Using C Programming

Define the following constants:

SIGN_SHIFT	how many bits to shift the sign field from the least signficant position to where the exponent bit field belongs.
EXPONENT_SHIFT	how many bits to shift the exponent bit field from the least signficant position to where the exponent bit field belongs.
MANTISSA_MASK	the mask to only keep the mantissa bit field.
MANTISSA_HIDDEN_BIT	the hidden bit in its proper position
MANTISSA_SHIFT	How many bits to shift the mantissa bit field from the least signficant position to where the mantissa bit field belongs.

Use those constants, and the others given, to finish the following functions:

int isPositive(float number)	Returns '1' if 'number' is positive, or '0' otherwise.
int obtainExponent(float number)	Returns the power-of-2 exponent of 'number'.
int obtainMantissa(float number)	Returns the mantissa of 'number'.
int isZero(float number)	Returns return '1' if 'number' is +0.0 or -0.0, or false otherwise.

/*-------------------------------------------------------------------------* *--- ---* *--- floatCompare.c ---* *--- ---* *--- This file defines a program that supports the function ---* *--- isLessThan(float lhs,float rhs). It compares 'lhs' and 'rhs' ---* *--- and implements the floating point '<' operator, but does so ---* *--- with only integer and bitwise operations. ---* *--- ---* 

// Compile with: // $ gcc floatCompare.c -o floatCompare -std=c99 -lm #include  #include  #include  #include  // PURPOSE: To define a nickname for type 'unsigned int'. typedef unsigned int uInt; //-- Sign related constants --// // PURPOSE: To tell how many bits to shift the sign field from the // least signficant position to where the exponent bit field belongs. const uInt SIGN_SHIFT = 0; // CHANGE THAT 0! // PURPOSE: To be the mask to only keep the sign bit field. #define SIGN_MASK (uInt)(0x1 << SIGN_SHIFT) //-- Exponent related constants --// // PURPOSE: To tell how many bits to shift the exponent bit field from the // least signficant position to where the exponent bit field belongs. const uInt EXPONENT_SHIFT = 0; // CHANGE THAT 0! // PURPOSE: To be the mask to only keep the exponent bit field. #define EXPONENT_MASK (uInt)(0xFF << EXPONENT_SHIFT) // PURPOSE: To tell the exponent bit pattern for denormalized numbers. const uInt EXPONENT_DENORMALIZED_BIT_PATTERN = 0x00; // PURPOSE: To tell the exponent value (*not* the bit pattern value) that // signifies a denormalized number. const int DENORMALIZE_EXPONENT = -127; // PURPOSE: To tell the 'bias' of the exponents: // exponent = (bit field number) - 'bias'. const uInt EXPONENT_BIAS = 0x7F; //-- Mantissa related constants --// // PURPOSE: To tell the mask to only keep the mantissa bit field. const uInt MANTISSA_MASK = 0; // CHANGE THAT 0! // PURPOSE: To tell give the hidden bit in its proper position. const uInt MANTISSA_HIDDEN_BIT = 0; // CHANGE THAT 0! // PURPOSE: To tell how many bits to shift the mantissa bit field from the // least signficant position to where the mantissa bit field belongs. const uInt MANTISSA_SHIFT = 0; // PERHAPS CHANGE THAT 0? // PURPOSE: To tell how many mantissa bits there are (including hidden bit) const uInt NUM_MANTISSA_BITS = 24; //-- Miscellaneous related constants --// // PURPOSE: To give the maximum length of C-strings. const uInt TEXT_LEN = 64; //-- Functions: --// // PURPOSE: To return '1' if 'number' is positive, or '0' otherwise. int isPositive (float number ) { // Make an integer with the same bit pattern as number // If that integer has SIGN_MASK on then return '0', otherwise '1' } // PURPOSE: To return the power-of-2 exponent of 'number'. int obtainExponent (float number ) { // Make an integer with the same bit pattern as number // Use EXPONENT_MASK to only keep only the exponent bits. // Shift the result over by EXPONENT_SHIFT // Subtract EXPONENT_BIAS from the shifted result, return() that value } // PURPOSE: To return the mantissa of 'number'. int obtainMantissa (float number ) { // Make an integer with the same bit pattern as number // Use MANTISSA_MASK to only keep only the exponent bits. // Shift the result over by MANTISSA_SHIFT // Only if (obtainExponent(number) != DENORMALIZE_EXPONENT) then turn the MANTISSA_HIDDEN_BIT on } // PURPOSE: To return '1' if 'number' is +0.0 or -0.0, or false otherwise. int isZero (float number ) { // If (obtainExponent(number) == DENORMALIZE_EXPONENT) and // (obtainMantissa(number) == 0x00) then return 1, otherwise 0. } // PURPOSE: To return '1' if 'lhs' is computed as being less than 'rhs' or // '0' otherwise. int isLessThan (float lhs, float rhs ) { // I. Application validity check: // II. Compare numbers: // II.A. Handle zero as a special case: if ( isZero(lhs) && isZero(rhs) ) return(0); // II.B. Compare signs: int isLhsPos = isPositive(lhs); int isRhsPos = isPositive(rhs); if (isLhsPos && !isRhsPos) return(0); if (!isLhsPos && isRhsPos) return(1); // II.C. Compare exponents: int lhsExp = obtainExponent(lhs); int rhsExp = obtainExponent(rhs); if (lhsExp > rhsExp) return( isLhsPos ? 0 : 1 ); if (lhsExp < rhsExp) return( isLhsPos ? 1 : 0 ); // II.D. Compare mantissas: int lhsMant = obtainMantissa(lhs); int rhsMant = obtainMantissa(rhs); if (lhsMant > rhsMant) return( isLhsPos ? 0 : 1 ); if (lhsMant < rhsMant) return( isLhsPos ? 1 : 0 ); // III. Finished, if get here they are equal: return(0); } // PURPOSE: To compare several floating point numbers with 'isLessThan()', // and to tell how accurate the function is. Ignores arguments. Returns // 'EXIT_SUCCESS' to OS. int main () { // I. Application validity check: // II. Do comparisons: // II.A. Define numbers to compare: const float NUMBER_ARRAY[] = {-INFINITY, -FLT_MAX, -1e+10, -1.0, -1e-10, -1.17549e-38, -5.87747e-39, -2.93874e-39, -1.4013e-45, -0.0, +0.0, +1.4013e-45, +2.93874e-39, +5.87747e-39, +1.17549e-38, +1e-10, +1.0, +1e+10, +FLT_MAX, +INFINITY }; const int NUM_NUMS = sizeof(NUMBER_ARRAY) / sizeof(float); // II.B. Decompose all numbers into sign, exponent and mantissa: int index; for (index = 0; index < NUM_NUMS; index++) { float number = NUMBER_ARRAY[index]; int isPos = isPositive(number); int exponent= obtainExponent(number); int mantissa= obtainMantissa(number); float reconstitute = (exponent == DENORMALIZE_EXPONENT) ? pow(2.0,exponent+1) * ((double)(mantissa))/MANTISSA_HIDDEN_BIT : pow(2.0,exponent) * ((double)(mantissa))/MANTISSA_HIDDEN_BIT; if (!isPos) reconstitute = -reconstitute; printf("%12g: %c\t%4d\t0x%06X\t%g ", number, isPositive(number) ? '+' : '-', exponent, mantissa, reconstitute ); } // II.C. Do comparisons: int indexOut; int indexIn; for (indexOut = 0; indexOut < NUM_NUMS; indexOut++) { float lhs = NUMBER_ARRAY[indexOut]; for (indexIn = 0; indexIn < NUM_NUMS; indexIn++) { float rhs = NUMBER_ARRAY[indexIn]; int result = isLessThan(lhs,rhs); printf("isLessThan(%12g,%12g) == %5s (%s) ",lhs,rhs, (result ? "true" : "false"), ( (result == (lhs < rhs)) ? "correct" : "WRONG") ); } } // III. Finished: return(EXIT_SUCCESS); }

