\input texinfo @c -*-texinfo-*-

@c %**start of header
@setfilename libquadmath.info
@settitle GCC libquadmath
@c %**end of header

@copying
Copyright @copyright{} 2010-2024 Free Software Foundation, Inc.

@quotation
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with no
Invariant Sections, with the Front-Cover Texts being ``A GNU Manual,''
and with the Back-Cover Texts as in (a) below.  A copy of the
license is included in the section entitled ``GNU Free Documentation
License.''

(a) The FSF's Back-Cover Text is: ``You have the freedom to
copy and modify this GNU manual.
@end quotation
@end copying

@ifinfo
@dircategory GNU Libraries
@direntry
* libquadmath: (libquadmath).                  GCC Quad-Precision Math Library
@end direntry

This manual documents the GCC Quad-Precision Math Library API.

Published by the Free Software Foundation
51 Franklin Street, Fifth Floor
Boston, MA 02110-1301 USA

@insertcopying
@end ifinfo


@setchapternewpage odd

@titlepage
@title The GCC Quad-Precision Math Library
@page
@vskip 0pt plus 1filll
@comment For the @value{version-GCC} Version*
@sp 1
Published by the Free Software Foundation @*
51 Franklin Street, Fifth Floor@*
Boston, MA 02110-1301, USA@*
@sp 1
@insertcopying
@end titlepage

@summarycontents
@contents
@page


@node Top
@top Introduction
@cindex Introduction

This manual documents the usage of libquadmath, the GCC Quad-Precision
Math Library Application Programming Interface (API).


@comment
@comment  When you add a new menu item, please keep the right hand
@comment  aligned to the same column.  Do not use tabs.  This provides
@comment  better formatting.
@comment
@menu
* Typedef and constants::      Defined data types and constants
* Math Library Routines::      The Libquadmath math runtime application
                               programming interface.
* I/O Library Routines::       The Libquadmath I/O runtime application
                               programming interface.
* GNU Free Documentation License::
                               How you can copy and share this manual.
* Reporting Bugs::             How to report bugs in GCC Libquadmath.
@c * Index::                      Index of this documentation.
@end menu


@c ---------------------------------------------------------------------
@c Defined macros
@c ---------------------------------------------------------------------

@node Typedef and constants
@chapter Typedef and constants

The following data type has been defined via @code{typedef}.

@table @asis
@item @code{__complex128}: @code{__float128}-based complex number
@end table

The following macros are defined, which give the numeric limits of the
@code{__float128} data type.

@table @asis
@item @code{FLT128_MAX}: largest finite number
@item @code{FLT128_MIN}: smallest positive number with full precision
@item @code{FLT128_EPSILON}: difference between 1 and the next larger
                             representable number
@item @code{FLT128_DENORM_MIN}: smallest positive denormalized number
@item @code{FLT128_MANT_DIG}: number of digits in the mantissa (bit precision)
@item @code{FLT128_MIN_EXP}: maximal negative exponent
@item @code{FLT128_MAX_EXP}: maximal positive exponent
@item @code{FLT128_DIG}: number of decimal digits in the mantissa
@item @code{FLT128_MIN_10_EXP}: maximal negative decimal exponent
@item @code{FLT128_MAX_10_EXP}: maximal positive decimal exponent
@end table

The following mathematical constants of type @code{__float128} are defined.

@table @asis
@item @code{M_Eq}: the constant e (Euler's number)
@item @code{M_LOG2Eq}: base 2 logarithm of e
@item @code{M_LOG10Eq}: decimal (base 10) logarithm of e
@item @code{M_LN2q}: natural logarithm of 2
@item @code{M_LN10q}: natural logarithm of 10
@item @code{M_PIq}: pi
@item @code{M_PI_2q}: pi divided by two
@item @code{M_PI_4q}: pi divided by four
@item @code{M_1_PIq}: one divided by pi
@item @code{M_2_PIq}: two divided by pi
@item @code{M_2_SQRTPIq}: two divided by square root of pi
@item @code{M_SQRT2q}: square root of 2
@item @code{M_SQRT1_2q}: one divided by square root of 2
@end table


