用于转换32位单精度IEEE 754浮点表示的程序

前提条件： IEEE标准754浮点数

编写程序以找出给定实际值的32位单精度IEEE 754浮点表示，反之亦然。

例子：

Input: real number = 16.75
Output: 0 | 10000011 | 00001100000000000000000

Input: floating point number = 0 | 10000011 | 00001100000000000000000
Output: 16.75

方法：
此实现基于C中的联合数据类型，并使用位字段的概念。

当我们不需要通常分配给某些变量的完整内存，但我们想限制这些变量占用的内存量时，便会分配位字段。在C中，一个Union的成员共享公共内存空间，因此我们一次只能访问一个成员。

下面是上述方法的实现：

程序1：将实数值转换为其浮点表示形式

C

// C program to convert a real value
// to IEEE 754 floating point representaion
  
#include 
  
void printBinary(int n, int i)
{
  
    // Prints the binary representation
    // of a number n up to i-bits.
    int k;
    for (k = i - 1; k >= 0; k--) {
  
        if ((n >> k) & 1)
            printf("1");
        else
            printf("0");
    }
}
  
typedef union {
  
    float f;
    struct
    {
  
        // Order is important.
        // Here the members of the union data structure
        // use the same memory (32 bits).
        // The ordering is taken
        // from the LSB to the MSB.
        unsigned int mantissa : 23;
        unsigned int exponent : 8;
        unsigned int sign : 1;
  
    } raw;
} myfloat;
  
// Function to convert real value
// to IEEE foating point representation
void printIEEE(myfloat var)
{
  
    // Prints the IEEE 754 representation
    // of a float value (32 bits)
  
    printf("%d | ", var.raw.sign);
    printBinary(var.raw.exponent, 8);
    printf(" | ");
    printBinary(var.raw.mantissa, 23);
    printf("\n");
}
  
// Driver Code
int main()
{
  
    // Instantiate the union
    myfloat var;
  
    // Get the real value
    var.f = -2.25;
  
    // Get the IEEE floating point representation
    printf("IEEE 754 representation of %f is : \n",
           var.f);
    printIEEE(var);
  
    return 0;
}

Python3

# Python program to convert a real value
# to IEEE 754 Floating Point Representation.
  
# Function to convert a 
# fraction to binary form.
def binaryOfFraction(fraction):
  
    # Declaring an empty string
    # to store binary bits.
    binary = str()
  
    # Iterating through 
    # fraction until it 
    # becomes Zero.
    while (fraction):
          
        # Multiplying fraction by 2.
        fraction *= 2
  
        # Storing Integer Part of
        # Fraction in int_part.
        if (fraction >= 1):
            int_part = 1
            fraction -= 1
        else:
            int_part = 0
      
        # Adding int_part to binary
        # after every iteration.
        binary += str(int_part)
  
    # Returning the binary string.
    return binary
  
# Function to get sign  bit,
# exp bits and mantissa bits,
# from given real no.
def floatingPoint(real_no):
  
    # Setting Sign bit
    # default to zero.
    sign_bit = 0
  
    # Sign bit will set to
    # 1 for negative no.
    if(real_no < 0):
        sign_bit = 1
  
    # converting given no. to
    # absolute value as we have
    # already set the sign bit.
    real_no = abs(real_no)
  
    # Converting Integer Part 
    # of Real no to Binary
    int_str = bin(int(real_no))[2 : ]
  
    # Function call to convert
    # Fraction part of real no
    # to Binary.
    fraction_str = binaryOfFraction(real_no - int(real_no))
  
    # Getting the index where
    # Bit was high for the first
    # Time in binary repres
    # of Integer part of real no.
    ind = int_str.index('1')
  
    # The Exponent is the no.
    # By which we have right 
    # Shifted the decimal and 
    # it is given below.
    # Also converting it to bias 
    # exp by adding 127.
    exp_str = bin((len(int_str) - ind - 1) + 127)[2 : ]
  
    # getting mantissa string
    # By adding int_str and fraction_str.
    # the zeroes in MSB of int_str
    # have no significance so they
    # are ignored by slicing.
    mant_str = int_str[ind + 1 : ] + fraction_str
  
    # Adding Zeroes in LSB of 
    # mantissa string so as to make
    # it's length of 23 bits.
    mant_str = mant_str + ('0' * (23 - len(mant_str)))
  
