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sys/sys/qmath.h
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1 /*- 2 * Copyright (c) 2018 Netflix, Inc. 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 * 26 * $FreeBSD$ 27 */ 28 29 /* 30 * Data types and APIs for fixed-point math based on the "Q" number format. 31 * 32 * Author: Lawrence Stewart <lstewart@netflix.com> 33 * 34 * The 3 LSBs of all base data types are reserved for embedded control data: 35 * bits 1-2 specify the radix point shift index i.e. 00,01,10,11 == 1,2,3,4 36 * bit 3 specifies the radix point shift index multiplier as 2 (0) or 16 (1) 37 * 38 * This scheme can therefore represent Q numbers with [2,4,6,8,16,32,48,64] bits 39 * of precision after the binary radix point. The number of bits available for 40 * the integral component depends on the underlying storage type chosen. 41 */ 42 43 #ifndef _SYS_QMATH_H_ 44 #define _SYS_QMATH_H_ 45 46 #include <machine/_stdint.h> 47 48 typedef int8_t s8q_t; 49 typedef uint8_t u8q_t; 50 typedef int16_t s16q_t; 51 typedef uint16_t u16q_t; 52 typedef int32_t s32q_t; 53 typedef uint32_t u32q_t; 54 typedef int64_t s64q_t; 55 typedef uint64_t u64q_t; 56 /* typedef int128_t s128q_t; Not yet */ 57 /* typedef uint128_t u128q_t; Not yet */ 58 typedef s64q_t smaxq_t; 59 typedef u64q_t umaxq_t; 60 61 #if defined(__GNUC__) && !defined(__clang__) 62 /* Ancient GCC hack to de-const, remove when GCC4 is removed. */ 63 #define Q_BT(q) __typeof(1 * q) 64 #else 65 /* The underlying base type of 'q'. */ 66 #define Q_BT(q) __typeof(q) 67 #endif 68 69 /* Type-cast variable 'v' to the same underlying type as 'q'. */ 70 #define Q_TC(q, v) ((__typeof(q))(v)) 71 72 /* Number of total bits associated with the data type underlying 'q'. */ 73 #define Q_NTBITS(q) ((uint32_t)(sizeof(q) << 3)) 74 75 /* Number of LSBs reserved for control data. */ 76 #define Q_NCBITS ((uint32_t)3) 77 78 /* Number of control-encoded bits reserved for fractional component data. */ 79 #define Q_NFCBITS(q) \ 80 ((uint32_t)(((Q_GCRAW(q) & 0x3) + 1) << ((Q_GCRAW(q) & 0x4) ? 4 : 1))) 81 82 /* Min/max number of bits that can be reserved for fractional component data. */ 83 #define Q_MINNFBITS(q) ((uint32_t)(2)) 84 #define Q_MAXNFBITS(q) ((uint32_t)(Q_NTBITS(q) - Q_SIGNED(q) - Q_NCBITS)) 85 86 /* 87 * Number of bits actually reserved for fractional component data. This can be 88 * less than the value returned by Q_NFCBITS() as we treat any excess 89 * control-encoded number of bits for the underlying data type as meaning all 90 * available bits are reserved for fractional component data i.e. zero int bits. 91 */ 92 #define Q_NFBITS(q) \ 93 (Q_NFCBITS(q) > Q_MAXNFBITS(q) ? Q_MAXNFBITS(q) : Q_NFCBITS(q)) 94 95 /* Number of bits