@c ---------------------------------------------------------------------
@c Math routines
@c ---------------------------------------------------------------------

@node Math Library Routines
@chapter Math Library Routines

The following mathematical functions are available:

@table @asis
@item @code{acosq}: arc cosine function
@item @code{acoshq}: inverse hyperbolic cosine function
@item @code{asinq}: arc sine function
@item @code{asinhq}: inverse hyperbolic sine function
@item @code{atanq}: arc tangent function
@item @code{atanhq}: inverse hyperbolic tangent function
@item @code{atan2q}: arc tangent function
@item @code{cbrtq}: cube root function
@item @code{ceilq}: ceiling value function
@item @code{copysignq}: copy sign of a number
@item @code{coshq}: hyperbolic cosine function
@item @code{cosq}: cosine function
@item @code{erfq}: error function
@item @code{erfcq}: complementary error function
@item @code{exp2q}: base 2 exponential function
@item @code{expq}: exponential function
@item @code{expm1q}: exponential minus 1 function
@need 800
@item @code{fabsq}: absolute value function
@item @code{fdimq}: positive difference function
@item @code{finiteq}: check finiteness of value
@item @code{floorq}: floor value function
@item @code{fmaq}: fused multiply and add
@item @code{fmaxq}: determine maximum of two values
@item @code{fminq}: determine minimum of two values
@item @code{fmodq}: remainder value function
@item @code{frexpq}: extract mantissa and exponent
@item @code{hypotq}: Eucledian distance function
@item @code{ilogbq}: get exponent of the value
@item @code{isinfq}: check for infinity
@item @code{isnanq}: check for not a number
@item @code{issignalingq}: check for signaling not a number
@item @code{j0q}: Bessel function of the first kind, first order
@item @code{j1q}: Bessel function of the first kind, second order
@item @code{jnq}: Bessel function of the first kind, @var{n}-th order
@item @code{ldexpq}: load exponent of the value
@item @code{lgammaq}: logarithmic gamma function
@item @code{llrintq}: round to nearest integer value
@item @code{llroundq}: round to nearest integer value away from zero
@item @code{logbq}: get exponent of the value
@item @code{logq}: natural logarithm function
@item @code{log10q}: base 10 logarithm function
@item @code{log1pq}: compute natural logarithm of the value plus one
@item @code{log2q}: base 2 logarithm function
@need 800
@item @code{lrintq}: round to nearest integer value
@item @code{lroundq}: round to nearest integer value away from zero
@item @code{modfq}: decompose the floating-point number
@item @code{nanq}: return quiet NaN
@item @code{nearbyintq}: round to nearest integer
@item @code{nextafterq}: next representable floating-point number
@item @code{powq}: power function
@item @code{remainderq}: remainder function
@item @code{remquoq}: remainder and part of quotient
@item @code{rintq}: round-to-nearest integral value
@item @code{roundq}: round-to-nearest integral value, return @code{__float128}
@item @code{scalblnq}: compute exponent using @code{FLT_RADIX}
@item @code{scalbnq}: compute exponent using @code{FLT_RADIX}
@item @code{signbitq}: return sign bit
@item @code{sincosq}: calculate sine and cosine simultaneously
@item @code{sinhq}: hyperbolic sine function
@item @code{sinq}: sine function
@item @code{sqrtq}: square root function
@item @code{tanq}: tangent function
@item @code{tanhq}: hyperbolic tangent function
@need 800
@item @code{tgammaq}: true gamma function
@item @code{truncq}: round to integer, towards zero
@item @code{y0q}: Bessel function of the second kind, first order
@item @code{y1q}: Bessel function of the second kind, second order
@item @code{ynq}: Bessel function of the second kind, @var{n}-th order
@item @code{cabsq} complex absolute value function
@item @code{cargq}: calculate the argument
@item @code{cimagq} imaginary part of complex number
@item @code{crealq}: real part of complex number
@item @code{cacoshq}: complex arc hyperbolic cosine function
@item @code{cacosq}: complex arc cosine function
@item @code{casinhq}: complex arc hyperbolic sine function
@item @code{casinq}: complex arc sine function
@item @code{catanhq}: complex arc hyperbolic tangent function
@item @code{catanq}: complex arc tangent function
@item @code{ccosq} complex cosine function:
@item @code{ccoshq}: complex hyperbolic cosine function
@item @code{cexpq}: complex exponential function
@need 800
@item @code{cexpiq}: computes the exponential function of ``i'' times a
                     real value
@item @code{clogq}: complex natural logarithm
@item @code{clog10q}: complex base 10 logarithm
@item @code{conjq}: complex conjugate function
@item @code{cpowq}: complex power function
@item @code{cprojq}: project into Riemann Sphere
@item @code{csinq}: complex sine function
@item @code{csinhq}: complex hyperbolic sine function
@item @code{csqrtq}: complex square root
@item @code{ctanq}: complex tangent function
@item @code{ctanhq}: complex hyperbolic tangent function
@end table