Correct output:

$ ./floatCompare isLessThan( -inf, -inf) == false (correct) isLessThan( -inf,-3.40282e+38) == true (correct) isLessThan( -inf, -1e+10) == true (correct) isLessThan( -inf, -1e-10) == true (correct) isLessThan( -inf,-1.17549e-38) == true (correct) isLessThan( -inf,-5.87747e-39) == true (correct) isLessThan( -inf,-2.93874e-39) == true (correct) isLessThan( -inf, -1.4013e-45) == true (correct) isLessThan( -inf, -0) == true (correct) isLessThan( -inf, 0) == true (correct) isLessThan( -inf, 1.4013e-45) == true (correct) isLessThan( -inf, 2.93874e-39) == true (correct) isLessThan( -inf, 5.87747e-39) == true (correct) isLessThan( -inf, 1.17549e-38) == true (correct) isLessThan( -inf, 1e-10) == true (correct) isLessThan( -inf, 1) == true (correct) isLessThan( -inf, 1e+10) == true (correct) isLessThan( -inf, 3.40282e+38) == true (correct) isLessThan( -inf, inf) == true (correct) isLessThan(-3.40282e+38, -inf) == false (correct) isLessThan(-3.40282e+38,-3.40282e+38) == false (correct) isLessThan(-3.40282e+38, -1e+10) == true (correct) isLessThan(-3.40282e+38, -1e-10) == true (correct) isLessThan(-3.40282e+38,-1.17549e-38) == true (correct) isLessThan(-3.40282e+38,-5.87747e-39) == true (correct) isLessThan(-3.40282e+38,-2.93874e-39) == true (correct)