available for integer component data. */ 96 #define Q_NIBITS(q) ((uint32_t)(Q_NTBITS(q) - Q_RPSHFT(q) - Q_SIGNED(q))) 97 98 /* The radix point offset relative to the LSB. */ 99 #define Q_RPSHFT(q) (Q_NCBITS + Q_NFBITS(q)) 100 101 /* The sign bit offset relative to the LSB. */ 102 #define Q_SIGNSHFT(q) (Q_NTBITS(q) - 1) 103 104 /* Set the sign bit to 0 ('isneg' is F) or 1 ('isneg' is T). */ 105 #define Q_SSIGN(q, isneg) \ 106 ((q) = ((Q_SIGNED(q) && (isneg)) ? (q) | (1ULL << Q_SIGNSHFT(q)) : \ 107 (q) & ~(1ULL << Q_SIGNSHFT(q)))) 108 109 /* Manipulate the 'q' bits holding control/sign data. */ 110 #define Q_CRAWMASK(q) 0x7ULL 111 #define Q_SRAWMASK(q) (1ULL << Q_SIGNSHFT(q)) 112 #define Q_GCRAW(q) ((q) & Q_CRAWMASK(q)) 113 #define Q_GCVAL(q) Q_GCRAW(q) 114 #define Q_SCVAL(q, cv) ((q) = ((q) & ~Q_CRAWMASK(q)) | (cv)) 115 116 /* Manipulate the 'q' bits holding combined integer/fractional data. */ 117 #define Q_IFRAWMASK(q) \ 118 Q_TC(q, Q_SIGNED(q) ? ~(Q_SRAWMASK(q) | Q_CRAWMASK(q)) : ~Q_CRAWMASK(q)) 119 #define Q_IFMAXVAL(q) Q_TC(q, Q_IFRAWMASK(q) >> Q_NCBITS) 120 #define Q_IFMINVAL(q) Q_TC(q, Q_SIGNED(q) ? -Q_IFMAXVAL(q) : 0) 121 #define Q_IFVALIMASK(q) Q_TC(q, ~Q_IFVALFMASK(q)) 122 #define Q_IFVALFMASK(q) Q_TC(q, (1ULL << Q_NFBITS(q)) - 1) 123 #define Q_GIFRAW(q) Q_TC(q, (q) & Q_IFRAWMASK(q)) 124 #define Q_GIFABSVAL(q) Q_TC(q, Q_GIFRAW(q) >> Q_NCBITS) 125 #define Q_GIFVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GIFABSVAL(q) : Q_GIFABSVAL(q)) 126 #define Q_SIFVAL(q, ifv) \ 127 ((q) = ((q) & (~(Q_SRAWMASK(q) | Q_IFRAWMASK(q)))) | \ 128 (Q_TC(q, Q_ABS(ifv)) << Q_NCBITS) | \ 129 (Q_LTZ(ifv) ? 1ULL << Q_SIGNSHFT(q) : 0)) 130 #define Q_SIFVALS(q, iv, fv) \ 131 ((q) = ((q) & (~(Q_SRAWMASK(q) | Q_IFRAWMASK(q)))) | \ 132 (Q_TC(q, Q_ABS(iv)) << Q_RPSHFT(q)) | \ 133 (Q_TC(q, Q_ABS(fv)) << Q_NCBITS) | \ 134 (Q_LTZ(iv) || Q_LTZ(fv) ? 1ULL << Q_SIGNSHFT(q) : 0)) 135 136 /* Manipulate the 'q' bits holding integer data. */ 137 #define Q_IRAWMASK(q) Q_TC(q, Q_IFRAWMASK(q) & ~Q_FRAWMASK(q)) 138 #define Q_IMAXVAL(q) Q_TC(q, Q_IRAWMASK(q) >> Q_RPSHFT(q)) 139 #define Q_IMINVAL(q) Q_TC(q, Q_SIGNED(q) ? -Q_IMAXVAL(q) : 0) 140 #define Q_GIRAW(q) Q_TC(q, (q) & Q_IRAWMASK(q)) 141 #define Q_GIABSVAL(q) Q_TC(q, Q_GIRAW(q) >> Q_RPSHFT(q)) 142 #define Q_GIVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GIABSVAL(q) : Q_GIABSVAL(q)) 143 #define Q_SIVAL(q, iv) \ 144 ((q) = ((q) & ~(Q_SRAWMASK(q) | Q_IRAWMASK(q))) | \ 145 (Q_TC(q, Q_ABS(iv)) << Q_RPSHFT(q)) | \ 146 (Q_LTZ(iv) ? 