text: /*
   * Copyright 2015 Advanced Micro Devices, Inc.
   *
   * Permission is hereby granted, free of charge, to any person obtaining a
   * copy of this software and associated documentation files (the "Software"),
   * to deal in the Software without restriction, including without limitation
   * the rights to use, copy, modify, merge, publish, distribute, sublicense,
   * and/or sell copies of the Software, and to permit persons to whom the
   * Software is furnished to do so, subject to the following conditions:
   *
   * The above copyright notice and this permission notice shall be included in
   * all copies or substantial portions of the Software.
   *
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
   * THE COPYRIGHT HOLDER(S) OR AUTHOR(S) BE LIABLE FOR ANY CLAIM, DAMAGES OR
   * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
   * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
   * OTHER DEALINGS IN THE SOFTWARE.
   *
   */
  #include <asm/div64.h>
  
  #define SHIFT_AMOUNT 16 /* We multiply all original integers with 2^SHIFT_AMOUNT to get the fInt representation */
  
  #define PRECISION 5 /* Change this value to change the number of decimal places in the final output - 5 is a good default */
  
  #define SHIFTED_2 (2 << SHIFT_AMOUNT)
  #define MAX (1 << (SHIFT_AMOUNT - 1)) - 1 /* 32767 - Might change in the future */
  
  /* -------------------------------------------------------------------------------
   * NEW TYPE - fINT
   * -------------------------------------------------------------------------------
   * A variable of type fInt can be accessed in 3 ways using the dot (.) operator
   * fInt A;
   * A.full => The full number as it is. Generally not easy to read
   * A.partial.real => Only the integer portion
   * A.partial.decimal => Only the fractional portion
   */
  typedef union _fInt {
      int full;
      struct _partial {
          unsigned int decimal: SHIFT_AMOUNT; /*Needs to always be unsigned*/
          int real: 32 - SHIFT_AMOUNT;
      } partial;
  } fInt;
  
  /* -------------------------------------------------------------------------------
   * Function Declarations
   *  -------------------------------------------------------------------------------
   */
  fInt ConvertToFraction(int);                       /* Use this to convert an INT to a FINT */
  fInt Convert_ULONG_ToFraction(uint32_t);              /* Use this to convert an uint32_t to a FINT */
  fInt GetScaledFraction(int, int);                  /* Use this to convert an INT to a FINT after scaling it by a factor */
  int ConvertBackToInteger(fInt);                    /* Convert a FINT back to an INT that is scaled by 1000 (i.e. last 3 digits are the decimal digits) */
  
  fInt fNegate(fInt);                                /* Returns -1 * input fInt value */
  fInt fAdd (fInt, fInt);                            /* Returns the sum of two fInt numbers */
  fInt fSubtract (fInt A, fInt B);                   /* Returns A-B - Sometimes easier than Adding negative numbers */
  fInt fMultiply (fInt, fInt);                       /* Returns the product of two fInt numbers */
  fInt fDivide (fInt A, fInt B);                     /* Returns A/B */
  fInt fGetSquare(fInt);                             /* Returns the square of a fInt number */
  fInt fSqrt(fInt);                                  /* Returns the Square Root of a fInt number */
  
  int uAbs(int);                                     /* Returns the Absolute value of the Int */
  fInt fAbs(fInt);                                   /* Returns the Absolute value of the fInt */
  int uPow(int base, int exponent);                  /* Returns base^exponent an INT */
  
  void SolveQuadracticEqn(fInt, fInt, fInt, fInt[]); /* Returns the 2 roots via the array */
  bool Equal(fInt, fInt);                         /* Returns true if two fInts are equal to each other */
  bool GreaterThan(fInt A, fInt B);               /* Returns true if A > B */
  
  fInt fExponential(fInt exponent);                  /* Can be used to calculate e^exponent */
  fInt fNaturalLog(fInt value);                      /* Can be used to calculate ln(value) */
  
  /* Fuse decoding functions
   * -------------------------------------------------------------------------------------
   */
  fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength);
  fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength);
  fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength);
  
