drivers/gpu/drm/amd/powerplay/hwmgr/ppevvmath.h

   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  */
  41 typedef 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  */
  53 static fInt ConvertToFraction(int);                       /* Use this to convert an INT to a FINT */
  54 static fInt Convert_ULONG_ToFraction(uint32_t);           /* Use this to convert an uint32_t to a FINT */
  55 static fInt GetScaledFraction(int, int);                  /* Use this to convert an INT to a FINT after scaling it by a factor */
  56 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) */
  57
  58 static fInt fNegate(fInt);                                /* Returns -1 * input fInt value */
  59 static fInt fAdd (fInt, fInt);                            /* Returns the sum of two fInt numbers */
  60 static fInt fSubtract (fInt A, fInt B);                   /* Returns A-B - Sometimes easier than Adding negative numbers */
  61 static fInt fMultiply (fInt, fInt);                       /* Returns the product of two fInt numbers */
  62 static fInt fDivide (fInt A, fInt B);                     /* Returns A/B */
  63 static fInt fGetSquare(fInt);                             /* Returns the square of a fInt number */
  64 static fInt fSqrt(fInt);                                  /* Returns the Square Root of a fInt number */
  65
  66 static int uAbs(int);                                     /* Returns the Absolute value of the Int */
  67 static fInt fAbs(fInt);                                   /* Returns the Absolute value of the fInt */
  68 static int uPow(int base, int exponent);                  /* Returns base^exponent an INT */
  69
  70 static void SolveQuadracticEqn(fInt, fInt, fInt, fInt[]); /* Returns the 2 roots via the array */
  71 static bool Equal(fInt, fInt);                            /* Returns true if two fInts are equal to each other */
  72 static bool GreaterThan(fInt A, fInt B);                  /* Returns true if A > B */
  73
  74 static fInt fExponential(fInt exponent);                  /* Can be used to calculate e^exponent */
  75 static fInt fNaturalLog(fInt value);                      /* Can be used to calculate ln(value) */
  76
  77 /* Fuse decoding functions
  78  * -------------------------------------------------------------------------------------
  79  */
  80 static fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength);
  81 static fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength);
  82 static fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength);
  83
  84 /* Internal Support Functions - Use these ONLY for testing or adding to internal functions
  85  * -------------------------------------------------------------------------------------
  86  * Some of the following functions take two INTs as their input - This is unsafe for a variety of reasons.
  87  */
  88 static fInt Add (int, int);                               /* Add two INTs and return Sum as FINT */
  89 static fInt Multiply (int, int);                          /* Multiply two INTs and return Product as FINT */
  90 static fInt Divide (int, int);                            /* You get the idea... */
  91 static fInt fNegate(fInt);
  92
  93 static int uGetScaledDecimal (fInt);                      /* Internal function */
  94 static int GetReal (fInt A);                              /* Internal function */
  95
  96 /* Future Additions and Incomplete Functions
  97  * -------------------------------------------------------------------------------------
  98  */
  99 static int GetRoundedValue(fInt);                         /* Incomplete function - Useful only when Precision is lacking */
 100                                                           /* Let us say we have 2.126 but can only handle 2 decimal points. We could */
 101                                                           /* either chop of 6 and keep 2.12 or use this function to get 2.13, which is more accurate */
 102
 103 /* -------------------------------------------------------------------------------------
 104  * TROUBLESHOOTING INFORMATION
 105  * -------------------------------------------------------------------------------------
 106  * 1) ConvertToFraction - InputOutOfRangeException: Only accepts numbers smaller than MAX (default: 32767)
 107  * 2) fAdd - OutputOutOfRangeException: Output bigger than MAX (default: 32767)
