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/*-
* Copyright (c) 2018 Netflix, Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $FreeBSD$
*/
/*
* Data types and APIs for fixed-point math based on the "Q" number format.
*
* Author: Lawrence Stewart <lstewart@netflix.com>
*
* The 3 LSBs of all base data types are reserved for embedded control data:
* bits 1-2 specify the radix point shift index i.e. 00,01,10,11 == 1,2,3,4
* bit 3 specifies the radix point shift index multiplier as 2 (0) or 16 (1)
*
* This scheme can therefore represent Q numbers with [2,4,6,8,16,32,48,64] bits
* of precision after the binary radix point. The number of bits available for
* the integral component depends on the underlying storage type chosen.
*/
#ifndef _SYS_QMATH_H_
#define _SYS_QMATH_H_
#include <machine/_stdint.h>
typedef int8_t s8q_t;
typedef uint8_t u8q_t;
typedef int16_t s16q_t;
typedef uint16_t u16q_t;
typedef int32_t s32q_t;
typedef uint32_t u32q_t;
typedef int64_t s64q_t;
typedef uint64_t u64q_t;
/* typedef int128_t s128q_t; Not yet */
/* typedef uint128_t u128q_t; Not yet */
typedef s64q_t smaxq_t;
typedef u64q_t umaxq_t;
#if defined(__GNUC__) && !defined(__clang__)
/* Ancient GCC hack to de-const, remove when GCC4 is removed. */
#define Q_BT(q) __typeof(1 * q)
#else
/* The underlying base type of 'q'. */
#define Q_BT(q) __typeof(q)
#endif
/* Type-cast variable 'v' to the same underlying type as 'q'. */
#define Q_TC(q, v) ((__typeof(q))(v))
/* Number of total bits associated with the data type underlying 'q'. */
#define Q_NTBITS(q) ((uint32_t)(sizeof(q) << 3))
/* Number of LSBs reserved for control data. */
#define Q_NCBITS ((uint32_t)3)
/* Number of control-encoded bits reserved for fractional component data. */
#define Q_NFCBITS(q) \
((uint32_t)(((Q_GCRAW(q) & 0x3) + 1) << ((Q_GCRAW(q) & 0x4) ? 4 : 1)))
/* Min/max number of bits that can be reserved for fractional component data. */
#define Q_MINNFBITS(q) ((uint32_t)(2))
#define Q_MAXNFBITS(q) ((uint32_t)(Q_NTBITS(q) - Q_SIGNED(q) - Q_NCBITS))
/*
* Number of bits actually reserved for fractional component data. This can be
* less than the value returned by Q_NFCBITS() as we treat any excess
* control-encoded number of bits for the underlying data type as meaning all
* available bits are reserved for fractional component data i.e. zero int bits.
*/
#define Q_NFBITS(q) \
(Q_NFCBITS(q) > Q_MAXNFBITS(q) ? Q_MAXNFBITS(q) : Q_NFCBITS(q))
/* Number of bits available for integer component data. */
#define Q_NIBITS(q) ((uint32_t)(Q_NTBITS(q) - Q_RPSHFT(q) - Q_SIGNED(q)))
/* The radix point offset relative to the LSB. */
#define Q_RPSHFT(q) (Q_NCBITS + Q_NFBITS(q))
/* The sign bit offset relative to the LSB. */
#define Q_SIGNSHFT(q) (Q_NTBITS(q) - 1)
/* Set the sign bit to 0 ('isneg' is F) or 1 ('isneg' is T). */
#define Q_SSIGN(q, isneg) \
((q) = ((Q_SIGNED(q) && (isneg)) ? (q) | (1ULL << Q_SIGNSHFT(q)) : \
