1/* 2 * Copyright 2015 Advanced Micro Devices, Inc. 3 * 4 * Permission is hereby granted, free of charge, to any person obtaining a 5 * copy of this software and associated documentation files (the "Software"), 6 * to deal in the Software without restriction, including without limitation 7 * the rights to use, copy, modify, merge, publish, distribute, sublicense, 8 * and/or sell copies of the Software, and to permit persons to whom the 9 * Software is furnished to do so, subject to the following conditions: 10 * 11 * The above copyright notice and this permission notice shall be included in 12 * all copies or substantial portions of the Software. 13 * 14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 17 * THE COPYRIGHT HOLDER(S) OR AUTHOR(S) BE LIABLE FOR ANY CLAIM, DAMAGES OR 18 * OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 19 * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 20 * OTHER DEALINGS IN THE SOFTWARE. 21 * 22 */ 23#include <asm/div64.h> 24 25#define SHIFT_AMOUNT 16 /* We multiply all original integers with 2^SHIFT_AMOUNT to get the fInt representation */ 26 27#define PRECISION 5 /* Change this value to change the number of decimal places in the final output - 5 is a good default */ 28 29#define SHIFTED_2 (2 << SHIFT_AMOUNT) 30#define MAX (1 << (SHIFT_AMOUNT - 1)) - 1 /* 32767 - Might change in the future */ 31 32/* ------------------------------------------------------------------------------- 33 * NEW TYPE - fINT 34 * ------------------------------------------------------------------------------- 35 * A variable of type fInt can be accessed in 3 ways using the dot (.) operator 36 * fInt A; 37 * A.full => The full number as it is. Generally not easy to read 38 * A.partial.real => Only the integer portion 39 * A.partial.decimal => Only the fractional portion 40 */ 41typedef union _fInt { 42 int full; 43 struct _partial { 44 unsigned int decimal: SHIFT_AMOUNT; /*Needs to always be unsigned*/ 45 int real: 32 - SHIFT_AMOUNT; 46 } partial; 47} fInt; 48 49/* ------------------------------------------------------------------------------- 50 * Function Declarations 51 * ------------------------------------------------------------------------------- 52 */ 53static fInt ConvertToFraction(int); /* Use this to convert an INT to a FINT */ 54static fInt Convert_ULONG_ToFraction(uint32_t); /* Use this to convert an uint32_t to a FINT */ 55static fInt GetScaledFraction(int, int); /* Use this to convert an INT to a FINT after scaling it by a factor */ 56static int ConvertBackToInteger(fInt); /* Convert a FINT back to an INT that is scaled by 1000 (i.e. last 3 digits are the decimal digits) */ 57 58static fInt fNegate(fInt); /* Returns -1 * input fInt value */ 59static fInt fAdd (fInt, fInt); /* Returns the sum of two fInt numbers */ 60static fInt fSubtract (fInt A, fInt B); /* Returns A-B - Sometimes easier than Adding negative numbers */ 61static fInt fMultiply (fInt, fInt); /* Returns the product of two fInt numbers */ 62static fInt fDivide (fInt A, fInt B); /* Returns A/B */ 63static fInt fGetSquare(fInt); /* Returns the square of a fInt number */ 64static fInt fSqrt(fInt); /* Returns the Square Root of a fInt number */ 65 66static int uAbs(int); /* Returns the Absolute value of the Int */ 67static int uPow(int base, int exponent); /* Returns base^exponent an INT */ 68 69static void SolveQuadracticEqn(fInt, fInt, fInt, fInt[]); /* Returns the 2 roots via the array */ 70static bool Equal(fInt, fInt); /* Returns true if two fInts are equal to each