  /* Internal Support Functions - Use these ONLY for testing or adding to internal functions
   * -------------------------------------------------------------------------------------
   * Some of the following functions take two INTs as their input - This is unsafe for a variety of reasons.
   */
  fInt Add (int, int);                               /* Add two INTs and return Sum as FINT */
  fInt Multiply (int, int);                          /* Multiply two INTs and return Product as FINT */
  fInt Divide (int, int);                            /* You get the idea... */
  fInt fNegate(fInt);
  
  int uGetScaledDecimal (fInt);                      /* Internal function */
  int GetReal (fInt A);                              /* Internal function */
  
  /* Future Additions and Incomplete Functions
   * -------------------------------------------------------------------------------------
   */
  int GetRoundedValue(fInt);                         /* Incomplete function - Useful only when Precision is lacking */
                                                     /* Let us say we have 2.126 but can only handle 2 decimal points. We could */
                                                     /* either chop of 6 and keep 2.12 or use this function to get 2.13, which is more accurate */
  
  /* -------------------------------------------------------------------------------------
   * TROUBLESHOOTING INFORMATION
   * -------------------------------------------------------------------------------------
   * 1) ConvertToFraction - InputOutOfRangeException: Only accepts numbers smaller than MAX (default: 32767)
   * 2) fAdd - OutputOutOfRangeException: Output bigger than MAX (default: 32767)
   * 3) fMultiply - OutputOutOfRangeException:
   * 4) fGetSquare - OutputOutOfRangeException:
   * 5) fDivide - DivideByZeroException
   * 6) fSqrt - NegativeSquareRootException: Input cannot be a negative number
   */
  
  /* -------------------------------------------------------------------------------------
   * START OF CODE
   * -------------------------------------------------------------------------------------
   */
  fInt fExponential(fInt exponent)        /*Can be used to calculate e^exponent*/
  {
  	uint32_t i;
  	bool bNegated = false;
  
  	fInt fPositiveOne = ConvertToFraction(1);
  	fInt fZERO = ConvertToFraction(0);
  
  	fInt lower_bound = Divide(78, 10000);
  	fInt solution = fPositiveOne; /*Starting off with baseline of 1 */
  	fInt error_term;
  
  	uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
  	uint32_t expk_array[11] = {2560000, 160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
  
  	if (GreaterThan(fZERO, exponent)) {
  		exponent = fNegate(exponent);
  		bNegated = true;
  	}
  
  	while (GreaterThan(exponent, lower_bound)) {
  		for (i = 0; i < 11; i++) {
  			if (GreaterThan(exponent, GetScaledFraction(k_array[i], 10000))) {
  				exponent = fSubtract(exponent, GetScaledFraction(k_array[i], 10000));
  				solution = fMultiply(solution, GetScaledFraction(expk_array[i], 10000));
  			}
  		}
  	}
  
  	error_term = fAdd(fPositiveOne, exponent);
  
  	solution = fMultiply(solution, error_term);
  
  	if (bNegated)
  		solution = fDivide(fPositiveOne, solution);
  
  	return solution;
  }
  
  fInt fNaturalLog(fInt value)
  {
  	uint32_t i;
  	fInt upper_bound = Divide(8, 1000);
  	fInt fNegativeOne = ConvertToFraction(-1);
  	fInt solution = ConvertToFraction(0); /*Starting off with baseline of 0 */
  	fInt error_term;
  
  	uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
  	uint32_t logk_array[10] = {27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
  
  	while (GreaterThan(fAdd(value, fNegativeOne), upper_bound)) {
  		for (i = 0; i < 10; i++) {
  			if (GreaterThan(value, GetScaledFraction(k_array[i], 10000))) {
  				value = fDivide(value, GetScaledFraction(k_array[i], 10000));
  				solution = fAdd(solution, GetScaledFraction(logk_array[i], 10000));
  			}
  		}
  	}
  
  	error_term = fAdd(fNegativeOne, value);
  
  	return (fAdd(solution, error_term));
  }
  
  fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength)
  {
  	fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
  	fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
  
  	fInt f_decoded_value;
  
  	f_decoded_value = fDivide(f_fuse_value, f_bit_max_value);
  	f_decoded_value = fMultiply(f_decoded_value, f_range);
  	f_decoded_value = fAdd(f_decoded_value, f_min);
  
  	return f_decoded_value;
  }
  
  
  fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength)
  {
  	fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
  	fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
  
  	fInt f_CONSTANT_NEG13 = ConvertToFraction(-13);
  	fInt f_CONSTANT1 = ConvertToFraction(1);
  
  	fInt f_decoded_value;
  
