IEE754

diff --git a/IEE754/Makefile b/IEE754/Makefile
new file mode 100644 (file)
index 0000000..09493a9
--- /dev/null
+++ b/IEE754/Makefile
@@ -0,0 +1,11 @@
+all: floatconverter doubleconverter
+
+floatconverter: floatconverter.c
+       g++ -Wall -g -o floatconverter floatconverter.c
+
+doubleconverter: doubleconverter.c
+       g++ -Wall -g -o doubleconverter doubleconverter.c
+
+clean:
+       rm -f floatconverter
+       rm -f doubleconverter

diff --git a/IEE754/doubleconverter.c b/IEE754/doubleconverter.c
new file mode 100644 (file)
index 0000000..a27e562
--- /dev/null
+++ b/IEE754/doubleconverter.c
@@ -0,0 +1,117 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <string>
+#include <iostream>
+#include <iomanip>
+#include <bitset>
+#include <stdint.h>
+
+//using namespace std;
+
+union Double_t
+{
+    Double_t(double num) : f(num) {}
+    // Portable extraction of components.
+    bool Negative() const { return (i >> 63) != 0; }
+    int64_t RawMantissa() const { return i & ((1LL << 52) - 1); }
+    int64_t RawExponent() const { return (i >> 52) & 0x7FF; }
+
+    int64_t i;
+    double f;
+#ifdef _DEBUG
+    struct
+    {
+        // Bitfields for exploration. Do not use in production code.
+        // least significant bit (LSB): 2^0
+        uint64_t mantissa : 52;  // mantissa also called significand
+        uint64_t exponent : 11;
+        uint64_t sign : 1;
+        // most significant bit (MSB): 2^64
+    } parts;
+#endif
+};
+
+
+int main (int argc, char *argv[])
+{
+    std::cout << "******************************************************************************" << std::endl;
+    std::cout << std::endl;
+    std::cout << "(SIGN) MANTISSA * 2^(EXPONENT-1023)     (using base 10)" << std::endl;
+    std::cout << std::endl;
+    std::cout << "******************************************************************************" << std::endl;
+    std::cout << std::endl;
+
+    double number = atof(argv[1]);
+    Double_t mydouble(number);
+
+    std::cout << std::setprecision(64);
+    std::cout << std::fixed;
+    std::cout << "Number after atof conversion (libc): ";
+    std::cout << number << std::endl;
+    std::cout.unsetf(std::ios::fixed);  
+
+    std::cout << std::endl;
+    std::string signo = mydouble.Negative() ? "negative" : "positive";
+    std::cout << "Sign: " + signo << std::endl;
+    std::cout << std::endl;
+
+    int64_t exponent = mydouble.RawExponent();
+    std::bitset<11> exponent_bits(exponent);
+    std::cout << "Exponent, binary value: " << exponent_bits << std::endl;
+    std::cout << "Exponent, decimal value: " << exponent << std::endl;
+    std::cout << "Exponent, real value: " << exponent << " - 1023 = " << (exponent - 1023) << std::endl;
+    std::cout << std::endl;
+
+    int64_t mantissa = mydouble.RawMantissa();
+    std::bitset<52> mantissa_bits(mantissa);
+    std::cout << "Mantissa, binary value: " << mantissa_bits << std::endl;
+    std::cout << "Mantissa, hexadecimal value: ";
+       std::cout << std::hex << std::uppercase << std::setw(13) << std::setfill('0') << mantissa << std::endl;
+    std::cout << "Mantissa, binary value (fraction in base 2): 1." << mantissa_bits << std::endl;
+    std::cout << "Mantissa, decimal value: TODO" << std::endl;
+    std::cout << std::endl;
+ 
+
+       std::cout << std::endl;
+    std::cout << "Hexadecimal value (integer representation): ";
+       std::cout << std::hex << std::setw(16) << std::setfill('0') << std::uppercase << mydouble.i << std::endl;
+
+
+    return 0;
+}
+
+
+
+
+/***************************************************************************************************
+
+
+
+          me@mycomputer:~$ ./floatconverter 0.01
+          ******************************************************************************
+          
+          (SIGN) MANTISSA * 2^(EXPONENT-127)     (using base 10)
+          
+          ******************************************************************************
+          
+          Sign: positive
+          
+          Exponent, binary value: 01111000
+          Exponent, decimal value: 120
+          Exponent, real value: 120 - 127 = -7
+          
+          Mantissa, binary value: 01000111101011100001010
+          Mantissa, binary value (fraction in base 2): 1.01000111101011100001010
+          Mantissa, decimal value: TODO
+          
+          
+          Hexadecimal value: 3C23D7A
+          me@mycomputer:~$ echo "ibase=2; 1.01000111101011100001010" | bc
+          1.27999997138977050781250
+          me@mycomputer:~$ echo "obase=10; scale=10; 1.27999997138977050781250*(2^-7)" | bc
+          .00999999977648258209228    <------------ closest integer (never 0.01)
+
+
+
+
+******************************************************************************************************/