(q) & ~(1ULL << Q_SIGNSHFT(q))))
/* Manipulate the 'q' bits holding control/sign data. */
#define Q_CRAWMASK(q) 0x7ULL
#define Q_SRAWMASK(q) (1ULL << Q_SIGNSHFT(q))
#define Q_GCRAW(q) ((q) & Q_CRAWMASK(q))
#define Q_GCVAL(q) Q_GCRAW(q)
#define Q_SCVAL(q, cv) ((q) = ((q) & ~Q_CRAWMASK(q)) | (cv))
/* Manipulate the 'q' bits holding combined integer/fractional data. */
#define Q_IFRAWMASK(q) \
Q_TC(q, Q_SIGNED(q) ? ~(Q_SRAWMASK(q) | Q_CRAWMASK(q)) : ~Q_CRAWMASK(q))
#define Q_IFMAXVAL(q) Q_TC(q, Q_IFRAWMASK(q) >> Q_NCBITS)
#define Q_IFMINVAL(q) Q_TC(q, Q_SIGNED(q) ? -Q_IFMAXVAL(q) : 0)
#define Q_IFVALIMASK(q) Q_TC(q, ~Q_IFVALFMASK(q))
#define Q_IFVALFMASK(q) Q_TC(q, (1ULL << Q_NFBITS(q)) - 1)
#define Q_GIFRAW(q) Q_TC(q, (q) & Q_IFRAWMASK(q))
#define Q_GIFABSVAL(q) Q_TC(q, Q_GIFRAW(q) >> Q_NCBITS)
#define Q_GIFVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GIFABSVAL(q) : Q_GIFABSVAL(q))
#define Q_SIFVAL(q, ifv) \
((q) = ((q) & (~(Q_SRAWMASK(q) | Q_IFRAWMASK(q)))) | \
(Q_TC(q, Q_ABS(ifv)) << Q_NCBITS) | \
(Q_LTZ(ifv) ? 1ULL << Q_SIGNSHFT(q) : 0))
#define Q_SIFVALS(q, iv, fv) \
((q) = ((q) & (~(Q_SRAWMASK(q) | Q_IFRAWMASK(q)))) | \
(Q_TC(q, Q_ABS(iv)) << Q_RPSHFT(q)) | \
(Q_TC(q, Q_ABS(fv)) << Q_NCBITS) | \
(Q_LTZ(iv) || Q_LTZ(fv) ? 1ULL << Q_SIGNSHFT(q) : 0))
/* Manipulate the 'q' bits holding integer data. */
#define Q_IRAWMASK(q) Q_TC(q, Q_IFRAWMASK(q) & ~Q_FRAWMASK(q))
#define Q_IMAXVAL(q) Q_TC(q, Q_IRAWMASK(q) >> Q_RPSHFT(q))
#define Q_IMINVAL(q) Q_TC(q, Q_SIGNED(q) ? -Q_IMAXVAL(q) : 0)
#define Q_GIRAW(q) Q_TC(q, (q) & Q_IRAWMASK(q))
#define Q_GIABSVAL(q) Q_TC(q, Q_GIRAW(q) >> Q_RPSHFT(q))
#define Q_GIVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GIABSVAL(q) : Q_GIABSVAL(q))
#define Q_SIVAL(q, iv) \
((q) = ((q) & ~(Q_SRAWMASK(q) | Q_IRAWMASK(q))) | \
(Q_TC(q, Q_ABS(iv)) << Q_RPSHFT(q)) | \
(Q_LTZ(iv) ? 1ULL << Q_SIGNSHFT(q) : 0))
/* Manipulate the 'q' bits holding fractional data. */
#define Q_FRAWMASK(q) Q_TC(q, ((1ULL << Q_NFBITS(q)) - 1) << Q_NCBITS)
#define Q_FMAXVAL(q) Q_TC(q, Q_FRAWMASK(q) >> Q_NCBITS)
#define Q_GFRAW(q) Q_TC(q, (q) & Q_FRAWMASK(q))
#define Q_GFABSVAL(q) Q_TC(q, Q_GFRAW(q) >> Q_NCBITS)
#define Q_GFVAL(q) Q_TC(q, Q_LTZ(q) ? -Q_GFABSVAL(q) : Q_GFABSVAL(q))
#define Q_SFVAL(q, fv) \
((q) = ((q) & ~(Q_SRAWMASK(q) | Q_FRAWMASK(q))) | \
(Q_TC(q, Q_ABS(fv)) << Q_NCBITS) | \
(Q_LTZ(fv) ? 1ULL << Q_SIGNSHFT(q) : 0))
/*
* Calculate the number of bits required per 'base' digit, rounding up or down
* for non power-of-two bases.
*/
#define Q_BITSPERBASEDOWN(base) (flsll(base) - 1)
#define Q_BITSPERBASEUP(base) (flsll(base) - (__builtin_popcountll(base) == 1))
#define Q_BITSPERBASE(base, rnd) Q_BITSPERBASE##rnd(base)
/*
* Upper bound number of digits required to render 'nbits' worth of integer
* component bits with numeric base 'base'. Overestimates for power-of-two
* bases.
