Decomposition of Single Precision Float Points , C++ (vc++)

Decomposition of Single Precision Float Points

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/**
 *   File:   decompose_binary32flt.cpp
 *   Author: Caio Rodrigues Soares Silva
 *   Brief:  Sample C++ program to decompose IEE754 32 bits floating point.
 *
 *   Note:   The results of this app can be checked with the online calculator:
 *           https://calculla.com/floating_point_numbers
 **************************************************************************/

#include <iostream>
#include <string>
#include <sstream>
#include <iomanip>
#include <limits>
#include <cmath>
#include <cstdint>
#include <map>

#define SHOW_FLOAT(expr) show_float(#expr, (expr))

template<typename T>
std::string num2hexstr(T number, int padding = 8)
{
    std::stringstream ss;
    if(padding != 0){
        ss << "0x" << std::hex
           <<  std::setfill('0') << std::setw(padding) << number;
    } else {
        ss << "0x" << std::hex  << number;
    }
    return ss.str();
}

std::string to_hexfloat(float number)
{
    std::stringstream ss;
    ss << std::hexfloat << number;
    return ss.str();
}

// Decompose float point
void show_float(const char* expr, float x)
{
    constexpr int w1 = 34;
    constexpr int w2 = 4;

// Float point classification constants
    static auto const fpmap = std::map<int, const char*>{
         {FP_INFINITE,  "FP_INFINITE"}
        ,{FP_NAN,       "FP_NAN"}
        ,{FP_NORMAL,    "PF_NORMAL"}
        ,{FP_SUBNORMAL, "FP_SUBNORMAL"}
        ,{FP_ZERO,      "FP_ZERO"}
    };

// Integer represetation extracted
    // through type punning aka memory reinterpretation
    std::uint32_t* pn       = reinterpret_cast<std::uint32_t*>(&x);
    std::uint32_t  value    = *pn;
    std::uint32_t  mantissa = value & ((1 << 23) - 1);
    std::uint32_t  raw_exp  = (value >> 23) & 0xFF;
    std::uint32_t  sign     = (value >> 31) & 0x01;

auto print_row = [&w1, &w2](const char* label, auto const& value)
    {
        std::cout << std::setw(w1) << std::right << label
                  << std::setw(w2) << std::left  << value
                  << "\n";
    };

print_row("Input Expression: ", expr);
    print_row("Classification: ", fpmap.at(std::fpclassify(x)));
    print_row("Decimal Representation: ", x);
    print_row("Hexadecimal Representation: ", to_hexfloat(x));
    print_row("Integer Representation (hex): ", num2hexstr(value));
    print_row("Sign bit: ", sign);
    print_row("Exponent: ", static_cast<std::int32_t>(raw_exp) - 127);
    print_row("Raw Exponent: ", raw_exp);
    print_row("Raw Exponent (hex): ", num2hexstr(raw_exp, 0));
    print_row("Mantissa (hex): ", num2hexstr(mantissa, 0));    
    std::cout << "\n\n";
}

int main()
{
    std::puts("\n==== Decomposition of Single Precision Float Points =====\n");

// Signed Zero
    SHOW_FLOAT(+0.0f);
    SHOW_FLOAT(-0.0f);

// NaN - Not a number
    SHOW_FLOAT(+std::numeric_limits<float>::quiet_NaN());
    SHOW_FLOAT(-std::numeric_limits<float>::quiet_NaN());

// Positive and negative Infinity
    SHOW_FLOAT(+std::numeric_limits<float>::infinity());
    SHOW_FLOAT(-std::numeric_limits<float>::infinity());

// Subnormal
    SHOW_FLOAT(+std::numeric_limits<float>::min());
    SHOW_FLOAT(+std::numeric_limits<float>::min() / 100.0f);
    SHOW_FLOAT(-std::numeric_limits<float>::min() / 1000000.0f);

// Epsilon
    SHOW_FLOAT(+std::numeric_limits<float>::epsilon());

// Normal Numbers
    SHOW_FLOAT(1.0f);
    SHOW_FLOAT(0.5f);
    SHOW_FLOAT(1E-5f);
    SHOW_FLOAT(1.051646E4f);
    SHOW_FLOAT(-99000134.3401f);
    SHOW_FLOAT(std::numeric_limits<float>::max());
    SHOW_FLOAT(std::numeric_limits<float>::lowest());

return 0;
}

Show compiler warnings [ + ] Compiler args [ + ] Show input
Compilation time: 2,12 sec, absolute running time: 0,33 sec, absolute service time: 2,46 sec