other */ 71static bool GreaterThan(fInt A, fInt B); /* Returns true if A > B */ 72 73static fInt fExponential(fInt exponent); /* Can be used to calculate e^exponent */ 74static fInt fNaturalLog(fInt value); /* Can be used to calculate ln(value) */ 75 76/* Fuse decoding functions 77 * ------------------------------------------------------------------------------------- 78 */ 79static fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength); 80static fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength); 81static fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength); 82 83/* Internal Support Functions - Use these ONLY for testing or adding to internal functions 84 * ------------------------------------------------------------------------------------- 85 * Some of the following functions take two INTs as their input - This is unsafe for a variety of reasons. 86 */ 87static fInt Divide (int, int); /* Divide two INTs and return result as FINT */ 88static fInt fNegate(fInt); 89 90static int uGetScaledDecimal (fInt); /* Internal function */ 91static int GetReal (fInt A); /* Internal function */ 92 93/* ------------------------------------------------------------------------------------- 94 * TROUBLESHOOTING INFORMATION 95 * ------------------------------------------------------------------------------------- 96 * 1) ConvertToFraction - InputOutOfRangeException: Only accepts numbers smaller than MAX (default: 32767) 97 * 2) fAdd - OutputOutOfRangeException: Output bigger than MAX (default: 32767) 98 * 3) fMultiply - OutputOutOfRangeException: 99 * 4) fGetSquare - OutputOutOfRangeException: 100 * 5) fDivide - DivideByZeroException 101 * 6) fSqrt - NegativeSquareRootException: Input cannot be a negative number 102 */ 103 104/* ------------------------------------------------------------------------------------- 105 * START OF CODE 106 * ------------------------------------------------------------------------------------- 107 */ 108static fInt fExponential(fInt exponent) /*Can be used to calculate e^exponent*/ 109{ 110 uint32_t i; 111 bool bNegated = false; 112 113 fInt fPositiveOne = ConvertToFraction(1); 114 fInt fZERO = ConvertToFraction(0); 115 116 fInt lower_bound = Divide(78, 10000); 117 fInt solution = fPositiveOne; /*Starting off with baseline of 1 */ 118 fInt error_term; 119 120 static const uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78}; 121 static const uint32_t expk_array[11] = {2560000, 160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078}; 122 123 if (GreaterThan(fZERO, exponent)) { 124 exponent = fNegate(exponent); 125 bNegated = true; 126 } 127 128 while (GreaterThan(exponent, lower_bound)) { 129 for (i = 0; i < 11; i++) { 130 if (GreaterThan(exponent, GetScaledFraction(k_array[i], 10000))) { 131 exponent = fSubtract(exponent, GetScaledFraction(k_array[i], 10000)); 132 solution = fMultiply(solution, GetScaledFraction(expk_array[i], 10000)); 133 } 134 } 135 } 136 137 error_term = fAdd(fPositiveOne, exponent); 138 139 solution = fMultiply(solution, error_term); 140 141 if (bNegated) 142 solution = fDivide(fPositiveOne, solution); 143 144 return solution; 145} 146 147static fInt fNaturalLog(fInt value) 148{ 149 uint32_t i; 150 fInt upper_bound = Divide(8, 1000); 151 fInt fNegativeOne = ConvertToFraction(-1); 152 fInt solution = ConvertToFraction(0); /*Starting off with baseline of 0 */ 153 fInt error_term; 154 155 static const uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078}; 156 static const uint32_t