*/
#define Q_NIBITS2NCHARS(nbits, base) \
({ \
int _bitsperbase = Q_BITSPERBASE(base, DOWN); \
(((nbits) + _bitsperbase - 1) / _bitsperbase); \
})
#define Q_NFBITS2NCHARS(nbits, base) (nbits)
/*
* Maximum number of chars required to render 'q' as a C-string of base 'base'.
* Includes space for sign, radix point and NUL-terminator.
*/
#define Q_MAXSTRLEN(q, base) \
(2 + Q_NIBITS2NCHARS(Q_NIBITS(q), base) + \
Q_NFBITS2NCHARS(Q_NFBITS(q), base) + Q_SIGNED(q))
/* Yield the next char from integer bits. */
#define Q_IBITS2CH(q, bits, base) \
({ \
__typeof(bits) _tmp = (bits) / (base); \
int _idx = (bits) - (_tmp * (base)); \
(bits) = _tmp; \
"0123456789abcdef"[_idx]; \
})
/* Yield the next char from fractional bits. */
#define Q_FBITS2CH(q, bits, base) \
({ \
int _carry = 0, _idx, _nfbits = Q_NFBITS(q), _shift = 0; \
/* \
* Normalise enough MSBs to yield the next digit, multiply by the \
* base, and truncate residual fractional bits post multiplication. \
*/ \
if (_nfbits > Q_BITSPERBASEUP(base)) { \
/* Break multiplication into two steps to ensure no overflow. */\
_shift = _nfbits >> 1; \
_carry = (((bits) & ((1ULL << _shift) - 1)) * (base)) >> _shift;\
} \
_idx = ((((bits) >> _shift) * (base)) + _carry) >> (_nfbits - _shift);\
(bits) *= (base); /* With _idx computed, no overflow concern. */ \
(bits) &= (1ULL << _nfbits) - 1; /* Exclude residual int bits. */ \
"0123456789abcdef"[_idx]; \
})
/*
* Render the C-string representation of 'q' into 's'. Returns a pointer to the
* final '\0' to allow for easy calculation of the rendered length and easy
* appending to the C-string.
*/
#define Q_TOSTR(q, prec, base, s, slen) \
({ \
char *_r, *_s = s; \
int _i; \
if (Q_LTZ(q) && ((ptrdiff_t)(slen)) > 0) \
*_s++ = '-'; \
Q_BT(q) _part = Q_GIABSVAL(q); \
_r = _s; \
do { \
/* Render integer chars in reverse order. */ \
if ((_s - (s)) < ((ptrdiff_t)(slen))) \
*_s++ = Q_IBITS2CH(q, _part, base); \
else \
_r = NULL; \
} while (_part > 0 && _r != NULL); \
if (!((_s - (s)) < ((ptrdiff_t)(slen)))) \
_r = NULL; \
_i = (_s - _r) >> 1; /* N digits requires int(N/2) swaps. */ \
while (_i-- > 0 && _r != NULL) { \
/* Work from middle out to reverse integer chars. */ \
*_s = *(_r + _i); /* Stash LHS char temporarily. */ \
*(_r + _i) = *(_s - _i - 1); /* Copy RHS char to LHS. */\
*(_s - _i - 1) = *_s; /* Copy LHS char to RHS. */ \
} \
_i = (prec); \
if (_i != 0 && _r != NULL) { \
if ((_s - (s)) < ((ptrdiff_t)(slen))) \
*_s++ = '.'; \
else \
_r = NULL; \
_part = Q_GFABSVAL(q); \
if (_i < 0 || _i > (int)Q_NFBITS(q)) \
_i = Q_NFBITS(q); \
while (_i-- > 0 && _r != NULL) { \
/* Render fraction chars in correct order. */ \
if ((_s - (s)) < ((ptrdiff_t)(slen))) \
*_s++ = Q_FBITS2CH(q, _part, base); \
else \
_r = NULL; \
} \
} \
if ((_s - (s)) < ((ptrdiff_t)(slen)) && _r != NULL) \
*_s = '\0'; \
else { \
_r = NULL; \
if (((ptrdiff_t)(slen)) > 0) \
*(s) = '\0'; \
} \
/* Return a pointer to the '\0' or NULL on overflow. */ \
(_r != NULL ? _s : _r); \
})
/* Left shift an integral value to align with the int bits of 'q'. */
#define Q_SHL(q, iv) \
(Q_LTZ(iv) ? -(int64_t)(Q_ABS(iv) << Q_NFBITS(q)) : \
Q_TC(q, iv) << Q_NFBITS(q))
/* Calculate the relative fractional precision between 'a' and 'b' in bits. */
#define Q_RELPREC(a, b) ((int)Q_NFBITS(a) - (int)Q_NFBITS(b))
/*
* Determine control bits for the desired 'rpshft' radix point shift. Rounds up
* to the nearest valid shift supported by the encoding scheme.