 108  * 3) fMultiply - OutputOutOfRangeException:
 109  * 4) fGetSquare - OutputOutOfRangeException:
 110  * 5) fDivide - DivideByZeroException
 111  * 6) fSqrt - NegativeSquareRootException: Input cannot be a negative number
 112  */
 113
 114 /* -------------------------------------------------------------------------------------
 115  * START OF CODE
 116  * -------------------------------------------------------------------------------------
 117  */
 118 static fInt fExponential(fInt exponent)        /*Can be used to calculate e^exponent*/
 119 {
 120         uint32_t i;
 121         bool bNegated = false;
 122
 123         fInt fPositiveOne = ConvertToFraction(1);
 124         fInt fZERO = ConvertToFraction(0);
 125
 126         fInt lower_bound = Divide(78, 10000);
 127         fInt solution = fPositiveOne; /*Starting off with baseline of 1 */
 128         fInt error_term;
 129
 130         static const uint32_t k_array[11] = {55452, 27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
 131         static const uint32_t expk_array[11] = {2560000, 160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
 132
 133         if (GreaterThan(fZERO, exponent)) {
 134                 exponent = fNegate(exponent);
 135                 bNegated = true;
 136         }
 137
 138         while (GreaterThan(exponent, lower_bound)) {
 139                 for (i = 0; i < 11; i++) {
 140                         if (GreaterThan(exponent, GetScaledFraction(k_array[i], 10000))) {
 141                                 exponent = fSubtract(exponent, GetScaledFraction(k_array[i], 10000));
 142                                 solution = fMultiply(solution, GetScaledFraction(expk_array[i], 10000));
 143                         }
 144                 }
 145         }
 146
 147         error_term = fAdd(fPositiveOne, exponent);
 148
 149         solution = fMultiply(solution, error_term);
 150
 151         if (bNegated)
 152                 solution = fDivide(fPositiveOne, solution);
 153
 154         return solution;
 155 }
 156
 157 static fInt fNaturalLog(fInt value)
 158 {
 159         uint32_t i;
 160         fInt upper_bound = Divide(8, 1000);
 161         fInt fNegativeOne = ConvertToFraction(-1);
 162         fInt solution = ConvertToFraction(0); /*Starting off with baseline of 0 */
 163         fInt error_term;
 164
 165         static const uint32_t k_array[10] = {160000, 40000, 20000, 15000, 12500, 11250, 10625, 10313, 10156, 10078};
 166         static const uint32_t logk_array[10] = {27726, 13863, 6931, 4055, 2231, 1178, 606, 308, 155, 78};
 167
 168         while (GreaterThan(fAdd(value, fNegativeOne), upper_bound)) {
 169                 for (i = 0; i < 10; i++) {
 170                         if (GreaterThan(value, GetScaledFraction(k_array[i], 10000))) {
 171                                 value = fDivide(value, GetScaledFraction(k_array[i], 10000));
 172                                 solution = fAdd(solution, GetScaledFraction(logk_array[i], 10000));
 173                         }
 174                 }
 175         }
 176
 177         error_term = fAdd(fNegativeOne, value);
 178
 179         return (fAdd(solution, error_term));
 180 }
 181
 182 static fInt fDecodeLinearFuse(uint32_t fuse_value, fInt f_min, fInt f_range, uint32_t bitlength)
 183 {
 184         fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
 185         fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
 186
 187         fInt f_decoded_value;
 188
 189         f_decoded_value = fDivide(f_fuse_value, f_bit_max_value);
 190         f_decoded_value = fMultiply(f_decoded_value, f_range);
 191         f_decoded_value = fAdd(f_decoded_value, f_min);
 192
 193         return f_decoded_value;
 194 }
 195
 196
 197 static fInt fDecodeLogisticFuse(uint32_t fuse_value, fInt f_average, fInt f_range, uint32_t bitlength)
 198 {
 199         fInt f_fuse_value = Convert_ULONG_ToFraction(fuse_value);
 200         fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
 201
 202         fInt f_CONSTANT_NEG13 = ConvertToFraction(-13);
 203         fInt f_CONSTANT1 = ConvertToFraction(1);
 204
 205         fInt f_decoded_value;
 206
 207         f_decoded_value = fSubtract(fDivide(f_bit_max_value, f_fuse_value), f_CONSTANT1);
 208         f_decoded_value = fNaturalLog(f_decoded_value);