logk_array[10] = {27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78}; 157 158 while (GreaterThan(fAdd(value, fNegativeOne), upper_bound)) { 159 for (i = 0; i < 10; i++) { 160 if (GreaterThan(value, GetScaledFraction(k_array[i], 10000))) { 161 value = fDivide(value, GetScaledFraction(k_array[i], 10000)); 162 solution = fAdd(solution, GetScaledFraction(logk_array[i], 10000)); 163 } 164 } 165 } 166 167 error_term = fAdd(fNegativeOne, value); 168 169 return fAdd(solution, error_term); 170} 171 172static fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength) 173{ 174 fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value); 175 fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1); 176 177 fInt f_decoded_value; 178 179 f_decoded_value = fDivide(f_fuse_value, f_bit_max_value); 180 f_decoded_value = fMultiply(f_decoded_value, f_range); 181 f_decoded_value = fAdd(f_decoded_value, f_min); 182 183 return f_decoded_value; 184} 185 186 187static fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength) 188{ 189 fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value); 190 fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1); 191 192 fInt f_CONSTANT_NEG13 = ConvertToFraction(-13); 193 fInt f_CONSTANT1 = ConvertToFraction(1); 194 195 fInt f_decoded_value; 196 197 f_decoded_value = fSubtract(fDivide(f_bit_max_value, f_fuse_value), f_CONSTANT1); 198 f_decoded_value = fNaturalLog(f_decoded_value); 199 f_decoded_value = fMultiply(f_decoded_value, fDivide(f_range, f_CONSTANT_NEG13)); 200 f_decoded_value = fAdd(f_decoded_value, f_average); 201 202 return f_decoded_value; 203} 204 205static fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength) 206{ 207 fInt fLeakage; 208 fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1); 209 210 fLeakage = fMultiply(ln_max_div_min, Convert_ULONG_ToFraction(leakageID_fuse)); 211 fLeakage = fDivide(fLeakage, f_bit_max_value); 212 fLeakage = fExponential(fLeakage); 213 fLeakage = fMultiply(fLeakage, f_min); 214 215 return fLeakage; 216} 217 218static fInt ConvertToFraction(int X) /*Add all range checking here. Is it possible to make fInt a private declaration? */ 219{ 220 fInt temp; 221 222 if (X <= MAX) 223 temp.full = (X << SHIFT_AMOUNT); 224 else 225 temp.full = 0; 226 227 return temp; 228} 229 230static fInt fNegate(fInt X) 231{ 232 fInt CONSTANT_NEGONE = ConvertToFraction(-1); 233 return fMultiply(X, CONSTANT_NEGONE); 234} 235 236static fInt Convert_ULONG_ToFraction(uint32_t X) 237{ 238 fInt temp; 239 240 if (X <= MAX) 241 temp.full = (X << SHIFT_AMOUNT); 242 else 243 temp.full = 0; 244 245 return temp; 246} 247 248static fInt GetScaledFraction(int X, int factor) 249{ 250 int times_shifted, factor_shifted; 251 bool bNEGATED; 252 fInt fValue; 253 254 times_shifted = 0; 255 factor_shifted = 0; 256 bNEGATED = false; 257 258 if (X < 0) { 259 X = -1*X; 260 bNEGATED = true; 261 } 262 263 if (factor < 0) { 264 factor = -1*factor; 265 bNEGATED = !bNEGATED; /*If bNEGATED = true due to X < 0, this will cover the case of negative cancelling negative */ 266 } 267 268 if ((X > MAX) || factor > MAX) { 269 if ((X/factor) <= MAX) { 270 while (X > MAX) { 271 X = X >> 1; 272 times_shifted++; 273 } 274 275 while (factor > MAX) { 276 factor = factor >> 1; 277 factor_shifted++; 278 } 279 } else { 280 fValue.full = 0; 281 return fValue; 282 } 283 } 284 285 if (factor == 1) 286 return ConvertToFraction(X); 287 288 fValue = fDivide(ConvertToFraction(X * uPow(-1, bNEGATED)), ConvertToFraction(factor)); 289 290 fValue.full = fValue.full << times_shifted; 