*/
#define Q_CTRLINI(rpshft) \
(((rpshft) <= 8) ? (((rpshft) - 1) >> 1) : (0x4 | (((rpshft) - 1) >> 4)))
/*
* Convert decimal fractional value 'dfv' to its binary-encoded representation
* with 'nfbits' of binary precision. 'dfv' must be passed as a preprocessor
* literal to preserve leading zeroes. The returned result can be used to set a
* Q number's fractional bits e.g. using Q_SFVAL().
*/
#define Q_DFV2BFV(dfv, nfbits) \
({ \
uint64_t _bfv = 0, _thresh = 5, _tmp = dfv; \
int _i = sizeof(""#dfv) - 1; \
/* \
* Compute decimal threshold to determine which \
* conversion rounds will yield a binary 1. \
*/ \
while (--_i > 0) {_thresh *= 10;} \
_i = (nfbits) - 1; \
while (_i >= 0) { \
if (_thresh <= _tmp) { \
_bfv |= 1ULL << _i; \
_tmp = _tmp - _thresh; \
} \
_i--; _tmp <<= 1; \
} \
_bfv; \
})
/*
* Initialise 'q' with raw integer value 'iv', decimal fractional value 'dfv',
* and radix point shift 'rpshft'. Must be done in two steps in case 'iv'
* depends on control bits being set e.g. when passing Q_INTMAX(q) as 'iv'.
*/
#define Q_INI(q, iv, dfv, rpshft) \
({ \
(*(q)) = Q_CTRLINI(rpshft); \
Q_SIFVALS(*(q), iv, Q_DFV2BFV(dfv, Q_NFBITS(*(q)))); \
})
/* Test if 'a' and 'b' fractional precision is the same (T) or not (F). */
#define Q_PRECEQ(a, b) (Q_NFBITS(a) == Q_NFBITS(b))
/* Test if 'n' is a signed type (T) or not (F). Works with any numeric type. */
#define Q_SIGNED(n) (Q_TC(n, -1) < 0)
/*
* Test if 'n' is negative. Works with any numeric type that uses the MSB as the
* sign bit, and also works with Q numbers.
*/
#define Q_LTZ(n) (Q_SIGNED(n) && ((n) & Q_SRAWMASK(n)))
/*
* Return absolute value of 'n'. Works with any standard numeric type that uses
* the MSB as the sign bit, and is signed/unsigned type safe.
* Does not work with Q numbers; use Q_QABS() instead.
*/
#define Q_ABS(n) (Q_LTZ(n) ? -(n) : (n))
/*
* Return an absolute value interpretation of 'q'.
*/
#define Q_QABS(q) (Q_SIGNED(q) ? (q) & ~Q_SRAWMASK(q) : (q))
/* Convert 'q' to float or double representation. */
#define Q_Q2F(q) ((float)Q_GIFVAL(q) / (float)(1ULL << Q_NFBITS(q)))
#define Q_Q2D(q) ((double)Q_GIFVAL(q) / (double)(1ULL << Q_NFBITS(q)))
/* Numerically compare 'a' and 'b' as whole numbers using provided operators. */
#define Q_QCMPQ(a, b, intcmp, fraccmp) \
((Q_GIVAL(a) intcmp Q_GIVAL(b)) || \
((Q_GIVAL(a) == Q_GIVAL(b)) && (Q_GFVAL(a) fraccmp Q_GFVAL(b))))
/* Test if 'a' is numerically less than 'b' (T) or not (F). */
#define Q_QLTQ(a, b) Q_QCMPQ(a, b, <, <)
/* Test if 'a' is numerically less than or equal to 'b' (T) or not (F). */
#define Q_QLEQ(a, b) Q_QCMPQ(a, b, <, <=)
/* Test if 'a' is numerically greater than 'b' (T) or not (F). */
#define Q_QGTQ(a, b) Q_QCMPQ(a, b, >, >)
/* Test if 'a' is numerically greater than or equal to 'b' (T) or not (F). */
#define Q_QGEQ(a, b) Q_QCMPQ(a, b, >, >=)
/* Test if 'a' is numerically equal to 'b' (T) or not (F). */
#define Q_QEQ(a, b) Q_QCMPQ(a, b, ==, ==)
/* Test if 'a' is numerically not equal to 'b' (T) or not (F). */
#define Q_QNEQ(a, b) Q_QCMPQ(a, b, !=, !=)
/* Returns the numerically larger of 'a' and 'b'. */
#define Q_QMAXQ(a, b) (Q_GT(a, b) ? (a) : (b))
/* Returns the numerically smaller of 'a' and 'b'. */
#define Q_QMINQ(a, b) (Q_LT(a, b) ? (a) : (b))
/*
* Test if 'a' can be represented by 'b' with full accuracy (T) or not (F).