==== Decomposition of Single Precision Float Points ===== Input Expression: +0.0f Classification: FP_ZERO Decimal Representation: 0 Hexadecimal Representation: 0x0.000000p+0 Integer Representation (hex): 0x00000000 Sign bit: 0 Exponent: -127 Raw Exponent: 0 Raw Exponent (hex): 0x0 Mantissa (hex): 0x0 Input Expression: -0.0f Classification: FP_ZERO Decimal Representation: -0 Hexadecimal Representation: -0x0.000000p+0 Integer Representation (hex): 0x80000000 Sign bit: 1 Exponent: -127 Raw Exponent: 0 Raw Exponent (hex): 0x0 Mantissa (hex): 0x0 Input Expression: +std::numeric_limits<float>::quiet_NaN() Classification: FP_NAN Decimal Representation: nan Hexadecimal Representation: nan Integer Representation (hex): 0x7fc00000 Sign bit: 0 Exponent: 128 Raw Exponent: 255 Raw Exponent (hex): 0xff Mantissa (hex): 0x400000 Input Expression: -std::numeric_limits<float>::quiet_NaN() Classification: FP_NAN Decimal Representation: -nan(ind) Hexadecimal Representation: -nan(ind) Integer Representation (hex): 0xffc00000 Sign bit: 1 Exponent: 128 Raw Exponent: 255 Raw Exponent (hex): 0xff Mantissa (hex): 0x400000 Input Expression: +std::numeric_limits<float>::infinity() Classification: FP_INFINITE Decimal Representation: inf Hexadecimal Representation: inf Integer Representation (hex): 0x7f800000 Sign bit: 0 Exponent: 128 Raw Exponent: 255 Raw Exponent (hex): 0xff Mantissa (hex): 0x0 Input Expression: -std::numeric_limits<float>::infinity() Classification: FP_INFINITE Decimal Representation: -inf Hexadecimal Representation: -inf Integer Representation (hex): 0xff800000 Sign bit: 1 Exponent: 128 Raw Exponent: 255 Raw Exponent (hex): 0xff Mantissa (hex): 0x0 Input Expression: +std::numeric_limits<float>::min() Classification: PF_NORMAL Decimal Representation: 1.17549e-38 Hexadecimal Representation: 0x1.000000p-126 Integer Representation (hex): 0x00800000 Sign bit: 0 Exponent: -126 Raw Exponent: 1 Raw Exponent (hex): 0x1 Mantissa (hex): 0x0 Input Expression: +std::numeric_limits<float>::min() / 100.0f Classification: FP_SUBNORMAL Decimal Representation: 1.17549e-40 Hexadecimal Representation: 0x1.47ae00p-133 Integer Representation (hex): 0x000147ae Sign bit: 0 Exponent: -127 Raw Exponent: 0 Raw Exponent (hex): 0x0 Mantissa (hex): 0x147ae Input Expression: -std::numeric_limits<float>::min() / 1000000.0f Classification: FP_SUBNORMAL Decimal Representation: -1.12104e-44 Hexadecimal Representation: -0x1.000000p-146 Integer Representation (hex): 0x80000008 Sign bit: 1 Exponent: -127 Raw Exponent: 0 Raw Exponent (hex): 0x0 Mantissa (hex): 0x8 Input Expression: +std::numeric_limits<float>::epsilon() Classification: PF_NORMAL Decimal Representation: 1.19209e-07 Hexadecimal Representation: 0x1.000000p-23 Integer Representation (hex): 0x34000000 Sign bit: 0 Exponent: -23 Raw Exponent: 104 Raw Exponent (hex): 0x68 Mantissa (hex): 0x0 Input Expression: 1.0f Classification: PF_NORMAL Decimal Representation: 1 Hexadecimal Representation: 0x1.000000p+0 Integer Representation (hex): 0x3f800000 Sign bit: 0 Exponent: 0 Raw Exponent: 127 Raw Exponent (hex): 0x7f Mantissa (hex): 0x0 Input Expression: 0.5f Classification: PF_NORMAL Decimal Representation: 0.5 Hexadecimal Representation: 0x1.000000p-1 Integer Representation (hex): 0x3f000000 Sign bit: 0 Exponent: -1 Raw Exponent: 126 Raw Exponent (hex): 0x7e Mantissa (hex): 0x0 Input Expression: 1E-5f Classification: PF_NORMAL Decimal Representation: 1e-05 Hexadecimal Representation: 0x1.4f8b58p-17 Integer Representation (hex): 0x3727c5ac Sign bit: 0 Exponent: -17 Raw Exponent: 110 Raw Exponent (hex): 0x6e Mantissa (hex): 0x27c5ac Input Expression: 1.051646E4f Classification: PF_NORMAL Decimal Representation: 10516.5 Hexadecimal Representation: 0x1.48a3aep+13 Integer Representation (hex): 0x462451d7 Sign bit: 0 Exponent: 13 Raw Exponent: 140 Raw Exponent (hex): 0x8c Mantissa (hex): 0x2451d7 Input Expression: -99000134.3401f Classification: PF_NORMAL Decimal Representation: -9.90001e+07 Hexadecimal Representation: -0x1.79a7d2p+26 Integer Representation (hex): 0xccbcd3e9 Sign bit: 1 Exponent: 26 Raw Exponent: 153 Raw Exponent (hex): 0x99 Mantissa (hex): 0x3cd3e9 Input Expression: std::numeric_limits<float>::max() Classification: PF_NORMAL Decimal Representation: 3.40282e+38 Hexadecimal Representation: 0x1.fffffep+127 Integer Representation (hex): 0x7f7fffff Sign bit: 0 Exponent: 127 Raw Exponent: 254 Raw Exponent (hex): 0xfe Mantissa (hex): 0x7fffff Input Expression: std::numeric_limits<float>::lowest() Classification: PF_NORMAL Decimal Representation: -3.40282e+38 Hexadecimal Representation: -0x1.fffffep+127 Integer Representation (hex): 0xff7fffff Sign bit: 1 Exponent: 127 Raw Exponent: 254 Raw Exponent (hex): 0xfe Mantissa (hex): 0x7fffff