1ULL << Q_SIGNSHFT(q) : 0)) 147 148 /* Manipulate the 'q' bits holding fractional data. */ 149 #define Q_FRAWMASK(q) Q_TC(q, ((1ULL << Q_NFBITS(q)) - 1) << Q_NCBITS) 150 #define Q_FMAXVAL(q) Q_TC(q, Q_FRAWMASK(q) >> Q_NCBITS) 151 #define Q_GFRAW(q) Q_TC(q, (q) & Q_FRAWMASK(q)) 152 #define Q_GFABSVAL(q) Q_TC(q, Q_GFRAW(q) >> Q_NCBITS) 153 #define Q_GFVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GFABSVAL(q) : Q_GFABSVAL(q)) 154 #define Q_SFVAL(q, fv) \ 155 ((q) = ((q) & ~(Q_SRAWMASK(q) | Q_FRAWMASK(q))) | \ 156 (Q_TC(q, Q_ABS(fv)) << Q_NCBITS) | \ 157 (Q_LTZ(fv) ? 1ULL << Q_SIGNSHFT(q) : 0)) 158 159 /* 160 * Calculate the number of bits required per 'base' digit, rounding up or down 161 * for non power-of-two bases. 162 */ 163 #define Q_BITSPERBASEDOWN(base) (flsll(base) - 1) 164 #define Q_BITSPERBASEUP(base) (flsll(base) - (__builtin_popcountll(base) == 1)) 165 #define Q_BITSPERBASE(base, rnd) Q_BITSPERBASE##rnd(base) 166 167 /* 168 * Upper bound number of digits required to render 'nbits' worth of integer 169 * component bits with numeric base 'base'. Overestimates for power-of-two 170 * bases. 171 */ 172 #define Q_NIBITS2NCHARS(nbits, base) \ 173 ({ \ 174 int _bitsperbase = Q_BITSPERBASE(base, DOWN); \ 175 (((nbits) + _bitsperbase - 1) / _bitsperbase); \ 176 }) 177 178 #define Q_NFBITS2NCHARS(nbits, base) (nbits) 179 180 /* 181 * Maximum number of chars required to render 'q' as a C-string of base 'base'. 182 * Includes space for sign, radix point and NUL-terminator. 183 */ 184 #define Q_MAXSTRLEN(q, base) \ 185 (2 + Q_NIBITS2NCHARS(Q_NIBITS(q), base) + \ 186 Q_NFBITS2NCHARS(Q_NFBITS(q), base) + Q_SIGNED(q)) 187 188 /* Yield the next char from integer bits. */ 189 #define Q_IBITS2CH(q, bits, base) \ 190 ({ \ 191 __typeof(bits) _tmp = (bits) / (base); \ 192 int _idx = (bits) - (_tmp * (base)); \ 193 (bits) = _tmp; \ 194 "0123456789abcdef"[_idx]; \ 195 }) 196 197 /* Yield the next char from fractional bits. */ 198 #define Q_FBITS2CH(q, bits, base) \ 199 ({ \ 200 int _carry = 0, _idx, _nfbits = Q_NFBITS(q), _shift = 0; \ 201 /* \ 202 * Normalise enough MSBs to yield the next digit, multiply by the \ 203 * base, and truncate residual fractional bits post multiplication. \ 204 */ \ 205 if (_nfbits > Q_BITSPERBASEUP(base)) { \ 206 /* Break multiplication into two steps to ensure no overflow. */\ 207 _shift = _nfbits >> 1; \ 208 _carry = (((bits) & ((1ULL << _shift) - 1)) * (base)) >> _shift;\ 209 } \ 210 _idx = ((((bits) >> _shift) * (base)) + _carry) >> (_nfbits - _shift);\ 211 (bits) *= (base); /* With _idx computed, no overflow concern. */ \ 212 (bits) &= (1ULL << _nfbits) - 1; /* Exclude residual int bits. */ \ 213 "0123456789abcdef"[_idx]; \ 214 }) 215 216 /* 217 * Render the C-string representation of 'q' into 's'. Returns a pointer to the 218 * final '\0' to allow for easy calculation of the rendered length and easy 219 * appending to the C-string. 