* The type casting has to be done to a's type so that any truncation caused by
* the casts will not affect the logic.
*/
#define Q_QCANREPQ(a, b) \
((((Q_LTZ(a) && Q_SIGNED(b)) || !Q_LTZ(a)) && \
Q_GIABSVAL(a) <= Q_TC(a, Q_IMAXVAL(b)) && \
Q_GFABSVAL(a) <= Q_TC(a, Q_FMAXVAL(b))) ? \
0 : EOVERFLOW)
/* Test if raw integer value 'i' can be represented by 'q' (T) or not (F). */
#define Q_QCANREPI(q, i) \
((((Q_LTZ(i) && Q_SIGNED(q)) || !Q_LTZ(i)) && \
Q_ABS(i) <= Q_TC(i, Q_IMAXVAL(q))) ? 0 : EOVERFLOW)
/*
* Returns a Q variable debug format string with appropriate modifiers and
* padding relevant to the underlying Q data type.
*/
#define Q_DEBUGFMT_(prefmt, postfmt, mod, hexpad) \
prefmt \
/* Var name + address. */ \
"\"%s\"@%p" \
/* Data type. */ \
"\n\ttype=%c%dq_t, " \
/* Qm.n notation; 'm' = # int bits, 'n' = # frac bits. */ \
"Qm.n=Q%d.%d, " \
/* Radix point shift relative to the underlying data type's LSB. */ \
"rpshft=%d, " \
/* Min/max integer values which can be represented. */ \
"imin=0x%0" #mod "x, " \
"imax=0x%0" #mod "x" \
/* Raw hex dump of all bits. */ \
"\n\tqraw=0x%0" #hexpad #mod "x" \
/* Bit masks for int/frac/ctrl bits. */ \
"\n\timask=0x%0" #hexpad #mod "x, " \
"fmask=0x%0" #hexpad #mod "x, " \
"cmask=0x%0" #hexpad #mod "x, " \
"ifmask=0x%0" #hexpad #mod "x" \
/* Hex dump of masked int bits; 'iraw' includes shift */ \
"\n\tiraw=0x%0" #hexpad #mod "x, " \
"iabsval=0x%" #mod "x, " \
"ival=0x%" #mod "x" \
/* Hex dump of masked frac bits; 'fraw' includes shift */ \
"\n\tfraw=0x%0" #hexpad #mod "x, " \
"fabsval=0x%" #mod "x, " \
"fval=0x%" #mod "x" \
"%s" \
postfmt
#define Q_DEBUGFMT(q, prefmt, postfmt) \
sizeof(q) == 8 ? Q_DEBUGFMT_(prefmt, postfmt, j, 16) : \
sizeof(q) == 4 ? Q_DEBUGFMT_(prefmt, postfmt, , 8) : \
sizeof(q) == 2 ? Q_DEBUGFMT_(prefmt, postfmt, h, 4) : \
sizeof(q) == 1 ? Q_DEBUGFMT_(prefmt, postfmt, hh, 2) : \
prefmt "\"%s\"@%p: invalid" postfmt \
/*
* Returns a format string and data suitable for printf-like rendering
* e.g. Print to console with a trailing newline: printf(Q_DEBUG(q, "", "\n"));
*/
#define Q_DEBUG(q, prefmt, postfmt, incfmt) \
Q_DEBUGFMT(q, prefmt, postfmt) \
, #q \
, &(q) \
, Q_SIGNED(q) ? 's' : 'u' \
, Q_NTBITS(q) \
, Q_NIBITS(q) \
, Q_NFBITS(q) \
, Q_RPSHFT(q) \
, Q_IMINVAL(q) \
, Q_IMAXVAL(q) \
, (q) \
, Q_IRAWMASK(q) \
, Q_FRAWMASK(q) \
, Q_TC(q, Q_CRAWMASK(q)) \
, Q_IFRAWMASK(q) \
, Q_GIRAW(q) \
, Q_GIABSVAL(q) \
, Q_GIVAL(q) \
, Q_GFRAW(q) \
, Q_GFABSVAL(q) \
, Q_GFVAL(q) \
, (incfmt) ? Q_DEBUGFMT(q, "\nfmt:", "") : "" \
/*
* If precision differs, attempt to normalise to the greater precision that
* preserves the integer component of both 'a' and 'b'.
