , EndFraction plus left parenthesis, "M" Subscript, 1 , Baseline left parenthesis, "Q" left parenthesis, "a" , right parenthesis , "R" left parenthesis, "b" , right parenthesis , right parenthesis plus "M" Subscript, 1 , Baseline left parenthesis, "Q" left parenthesis, "b" , right parenthesis , "R" left parenthesis, "a" , right parenthesis , right parenthesis , right parenthesis StartRoot, StartFraction, "N" Over 4 , EndFraction , EndRoot plus "M" Subscript, 1 , Baseline left parenthesis, "R" left parenthesis, "a" , right parenthesis , "R" left parenthesis, "b" , right parenthesis , right parenthesis , right parenthesisM2a,b=FQaQbN4+M1Qa,Rb+M1Qb,RaN4+M1Ra,Rb
28
Expression 29: "M" Subscript, 2 , Baseline left parenthesis, floor left parenthesis, "x" , right parenthesis , "B" , right parenthesis "I" left parenthesis, "x" , right parenthesisM2floorx,BIx