十六进制的HEX字符串 转换成 浮点数

function hexToFloat( hexString )
	if hexString == nil then
		return 0
	end
	local t = type( hexString )
	if t == "string" then
		hexString = tonumber(hexString , 16)
	end
 
	local hexNums = hexString
 
	local sign = math.modf(hexNums/(2^31))
 
	local exponent = hexNums % (2^31)
	exponent = math.modf(exponent/(2^23)) -127
 
	local mantissa = hexNums % (2^23)
 
	for i=1,23 do
		mantissa = mantissa / 2
	end
	mantissa = 1+mantissa
--	print(mantissa)
	local result = (-1)^sign * mantissa * 2^exponent
	result = tonumber(string.format('%.3f', result))
	return result
end

浮点数转换成 十六进制字符串

function floattohex(floatNum)
	if(floatNum == 0)then
		return 0;
	end
---给一个浮点数 33.758
--1.将浮点数分成整数和小数
	num_z,num_x= math.modf(floatNum/1)
	--print("整数:" .. num_z  .. "  小数:".. num_x)
--2.将整数部分化成二进制
	str_z = ""
	intercount = 0;  --转换成二进制一共多少位
	num1 = num_z
	if(num1 == 0)then
		intercount = 0
		str_z = "0"
	else
		repeat
		num = num1
		num1= math.modf(num1/2)
		num2 = num - num1*2
		intercount = intercount + 1  --阶乘
		str_z = str_z .. num2
		until (num1 == 0)
	end
	str_z = string.reverse(str_z)
	--print("整数:" .. str_z)
--3.将小数转换成二进制
	str_x = ""
	num2 = num_x
	repeat
	num2 = num2 *2
	num1,num2 = math.modf(num2/1)
	str_x = str_x .. num1
	until(num2 == 0 or #str_x >=40)
	--print("小数:"..str_x)
--4.浮点数的二进制表示
	--print("浮点数的二进制表示 :" .. str_z .. "."  .. str_x)

--浮点数的二进制表示 :一种：0.00110101110000101000111
                    --两种：1011.01101011100001010
--5.首先确认整数是否大于0，
        --（1）==0 右移  查找小数二进制何时有1
		--（2） >0 左移  
	
	e = 0
	str_m =""
	if(num_z == 0)then
		num_1 =string.find(str_x,"1")  --阶
		e = -num_1
		str_m = string.sub(str_x,num_1+1,-1)
	else
		e = intercount - 1
		str_m = string.sub(str_z,2,-1) .. str_x
	end	
	--？？考虑str_m是否有23位
	if(#str_m ~= 23)then
		if(#str_m > 23)then
			str_m = string.sub(str_m,1,23)
		end
		if(#str_m <23)then
			len_m = 23 - #str_m
			for i = 1,len_m do
				str_m =  str_m .."0"
			end
		end
	
	end
	M = str_m
	--print("M = " .. M)    
	
	--考虑把它转换成二进制
	E = e + 127  
	str_e = ""  --E的二进制
	intercount_e = 0
	num1 = E
	repeat
		num = num1
		num1= math.modf(num1/2)
		num2 = num - num1*2
		intercount_e = intercount_e + 1  --阶乘
		str_e = str_e .. num2
	until (num1 == 0)
	
	if(#str_e ~= 8)then
		len_e = 8 - #str_e
		for i = 1,len_e do
			str_e =  str_e .."0"
		end
	end
	E = string.reverse(str_e)
	--print("E的二进制字符串:" .. E)--此时str_e 是E的二进制字符串
		
	
	
--6.确定 S
	if(floatNum > 0)then
		S = 0
	else	
		S = 1
	end
	--print("S:" .. S)
--7.将S E M 二进制转换
	str = S .. E .. M
	result = string.format("%08X",tonumber(str,2))
	
	--print ("result =" .. result)
	--print("**************************************************")
	return result;
end

用30000组数据测试数据的正确性

for i= 1,30000 do
	num = 0;
	--math.randomseed(os.time())
	num = tonumber(string.format('%.3f', math.random() + math.random(0,10) ))
 	num_result = num;
	print("i = " .. i.. " num :" .. num_result )
	str_hex = floattohex(num_result)
	num_str =hexToFloat(str_hex)
	if(num_result == tonumber(num_str))then
		--print("i = " .. i.. "  对比正确true")
	else
		print("对比错误false")
	end
	--print("**************************************************")
end