*/
#define Q_NORMPREC(a, b) \
({ \
int _perr = 0, _relprec = Q_RELPREC(*(a), b); \
if (_relprec != 0) \
_perr = ERANGE; /* XXXLAS: Do precision normalisation! */\
_perr; \
})
/* Clone r's control bits and int/frac value into 'l'. */
#define Q_QCLONEQ(l, r) \
({ \
Q_BT(*(l)) _l = Q_GCVAL(r); \
int _err = Q_QCANREPQ(r, _l); \
if (!_err) { \
*(l) = _l; \
Q_SIFVAL(*(l), Q_GIFVAL(r)); \
} \
_err; \
})
/* Copy r's int/frac vals into 'l', retaining 'l's precision and signedness. */
#define Q_QCPYVALQ(l, r) \
({ \
int _err = Q_QCANREPQ(r, *(l)); \
if (!_err) \
Q_SIFVALS(*(l), Q_GIVAL(r), Q_GFVAL(r)); \
_err; \
})
#define Q_QADDSUBQ(a, b, eop) \
({ \
int _aserr; \
if ((_aserr = Q_NORMPREC(a, b))) while(0); /* NOP */ \
else if ((eop) == '+') { \
if (Q_IFMAXVAL(*(a)) - Q_GIFABSVAL(b) < Q_GIFVAL(*(a))) \
_aserr = EOVERFLOW; /* [+/-a + +b] > max(a) */ \
else \
Q_SIFVAL(*(a), Q_GIFVAL(*(a)) + Q_TC(*(a), \
Q_GIFABSVAL(b))); \
} else { /* eop == '-' */ \
if (Q_IFMINVAL(*(a)) + Q_GIFABSVAL(b) > Q_GIFVAL(*(a))) \
_aserr = EOVERFLOW; /* [+/-a - +b] < min(a) */ \
else \
Q_SIFVAL(*(a), Q_GIFVAL(*(a)) - Q_TC(*(a), \
Q_GIFABSVAL(b))); \
} \
_aserr; \
})
#define Q_QADDQ(a, b) Q_QADDSUBQ(a, b, (Q_LTZ(b) ? '-' : '+'))
#define Q_QSUBQ(a, b) Q_QADDSUBQ(a, b, (Q_LTZ(b) ? '+' : '-'))
#define Q_QDIVQ(a, b) \
({ \
int _err; \
if ((_err = Q_NORMPREC(a, b))) while(0); /* NOP */ \
else if (Q_GIFABSVAL(b) == 0 || (!Q_SIGNED(*(a)) && Q_LTZ(b))) \
_err = EINVAL; /* Divide by zero or cannot represent. */\
/* XXXLAS: Handle overflow. */ \
else if (Q_GIFABSVAL(*(a)) != 0) { /* Result expected. */ \
Q_SIFVAL(*(a), \
((Q_GIVAL(*(a)) << Q_NFBITS(*(a))) / Q_GIFVAL(b)) + \
(Q_GFVAL(b) == 0 ? 0 : \
((Q_GFVAL(*(a)) << Q_NFBITS(*(a))) / Q_GFVAL(b)))); \
} \
_err; \
})
#define Q_QMULQ(a, b) \
({ \
int _mulerr; \
if ((_mulerr = Q_NORMPREC(a, b))) while(0); /* NOP */ \
else if (!Q_SIGNED(*(a)) && Q_LTZ(b)) \
_mulerr = EINVAL; \
else if (Q_GIFABSVAL(b) != 0 && \
Q_IFMAXVAL(*(a)) / Q_GIFABSVAL(b) < Q_GIFABSVAL(*(a))) \
_mulerr = EOVERFLOW; \
else \
Q_SIFVAL(*(a), (Q_GIFVAL(*(a)) * Q_GIFVAL(b)) >> \
Q_NFBITS(*(a))); \
_mulerr; \
})
#define Q_QCPYVALI(q, i) \
