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FloatAdd.c
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FloatAdd.c
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/**File: FloatAdd.c
* Name: Jay Ofemi
* Date: 02/15/2017
* Collaboration Declaration:
* Online resources.
*/
#include <stdio.h>
//This is a FloatAdd routine,
//meant to emulate IEEE 32-bit floating point addition.
///Function Declarations
//FloatAdd Function
int FloatAdd(int op1, int op2);
//Function to break out the three components (Sign, Exponent,
//and Significand) and categorize the value.
unsigned int categorize(int operand, unsigned int sign,
unsigned int exponent, unsigned int significand);
//Function to handle zero inputs
int zeroInputs(int op1, int op2, unsigned int category1,
unsigned int category2, unsigned int sign1,
unsigned int sign2);
//Function to handle infinty inputs
int infintyInputs(int op1, int op2, unsigned int sign1, unsigned int sign2,
unsigned int category1, unsigned int category2);
//Function to handle NaN inputs
int NaNInputs(int op1, int op2, unsigned int category1,
unsigned int category2);
//Function to add Normalized inputs
int addNormalized(int op1, int op2, unsigned int sign1, unsigned int sign2,
unsigned int exponent1, unsigned int exponent2,
unsigned int significand1, unsigned int significand2,
unsigned int denorm);
//Function to check for underflow
int checkForUnderflow(unsigned int exponent);
//Function to check for overflow
int checkForOverflow(unsigned int exponent);
//Function to get rounding factor (guard + sticky)
int guardPlusSticky(unsigned int significand, unsigned int sticky);
//FloatAdd Function
int FloatAdd(int op1, int op2)
{
//local variables definition
int result;
unsigned int category1, category2, denorm;
unsigned int sign1, exponent1, significand1;
unsigned int sign2, exponent2, significand2;
//turn debugging on (1) or off (0)
#define DO_DEBUGGING_PRINTS 0
//for operand 1
//sign bit
sign1 = (op1 & 0x80000000) >> 31;
//Exponent bits
exponent1 = (op1 & 0x7F800000) >> 23;
//Significand bits
significand1 = ((op1 << 9) >> 9) & 0x007FFFFF;
//categorize the operand
category1 = categorize(op1, sign1, exponent1, significand1);
//for operand 2
//sign bit
sign2 = (op2 & 0x80000000) >> 31;
//Exponent bits
exponent2 = (op2 & 0x7F800000) >> 23;
//Significand bits
significand2 = ((op2 << 9) >> 9) & 0x007FFFFF;
//categorize the operand
category2 = categorize(op2, sign2, exponent2, significand2);
//Input Handling
denorm = 0;
//handle NaN inputs
if(category1 == 2 || category2 == 2)
{
result = NaNInputs(op1, op2, category1, category2);
}
//handle infinty inputs
else if(category1 == 1 || category2 == 1)
{
result = infintyInputs(op1, op2, sign1, sign2, category1, category2);
}
//handle zero inputs
else if(category1 == 0 || category2 == 0)
{
result = zeroInputs(op1, op2, category1, category2, sign1, sign2);
}
//handle De-Normalized inputs
else if(category1 == 4 && category2 == 4)
{
denorm = 1;
exponent1 = exponent1 + 1;
exponent2 = exponent2 + 1;
//add
result = addNormalized(op1, op2, sign1, sign2, exponent1,
exponent2, significand1, significand2, denorm);
}
//handle Normalized inputs
//if op1 is normalized and op2 is not
if(category1 == 3 && category2 == 4)
{
exponent2 = exponent2 + 1;
//add 1 to significand 1
significand1 = significand1 | 0x00800000;
//add
result = addNormalized(op1, op2, sign1, sign2, exponent1,
exponent2, significand1, significand2, denorm);
}
//if op2 is normalized and op1 is not
else if(category1 == 4 && category2 == 3)
{
exponent1 = exponent1 + 1;
//add 1 to significand 2
significand2 = significand2 | 0x00800000;
//add
result = addNormalized(op1, op2, sign1, sign2, exponent1,
exponent2, significand1, significand2, denorm);
}
//if op1 is normalized and op2 is as well
else if(category1 == 3 && category2 == 3)
{
//add 1 to significand 1
significand1 = significand1 | 0x00800000;
//add 1 to significand 2
significand2 = significand2 | 0x00800000;
//add
result = addNormalized(op1, op2, sign1, sign2, exponent1,
exponent2, significand1, significand2, denorm);
}
//display necessary information to user
//for operand 1
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "-----Operand 1-----\n");
fprintf(stderr, "Sign: %01x\n", sign1);
fprintf(stderr, "Exponent: %08x\n", exponent1);
fprintf(stderr, "Significand: %08x\n", significand1);
#endif
//for operand 2
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "-----Operand 2-----\n");
fprintf(stderr, "Sign: %01x\n", sign2);
fprintf(stderr, "Exponent: %08x\n", exponent2);
fprintf(stderr, "Significand: %08x\n", significand2);
#endif
return result;
}
/*Function to break out the three components (Sign, Exponent,
*and Significand) and categorize the value.
