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N = 16 FFT module

Module by: Howard Johnson, C. Sidney Burrus. E-mail the authors

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Summary: A very efficient length N = 16 FFT module that can be use alone or with the PFA or the WFTA.

N=16 FFT module

A FORTRAN implementation of a length-16 FFT module to be used in a Prime Factor Algorithm program.

C
C-------------------WFTA N=16----------------------------
C
  116   R1 = X(I(1)) + X(I(9))
    R2 = X(I(1)) - X(I(9))
    S1 = Y(I(1)) + Y(I(9))
    S2 = Y(I(1)) - Y(I(9))
    R3 = X(I(2)) + X(I(10))
    R4 = X(I(2)) - X(I(10))
    S3 = Y(I(2)) + Y(I(10))
    S4 = Y(I(2)) - Y(I(10))
    R5 = X(I(3)) + X(I(11))
    R6 = X(I(3)) - X(I(11))
    S5 = Y(I(3)) + Y(I(11))
    S6 = Y(I(3)) - Y(I(11))
    R7 = X(I(4)) + X(I(12))
    R8 = X(I(4)) - X(I(12))
    S7 = Y(I(4)) + Y(I(12))
    S8 = Y(I(4)) - Y(I(12))
    R9 = X(I(5)) + X(I(13))
    R10= X(I(5)) - X(I(13))
    S9 = Y(I(5)) + Y(I(13))
    S10= Y(I(5)) - Y(I(13))
    R11 = X(I(6)) + X(I(14))
    R12 = X(I(6)) - X(I(14))
    S11 = Y(I(6)) + Y(I(14))
    S12 = Y(I(6)) - Y(I(14))
    R13 = X(I(7)) + X(I(15))
    R14 = X(I(7)) - X(I(15))
    S13 = Y(I(7)) + Y(I(15))
    S14 = Y(I(7)) - Y(I(15))
    R15 = X(I(8)) + X(I(16))
    R16 = X(I(8)) - X(I(16))
    S15 = Y(I(8)) + Y(I(16))
    S16 = Y(I(8)) - Y(I(16))
    T1 = R1 + R9
    T2 = R1 - R9
    U1 = S1 + S9
    U2 = S1 - S9
    T3 = R3 + R11
    T4 = R3 - R11
    U3 = S3 + S11
    U4 = S3 - S11
    T5 = R5 + R13
    T6 = R5 - R13
    U5 = S5 + S13
    U6 = S5 - S13
    T7 = R7 + R15
    T8 = R7 - R15
    U7 = S7 + S15
    U8 = S7 - S15
    T9 = C81 * (T4 + T8)
    T10= C81 * (T4 - T8)
    U9 = C81 * (U4 + U8)
    U10= C81 * (U4 - U8)
    R1 = T1 + T5
    R3 = T1 - T5
    S1 = U1 + U5
    S3 = U1 - U5
    R5 = T3 + T7
    R7 = T3 - T7
    S5 = U3 + U7
    S7 = U3 - U7
    R9 = T2 + T10
    R11= T2 - T10
    S9 = U2 + U10
    S11= U2 - U10
    R13 = T6 + T9
    R15 = T6 - T9
    S13 = U6 + U9
    S15 = U6 - U9
    T1 = R4 + R16
    T2 = R4 - R16
    U1 = S4 + S16
    U2 = S4 - S16
    T3 = C81 * (R6 + R14)
    T4 = C81 * (R6 - R14)
    U3 = C81 * (S6 + S14)
    U4 = C81 * (S6 - S14)
    T5 = R8 + R12
    T6 = R8 - R12
    U5 = S8 + S12
    U6 = S8 - S12
    T7 = C162 * (T2 - T6)
    T8 = C163 * T2 - T7
    T9 = C164 * T6 - T7
    T10 = R2 + T4
    T11 = R2 - T4
    R2 = T10 + T8
    R4 = T10 - T8
    R6 = T11 + T9
    R8 = T11 - T9
    U7 = C162 * (U2 - U6)
    U8 = C163 * U2 - U7
    U9 = C164 * U6 - U7
    U10 = S2 + U4
    U11 = S2 - U4
    S2 = U10 + U8
    S4 = U10 - U8
    S6 = U11 + U9
    S8 = U11 - U9
    T7 = C165 * (T1 + T5)
    T8 = T7 - C164 * T1
    T9 = T7 - C163 * T5
    T10 = R10 + T3
    T11 = R10 - T3
    R10 = T10 + T8
    R12 = T10 - T8
    R14 = T11 + T9
    R16 = T11 - T9
    U7 = C165 * (U1 + U5)
    U8 = U7 - C164 * U1
    U9 = U7 - C163 * U5
    U10 = S10 + U3
    U11 = S10 - U3
    S10 = U10 + U8
    S12 = U10 - U8
    S14 = U11 + U9
    S16 = U11 - U9
C
    X(I( 1)) = R1 + R5
    X(I( 9)) = R1 - R5
    Y(I( 1)) = S1 + S5
    Y(I( 9)) = S1 - S5
    X(I( 2)) = R2 + S10
    X(I(16)) = R2 - S10
    Y(I( 2)) = S2 - R10
    Y(I(16)) = S2 + R10
    X(I( 3)) = R9 + S13
    X(I(15)) = R9 - S13
    Y(I( 3)) = S9 - R13
    Y(I(15)) = S9 + R13
    X(I( 4)) = R8 - S16
    X(I(14)) = R8 + S16
    Y(I( 4)) = S8 + R16
    Y(I(14)) = S8 - R16
    X(I( 5)) = R3 + S7
    X(I(13)) = R3 - S7
    Y(I( 5)) = S3 - R7
    Y(I(13)) = S3 + R7
    X(I( 6)) = R6 + S14
    X(I(12)) = R6 - S14
    Y(I( 6)) = S6 - R14
    Y(I(12)) = S6 + R14
    X(I( 7)) = R11 - S15
    X(I(11)) = R11 + S15
    Y(I( 7)) = S11 + R15
    Y(I(11)) = S11 - R15
    X(I( 8)) = R4 - S12
    X(I(10)) = R4 + S12
    Y(I( 8)) = S4 + R12
    Y(I(10)) = S4 - R12
C
    GOTO 20
C
 
Figure. Length-16 FFT Module

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