220 */ 221 #define Q_TOSTR(q, prec, base, s, slen) \ 222 ({ \ 223 char *_r, *_s = s; \ 224 int _i; \ 225 if (Q_LTZ(q) && ((ptrdiff_t)(slen)) > 0) \ 226 *_s++ = '-'; \ 227 Q_BT(q) _part = Q_GIABSVAL(q); \ 228 _r = _s; \ 229 do { \ 230 /* Render integer chars in reverse order. */ \ 231 if ((_s - (s)) < ((ptrdiff_t)(slen))) \ 232 *_s++ = Q_IBITS2CH(q, _part, base); \ 233 else \ 234 _r = NULL; \ 235 } while (_part > 0 && _r != NULL); \ 236 if (!((_s - (s)) < ((ptrdiff_t)(slen)))) \ 237 _r = NULL; \ 238 _i = (_s - _r) >> 1; /* N digits requires int(N/2) swaps. */ \ 239 while (_i-- > 0 && _r != NULL) { \ 240 /* Work from middle out to reverse integer chars. */ \ 241 *_s = *(_r + _i); /* Stash LHS char temporarily. */ \ 242 *(_r + _i) = *(_s - _i - 1); /* Copy RHS char to LHS. */\ 243 *(_s - _i - 1) = *_s; /* Copy LHS char to RHS. */ \ 244 } \ 245 _i = (prec); \ 246 if (_i != 0 && _r != NULL) { \ 247 if ((_s - (s)) < ((ptrdiff_t)(slen))) \ 248 *_s++ = '.'; \ 249 else \ 250 _r = NULL; \ 251 _part = Q_GFABSVAL(q); \ 252 if (_i < 0 || _i > (int)Q_NFBITS(q)) \ 253 _i = Q_NFBITS(q); \ 254 while (_i-- > 0 && _r != NULL) { \ 255 /* Render fraction chars in correct order. */ \ 256 if ((_s - (s)) < ((ptrdiff_t)(slen))) \ 257 *_s++ = Q_FBITS2CH(q, _part, base); \ 258 else \ 259 _r = NULL; \ 260 } \ 261 } \ 262 if ((_s - (s)) < ((ptrdiff_t)(slen)) && _r != NULL) \ 263 *_s = '\0'; \ 264 else { \ 265 _r = NULL; \ 266 if (((ptrdiff_t)(slen)) > 0) \ 267 *(s) = '\0'; \ 268 } \ 269 /* Return a pointer to the '\0' or NULL on overflow. */ \ 270 (_r != NULL ? _s : _r); \ 271 }) 272 273 /* Left shift an integral value to align with the int bits of 'q'. */ 274 #define Q_SHL(q, iv) \ 275 (Q_LTZ(iv) ? -(int64_t)(Q_ABS(iv) << Q_NFBITS(q)) : \ 276 Q_TC(q, iv) << Q_NFBITS(q)) 277 278 /* Calculate the relative fractional precision between 'a' and 'b' in bits. */ 279 #define Q_RELPREC(a, b) ((int)Q_NFBITS(a) - (int)Q_NFBITS(b)) 280 281 /* 282 * Determine control bits for the desired 'rpshft' radix point shift. Rounds up 283 * to the nearest valid shift supported by the encoding scheme. 284 */ 285 #define Q_CTRLINI(rpshft) \ 286 (((rpshft) <= 8) ? (((rpshft) - 1) >> 1) : (0x4 | (((rpshft) - 1) >> 4))) 287 288 /* 289 * Convert decimal fractional value 'dfv' to its binary-encoded representation 290 * with 'nfbits' of binary precision. 'dfv' must be passed as a preprocessor 291 * literal to preserve leading zeroes. The returned result can be used to set a 292 * Q number's fractional bits e.g. using Q_SFVAL(). 