* param: operand
* param: sign
* param: exponent
* param: significand
* return: 0 for zero value, 1 for Infinity, 2 for NaN,
* 3 for Normalized, and 4 for De-Normalized
*/
unsigned int categorize(int operand, unsigned int sign,
unsigned int exponent, unsigned int significand)
{
unsigned int value = 5;
//check if exponent is all 0 bits
if(exponent == 0x00)
{
//check if significand is also all 0 bits
if(significand == 0x000000)
{
//then value is +/- zero
value = 0;
if(sign == 0)
{
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x = +0\n", operand);
#endif
}
else if(sign == 1)
{
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x = -0\n", operand);
#endif
}
}
//if significand is not all 0 bits
else
{
//value is denormalized
value = 4;
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x is De-Normalized\n", operand);
#endif
}
}
//check if exponent is all 1 bits
else if(exponent == 0xFF)
{
//check if significand is all 0 bits
if(significand == 0x000000)
{
//then value is +/- infinity
value = 1;
if(sign == 0)
{
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x = +Infinity\n", operand);
#endif
}
else if(sign == 1)
{
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x = -Infinity\n", operand);
#endif
}
}
//if significand is not all 0 bits
else
{
//value is Not a Number(NaN)
value = 2;
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x is NaN\n", operand);
#endif
}
}
//if exponent is neither all 0s nor all 1s
else
{
//exponent is biased and value is Normalized
value = 3;
#if DO_DEBUGGING_PRINTS
fprintf(stderr, "Value %08x is Normalized\n", operand);
#endif
}
return value;
}
/*Function to handle zero inputs
* param: operand 1
* param: operand 2
* param: category 1
* param: category 2
* param: sign 1
* param: sign 2
* return: zero value
*/
int zeroInputs(int op1, int op2, unsigned int category1,
unsigned int category2, unsigned int sign1,
unsigned int sign2)
{
//local variables
int value;
unsigned int sign;
//if operand 1 is zero and operand 2 is not
if(category1 == 0 && category2 != 0)
{
//value is operand 2
value = op2;
}
//if operand 2 is zero and operand 1 is not
else if(category2 == 0 && category1 != 0)
{
//value is operand 1
value = op1;
}
//if operand 1 is zero and so is operand 2
else if(category2 == 0 && category1 == 0)
{
//determine sign: positive takes priority over negative
//if sign 1 is positive
if(sign1 < sign2)
{
//use sign 1
sign = sign1;
}
//if sign 2 is positive
else if(sign1 > sign2)
{
//use sign 2
sign = sign2;
}
//if sign 1 and 2 are the same
else
{
//use sign 1
sign = sign1;
}
//mask then or with the new sign bit
value = ((op1 & 0x7FFFFFFF) | (sign << 31));
}
return value;
}
/*Function to handle infinty inputs
* param: operand 1
* param: operand 2
* param: sign 1
* param: sign 2
* param: category 1
* param: category 2
* return: infinty value
*/
int infintyInputs(int op1, int op2, unsigned int sign1, unsigned int sign2,
unsigned int category1, unsigned int category2)
{
//local variables
int value;
//if operand 1 is infinty and operand 2 is not
if(category1 == 1 && category2 != 1)
{
//value is operand 1
value = op1;
}
//if operand 2 is infinty and operand 1 is not
else if(category2 == 1 && category1 != 1)
{
//value is operand 2
value = op2;
}
//if operand 1 is infinity and so is operand 2
else if(category2 == 1 && category1 == 1)
{
//and they both have the same signs
if(sign1 == sign2)
{
//value is either operand
value = op1;
}
//if their signs are different
else
{
//value is Not a Number (NaN) : FFC00000
value = 0xFFC00000;
}
}
return value;
}
/*Function to handle Not a Number (NaN) inputs
* param: operand 1
* param: operand 2
* param: category 1
* param: category 2
* return: NaN value
*/
int NaNInputs(int op1, int op2, unsigned int category1,
unsigned int category2)
{
//local variables
int value;
//if operand 1 is NaN and operand 2 is not
if(category1 == 2 && category2 != 2)
