5a38af1fb8
This makes it possible to perform mathematical operations on fractional values without using floating point. It operates on Q numbers, which are integer-sized, opaque structures initialized to hold a chosen number of integer and fractional bits. For a general description of the Q number system, see the "Fixed Point Representation & Fractional Math" whitepaper[1]; for the actual API see the qmath(3) man page. This is one of dependencies for the upcoming stats(3) framework[2] that will be applied to the TCP stack in a later commit. 1. https://www.superkits.net/whitepapers/Fixed%20Point%20Representation%20&%20Fractional%20Math.pdf 2. https://reviews.freebsd.org/D20477 Reviewed by: bcr (man pages, earlier version), sef (earlier version) Discussed with: cem, dteske, imp, lstewart Sponsored By: Klara Inc, Netflix Obtained from: Netflix Differential Revision: https://reviews.freebsd.org/D20116
262 lines
6.0 KiB
Groff
262 lines
6.0 KiB
Groff
.\"
|
|
.\" 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,
|
|
.\" without modification, immediately at the beginning of the file.
|
|
.\" 2. The name of the author may not be used to endorse or promote products
|
|
.\" derived from this software without specific prior written permission.
|
|
.\"
|
|
.\" 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.
|
|
.\"
|
|
.\" $FreeBSD$
|
|
.\"
|
|
.Dd July 8, 2018
|
|
.Dt Q_INI 3
|
|
.Os
|
|
.Sh NAME
|
|
.Nm Q_INI ,
|
|
.Nm Q_NCBITS ,
|
|
.Nm Q_BT ,
|
|
.Nm Q_TC ,
|
|
.Nm Q_NTBITS ,
|
|
.Nm Q_NFCBITS ,
|
|
.Nm Q_MAXNFBITS ,
|
|
.Nm Q_NFBITS ,
|
|
.Nm Q_NIBITS ,
|
|
.Nm Q_RPSHFT ,
|
|
.Nm Q_ABS ,
|
|
.Nm Q_MAXSTRLEN ,
|
|
.Nm Q_TOSTR ,
|
|
.Nm Q_SHL ,
|
|
.Nm Q_SHR ,
|
|
.Nm Q_DEBUG
|
|
.Nd fixed-point math miscellaneous functions/variables
|
|
.Sh SYNOPSIS
|
|
.In sys/qmath.h
|
|
.Ft QTYPE
|
|
.Fn Q_INI "QTYPE *q" "ITYPE iv" "ITYPE dfv" "int rpshft"
|
|
.Fd Q_NCBITS
|
|
.Ft __typeof(q)
|
|
.Fn Q_BT "QTYPE q"
|
|
.Ft ITYPE
|
|
.Fn Q_TC "QTYPE q" "ITYPE v"
|
|
.Ft uint32_t
|
|
.Fn Q_NTBITS "QTYPE q"
|
|
.Ft uint32_t
|
|
.Fn Q_NFCBITS "QTYPE q"
|
|
.Ft uint32_t
|
|
.Fn Q_MAXNFBITS "QTYPE q"
|
|
.Ft uint32_t
|
|
.Fn Q_NFBITS "QTYPE q"
|
|
.Ft uint32_t
|
|
.Fn Q_NIBITS "QTYPE q"
|
|
.Ft uint32_t
|
|
.Fn Q_RPSHFT "QTYPE q"
|
|
.Ft NTYPE
|
|
.Fn Q_ABS "NTYPE n"
|
|
.Ft uint32_t
|
|
.Fn Q_MAXSTRLEN "QTYPE q" "int base"
|
|
.Ft char *
|
|
.Fn Q_TOSTR "QTYPE q" "int prec" "int base" "char *s" "int slen"
|
|
.Ft ITYPE
|
|
.Fn Q_SHL "QTYPE q" "ITYPE iv"
|
|
.Ft ITYPE
|
|
.Fn Q_SHR "QTYPE q" "ITYPE iv"
|
|
.Ft char *, ...
|
|
.Fn Q_DEBUG "QTYPE q" "char *prefmt" "char *postfmt" "incfmt"
|
|
.Ft ITYPE
|
|
.Fn Q_DFV2BFV "ITYPE dfv" "int nfbits"
|
|
.Sh DESCRIPTION
|
|
.Fn Q_INI
|
|
initialises a Q number with the supplied integral value
|
|
.Fa iv
|
|
and decimal fractional value
|
|
.Fa dfv ,
|
|
with appropriate control bits based on the requested radix shift point
|
|
.Fa rpshft .
|
|
.Fa dfv
|
|
must be passed as a preprocessor literal to preserve leading zeroes.
|
|
.Pp
|
|
The
|
|
.Dv Q_NCBITS
|
|
defined constant specifies the number of reserved control bits, currently 3.
|
|
.Pp
|
|
.Fn Q_NTBITS ,
|
|
.Fn Q_NFCBITS ,
|
|
.Fn Q_MAXNFBITS ,
|
|
.Fn Q_NFBITS
|
|
and
|
|
.Fn Q_NIBITS
|
|
return the
|
|
.Fa q Ns -specific
|
|
count of total, control-encoded fractional, maximum fractional, effective
|
|
fractional, and integer bits applicable to
|
|
.Fa q
|
|
respectively.