293 */ 294 #define Q_DFV2BFV(dfv, nfbits) \ 295 ({ \ 296 uint64_t _bfv = 0, _thresh = 5, _tmp = dfv; \ 297 int _i = sizeof(""#dfv) - 1; \ 298 /* \ 299 * Compute decimal threshold to determine which \ 300 * conversion rounds will yield a binary 1. \ 301 */ \ 302 while (--_i > 0) {_thresh *= 10;} \ 303 _i = (nfbits) - 1; \ 304 while (_i >= 0) { \ 305 if (_thresh <= _tmp) { \ 306 _bfv |= 1ULL << _i; \ 307 _tmp = _tmp - _thresh; \ 308 } \ 309 _i--; _tmp <<= 1; \ 310 } \ 311 _bfv; \ 312 }) 313 314 /* 315 * Initialise 'q' with raw integer value 'iv', decimal fractional value 'dfv', 316 * and radix point shift 'rpshft'. Must be done in two steps in case 'iv' 317 * depends on control bits being set e.g. when passing Q_INTMAX(q) as 'iv'. 318 */ 319 #define Q_INI(q, iv, dfv, rpshft) \ 320 ({ \ 321 (*(q)) = Q_CTRLINI(rpshft); \ 322 Q_SIFVALS(*(q), iv, Q_DFV2BFV(dfv, Q_NFBITS(*(q)))); \ 323 }) 324 325 /* Test if 'a' and 'b' fractional precision is the same (T) or not (F). */ 326 #define Q_PRECEQ(a, b) (Q_NFBITS(a) == Q_NFBITS(b)) 327 328 /* Test if 'n' is a signed type (T) or not (F). Works with any numeric type. */ 329 #define Q_SIGNED(n) (Q_TC(n, -1) < 0) 330 331 /* 332 * Test if 'n' is negative. Works with any numeric type that uses the MSB as the 333 * sign bit, and also works with Q numbers. 334 */ 335 #define Q_LTZ(n) (Q_SIGNED(n) && ((n) & Q_SRAWMASK(n))) 336 337 /* 338 * Return absolute value of 'n'. Works with any standard numeric type that uses 339 * the MSB as the sign bit, and is signed/unsigned type safe. 340 * Does not work with Q numbers; use Q_QABS() instead. 341 */ 342 #define Q_ABS(n) (Q_LTZ(n) ? -(n) : (n)) 343 344 /* 345 * Return an absolute value interpretation of 'q'. 346 */ 347 #define Q_QABS(q) (Q_SIGNED(q) ? (q) & ~Q_SRAWMASK(q) : (q)) 348 349 /* Convert 'q' to float or double representation. */ 350 #define Q_Q2F(q) ((float)Q_GIFVAL(q) / (float)(1ULL << Q_NFBITS(q))) 351 #define Q_Q2D(q) ((double)Q_GIFVAL(q) / (double)(1ULL << Q_NFBITS(q))) 352 353 /* Numerically compare 'a' and 'b' as whole numbers using provided operators. */ 354 #define Q_QCMPQ(a, b, intcmp, fraccmp) \ 355 ((Q_GIVAL(a) intcmp Q_GIVAL(b)) || \ 356 ((Q_GIVAL(a) == Q_GIVAL(b)) && (Q_GFVAL(a) fraccmp Q_GFVAL(b)))) 357 358 /* Test if 'a' is numerically less than 'b' (T) or not (F). */ 359 #define Q_QLTQ(a, b) Q_QCMPQ(a, b, <, <) 360 361 /* Test if 'a' is numerically less than or equal to 'b' (T) or not (F). */ 362 #define Q_QLEQ(a, b) Q_QCMPQ(a, b, <, <=) 363 364 /* Test if 'a' is numerically greater than 'b' (T) or not (F). */ 365 #define Q_QGTQ(a, b) Q_QCMPQ(a, b, >, >) 366 367 /* Test if 'a' is numerically greater than or equal to 'b' (T) or not (F). */ 368 #define Q_QGEQ(a, b) Q_QCMPQ(a, b, >, >=) 369 370 /* Test if 'a' is numerically equal to 'b' (T) or not (F). */ 371 #define Q_QEQ(a, b) Q_QCMPQ(a, b, ==, ==) 372 373 /* Test if 'a' is numerically not equal to 'b' (T) or not (F). */ 374 #define Q_QNEQ(a, b) Q_QCMPQ(a, b, !=, !