diff --git a/IEE754/floatconverter.c b/IEE754/floatconverter.c
new file mode 100644 (file)
index 0000000..f88dc34
--- /dev/null
+++ b/IEE754/floatconverter.c
@@ -0,0 +1,141 @@
+#include <stdlib.h>
+#include <stdio.h>
+#include <string>
+#include <iostream>
+#include <iomanip>
+#include <bitset>
+#include <stdint.h>
+
+//using namespace std;
+
+union Float_t
+{
+    Float_t(float num = 0.0f) : f(num) {}
+    // Portable extraction of components.
+    bool Negative() const { return (i >> 31) != 0; }
+    int32_t RawMantissa() const { return i & ((1 << 23) - 1); }
+    int32_t RawExponent() const { return (i >> 23) & 0xFF; }
+
+    int32_t i;
+    float f;
+#ifdef _DEBUG
+    struct
+    {
+        // Bitfields for exploration. Do not use in production code.
+        // least significant bit (LSB): 2^0
+        uint32_t mantissa : 23;  // mantissa also called significand
+        uint32_t exponent : 8;
+        uint32_t sign : 1;
+        // most significant bit (MSB): 2^31
+    } parts;
+#endif
+};
+
+
+int main (int argc, char *argv[])
+{
+    std::cout << "******************************************************************************" << std::endl;
+    std::cout << std::endl;
+    std::cout << "(SIGN) MANTISSA * 2^(EXPONENT-127)     (using base 10)" << std::endl;
+    std::cout << std::endl;
+    std::cout << "******************************************************************************" << std::endl;
+    std::cout << std::endl;
+
+    float number = atof(argv[1]);
+    Float_t myfloat(number);
+
+       std::cout << "Number after atof conversion (libc): ";
+    std::cout << std::setprecision(32) << std::fixed << number << std::endl;
+    //std::cout.unsetf(std::ios::fixed);  
+
+    std::cout << std::endl;
+    std::string signo = myfloat.Negative() ? "negative" : "positive";
+    std::cout << "Sign: " + signo << std::endl;
+    std::cout << std::endl;
+
+    int32_t exponent = myfloat.RawExponent();
+       int32_t mantissa = myfloat.RawMantissa();
+
+       // See: http://docs.oracle.com/cd/E19957-01/806-3568/ncgTOC.html
+       // NORMAL NUMBER
+       if (exponent > 0 && exponent < 255) {
+               std::cout << "NORMAL NUMBER" << std::endl;
+       }
+
+       // SUBNORMAL NUMBER
+       if (exponent == 0 && mantissa != 0) {
+               std::cout << "SUBNORMAL NUMBER" << std::endl;
+       }
+
+       // SIGNED ZERO
+       if (exponent == 0 && mantissa == 0) {
+        std::cout << "SIGNED ZERO" << std::endl;
+    }
+
+       // INFINITY
+    if (exponent == 255 && mantissa == 0) {
+               std::cout << "INFINITY, SEE SIGN" << std::endl;
+       }       
+
+       // NAN
+       if (exponent == 255 && mantissa != 0) {
+        std::cout << "NAN" << std::endl;
+    }
+
+    std::bitset<8> exponent_bits(exponent);
+    std::cout << "Exponent, binary value: " << exponent_bits << std::endl;
+    std::cout << "Exponent, decimal value: " << exponent << std::endl;
+    std::cout << "Exponent, real value: " << exponent << " - 127 = " << (exponent - 127) << std::endl;
+    std::cout << std::endl;
+
+    std::bitset<23> mantissa_bits(mantissa);
+    std::cout << "Mantissa, binary value: " << mantissa_bits << std::endl;
+    std::cout << "Mantissa, hexadecimal value: ";
+    std::cout << std::hex << std::uppercase << std::setw(6) << std::setfill('0') << mantissa << std::endl;
+    std::cout << "Mantissa, binary value (fraction in base 2): 1." << mantissa_bits << std::endl;
+    std::cout << "Mantissa, decimal value: TODO" << std::endl;
+    std::cout << std::endl;
+ 
+
+    std::cout << std::endl;
+    std::cout << "Hexadecimal value (integer representation): ";
+    std::cout << std::hex << std::setw(8) << std::setfill('0') << std::uppercase << myfloat.i << std::endl;
+
+    return 0;
+}
+
+
+
+
+/***************************************************************************************************
+
+
+
+          me@mycomputer:~$ ./floatconverter 0.01
+          ******************************************************************************
+          
+          (SIGN) MANTISSA * 2^(EXPONENT-127)     (using base 10)
+          
+          ******************************************************************************
+          
+          Sign: positive
+          
+          Exponent, binary value: 01111000
+          Exponent, decimal value: 120
+          Exponent, real value: 120 - 127 = -7
+          
+          Mantissa, binary value: 01000111101011100001010
+          Mantissa, binary value (fraction in base 2): 1.01000111101011100001010
+          Mantissa, decimal value: TODO
+          
+          
+          Hexadecimal value: 3C23D7A
+          me@mycomputer:~$ echo "ibase=2; 1.01000111101011100001010" | bc
+          1.27999997138977050781250
+          me@mycomputer:~$ echo "obase=10; scale=10; 1.27999997138977050781250*(2^-7)" | bc
+          .00999999977648258209228    <------------ closest integer (never 0.01)
+
+
+
+
+******************************************************************************************************/