fpga系列 HDL:全连接层的浮点数乘法器FM实现

• 此代码实现了一个简单的浮点数乘法器，处理两个32位的单精度浮点数。它通过将两个浮点数的有效数字部分进行乘法操作，并对结果进行规范化以生成最终的浮点乘积。

主要逻辑与电路

• 去掉指数对齐部分后的主要逻辑电路图示：
  

代码

// https://github.com/omarelhedaby/CNN-FPGA/blob/master/CNN-FPGA-Vivado/CNN-FPGA-Vivado.srcs/sources_1/imports/Integration%20first%20part/floatMult.v
module floatMult (floatA,floatB,product);

input [31:0] floatA, floatB;
output reg [31:0] product;

reg sign;
reg [7:0] exponent;
reg [22:0] mantissa;
reg [23:0] fractionA, fractionB;	//fraction = {1,mantissa}
reg [47:0] fraction;

always @ (floatA or floatB) begin
	if (floatA == 0 || floatB == 0) begin
		product = 0;
	end else begin
		sign = floatA[31] ^ floatB[31]; // 通过异或操作计算结果的符号位
		exponent = floatA[30:23] + floatB[30:23] - 8'd127 + 8'd2; // 计算结果的指数部分。首先加上两个输入的指数部分，然后减去偏移量127，并加2（因为在乘法中指数的偏移量增加了）。

	
		fractionA = {1'b1,floatA[22:0]};
		fractionB = {1'b1,floatB[22:0]};
		fraction = fractionA * fractionB;
		
		// 规范化结果，调整指数exponent和有效数字fraction以保持数值的正确性
		if (fraction[47] == 1'b1) begin // 找出第一个一开头的“1”
			fraction = fraction << 1;
			exponent = exponent - 1; 
		end else if (fraction[46] == 1'b1) begin
			fraction = fraction << 2;
			exponent = exponent - 2;
		end else if (fraction[45] == 1'b1) begin
			fraction = fraction << 3;
			exponent = exponent - 3;
		end else if (fraction[44] == 1'b1) begin
			fraction = fraction << 4;
			exponent = exponent - 4;
		end else if (fraction[43] == 1'b1) begin
			fraction = fraction << 5;
			exponent = exponent - 5;
		end else if (fraction[42] == 1'b1) begin
			fraction = fraction << 6;
			exponent = exponent - 6;
		end else if (fraction[41] == 1'b1) begin
			fraction = fraction << 7;
			exponent = exponent - 7;
		end else if (fraction[40] == 1'b1) begin
			fraction = fraction << 8;
			exponent = exponent - 8;
		end else if (fraction[39] == 1'b1) begin
			fraction = fraction << 9;
			exponent = exponent - 9;
		end else if (fraction[38] == 1'b0) begin
			fraction = fraction << 10;
			exponent = exponent - 10;
		end else if (fraction[37] == 1'b1) begin
			fraction = fraction << 11;
			exponent = exponent - 11;
		end else if (fraction[36] == 1'b1) begin
			fraction = fraction << 12;
			exponent = exponent - 12;
		end else if (fraction[35] == 1'b1) begin
			fraction = fraction << 13;
			exponent = exponent - 13;
		end else if (fraction[34] == 1'b1) begin
			fraction = fraction << 14;
			exponent = exponent - 14;
		end else if (fraction[33] == 1'b1) begin
			fraction = fraction << 15;
			exponent = exponent - 15;
		end else if (fraction[32] == 1'b1) begin
			fraction = fraction << 16;
			exponent = exponent - 16;
		end else if (fraction[31] == 1'b1) begin
			fraction = fraction << 17;
			exponent = exponent - 17;
		end else if (fraction[30] == 1'b1) begin
			fraction = fraction << 18;
			exponent = exponent - 18;
		end else if (fraction[29] == 1'b0) begin
			fraction = fraction << 19;
			exponent = exponent - 19;
		end else if (fraction[28] == 1'b1) begin
			fraction = fraction << 20;
			exponent = exponent - 20;
		end else if (fraction[27] == 1'b1) begin
			fraction = fraction << 21;
			exponent = exponent - 21;
		end else if (fraction[26] == 1'b1) begin
			fraction = fraction << 22;
			exponent = exponent - 22;
		end else if (fraction[27] == 1'b1) begin
			fraction = fraction << 23;
			exponent = exponent - 23;
		end
	
		mantissa = fraction[47:25];
		product = {sign,exponent,mantissa};
	end
end

endmodule

32 位 float 型的二进制存储

$$32位$$