=) 375 376 /* Returns the numerically larger of 'a' and 'b'. */ 377 #define Q_QMAXQ(a, b) (Q_GT(a, b) ? (a) : (b)) 378 379 /* Returns the numerically smaller of 'a' and 'b'. */ 380 #define Q_QMINQ(a, b) (Q_LT(a, b) ? (a) : (b)) 381 382 /* 383 * Test if 'a' can be represented by 'b' with full accuracy (T) or not (F). 384 * The type casting has to be done to a's type so that any truncation caused by 385 * the casts will not affect the logic. 386 */ 387 #define Q_QCANREPQ(a, b) \ 388 ((((Q_LTZ(a) && Q_SIGNED(b)) || !Q_LTZ(a)) && \ 389 Q_GIABSVAL(a) <= Q_TC(a, Q_IMAXVAL(b)) && \ 390 Q_GFABSVAL(a) <= Q_TC(a, Q_FMAXVAL(b))) ? \ 391 0 : EOVERFLOW) 392 393 /* Test if raw integer value 'i' can be represented by 'q' (T) or not (F). */ 394 #define Q_QCANREPI(q, i) \ 395 ((((Q_LTZ(i) && Q_SIGNED(q)) || !Q_LTZ(i)) && \ 396 Q_ABS(i) <= Q_TC(i, Q_IMAXVAL(q))) ? 0 : EOVERFLOW) 397 398 /* 399 * Returns a Q variable debug format string with appropriate modifiers and 400 * padding relevant to the underlying Q data type. 401 */ 402 #define Q_DEBUGFMT_(prefmt, postfmt, mod, hexpad) \ 403 prefmt \ 404 /* Var name + address. */ \ 405 "\"%s\"@%p" \ 406 /* Data type. */ \ 407 "\n\ttype=%c%dq_t, " \ 408 /* Qm.n notation; 'm' = # int bits, 'n' = # frac bits. */ \ 409 "Qm.n=Q%d.%d, " \ 410 /* Radix point shift relative to the underlying data type's LSB. */ \ 411 "rpshft=%d, " \ 412 /* Min/max integer values which can be represented. */ \ 413 "imin=0x%0" #mod "x, " \ 414 "imax=0x%0" #mod "x" \ 415 /* Raw hex dump of all bits. */ \ 416 "\n\tqraw=0x%0" #hexpad #mod "x" \ 417 /* Bit masks for int/frac/ctrl bits. */ \ 418 "\n\timask=0x%0" #hexpad #mod "x, " \ 419 "fmask=0x%0" #hexpad #mod "x, " \ 420 "cmask=0x%0" #hexpad #mod "x, " \ 421 "ifmask=0x%0" #hexpad #mod "x" \ 422 /* Hex dump of masked int bits; 'iraw' includes shift */ \ 423 "\n\tiraw=0x%0" #hexpad #mod "x, " \ 424 "iabsval=0x%" #mod "x, " \ 425 "ival=0x%" #mod "x" \ 426 /* Hex dump of masked frac bits; 'fraw' includes shift */ \ 427 "\n\tfraw=0x%0" #hexpad #mod "x, " \ 428 "fabsval=0x%" #mod "x, " \ 429 "fval=0x%" #mod "x" \ 430 "%s" \ 431 postfmt 432 433 #define Q_DEBUGFMT(q, prefmt, postfmt) \ 434 sizeof(q) == 8 ? Q_DEBUGFMT_(prefmt, postfmt, j, 16) : \ 435 sizeof(q) == 4 ? Q_DEBUGFMT_(prefmt, postfmt, , 8) : \ 436 sizeof(q) == 2 ? Q_DEBUGFMT_(prefmt, postfmt, h, 4) : \ 437 sizeof(q) == 1 ? Q_DEBUGFMT_(prefmt, postfmt, hh, 2) : \ 438 prefmt "\"%s\"@%p: invalid" postfmt \ 439 440 /* 441 * Returns a format string and data suitable for printf-like rendering 442 * e.g. Print to console with a trailing newline: printf(Q_DEBUG(q, "", "\n")); 443 */ 444 #define Q_DEBUG(q, prefmt, postfmt, incfmt) \ 445 Q_DEBUGFMT(q, prefmt, postfmt) \ 446 , #q \ 447 , &(q) \ 448 , Q_SIGNED(q) ? 