|
|
.Pp
|
|
.Fn Q_BT
|
|
returns the C data type of
|
|
.Fa q ,
|
|
while
|
|
.Fn Q_TC
|
|
returns
|
|
.Fa v
|
|
type casted to the C data type of
|
|
.Fa q .
|
|
.Pp
|
|
.Fn Q_RPSHFT
|
|
returns the bit position of
|
|
.Fa q Ap s
|
|
binary radix point relative to bit zero.
|
|
.Pp
|
|
.Fn Q_ABS
|
|
returns the absolute value of any standard numeric type
|
|
.Pq that uses the MSB as a sign bit, but not Q numbers
|
|
passed in as
|
|
.Fa n .
|
|
The function is signed/unsigned type safe.
|
|
.Pp
|
|
.Fn Q_SHL
|
|
and
|
|
.Fn Q_SHR
|
|
return the integral value
|
|
.Fa v
|
|
left or right shifted by the appropriate amount for
|
|
.Fa q .
|
|
.Pp
|
|
.Fn Q_MAXSTRLEN
|
|
calculates the maximum number of characters that may be required to render the
|
|
C-string representation of
|
|
.Fa q
|
|
with numeric base
|
|
.Fa base .
|
|
.Pp
|
|
.Fn Q_TOSTR
|
|
renders the C-string representation of
|
|
.Fa q
|
|
with numeric base
|
|
.Fa base
|
|
and fractional precision
|
|
.Fa prec
|
|
into
|
|
.Fa s
|
|
which has an available capacity of
|
|
.Fa slen
|
|
characters.
|
|
.Fa base
|
|
must be in range
|
|
.Bq 2,16 .
|
|
Specifying
|
|
.Fa prec
|
|
as -1 renders the number's fractional component with maximum precision.
|
|
If
|
|
.Fa slen
|
|
is greater than zero but insufficient to hold the complete C-string, the '\\0'
|
|
C-string terminator will be written to
|
|
.Fa *s ,
|
|
thereby returning a zero length C-string.
|
|
.Pp
|
|
.Fn Q_DEBUG
|
|
returns a format string and associated data suitable for printf-like rendering
|
|
of debugging information pertaining to
|
|
.Fa q .
|
|
If either
|
|
.Fa prefmt
|
|
and/or
|
|
.Fa postfmt
|
|
are specified, they are prepended and appended to the resulting format string
|
|
respectively.
|
|
The
|
|
.Fa incfmt
|
|
boolean specifies whether to include
|
|
.Pq Vt true
|
|
or exclude
|
|
.Pq Vt false
|
|
the raw format string itself in the debugging output.
|
|
.Pp
|
|
.Fn Q_DFV2BFV
|
|
converts decimal fractional value
|
|
.Fa dfv
|
|
to its binary-encoded representation with
|
|
.Fa nfbits
|
|
of binary precision.
|
|
.Fa dfv
|
|
must be passed as a preprocessor literal to preserve leading zeroes.
|
|
The returned value can be used to set a Q number's fractional bits, for example
|
|
using
|
|
.Fn Q_SFVAL .
|
|
.Pp
|
|
All of those functions operate on
|
|
the following data types:
|
|
.Vt s8q_t ,
|
|
.Vt u8q_t ,
|
|
.Vt s16q_t ,
|
|
.Vt u16q_t ,
|
|
.Vt s32q_t ,
|
|
.Vt u32q_t ,
|
|
.Vt s64q_t ,
|
|
and
|
|
.Vt u64q_t ,
|
|
which are referred to generically as
|
|
.Fa QTYPE .
|
|
The
|
|
.Fa ITYPE
|
|
refers to the
|
|
.Xr stdint 7
|
|
integer types.
|
|
.Fa NTYPE
|
|
is used to refer to any numeric type and is therefore a superset of
|
|
.Fa QTYPE
|
|
and
|
|
.Fa ITYPE .
|
|
.Pp
|
|
For more details, see
|
|
.Xr qmath 3 .
|
|
.Sh RETURN VALUES
|
|
.Fn Q_INI
|
|
returns the initialised Q number which can be used to chain initialise
|
|
additional Q numbers.
|
|
.Pp
|
|
.Fn Q_TOSTR
|
|
returns a pointer to the '\\0' C-string terminator appended to
|
|
.Fa s
|
|
after the rendered numeric data, or NULL on buffer overflow.
|
|
.Pp
|
|
.Fn Q_DFV2BFV
|
|
returns the binary-encoded representation of decimal fractional value
|
|
.Fa dfv
|
|
with
|
|
.Fa nfbits
|
|
of binary precision.
|
|
.Sh SEE ALSO
|
|
.Xr errno 2 ,
|
|
.Xr qmath 3 ,
|
|
.Xr stdint 7
|
|
.Sh HISTORY
|
|
The
|
|
.Xr qmath 3
|
|
functions first appeared in
|
|
.Fx 13.0 .
|
|
.Sh AUTHORS
|
|
.An -nosplit
|
|
The
|
|
.Xr qmath 3
|
|
functions and this manual page were written by
|
|
.An Lawrence Stewart Aq Mt lstewart@FreeBSD.org
|
|
and sponsored by Netflix, Inc.
|