hls-softmax-cordic

• ap_fixed<24,8> FW 16 Resolution 2^-16 = 0.0000152587890625 - Data type is used for internal calculations to ensure sufficient precision.

List of Fixed-Point Data Types Used

• ap_fixed<8,7> FW 1 -> Resolution 2^-1 = 0.5

  • Just works for iteration 1
  • Does not work for this implementation because the range is too small for hyperbolic functions.
  • Initially, it does not work with the max reduced value because 0.347 cannot be represented with this data type.
  • It will loss representation in LN(2) and INV_LN2 constants.

• ap_fixed<10,7> FW 3 -> Resolution 2^-3 = 0.125

  • Just works for iterations 1 to 3

• ap_fixed<12,7> FW 5 -> Resolution 2^-5 = 0.03125 - Just works for iterations 1 to 5

• ap_fixed<14,7> FW 7 -> Resolution 2^-7 = 0.0078125 - Just works for iterations 1 to 7

• ap_fixed<16,7> FW 9 -> Resolution 2^-9 = 0.001953125 - Just works for iterations 1 to 9

• ap_fixed<18,7> FW 11 -> Resolution 2^-11 = 0.00048828125 - Just works for iterations 1 to 11

• ap_fixed<20,7> FW 13 -> Resolution 2^-13 = 0.0001220703125 - Just works for iterations 1 to 13

• ap_fixed<24,7> FW 17 -> Resolution 2^-17 = 7.62939453125e-05 - Just works for iterations 1 to 17

CORDIC Hiperbolic Angles Table (atanh(2^-i)):

iterations | Angle (radians) |

1 | 0.5493061443340549 2 | 0.25541281188299536 3 | 0.12565721414045302 4 | 0.06258157147700301 5 | 0.031260178490666998 6 | 0.015626271752052288 7 | 0.0078126589515404865 8 | 0.003906269868396825 9 | 0.001953127483532549 10 | 0.0009765628104410351 11 | 0.00048828128880511277 12 | 0.0002441406298506382 13 | 0.0001220703131063298 14 | 0.0000610351563257915 15 | 0.0000305175781344738 16 | 0.00001525878906131576 17 | 0.00000762939453110197 18 | 0.0000038146972656065

Important Notes for CORDIC Implementation

CORDIC Constants

LN(2) = 0.6931471805599453 INV_LN2 = 1.4426950408889634 MAX_REDUCED = 0.347

Range Expansion