 209         f_decoded_value = fMultiply(f_decoded_value, fDivide(f_range, f_CONSTANT_NEG13));
 210         f_decoded_value = fAdd(f_decoded_value, f_average);
 211
 212         return f_decoded_value;
 213 }
 214
 215 static fInt fDecodeLeakageID (uint32_t leakageID_fuse, fInt ln_max_div_min, fInt f_min, uint32_t bitlength)
 216 {
 217         fInt fLeakage;
 218         fInt f_bit_max_value = Convert_ULONG_ToFraction((uPow(2, bitlength)) - 1);
 219
 220         fLeakage = fMultiply(ln_max_div_min, Convert_ULONG_ToFraction(leakageID_fuse));
 221         fLeakage = fDivide(fLeakage, f_bit_max_value);
 222         fLeakage = fExponential(fLeakage);
 223         fLeakage = fMultiply(fLeakage, f_min);
 224
 225         return fLeakage;
 226 }
 227
 228 static fInt ConvertToFraction(int X) /*Add all range checking here. Is it possible to make fInt a private declaration? */
 229 {
 230         fInt temp;
 231
 232         if (X <= MAX)
 233                 temp.full = (X << SHIFT_AMOUNT);
 234         else
 235                 temp.full = 0;
 236
 237         return temp;
 238 }
 239
 240 static fInt fNegate(fInt X)
 241 {
 242         fInt CONSTANT_NEGONE = ConvertToFraction(-1);
 243         return (fMultiply(X, CONSTANT_NEGONE));
 244 }
 245
 246 static fInt Convert_ULONG_ToFraction(uint32_t X)
 247 {
 248         fInt temp;
 249
 250         if (X <= MAX)
 251                 temp.full = (X << SHIFT_AMOUNT);
 252         else
 253                 temp.full = 0;
 254
 255         return temp;
 256 }
 257
 258 static fInt GetScaledFraction(int X, int factor)
 259 {
 260         int times_shifted, factor_shifted;
 261         bool bNEGATED;
 262         fInt fValue;
 263
 264         times_shifted = 0;
 265         factor_shifted = 0;
 266         bNEGATED = false;
 267
 268         if (X < 0) {
 269                 X = -1*X;
 270                 bNEGATED = true;
 271         }
 272
 273         if (factor < 0) {
 274                 factor = -1*factor;
 275                 bNEGATED = !bNEGATED; /*If bNEGATED = true due to X < 0, this will cover the case of negative cancelling negative */
 276         }
 277
 278         if ((X > MAX) || factor > MAX) {
 279                 if ((X/factor) <= MAX) {
 280                         while (X > MAX) {
 281                                 X = X >> 1;
 282                                 times_shifted++;
 283                         }
 284
 285                         while (factor > MAX) {
 286                                 factor = factor >> 1;
 287                                 factor_shifted++;
 288                         }
 289                 } else {
 290                         fValue.full = 0;
 291                         return fValue;
 292                 }
 293         }
 294
 295         if (factor == 1)
 296                 return ConvertToFraction(X);
 297
 298         fValue = fDivide(ConvertToFraction(X * uPow(-1, bNEGATED)), ConvertToFraction(factor));
 299
 300         fValue.full = fValue.full << times_shifted;
 301         fValue.full = fValue.full >> factor_shifted;
 302
 303         return fValue;
 304 }
 305
 306 /* Addition using two fInts */
 307 static fInt fAdd (fInt X, fInt Y)
 308 {
 309         fInt Sum;
 310
 311         Sum.full = X.full + Y.full;
 312
 313         return Sum;
 314 }
 315
 316 /* Addition using two fInts */
 317 static fInt fSubtract (fInt X, fInt Y)
 318 {
 319         fInt Difference;
 320
 321         Difference.full = X.full - Y.full;
 322
 323         return Difference;
 324 }
 325
 326 static bool Equal(fInt A, fInt B)
 327 {
 328         if (A.full == B.full)
 329                 return true;
 330         else
 331                 return false;
 332 }
 333
 334 static bool GreaterThan(fInt A, fInt B)
 335 {
 336         if (A.full > B.full)
 337                 return true;
 338         else
 339                 return false;
 340 }
 341
 342 static fInt fMultiply (fInt X, fInt Y) /* Uses 64-bit integers (int64_t) */
 343 {
 344         fInt Product;
 345         int64_t tempProduct;
 346         bool X_LessThanOne, Y_LessThanOne;
 347
 348         X_LessThanOne = (X.partial.real == 0 && X.partial.decimal != 0 && X.full >= 0);
 349         Y_LessThanOne = (Y.partial.real == 0 && Y.partial.decimal != 0 && Y.full >= 0);
 350
 351         /*The following is for a very specific common case: Non-zero number with ONLY fractional portion*/