{
//value is operand 1
value = (op1 | 0x7FC00000);
}
//if operand 2 is NaN and operand 1 is not
else if(category2 == 2 && category1 != 2)
{
//value is operand 2
value = (op2 | 0x7FC00000);
}
//if operand 1 is NaN and so is operand 2
else if(category2 == 2 && category1 == 2)
{
//value is Not a Number (NaN) : FFC00000
value = (op2 | 0x7FC00000);
}
return value;
}
/*Function to add Normalized inputs
* param: operand 1
* param: operand 2
* param: sign 1
* param: sign 2
* param: exponent 1
* param: exponent 2
* param: Significand 1
* param: Significand 2
* param: denorm
* return: addition result value
*/
int addNormalized(int op1, int op2, unsigned int sign1, unsigned int sign2,
unsigned int exponent1, unsigned int exponent2,
unsigned int significand1, unsigned int significand2,
unsigned int denorm)
{
//local variable Declarations
unsigned int sign, exponent, significand, ogsignificand;
unsigned int sticky, delta, value, roundFactor, subtracted;
//handle special cases
unsigned int specCase = 0;
//determine the bigger value and use its sign
//if value 1 is greater
if(exponent1 > exponent2)
{
//use sign of value 1
sign = sign1;
//difference between the exponents
delta = exponent1 - exponent2;
//take significand of the smaller value for shifting
significand = ((significand2 << 2) & 0x03FFFFFC);
//take significand of bigger value for storage
ogsignificand = ((significand1 << 2) & 0x03FFFFFC);
//take exponent of smaller value for storage
exponent = exponent2;
}
//if value 2 is greater
else if(exponent1 < exponent2)
{
//use sign of value 2
sign = sign2;
//difference between the exponents
delta = exponent2 - exponent1;
//take significand of the smaller value for shifting
significand = ((significand1 << 2) & 0x03FFFFFC);
//take significand of bigger value for storage
ogsignificand = ((significand2 << 2) & 0x03FFFFFC);
//take exponent of smaller value for storage
exponent = exponent1;
}
//if the values are the same
else
{
//difference of the exponents
delta = 0;
//no need to shift significand
if(significand1 < significand2)
{
//use sign of bigger value
sign = sign2;
//take smaller significand for storage
significand = ((significand1 << 2) & 0x03FFFFFC);
//take bigger significand for storage
ogsignificand = ((significand2 << 2) & 0x03FFFFFC);
}
else if(significand1 > significand2)
{
//use sign of bigger value
sign = sign1;
//take smaller significand for storage
significand = ((significand2 << 2) & 0x03FFFFFC);
//take bigger significand for storage
ogsignificand = ((significand1 << 2) & 0x03FFFFFC);
}
//if significands are the same
else
{
//check to see if signs are the same
if(sign1 == sign2)
{
//use either sign
sign = sign1;
//take either significand for storage
significand = ((significand2 << 2) & 0x03FFFFFC);
//take other significand for storage
ogsignificand = ((significand1 << 2) & 0x03FFFFFC);
}
//if signs are different
else
{
//sign is positive since value is zero
sign = 0;
//take either significand for storage
significand = 0x00000000;
//take other significand for storage
ogsignificand = 0x00000000;
specCase = 1;
}
}
//take exponent of either value for storage
exponent = exponent1;
}
//if delta is negative
if(delta < 0)
{
//make delta positive
delta = -delta;
}
sticky = 0;
roundFactor = 0;
//shift bits to match
int i = 0;
while(i < delta)
{
//sticky bit
if((significand & 0x00000001) == 0x00000001)
{
sticky = 1;
}
//shift significand to right by one bit
significand = significand >> 1;
//increase exponent to match
exponent++;
//get round factor
roundFactor = guardPlusSticky(significand, sticky);
i++;
}
//add the significands if signs are the same
if(sign1 == sign2)
{
significand = ogsignificand + significand;
subtracted = 0;
}
//subtract the significands if signs are different
else
{
significand = ogsignificand - significand;
subtracted = 1;
}
//get round factor
roundFactor = guardPlusSticky(significand, sticky);