291 fValue.full = fValue.full >> factor_shifted; 292 293 return fValue; 294} 295 296/* Addition using two fInts */ 297static fInt fAdd (fInt X, fInt Y) 298{ 299 fInt Sum; 300 301 Sum.full = X.full + Y.full; 302 303 return Sum; 304} 305 306/* Addition using two fInts */ 307static fInt fSubtract (fInt X, fInt Y) 308{ 309 fInt Difference; 310 311 Difference.full = X.full - Y.full; 312 313 return Difference; 314} 315 316static bool Equal(fInt A, fInt B) 317{ 318 if (A.full == B.full) 319 return true; 320 else 321 return false; 322} 323 324static bool GreaterThan(fInt A, fInt B) 325{ 326 if (A.full > B.full) 327 return true; 328 else 329 return false; 330} 331 332static fInt fMultiply (fInt X, fInt Y) /* Uses 64-bit integers (int64_t) */ 333{ 334 fInt Product; 335 int64_t tempProduct; 336 337 /*The following is for a very specific common case: Non-zero number with ONLY fractional portion*/ 338 /* TEMPORARILY DISABLED - CAN BE USED TO IMPROVE PRECISION 339 bool X_LessThanOne, Y_LessThanOne; 340 341 X_LessThanOne = (X.partial.real == 0 && X.partial.decimal != 0 && X.full >= 0); 342 Y_LessThanOne = (Y.partial.real == 0 && Y.partial.decimal != 0 && Y.full >= 0); 343 344 if (X_LessThanOne && Y_LessThanOne) { 345 Product.full = X.full * Y.full; 346 return Product 347 }*/ 348 349 tempProduct = ((int64_t)X.full) * ((int64_t)Y.full); /*Q(16,16)*Q(16,16) = Q(32, 32) - Might become a negative number! */ 350 tempProduct = tempProduct >> 16; /*Remove lagging 16 bits - Will lose some precision from decimal; */ 351 Product.full = (int)tempProduct; /*The int64_t will lose the leading 16 bits that were part of the integer portion */ 352 353 return Product; 354} 355 356static fInt fDivide (fInt X, fInt Y) 357{ 358 fInt fZERO, fQuotient; 359 int64_t longlongX, longlongY; 360 361 fZERO = ConvertToFraction(0); 362 363 if (Equal(Y, fZERO)) 364 return fZERO; 365 366 longlongX = (int64_t)X.full; 367 longlongY = (int64_t)Y.full; 368 369 longlongX = longlongX << 16; /*Q(16,16) -> Q(32,32) */ 370 371 div64_s64(longlongX, longlongY); /*Q(32,32) divided by Q(16,16) = Q(16,16) Back to original format */ 372 373 fQuotient.full = (int)longlongX; 374 return fQuotient; 375} 376 377static int ConvertBackToInteger (fInt A) /*THIS is the function that will be used to check with the Golden settings table*/ 378{ 379 fInt fullNumber, scaledDecimal, scaledReal; 380 381 scaledReal.full = GetReal(A) * uPow(10, PRECISION-1); /* DOUBLE CHECK THISSSS!!! */ 382 383 scaledDecimal.full = uGetScaledDecimal(A); 384 385 fullNumber = fAdd(scaledDecimal, scaledReal); 386 387 return fullNumber.full; 388} 389 390static fInt fGetSquare(fInt A) 391{ 392 return fMultiply(A, A); 393} 394 395/* x_new = x_old - (x_old^2 - C) / (2 * x_old) */ 396static fInt fSqrt(fInt num) 397{ 398 fInt F_divide_Fprime, Fprime; 399 fInt test; 400 fInt twoShifted; 401 int seed, counter, error; 402 fInt x_new, x_old, C, y; 403 404 fInt fZERO = ConvertToFraction(0); 405 406 /* (0 > num) is the same as (num < 0), i.e., num is negative */ 407 408 if (GreaterThan(fZERO, num) || Equal(fZERO, num)) 409 return fZERO; 410 411 C = num; 412 413 if (num.partial.real > 3000) 414 seed = 60; 415 else if (num.partial.real > 1000) 416 seed = 30; 417 else if (num.partial.real > 100) 418 seed = 10; 419 else 420 seed = 2; 421 422 counter = 0; 423 424 if (Equal(num, fZERO)) /*Square Root of Zero is zero */ 425 return fZERO; 426 427 twoShifted = ConvertToFraction(2); 428 x_new = ConvertToFraction(seed); 429 430 do { 431 counter++; 432 433 x_old.full = x_new.full; 434 435 