/* * 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 #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 * ------------------------------------------------------------------------------- */ static fInt ConvertToFraction(int); /* Use this to convert an INT to a FINT */ static fInt Convert_ULONG_ToFraction(uint32_t); /* Use this to convert an uint32_t to a FINT */ static fInt GetScaledFraction(int, int); /* Use this to convert an INT to a FINT after scaling it by a factor */ 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) */ static fInt fNegate(fInt); /* Returns -1 * input fInt value */ static fInt fAdd (fInt, fInt); /* Returns the sum of two fInt numbers */ static fInt fSubtract (fInt A, fInt B); /* Returns A-B - Sometimes easier than Adding negative numbers */ static fInt fMultiply (fInt, fInt); /* Returns the product of two fInt numbers */ static fInt fDivide (fInt A, fInt B); /* Returns A/B */ static fInt fGetSquare(fInt); /* Returns the square of a fInt number */ static fInt fSqrt(fInt); /* Returns the Square Root of a fInt number */ static int uAbs(int); /* Returns the Absolute value of the Int */ static int uPow(int base, int exponent); /* Returns base^exponent an INT */ static void SolveQuadracticEqn(fInt, fInt, fInt, fInt[]); /* Returns the 2 roots via the array */ static bool Equal(fInt, fInt); /* Returns true if two fInts are equal to each other */ static bool GreaterThan(fInt A, fInt B); /* Returns true if A > B */ static fInt fExponential(fInt exponent); /* Can be used to calculate e^exponent */ static fInt fNaturalLog(fInt value); /* Can be used to calculate ln(value) */ /* Fuse decoding functions * ------------------------------------------------------------------------------------- */ static fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength); static fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength); static 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. */ static fInt Divide (int, int); /* Divide two INTs and return result as FINT */ static fInt fNegate(fInt); static int uGetScaledDecimal (fInt); /* Internal function */ static int GetReal (fInt A); /* Internal function */ /* ------------------------------------------------------------------------------------- * 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 * ------------------------------------------------------------------------------------- */ static 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; static const uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78}; static const 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; } static 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; static const uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078}; static const 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)); } static 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; } static 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; } static 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; } static 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; } static fInt fNegate(fInt X) { fInt CONSTANT_NEGONE = ConvertToFraction(-1); return (fMultiply(X, CONSTANT_NEGONE)); } static fInt Convert_ULONG_ToFraction(uint32_t X) { fInt temp; if (X <= MAX) temp.full = (X << SHIFT_AMOUNT); else temp.full = 0; return temp; } static 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 */ static fInt fAdd (fInt X, fInt Y) { fInt Sum; Sum.full = X.full + Y.full; return Sum; } /* Addition using two fInts */ static fInt fSubtract (fInt X, fInt Y) { fInt Difference; Difference.full = X.full - Y.full; return Difference; } static bool Equal(fInt A, fInt B) { if (A.full == B.full) return true; else return false; } static bool GreaterThan(fInt A, fInt B) { if (A.full > B.full) return true; else return false; } static 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; } static 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; } static 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; } static fInt fGetSquare(fInt A) { return fMultiply(A,A); } /* x_new = x_old - (x_old^2 - C) / (2 * x_old) */ static 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); } static 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 * ----------------------------------------------------------------------------- */ /* 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; }