// // File name : fpadd // Title : Floating-Point Adder/Subtractor // project : FPU // Library : fpadd // Author(s) : James E. Stine, Jr., Brett Mathis // Purpose : definition of main unit to floating-point add/sub // notes : // // Copyright Oklahoma State University // Copyright AFRL // // Basic and Denormalized Operations // // Step 1: Load operands, set flags, and convert SP to DP // Step 2: Check for special inputs ( +/- Infinity, NaN) // Step 3: Compare exponents. Swap the operands of exp1 < exp2 // or of (exp1 = exp2 AND mnt1 < mnt2) // Step 4: Shift the mantissa corresponding to the smaller exponent, // and extend precision by three bits to the right. // Step 5: Add or subtract the mantissas. // Step 6: Normalize the result.// // Shift left until normalized. Normalized when the value to the // left of the binrary point is 1. // Step 7: Round the result.// // Step 8: Put sum onto output. // module fpuaddcvt1 (sum, sum_tc, sel_inv, exponent_postsum, corr_sign, op1_Norm, op2_Norm, opA_Norm, opB_Norm, Invalid, DenormIn, convert, swap, normal_overflow, signA, Float1, Float2, exp1_denorm, exp2_denorm, exponent, op1, op2, rm, op_type, Pin); input logic [63:0] op1; // 1st input operand (A) input logic [63:0] op2; // 2nd input operand (B) input logic [2:0] rm; // Rounding mode - specify values input logic [3:0] op_type; // Function opcode input logic Pin; // Result Precision (1 for double, 0 for single) wire P; assign P = ~Pin | op_type[2]; wire [63:0] IntValue; wire [11:0] exp1, exp2; wire [11:0] exp_diff1, exp_diff2; wire [11:0] exp_shift; wire [51:0] mantissaA; wire [56:0] mantissaA1; wire [63:0] mantissaA3; wire [51:0] mantissaB; wire [56:0] mantissaB1, mantissaB2; wire [63:0] mantissaB3; wire exp_gt63; wire Sticky_out; wire sub; wire zeroB; wire [5:0] align_shift; output logic [63:0] Float1; output logic [63:0] Float2; output logic [10:0] exponent; output logic [10:0] exponent_postsum; output logic [11:0] exp1_denorm, exp2_denorm;//KEP used to be [10:0] output logic [63:0] sum, sum_tc; output logic [3:0] sel_inv; output logic corr_sign; output logic signA; output logic op1_Norm, op2_Norm; output logic opA_Norm, opB_Norm; output logic Invalid; output logic DenormIn; // output logic exp_valid; output logic convert; output logic swap; output logic normal_overflow; wire [5:0] ZP_mantissaA; wire [5:0] ZP_mantissaB; wire ZV_mantissaA; wire ZV_mantissaB; // Convert the input operands to their appropriate forms based on // the orignal operands, the op_type , and their precision P. // Single precision inputs are converted to double precision // and the sign of the first operand is set appropratiately based on // if the operation is absolute value or negation. convert_inputs conv1 (Float1, Float2, op1, op2, op_type, P); // Test for exceptions and return the "Invalid Operation" and // "Denormalized" Input Flags. The "sel_inv" is used in // the third pipeline stage to select the result. Also, op1_Norm // and op2_Norm are one if op1 and op2 are not zero or denormalized. // sub is one if the effective operation is subtaction. exception exc1 (sel_inv, Invalid, DenormIn, op1_Norm, op2_Norm, sub, Float1, Float2, op_type); // Perform Exponent Subtraction (used for alignment). For performance // both exponent subtractions are performed in parallel. This was // changed to a behavior level to allow the tools to try to optimize // the two parallel additions. The input values are zero-extended to 12 // bits prior to performing the addition. assign exp1 = {1'b0, Float1[62:52]}; assign exp2 = {1'b0, Float2[62:52]}; assign exp_diff1 = exp1 - exp2; assign exp_diff2 = DenormIn ? ({Float2[63], exp2[10:0]} - {Float1[63], exp1[10:0]}): exp2 - exp1; // The second operand (B) should be set to zero, if op_type does not // specify addition or subtraction assign zeroB = op_type[2] | op_type[1]; // Swapped operands if zeroB is not one and exp1 < exp2. // Swapping causes exp2 to be used for the result exponent. // Only the exponent of the larger operand is used to determine // the final result. assign swap = exp_diff1[11] & ~zeroB; assign exponent = swap ? exp2[10:0] : exp1[10:0]; assign exponent_postsum = swap ? exp2[10:0] : exp1[10:0]; assign mantissaA = swap ? Float2[51:0] : Float1[51:0]; assign mantissaB = swap ? Float1[51:0] : Float2[51:0]; assign signA = swap ? Float2[63] : Float1[63]; // Leading-Zero Detector. Determine the size of the shift needed for // normalization. If sum_corrected is all zeros, the exp_valid is // zero; otherwise, it is one. // modified to 52 bits to detect leading zeroes on denormalized mantissas lz52 lz_norm_1 (ZP_mantissaA, ZV_mantissaA, mantissaA); lz52 lz_norm_2 (ZP_mantissaB, ZV_mantissaB, mantissaB); // Denormalized exponents created by subtracting the leading zeroes from the original exponents assign exp1_denorm = swap ? (exp1 - {6'b0, ZP_mantissaB}) : (exp1 - {6'b0, ZP_mantissaA}); //KEP extended ZP_mantissa assign exp2_denorm = swap ? (exp2 - {6'b0, ZP_mantissaA}) : (exp2 - {6'b0, ZP_mantissaB}); // Determine the alignment shift and limit it to 63. If any bit from // exp_shift[6] to exp_shift[11] is one, then shift is set to all ones. assign exp_shift = swap ? exp_diff2 : exp_diff1; assign exp_gt63 = exp_shift[11] | exp_shift[10] | exp_shift[9] | exp_shift[8] | exp_shift[7] | exp_shift[6]; assign align_shift = exp_shift[5:0] | {6{exp_gt63}}; //KEP used to be all of exp_shift // Unpack the 52-bit mantissas to 57-bit numbers of the form. // 001.M[51]M[50] ... M[1]M[0]00 // Unless the number has an exponent of zero, in which case it // is unpacked as // 000.00 ... 00 // This effectively flushes denormalized values to zero. // The three bits of to the left of the binary point prevent overflow // and loss of sign information. The two bits to the right of the // original mantissa form the "guard" and "round" bits that are used // to round the result. assign opA_Norm = swap ? op2_Norm : op1_Norm; assign opB_Norm = swap ? op1_Norm : op2_Norm; assign mantissaA1 = {2'h0, opA_Norm, mantissaA[51:0]&{52{opA_Norm}}, 2'h0}; assign mantissaB1 = {2'h0, opB_Norm, mantissaB[51:0]&{52{opB_Norm}}, 2'h0}; // Perform mantissa alignment using a 57-bit barrel shifter // If any of the bits shifted out are one, Sticky_out is set. // The size of the barrel shifter could be reduced by two bits // by not adding the leading two zeros until after the shift. barrel_shifter_r57 bs1 (mantissaB2, Sticky_out, mantissaB1, align_shift); // Place either the sign-extened 32-bit value or the original 64-bit value // into IntValue (to be used for integer to floating point conversion) assign IntValue [31:0] = op1[31:0]; assign IntValue [63:32] = op_type[0] ? {32{op1[31]}} : op1[63:32]; // If doing an integer to floating point conversion, mantissaA3 is set to // IntVal and the prenomalized exponent is set to 1084. Otherwise, // mantissaA3 is simply extended to 64-bits by setting the 7 LSBs to zero, // and the exponent value is left unchanged. // Under denormalized cases, the exponent before the rounder is set to 1 // if the normal shift value is 11. assign convert = ~op_type[2] & op_type[1]; assign mantissaA3 = (op_type[3]) ? (op_type[0] ? Float1 : ~Float1) : (DenormIn ? ({12'h0, mantissaA}) : (convert ? IntValue : {mantissaA1, 7'h0})); // Put zero in for mantissaB3, if zeroB is one. Otherwise, B is extended to // 64-bits by setting the 7 LSBs to the Sticky_out bit followed by six // zeros. assign mantissaB3[63:7] = (op_type[3]) ? (57'h0) : (DenormIn ? {12'h0, mantissaB[51:7]} : mantissaB2 & {57{~zeroB}}); assign mantissaB3[6] = (op_type[3]) ? (1'b0) : (DenormIn ? mantissaB[6] : Sticky_out & ~zeroB); assign mantissaB3[5:0] = (op_type[3]) ? (6'h01) : (DenormIn ? mantissaB[5:0] : 6'h0); // The sign of the result needs to be corrected if the true // operation is subtraction and the input operands were swapped. assign corr_sign = ~op_type[2]&~op_type[1]&op_type[0]&swap; // 64-bit Mantissa Adder/Subtractor cla64 add1 (sum, mantissaA3, mantissaB3, sub); // 64-bit Mantissa Subtractor - to get the two's complement of the // result when the sign from the adder/subtractor is negative. cla_sub64 sub1 (sum_tc, mantissaB3, mantissaA3); // Finds normal underflow result to determine whether to round final exponent down //***KEP used to be (sum == 16'h0) I am unsure what it's supposed to be assign normal_overflow = (DenormIn & (sum == 64'h0) & (opA_Norm | opB_Norm) & ~op_type[0]) ? 1'b1 : (sum[63] ? sum_tc[52] : sum[52]); endmodule // fpadd