's' : 'u' \ 449 , Q_NTBITS(q) \ 450 , Q_NIBITS(q) \ 451 , Q_NFBITS(q) \ 452 , Q_RPSHFT(q) \ 453 , Q_IMINVAL(q) \ 454 , Q_IMAXVAL(q) \ 455 , (q) \ 456 , Q_IRAWMASK(q) \ 457 , Q_FRAWMASK(q) \ 458 , Q_TC(q, Q_CRAWMASK(q)) \ 459 , Q_IFRAWMASK(q) \ 460 , Q_GIRAW(q) \ 461 , Q_GIABSVAL(q) \ 462 , Q_GIVAL(q) \ 463 , Q_GFRAW(q) \ 464 , Q_GFABSVAL(q) \ 465 , Q_GFVAL(q) \ 466 , (incfmt) ? Q_DEBUGFMT(q, "\nfmt:", "") : "" \ 467 468 /* 469 * If precision differs, attempt to normalise to the greater precision that 470 * preserves the integer component of both 'a' and 'b'. 471 */ 472 #define Q_NORMPREC(a, b) \ 473 ({ \ 474 int _perr = 0, _relprec = Q_RELPREC(*(a), b); \ 475 if (_relprec != 0) \ 476 _perr = ERANGE; /* XXXLAS: Do precision normalisation! */\ 477 _perr; \ 478 }) 479 480 /* Clone r's control bits and int/frac value into 'l'. */ 481 #define Q_QCLONEQ(l, r) \ 482 ({ \ 483 Q_BT(*(l)) _l = Q_GCVAL(r); \ 484 int _err = Q_QCANREPQ(r, _l); \ 485 if (!_err) { \ 486 *(l) = _l; \ 487 Q_SIFVAL(*(l), Q_GIFVAL(r)); \ 488 } \ 489 _err; \ 490 }) 491 492 /* Copy r's int/frac vals into 'l', retaining 'l's precision and signedness. */ 493 #define Q_QCPYVALQ(l, r) \ 494 ({ \ 495 int _err = Q_QCANREPQ(r, *(l)); \ 496 if (!_err) \ 497 Q_SIFVALS(*(l), Q_GIVAL(r), Q_GFVAL(r)); \ 498 _err; \ 499 }) 500 501 #define Q_QADDSUBQ(a, b, eop) \ 502 ({ \ 503 int _aserr; \ 504 if ((_aserr = Q_NORMPREC(a, b))) while (0); /* NOP */ \ 505 else if ((eop) == '+') { \ 506 if (Q_IFMAXVAL(*(a)) - Q_GIFABSVAL(b) < Q_GIFVAL(*(a))) \ 507 _aserr = EOVERFLOW; /* [+/-a + +b] > max(a) */ \ 508 else \ 509 Q_SIFVAL(*(a), Q_GIFVAL(*(a)) + Q_TC(*(a), \ 510 Q_GIFABSVAL(b))); \ 511 } else { /* eop == '-' */ \ 512 if (Q_IFMINVAL(*(a)) + Q_GIFABSVAL(b) > Q_GIFVAL(*(a))) \ 513 _aserr = EOVERFLOW; /* [+/-a - +b] < min(a) */ \ 514 else \ 515 Q_SIFVAL(*(a), Q_GIFVAL(*(a)) - Q_TC(*(a), \ 516 Q_GIFABSVAL(b))); \ 517 } \ 518 _aserr; \ 519 }) 520 #define Q_QADDQ(a, b) Q_QADDSUBQ(a, b, (Q_LTZ(b) ? '-' : '+')) 521 #define Q_QSUBQ(a, b) Q_QADDSUBQ(a, b, (Q_LTZ(b) ? '+' : '-')) 522 523 #define Q_QDIVQ(a, b) \ 524 ({ \ 525 int _err; \ 526 if ((_err = Q_NORMPREC(a, b))) while (0); /* NOP */ \ 527 else if (Q_GIFABSVAL(b) == 0 || (!Q_SIGNED(*(a)) && Q_LTZ(b))) \ 528 _err = EINVAL; /* Divide by zero or cannot represent. */\ 529 /* XXXLAS: Handle overflow. */ \ 530 else if (Q_GIFABSVAL(*(a)) != 0) { /* Result expected. */ \ 531 Q_SIFVAL(*(a), \ 532 ((Q_GIVAL(*(a)) << Q_NFBITS(*(a))) / Q_GIFVAL(b)) + \ 533 (Q_GFVAL(b) == 0 ? 