    # Returning the sign, Exp
    # and Mantissa Bit strings.
    return sign_bit, exp_str, mant_str
  
# Driver Code
if __name__ == "__main__":
  
    # Function call to get
    # Sign, Exponent and 
    # Mantissa Bit Strings.
    sign_bit, exp_str, mant_str = floatingPoint(-2.250000)
  
    # Final Floating point Representation.
    ieee_32 = str(sign_bit) + '|' + exp_str + '|' + mant_str
  
    # Printing the ieee 32 represenation.
    print("IEEE 754 representation of -2.250000 is :")
    print(ieee_32)

输出：

IEEE 754 representation of -2.250000 is : 
1 | 10000000 | 00100000000000000000000

程序2：将浮点表示形式转换为其实际值

C

// C program to convert
// IEEE 754 floating point representaion
// into real value
  
#include 
#include 
  
typedef union {
  
    float f;
    struct
    {
  
        // Order is important.
        // Here the members of the union data structure
        // use the same memory (32 bits).
        // The ordering is taken
        // from the LSB to the MSB.
  
        unsigned int mantissa : 23;
        unsigned int exponent : 8;
        unsigned int sign : 1;
  
    } raw;
} myfloat;
  
// Function to convert a binary array
// to the corresponding integer
unsigned int convertToInt(int* arr, int low, int high)
{
    unsigned f = 0, i;
    for (i = high; i >= low; i--) {
        f = f + arr[i] * pow(2, high - i);
    }
    return f;
}
  
// Driver Code
int main()
{
  
    // Get the 32-bit floating point number
    unsigned int ieee[32]
        = { 1,
            1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
            0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
            0, 0, 0, 0, 0, 0, 0, 0, 0 };
  
    myfloat var;
  
    // Convert the least significant
    // mantissa part (23 bits)
    // to corresponding decimal integer
    unsigned f = convertToInt(ieee, 9, 31);
  
    // Assign integer representation of mantissa
    var.raw.mantissa = f;
  
    // Convert the exponent part (8 bits)
    // to a corresponding decimal integer
    f = convertToInt(ieee, 1, 8);
  
    // Assign integer representation
    // of the exponent
    var.raw.exponent = f;
  
    // Assign sign bit
    var.raw.sign = ieee[0];
  
    printf("The float value of the given"
           " IEEE-754 representation is : \n");
    printf("%f", var.f);
}

Python3

# Python program to convert
# IEEE 754 floating point representation
# into real value
  
# Function to convert Binary
# of Mantissa to float value.
def convertToInt(mantissa_str):
  
    # variable to make a count
    # of negative power of 2.
    power_count = -1
  
    # variable to store
    # float value of mantissa.
    mantissa_int = 0
  
    # Iterations through binary
    # Number. Standard form of 
    # Mantissa is 1.M so we have 
    # 0.M therefore we are taking
    # negative powers on 2 for 
    # conversion.
    for i in mantissa_str:
  
        # Adding converted value of
        # Binary bits in every 
        # iteration to float mantissa.
        mantissa_int += (int(i) * pow(2, power_count))
  
        # count will decrease by 1
        # as we move toward right.
        power_count -= 1
          
    # returning mantissa in 1.M form.
    return (mantissa_int + 1)
  
if __name__ == "__main__":
    # Floating Point Representation
    # to be converted into real 
    # value.
    ieee_32 = '1|10000000|00100000000000000000000'
  
    # First bit will be sign bit.
    sign_bit = int(ieee_32[0])
  
    # Next 8 bits will be 
    # Exponent Bits in Biased
    # form.
    exponent_bias = int(ieee_32[2 : 10], 2)
  
    # In 32 Bit format bias
    # value is 127 so to have
    # unbiased exponent
    # subtract 127.
    exponent_unbias = exponent_bias - 127
  
    # Next 23 Bits will be
    # Mantissa (1.M format)
    mantissa_str = ieee_32[11 : ]
  
    # Function call to convert
    # 23 binary bits into 
    # 1.M real no. form
    mantissa_int = convertToInt(mantissa_str)
  
    # The final real no. obtained
    # by sign bit, mantissa and
    # Exponent.
    real_no = pow(-1, sign_bit) * mantissa_int * pow(2, exponent_unbias)
  
    # Printing the obtained
    # Real value of floating
    # Point Representaion.
    print("The float value of the given IEEE-754 representation is :",real_no)

输出：

The float value of the given IEEE-754 representation is : 
-2.250000

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