//check if significand is all zeros
if(significand == 0x00000000)
{
//if so, return value is 0
value = 0x00000000;
}
else
{
///check to see if significand result is normalized
//if value is De-Normalized
//and significand must be shifted left
if((significand & 0xFFFFFFFF) < 0x02000000)
{
while((significand & 0xFFFFFFFF) < 0x02000000)
{
if(denorm == 1 && exponent <= 0x01)
{
exponent = 0x00;
specCase = 1;
break;
}
//shift significand left by one bit
significand = significand << 1;
exponent--;
//get round factor
roundFactor = guardPlusSticky(significand, sticky);
//check for Underflow
if (checkForUnderflow(exponent) == 1)
{
//if underflow occurs, value is zero
exponent = 0x00;
//get rid of guard bits
significand = 0x00000000;
specCase = 1;
break;
}
}
}
//if significand must be shifted right
if((significand & 0xFFFFFFFF) > 0x03FFFFFF)
{
while((significand & 0xFFFFFFFF) > 0x03FFFFFF)
{
//sticky bit
if((significand & 0x00000001) == 0x00000001)
{
sticky = 1;
}
//shift significand right by one bit
significand = ((significand >> 1) & 0x7FFFFFFF);
exponent++;
//get round factor
roundFactor = guardPlusSticky(significand, sticky);
//check for Overflow
if (checkForOverflow(exponent) == 1)
{
//if overflow occurs, value is infinty
exponent = 0xFF;
//get rid of sig bits
significand = 0x00000000;
specCase = 1;
break;
}
}
}
//get rid of guard bits
significand = ((significand >> 2) & 0x00FFFFFF);
//Handle rounding and re-normalization
if(specCase != 1)
{
//if guard bits are 10 and sticky bit is 0
if(roundFactor == 2)
{
//round to even
if((significand & 0x00000001) == 0x00000001)
{
significand = significand + 1;
}
}
//if guard bits are 10 and sticky is 1 and we added
else if((roundFactor == 3) && (subtracted == 0))
{
significand = significand + 1;
}
//if guard bits are 11, regardless of sticky
else if(roundFactor == 4)
{
significand = significand + 1;
}
///check to see if significand result is still normalized
//if value is De-Normalized
//if significand must be shifted right
if((significand & 0xFFFFFFFF) > 0x00FFFFFF)
{
while((significand & 0xFFFFFFFF) > 0x00FFFFFF)
{
//shift significand right by one bit
significand = ((significand >> 1) & 0x7FFFFFFF);
exponent++;
//check for Overflow
if (checkForOverflow(exponent) == 1)
{
//if overflow occurs, value is infinty
exponent = 0xFF;
//get rid of sig bits
significand = 0x00000000;
specCase = 1;
break;
}
}
}
}
significand = (significand & 0x007FFFFF);
//put all three components together
//if significand is normalized or after shifting
value = (significand | ((exponent << 23) & 0x7F800000));
//add sign
value = ((value & 0x7FFFFFFF) | ((sign & 0x00000001) << 31));
}
return value;
}
/*Function to check for underflow
* param: exponent
* return: 0 if there is no underflow and 1 if there is underflow
*/
int checkForUnderflow(unsigned int exponent)
{
unsigned int value = 0;
if(exponent > 0x800000FE)
{
value = 1;
}
return value;
}
/*Function to check for overflow
* param: exponent
* return: 0 if there is no overflow and 1 if there is overflow
*/
int checkForOverflow(unsigned int exponent)
{
unsigned int value = 0;
if(exponent >= 0x000000FF)
{
value = 1;
}
return value;
}
/*Function to get rounding factor (guard + sticky)
* param: significand
* param: sticky
* return: rounding factor (1 = truncate, 2 = RTE (except in one case)
* 3 = add 1 (except in one case))
*/
int guardPlusSticky(unsigned int significand, unsigned int sticky)
{
//local variables declaration
unsigned int guard, value;
//set guard bits
guard = (significand & 0x00000003);
//rounding factor
value = guard + sticky;
//special cases:
//if guard is 01 and sticky is 1
if((value == 2) && (guard == 1))
{
//set value to 1 so it is truncated
//and not rounded to even
value = 1;
}
//if guard is 11 and sticky is 0
else if((value == 3) && (guard == 3))
{
//set value to 4 so it always adds 1
value = 4;
}
return value;
}