  	f_decoded_value = fSubtract(fDivide(f_bit_max_value, f_fuse_value), f_CONSTANT1);
  	f_decoded_value = fNaturalLog(f_decoded_value);
  	f_decoded_value = fMultiply(f_decoded_value, fDivide(f_range, f_CONSTANT_NEG13));
  	f_decoded_value = fAdd(f_decoded_value, f_average);
  
  	return f_decoded_value;
  }
  
  fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength)
  {
  	fInt fLeakage;
  	fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
  
  	fLeakage = fMultiply(ln_max_div_min, Convert_ULONG_ToFraction(leakageID_fuse));
  	fLeakage = fDivide(fLeakage, f_bit_max_value);
  	fLeakage = fExponential(fLeakage);
  	fLeakage = fMultiply(fLeakage, f_min);
  
  	return fLeakage;
  }
  
  fInt ConvertToFraction(int X) /*Add all range checking here. Is it possible to make fInt a private declaration? */
  {
  	fInt temp;
  
  	if (X <= MAX)
  		temp.full = (X << SHIFT_AMOUNT);
  	else
  		temp.full = 0;
  
  	return temp;
  }
  
  fInt fNegate(fInt X)
  {
  	fInt CONSTANT_NEGONE = ConvertToFraction(-1);
  	return (fMultiply(X, CONSTANT_NEGONE));
  }
  
  fInt Convert_ULONG_ToFraction(uint32_t X)
  {
  	fInt temp;
  
  	if (X <= MAX)
  		temp.full = (X << SHIFT_AMOUNT);
  	else
  		temp.full = 0;
  
  	return temp;
  }
  
  fInt GetScaledFraction(int X, int factor)
  {
  	int times_shifted, factor_shifted;
  	bool bNEGATED;
  	fInt fValue;
  
  	times_shifted = 0;
  	factor_shifted = 0;
  	bNEGATED = false;
  
  	if (X < 0) {
  		X = -1*X;
  		bNEGATED = true;
  	}
  
  	if (factor < 0) {
  		factor = -1*factor;
  		bNEGATED = !bNEGATED; /*If bNEGATED = true due to X < 0, this will cover the case of negative cancelling negative */
  	}
  
  	if ((X > MAX) || factor > MAX) {
  		if ((X/factor) <= MAX) {
  			while (X > MAX) {
  				X = X >> 1;
  				times_shifted++;
  			}
  
  			while (factor > MAX) {
  				factor = factor >> 1;
  				factor_shifted++;
  			}
  		} else {
  			fValue.full = 0;
  			return fValue;
  		}
  	}
  
  	if (factor == 1)
  	return (ConvertToFraction(X));
  
  	fValue = fDivide(ConvertToFraction(X * uPow(-1, bNEGATED)), ConvertToFraction(factor));
  
  	fValue.full = fValue.full << times_shifted;
  	fValue.full = fValue.full >> factor_shifted;
  
  	return fValue;
  }
  
  /* Addition using two fInts */
  fInt fAdd (fInt X, fInt Y)
  {
  	fInt Sum;
  
  	Sum.full = X.full + Y.full;
  
  	return Sum;
  }
  
  /* Addition using two fInts */
  fInt fSubtract (fInt X, fInt Y)
  {
  	fInt Difference;
  
  	Difference.full = X.full - Y.full;
  
  	return Difference;
  }
  
  bool Equal(fInt A, fInt B)
  {
  	if (A.full == B.full)
  		return true;
  	else
  		return false;
  }
  
  bool GreaterThan(fInt A, fInt B)
  {
  	if (A.full > B.full)
  		return true;
  	else
  		return false;
  }
  
  fInt fMultiply (fInt X, fInt Y) /* Uses 64-bit integers (int64_t) */
  {
  	fInt Product;
  	int64_t tempProduct;
  	bool X_LessThanOne, Y_LessThanOne;
  
  	X_LessThanOne = (X.partial.real == 0 && X.partial.decimal != 0 && X.full >= 0);
  	Y_LessThanOne = (Y.partial.real == 0 && Y.partial.decimal != 0 && Y.full >= 0);
  