test = fGetSquare(x_old); /*1.75*1.75 is reverting back to 1 when shifted down */ 436 y = fSubtract(test, C); /*y = f(x) = x^2 - C; */ 437 438 Fprime = fMultiply(twoShifted, x_old); 439 F_divide_Fprime = fDivide(y, Fprime); 440 441 x_new = fSubtract(x_old, F_divide_Fprime); 442 443 error = ConvertBackToInteger(x_new) - ConvertBackToInteger(x_old); 444 445 if (counter > 20) /*20 is already way too many iterations. If we dont have an answer by then, we never will*/ 446 return x_new; 447 448 } while (uAbs(error) > 0); 449 450 return x_new; 451} 452 453static void SolveQuadracticEqn(fInt A, fInt B, fInt C, fInt Roots[]) 454{ 455 fInt *pRoots = &Roots[0]; 456 fInt temp, root_first, root_second; 457 fInt f_CONSTANT10, f_CONSTANT100; 458 459 f_CONSTANT100 = ConvertToFraction(100); 460 f_CONSTANT10 = ConvertToFraction(10); 461 462 while (GreaterThan(A, f_CONSTANT100) || GreaterThan(B, f_CONSTANT100) || GreaterThan(C, f_CONSTANT100)) { 463 A = fDivide(A, f_CONSTANT10); 464 B = fDivide(B, f_CONSTANT10); 465 C = fDivide(C, f_CONSTANT10); 466 } 467 468 temp = fMultiply(ConvertToFraction(4), A); /* root = 4*A */ 469 temp = fMultiply(temp, C); /* root = 4*A*C */ 470 temp = fSubtract(fGetSquare(B), temp); /* root = b^2 - 4AC */ 471 temp = fSqrt(temp); /*root = Sqrt (b^2 - 4AC); */ 472 473 root_first = fSubtract(fNegate(B), temp); /* b - Sqrt(b^2 - 4AC) */ 474 root_second = fAdd(fNegate(B), temp); /* b + Sqrt(b^2 - 4AC) */ 475 476 root_first = fDivide(root_first, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */ 477 root_first = fDivide(root_first, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */ 478 479 root_second = fDivide(root_second, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */ 480 root_second = fDivide(root_second, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */ 481 482 *(pRoots + 0) = root_first; 483 *(pRoots + 1) = root_second; 484} 485 486/* ----------------------------------------------------------------------------- 487 * SUPPORT FUNCTIONS 488 * ----------------------------------------------------------------------------- 489 */ 490 491/* Conversion Functions */ 492static int GetReal (fInt A) 493{ 494 return (A.full >> SHIFT_AMOUNT); 495} 496 497static fInt Divide (int X, int Y) 498{ 499 fInt A, B, Quotient; 500 501 A.full = X << SHIFT_AMOUNT; 502 B.full = Y << SHIFT_AMOUNT; 503 504 Quotient = fDivide(A, B); 505 506 return Quotient; 507} 508 509static int uGetScaledDecimal (fInt A) /*Converts the fractional portion to whole integers - Costly function */ 510{ 511 int dec[PRECISION]; 512 int i, scaledDecimal = 0, tmp = A.partial.decimal; 513 514 for (i = 0; i < PRECISION; i++) { 515 dec[i] = tmp / (1 << SHIFT_AMOUNT); 516 tmp = tmp - ((1 << SHIFT_AMOUNT)*dec[i]); 517 tmp *= 10; 518 scaledDecimal = scaledDecimal + dec[i]*uPow(10, PRECISION - 1 - i); 519 } 520 521 return scaledDecimal; 522} 523 524static int uPow(int base, int power) 525{ 526 if (power == 0) 527 return 1; 528 else 529 return (base)*uPow(base, power - 1); 530} 531 532static int uAbs(int X) 533{ 534 if (X < 0) 535 return (X * -1); 536 else 537 return X; 538} 539 540static fInt fRoundUpByStepSize(fInt A, fInt fStepSize, bool error_term) 541{ 542 fInt solution; 543 544 solution = fDivide(A, fStepSize); 545 solution.partial.decimal = 0; /*All fractional digits changes to 0 */ 546 547 if (error_term) 548 solution.partial.real += 1; /*Error term of 1 added */ 549 550 solution = fMultiply(solution, fStepSize); 551 solution = fAdd(solution, fStepSize); 552 553 return solution; 554} 555 556