 352         /* TEMPORARILY DISABLED - CAN BE USED TO IMPROVE PRECISION
 353
 354         if (X_LessThanOne && Y_LessThanOne) {
 355                 Product.full = X.full * Y.full;
 356                 return Product
 357         }*/
 358
 359         tempProduct = ((int64_t)X.full) * ((int64_t)Y.full); /*Q(16,16)*Q(16,16) = Q(32, 32) - Might become a negative number! */
 360         tempProduct = tempProduct >> 16; /*Remove lagging 16 bits - Will lose some precision from decimal; */
 361         Product.full = (int)tempProduct; /*The int64_t will lose the leading 16 bits that were part of the integer portion */
 362
 363         return Product;
 364 }
 365
 366 static fInt fDivide (fInt X, fInt Y)
 367 {
 368         fInt fZERO, fQuotient;
 369         int64_t longlongX, longlongY;
 370
 371         fZERO = ConvertToFraction(0);
 372
 373         if (Equal(Y, fZERO))
 374                 return fZERO;
 375
 376         longlongX = (int64_t)X.full;
 377         longlongY = (int64_t)Y.full;
 378
 379         longlongX = longlongX << 16; /*Q(16,16) -> Q(32,32) */
 380
 381         div64_s64(longlongX, longlongY); /*Q(32,32) divided by Q(16,16) = Q(16,16) Back to original format */
 382
 383         fQuotient.full = (int)longlongX;
 384         return fQuotient;
 385 }
 386
 387 static int ConvertBackToInteger (fInt A) /*THIS is the function that will be used to check with the Golden settings table*/
 388 {
 389         fInt fullNumber, scaledDecimal, scaledReal;
 390
 391         scaledReal.full = GetReal(A) * uPow(10, PRECISION-1); /* DOUBLE CHECK THISSSS!!! */
 392
 393         scaledDecimal.full = uGetScaledDecimal(A);
 394
 395         fullNumber = fAdd(scaledDecimal,scaledReal);
 396
 397         return fullNumber.full;
 398 }
 399
 400 static fInt fGetSquare(fInt A)
 401 {
 402         return fMultiply(A,A);
 403 }
 404
 405 /* x_new = x_old - (x_old^2 - C) / (2 * x_old) */
 406 static fInt fSqrt(fInt num)
 407 {
 408         fInt F_divide_Fprime, Fprime;
 409         fInt test;
 410         fInt twoShifted;
 411         int seed, counter, error;
 412         fInt x_new, x_old, C, y;
 413
 414         fInt fZERO = ConvertToFraction(0);
 415
 416         /* (0 > num) is the same as (num < 0), i.e., num is negative */
 417
 418         if (GreaterThan(fZERO, num) || Equal(fZERO, num))
 419                 return fZERO;
 420
 421         C = num;
 422
 423         if (num.partial.real > 3000)
 424                 seed = 60;
 425         else if (num.partial.real > 1000)
 426                 seed = 30;
 427         else if (num.partial.real > 100)
 428                 seed = 10;
 429         else
 430                 seed = 2;
 431
 432         counter = 0;
 433
 434         if (Equal(num, fZERO)) /*Square Root of Zero is zero */
 435                 return fZERO;
 436
 437         twoShifted = ConvertToFraction(2);
 438         x_new = ConvertToFraction(seed);
 439
 440         do {
 441                 counter++;
 442
 443                 x_old.full = x_new.full;
 444
 445                 test = fGetSquare(x_old); /*1.75*1.75 is reverting back to 1 when shifted down */
 446                 y = fSubtract(test, C); /*y = f(x) = x^2 - C; */
 447
 448                 Fprime = fMultiply(twoShifted, x_old);
 449                 F_divide_Fprime = fDivide(y, Fprime);
 450
 451                 x_new = fSubtract(x_old, F_divide_Fprime);
 452
 453                 error = ConvertBackToInteger(x_new) - ConvertBackToInteger(x_old);
 454
 455                 if (counter > 20) /*20 is already way too many iterations. If we dont have an answer by then, we never will*/
 456                         return x_new;
 457
 458         } while (uAbs(error) > 0);
 459
 460         return (x_new);
 461 }
 462
 463 static void SolveQuadracticEqn(fInt A, fInt B, fInt C, fInt Roots[])
 464 {
 465         fInt *pRoots = &Roots[0];
 466         fInt temp, root_first, root_second;
 467         fInt f_CONSTANT10, f_CONSTANT100;
 468
 469         f_CONSTANT100 = ConvertToFraction(100);
 470         f_CONSTANT10 = ConvertToFraction(10);
 471
 472         while(GreaterThan(A, f_CONSTANT100) || GreaterThan(B, f_CONSTANT100) || GreaterThan(C, f_CONSTANT100)) {
 473                 A = fDivide(A, f_CONSTANT10);
 474                 B = fDivide(B, f_CONSTANT10);