({ \
int _err = Q_QCANREPI(*(q), i); \
if (!_err) \
Q_SIFVAL(*(q), Q_SHL(*(q), i)); \
_err; \
})
#define Q_QADDSUBI(q, i, eop) \
({ \
int _aserr = 0; \
if (Q_NTBITS(*(q)) < (uint32_t)flsll(Q_ABS(i))) \
_aserr = EOVERFLOW; /* i cannot fit in q's type. */ \
else if ((eop) == '+') { \
if (Q_IMAXVAL(*(q)) - Q_TC(*(q), Q_ABS(i)) < \
Q_GIVAL(*(q))) \
_aserr = EOVERFLOW; /* [+/-q + +i] > max(q) */ \
else \
Q_SIFVAL(*(q), Q_GIFVAL(*(q)) + \
Q_SHL(*(q), Q_ABS(i))); \
} else { /* eop == '-' */ \
if (Q_IMINVAL(*(q)) + Q_ABS(i) > Q_GIVAL(*(q))) \
_aserr = EOVERFLOW; /* [+/-q - +i] < min(q) */ \
else \
Q_SIFVAL(*(q), Q_GIFVAL(*(q)) - \
Q_SHL(*(q), Q_ABS(i))); \
} \
_aserr; \
})
#define Q_QADDI(q, i) Q_QADDSUBI(q, i, (Q_LTZ(i) ? '-' : '+'))
#define Q_QSUBI(q, i) Q_QADDSUBI(q, i, (Q_LTZ(i) ? '+' : '-'))
#define Q_QDIVI(q, i) \
({ \
int _diverr = 0; \
if ((i) == 0 || (!Q_SIGNED(*(q)) && Q_LTZ(i))) \
_diverr = EINVAL; /* Divide by zero or cannot represent. */\
else if (Q_GIFABSVAL(*(q)) != 0) { /* Result expected. */ \
Q_SIFVAL(*(q), Q_GIFVAL(*(q)) / Q_TC(*(q), i)); \
if (Q_GIFABSVAL(*(q)) == 0) \
_diverr = ERANGE; /* q underflow. */ \
} \
_diverr; \
})
#define Q_QMULI(q, i) \
({ \
int _mulerr = 0; \
if (!Q_SIGNED(*(q)) && Q_LTZ(i)) \
_mulerr = EINVAL; /* Cannot represent. */ \
else if ((i) != 0 && Q_IFMAXVAL(*(q)) / Q_TC(*(q), Q_ABS(i)) < \
Q_GIFABSVAL(*(q))) \
_mulerr = EOVERFLOW; \
else \
Q_SIFVAL(*(q), Q_GIFVAL(*(q)) * Q_TC(*(q), i)); \
_mulerr; \
})
#define Q_QFRACI(q, in, id) \
({ \
uint64_t _tmp; \
int _err = 0; \
if ((id) == 0) \
_err = EINVAL; /* Divide by zero. */ \
else if ((in) == 0) \
Q_SIFVAL(*(q), in); \
else if ((_tmp = Q_ABS(in)) > (UINT64_MAX >> Q_RPSHFT(*(q)))) \
_err = EOVERFLOW; /* _tmp overflow. */ \
else { \
_tmp = Q_SHL(*(q), _tmp) / Q_ABS(id); \
if (Q_QCANREPI(*(q), _tmp & Q_IFVALIMASK(*(q)))) \
_err = EOVERFLOW; /* q overflow. */ \
else { \
Q_SIFVAL(*(q), _tmp); \
Q_SSIGN(*(q), (Q_LTZ(in) && !Q_LTZ(id)) || \
(!Q_LTZ(in) && Q_LTZ(id))); \
if (_tmp == 0) \
_err = ERANGE; /* q underflow. */ \
} \
} \
_err; \
})
#endif /* _SYS_QMATH_H_ */
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