  	/*The following is for a very specific common case: Non-zero number with ONLY fractional portion*/
  	/* TEMPORARILY DISABLED - CAN BE USED TO IMPROVE PRECISION
  
  	if (X_LessThanOne && Y_LessThanOne) {
  		Product.full = X.full * Y.full;
  		return Product
  	}*/
  
  	tempProduct = ((int64_t)X.full) * ((int64_t)Y.full); /*Q(16,16)*Q(16,16) = Q(32, 32) - Might become a negative number! */
  	tempProduct = tempProduct >> 16; /*Remove lagging 16 bits - Will lose some precision from decimal; */
  	Product.full = (int)tempProduct; /*The int64_t will lose the leading 16 bits that were part of the integer portion */
  
  	return Product;
  }
  
  fInt fDivide (fInt X, fInt Y)
  {
  	fInt fZERO, fQuotient;
  	int64_t longlongX, longlongY;
  
  	fZERO = ConvertToFraction(0);
  
  	if (Equal(Y, fZERO))
  	return fZERO;
  
  	longlongX = (int64_t)X.full;
  	longlongY = (int64_t)Y.full;
  
  	longlongX = longlongX << 16; /*Q(16,16) -> Q(32,32) */
  
  	div64_s64(longlongX, longlongY); /*Q(32,32) divided by Q(16,16) = Q(16,16) Back to original format */
  
  	fQuotient.full = (int)longlongX;
  	return fQuotient;
  }
  
  int ConvertBackToInteger (fInt A) /*THIS is the function that will be used to check with the Golden settings table*/
  {
  	fInt fullNumber, scaledDecimal, scaledReal;
  
  	scaledReal.full = GetReal(A) * uPow(10, PRECISION-1); /* DOUBLE CHECK THISSSS!!! */
  
  	scaledDecimal.full = uGetScaledDecimal(A);
  
  	fullNumber = fAdd(scaledDecimal,scaledReal);
  
  	return fullNumber.full;
  }
  
  fInt fGetSquare(fInt A)
  {
  	return fMultiply(A,A);
  }
  
  /* x_new = x_old - (x_old^2 - C) / (2 * x_old) */
  fInt fSqrt(fInt num)
  {
  	fInt F_divide_Fprime, Fprime;
  	fInt test;
  	fInt twoShifted;
  	int seed, counter, error;
  	fInt x_new, x_old, C, y;
  
  	fInt fZERO = ConvertToFraction(0);
  
  	/* (0 > num) is the same as (num < 0), i.e., num is negative */
  
  	if (GreaterThan(fZERO, num) || Equal(fZERO, num))
  		return fZERO;
  
  	C = num;
  
  	if (num.partial.real > 3000)
  		seed = 60;
  	else if (num.partial.real > 1000)
  		seed = 30;
  	else if (num.partial.real > 100)
  		seed = 10;
  	else
  		seed = 2;
  
  	counter = 0;
  
  	if (Equal(num, fZERO)) /*Square Root of Zero is zero */
  		return fZERO;
  
  	twoShifted = ConvertToFraction(2);
  	x_new = ConvertToFraction(seed);
  
  	do {
  		counter++;
  
  		x_old.full = x_new.full;
  
  		test = fGetSquare(x_old); /*1.75*1.75 is reverting back to 1 when shifted down */
  		y = fSubtract(test, C); /*y = f(x) = x^2 - C; */
  
  		Fprime = fMultiply(twoShifted, x_old);
  		F_divide_Fprime = fDivide(y, Fprime);
  
  		x_new = fSubtract(x_old, F_divide_Fprime);
  
  		error = ConvertBackToInteger(x_new) - ConvertBackToInteger(x_old);
  
  		if (counter > 20) /*20 is already way too many iterations. If we dont have an answer by then, we never will*/
  			return x_new;
  
  	} while (uAbs(error) > 0);
  
  	return (x_new);
  }
  
  void SolveQuadracticEqn(fInt A, fInt B, fInt C, fInt Roots[])
  {
  	fInt *pRoots = &Roots[0];
  	fInt temp, root_first, root_second;
  	fInt f_CONSTANT10, f_CONSTANT100;
  
  	f_CONSTANT100 = ConvertToFraction(100);
  	f_CONSTANT10 = ConvertToFraction(10);
  
  	while(GreaterThan(A, f_CONSTANT100) || GreaterThan(B, f_CONSTANT100) || GreaterThan(C, f_CONSTANT100)) {
  		A = fDivide(A, f_CONSTANT10);
  		B = fDivide(B, f_CONSTANT10);
  		C = fDivide(C, f_CONSTANT10);
  	}
  
