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