0 : \ 534 ((Q_GFVAL(*(a)) << Q_NFBITS(*(a))) / Q_GFVAL(b)))); \ 535 } \ 536 _err; \ 537 }) 538 539 #define Q_QMULQ(a, b) \ 540 ({ \ 541 int _mulerr; \ 542 if ((_mulerr = Q_NORMPREC(a, b))) while (0); /* NOP */ \ 543 else if (!Q_SIGNED(*(a)) && Q_LTZ(b)) \ 544 _mulerr = EINVAL; \ 545 else if (Q_GIFABSVAL(b) != 0 && \ 546 Q_IFMAXVAL(*(a)) / Q_GIFABSVAL(b) < Q_GIFABSVAL(*(a))) \ 547 _mulerr = EOVERFLOW; \ 548 else \ 549 Q_SIFVAL(*(a), (Q_GIFVAL(*(a)) * Q_GIFVAL(b)) >> \ 550 Q_NFBITS(*(a))); \ 551 _mulerr; \ 552 }) 553 554 #define Q_QCPYVALI(q, i) \ 555 ({ \ 556 int _err = Q_QCANREPI(*(q), i); \ 557 if (!_err) \ 558 Q_SIFVAL(*(q), Q_SHL(*(q), i)); \ 559 _err; \ 560 }) 561 562 #define Q_QADDSUBI(q, i, eop) \ 563 ({ \ 564 int _aserr = 0; \ 565 if (Q_NTBITS(*(q)) < (uint32_t)flsll(Q_ABS(i))) \ 566 _aserr = EOVERFLOW; /* i cannot fit in q's type. */ \ 567 else if ((eop) == '+') { \ 568 if (Q_IMAXVAL(*(q)) - Q_TC(*(q), Q_ABS(i)) < \ 569 Q_GIVAL(*(q))) \ 570 _aserr = EOVERFLOW; /* [+/-q + +i] > max(q) */ \ 571 else \ 572 Q_SIFVAL(*(q), Q_GIFVAL(*(q)) + \ 573 Q_SHL(*(q), Q_ABS(i))); \ 574 } else { /* eop == '-' */ \ 575 if (Q_IMINVAL(*(q)) + Q_ABS(i) > Q_GIVAL(*(q))) \ 576 _aserr = EOVERFLOW; /* [+/-q - +i] < min(q) */ \ 577 else \ 578 Q_SIFVAL(*(q), Q_GIFVAL(*(q)) - \ 579 Q_SHL(*(q), Q_ABS(i))); \ 580 } \ 581 _aserr; \ 582 }) 583 #define Q_QADDI(q, i) Q_QADDSUBI(q, i, (Q_LTZ(i) ? '-' : '+')) 584 #define Q_QSUBI(q, i) Q_QADDSUBI(q, i, (Q_LTZ(i) ? '+' : '-')) 585 586 #define Q_QDIVI(q, i) \ 587 ({ \ 588 int _diverr = 0; \ 589 if ((i) == 0 || (!Q_SIGNED(*(q)) && Q_LTZ(i))) \ 590 _diverr = EINVAL; /* Divide by zero or cannot represent. */\ 591 else if (Q_GIFABSVAL(*(q)) != 0) { /* Result expected. */ \ 592 Q_SIFVAL(*(q), Q_GIFVAL(*(q)) / Q_TC(*(q), i)); \ 593 if (Q_GIFABSVAL(*(q)) == 0) \ 594 _diverr = ERANGE; /* q underflow. */ \ 595 } \ 596 _diverr; \ 597 }) 598 599 #define Q_QMULI(q, i) \ 600 ({ \ 601 int _mulerr = 0; \ 602 if (!Q_SIGNED(*(q)) && Q_LTZ(i)) \ 603 _mulerr = EINVAL; /* Cannot represent. */ \ 604 else if ((i) != 0 && Q_IFMAXVAL(*(q)) / Q_TC(*(q), Q_ABS(i)) < \ 605 Q_GIFABSVAL(*(q))) \ 606 _mulerr = EOVERFLOW; \ 607 else \ 608 Q_SIFVAL(*(q), Q_GIFVAL(*(q)) * Q_TC(*(q), i)); \ 609 _mulerr; \ 610 }) 611 612 #define Q_QFRACI(q, in, id) \ 613 ({ \ 614 uint64_t _tmp; \ 615 int _err = 0; \ 616 if ((id) == 0) \ 617 _err = EINVAL; /* Divide by zero. */ \ 618 else if ((in) == 0) \ 619 Q_SIFVAL(*(q), in); \ 620 else if ((_tmp = Q_ABS(in)) > (UINT64_MAX >> Q_RPSHFT(*(q)))) \ 621 _err = EOVERFLOW; /* _tmp overflow. */ \ 622 else { \ 623 _tmp = Q_SHL(*(q), _tmp) / Q_ABS(id); \ 624 if (Q_QCANREPI(*(q), _tmp & Q_IFVALIMASK(*(q)))) \ 625 _err = EOVERFLOW; /* q overflow. */ \ 626 else { \ 627 Q_SIFVAL(*(q), _tmp); \ 628 Q_SSIGN(*(q), (Q_LTZ(in) && !Q_LTZ(id)) || \ 629 (!Q_LTZ(in) && Q_LTZ(id))); \ 630 if (_tmp == 0) \ 631 _err = ERANGE; /* q underflow. */ \ 632 } \ 633 } \ 634 _err; \ 635 }) 636 637 #endif /* _SYS_QMATH_H_ */
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