 475                 C = fDivide(C, f_CONSTANT10);
 476         }
 477
 478         temp = fMultiply(ConvertToFraction(4), A); /* root = 4*A */
 479         temp = fMultiply(temp, C); /* root = 4*A*C */
 480         temp = fSubtract(fGetSquare(B), temp); /* root = b^2 - 4AC */
 481         temp = fSqrt(temp); /*root = Sqrt (b^2 - 4AC); */
 482
 483         root_first = fSubtract(fNegate(B), temp); /* b - Sqrt(b^2 - 4AC) */
 484         root_second = fAdd(fNegate(B), temp); /* b + Sqrt(b^2 - 4AC) */
 485
 486         root_first = fDivide(root_first, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
 487         root_first = fDivide(root_first, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
 488
 489         root_second = fDivide(root_second, ConvertToFraction(2)); /* [b +- Sqrt(b^2 - 4AC)]/[2] */
 490         root_second = fDivide(root_second, A); /*[b +- Sqrt(b^2 - 4AC)]/[2*A] */
 491
 492         *(pRoots + 0) = root_first;
 493         *(pRoots + 1) = root_second;
 494 }
 495
 496 /* -----------------------------------------------------------------------------
 497  * SUPPORT FUNCTIONS
 498  * -----------------------------------------------------------------------------
 499  */
 500
 501 /* Addition using two normal ints - Temporary - Use only for testing purposes?. */
 502 static fInt Add (int X, int Y)
 503 {
 504         fInt A, B, Sum;
 505
 506         A.full = (X << SHIFT_AMOUNT);
 507         B.full = (Y << SHIFT_AMOUNT);
 508
 509         Sum.full = A.full + B.full;
 510
 511         return Sum;
 512 }
 513
 514 /* Conversion Functions */
 515 static int GetReal (fInt A)
 516 {
 517         return (A.full >> SHIFT_AMOUNT);
 518 }
 519
 520 /* Temporarily Disabled */
 521 static int GetRoundedValue(fInt A) /*For now, round the 3rd decimal place */
 522 {
 523         /* ROUNDING TEMPORARLY DISABLED
 524         int temp = A.full;
 525         int decimal_cutoff, decimal_mask = 0x000001FF;
 526         decimal_cutoff = temp & decimal_mask;
 527         if (decimal_cutoff > 0x147) {
 528                 temp += 673;
 529         }*/
 530
 531         return ConvertBackToInteger(A)/10000; /*Temporary - in case this was used somewhere else */
 532 }
 533
 534 static fInt Multiply (int X, int Y)
 535 {
 536         fInt A, B, Product;
 537
 538         A.full = X << SHIFT_AMOUNT;
 539         B.full = Y << SHIFT_AMOUNT;
 540
 541         Product = fMultiply(A, B);
 542
 543         return Product;
 544 }
 545
 546 static fInt Divide (int X, int Y)
 547 {
 548         fInt A, B, Quotient;
 549
 550         A.full = X << SHIFT_AMOUNT;
 551         B.full = Y << SHIFT_AMOUNT;
 552
 553         Quotient = fDivide(A, B);
 554
 555         return Quotient;
 556 }
 557
 558 static int uGetScaledDecimal (fInt A) /*Converts the fractional portion to whole integers - Costly function */
 559 {
 560         int dec[PRECISION];
 561         int i, scaledDecimal = 0, tmp = A.partial.decimal;
 562
 563         for (i = 0; i < PRECISION; i++) {
 564                 dec[i] = tmp / (1 << SHIFT_AMOUNT);
 565                 tmp = tmp - ((1 << SHIFT_AMOUNT)*dec[i]);
 566                 tmp *= 10;
 567                 scaledDecimal = scaledDecimal + dec[i]*uPow(10, PRECISION - 1 -i);
 568         }
 569
 570         return scaledDecimal;
 571 }
 572
 573 static int uPow(int base, int power)
 574 {
 575         if (power == 0)
 576                 return 1;
 577         else
 578                 return (base)*uPow(base, power - 1);
 579 }
 580
 581 static fInt fAbs(fInt A)
 582 {
 583         if (A.partial.real < 0)
 584                 return (fMultiply(A, ConvertToFraction(-1)));
 585         else
 586                 return A;
 587 }
 588
 589 static int uAbs(int X)
 590 {
 591         if (X < 0)
 592                 return (X * -1);
 593         else
 594                 return X;
 595 }
 596
 597 static fInt fRoundUpByStepSize(fInt A, fInt fStepSize, bool error_term)
 598 {
 599         fInt solution;
 600
 601         solution = fDivide(A, fStepSize);
 602         solution.partial.decimal = 0; /*All fractional digits changes to 0 */
 603
 604         if (error_term)
 605                 solution.partial.real += 1; /*Error term of 1 added */
 606
 607         solution = fMultiply(solution, fStepSize);
 608         solution = fAdd(solution, fStepSize);
 609
 610         return solution;
 611 }
 612