  	temp = fMultiply(ConvertToFraction(4), A); /* root = 4*A */
  	temp = fMultiply(temp, C); /* root = 4*A*C */
  	temp = fSubtract(fGetSquare(B), temp); /* root = b^2 - 4AC */
  	temp = fSqrt(temp); /*root = Sqrt (b^2 - 4AC); */
  
  	root_first = fSubtract(fNegate(B), temp); /* b - Sqrt(b^2 - 4AC) */
  	root_second = fAdd(fNegate(B), temp); /* b + Sqrt(b^2 - 4AC) */
  
  	root_first = fDivide(root_first, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
  	root_first = fDivide(root_first, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
  
  	root_second = fDivide(root_second, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
  	root_second = fDivide(root_second, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
  
  	*(pRoots + 0) = root_first;
  	*(pRoots + 1) = root_second;
  }
  
  /* -----------------------------------------------------------------------------
   * SUPPORT FUNCTIONS
   * -----------------------------------------------------------------------------
   */
  
  /* Addition using two normal ints - Temporary - Use only for testing purposes?. */
  fInt Add (int X, int Y)
  {
  	fInt A, B, Sum;
  
  	A.full = (X << SHIFT_AMOUNT);
  	B.full = (Y << SHIFT_AMOUNT);
  
  	Sum.full = A.full + B.full;
  
  	return Sum;
  }
  
  /* Conversion Functions */
  int GetReal (fInt A)
  {
  	return (A.full >> SHIFT_AMOUNT);
  }
  
  /* Temporarily Disabled */
  int GetRoundedValue(fInt A) /*For now, round the 3rd decimal place */
  {
  	/* ROUNDING TEMPORARLY DISABLED
  	int temp = A.full;
  	int decimal_cutoff, decimal_mask = 0x000001FF;
  	decimal_cutoff = temp & decimal_mask;
  	if (decimal_cutoff > 0x147) {
  		temp += 673;
  	}*/
  
  	return ConvertBackToInteger(A)/10000; /*Temporary - in case this was used somewhere else */
  }
  
  fInt Multiply (int X, int Y)
  {
  	fInt A, B, Product;
  
  	A.full = X << SHIFT_AMOUNT;
  	B.full = Y << SHIFT_AMOUNT;
  
  	Product = fMultiply(A, B);
  
  	return Product;
  }
  
  fInt Divide (int X, int Y)
  {
  	fInt A, B, Quotient;
  
  	A.full = X << SHIFT_AMOUNT;
  	B.full = Y << SHIFT_AMOUNT;
  
  	Quotient = fDivide(A, B);
  
  	return Quotient;
  }
  
  int uGetScaledDecimal (fInt A) /*Converts the fractional portion to whole integers - Costly function */
  {
  	int dec[PRECISION];
  	int i, scaledDecimal = 0, tmp = A.partial.decimal;
  
  	for (i = 0; i < PRECISION; i++) {
  		dec[i] = tmp / (1 << SHIFT_AMOUNT);
  		tmp = tmp - ((1 << SHIFT_AMOUNT)*dec[i]);
  		tmp *= 10;
  		scaledDecimal = scaledDecimal + dec[i]*uPow(10, PRECISION - 1 -i);
  	}
  
  	return scaledDecimal;
  }
  
  int uPow(int base, int power)
  {
  	if (power == 0)
  		return 1;
  	else
  		return (base)*uPow(base, power - 1);
  }
  
  fInt fAbs(fInt A)
  {
  	if (A.partial.real < 0)
  		return (fMultiply(A, ConvertToFraction(-1)));
  	else
  		return A;
  }
  
  int uAbs(int X)
  {
  	if (X < 0)
  		return (X * -1);
  	else
  		return X;
  }
  
  fInt fRoundUpByStepSize(fInt A, fInt fStepSize, bool error_term)
  {
  	fInt solution;
  
  	solution = fDivide(A, fStepSize);
  	solution.partial.decimal = 0; /*All fractional digits changes to 0 */
  
  	if (error_term)
  		solution.partial.real += 1; /*Error term of 1 added */
  
  	solution = fMultiply(solution, fStepSize);
  	solution = fAdd(solution, fStepSize);
  
  	return solution;
  }
  
  