@c ---------------------------------------------------------------------
@c I/O routines
@c ---------------------------------------------------------------------

@node I/O Library Routines
@chapter I/O Library Routines

@menu
* @code{strtoflt128}:          strtoflt128,          Convert from string
* @code{quadmath_snprintf}:    quadmath_snprintf,    Convert to string
@end menu


@node strtoflt128
@section @code{strtoflt128} --- Convert from string

The function @code{strtoflt128} converts a string into a
@code{__float128} number.

@table @asis
@item Syntax
@code{__float128 strtoflt128 (const char *s, char **sp)}

@item @emph{Arguments}:
@multitable @columnfractions .15 .70
@item @var{s}  @tab input string
@item @var{sp} @tab the address of the next character in the string
@end multitable

The argument @var{sp} contains, if not @code{NULL}, the address of the
next character following the parts of the string, which have been read.

@item Example
@smallexample
#include <quadmath.h>

int main ()
@{
  __float128 r;

  r = strtoflt128 ("1.2345678", NULL);

  return 0;
@}
@end smallexample
@end table


@node quadmath_snprintf
@section @code{quadmath_snprintf} --- Convert to string

The function @code{quadmath_snprintf} converts a @code{__float128} floating-point
number into a string.  It is a specialized alternative to @code{snprintf}, where
the format string is restricted to a single conversion specifier with @code{Q}
modifier and conversion specifier @code{e}, @code{E}, @code{f}, @code{F}, @code{g},
@code{G}, @code{a} or @code{A}, with no extra characters before or after the
conversion specifier.  The @code{%m$} or @code{*m$} style must not be used in
the format.

@table @asis
@item Syntax
@code{int quadmath_snprintf (char *s, size_t size, const char *format, ...)}

@item @emph{Arguments}:
@multitable @columnfractions .15 .70
@item @var{s}    @tab output string
@item @var{size} @tab byte size of the string, including trailing NUL
@item @var{format} @tab conversion specifier string
@end multitable

@item Note
On some targets when supported by the C library hooks are installed
for @code{printf} family of functions, so that @code{printf ("%Qe", 1.2Q);}
etc.@: works too.

@item Example
@smallexample
#include <quadmath.h>
#include <stdlib.h>
#include <stdio.h>

int main ()
@{
  __float128 r;
  int prec = 20;
  int width = 46;
  char buf[128];

  r = 2.0q;
  r = sqrtq (r);
  int n = quadmath_snprintf (buf, sizeof buf, "%+-#*.20Qe", width, r);
  if ((size_t) n < sizeof buf)
    printf ("%s\n", buf);
    /* Prints: +1.41421356237309504880e+00 */
  quadmath_snprintf (buf, sizeof buf, "%Qa", r);
  if ((size_t) n < sizeof buf)
    printf ("%s\n", buf);
    /* Prints: 0x1.6a09e667f3bcc908b2fb1366ea96p+0 */
  n = quadmath_snprintf (NULL, 0, "%+-#46.*Qe", prec, r);
  if (n > -1)
    @{
      char *str = malloc (n + 1);
      if (str)
        @{
          quadmath_snprintf (str, n + 1, "%+-#46.*Qe", prec, r);
          printf ("%s\n", str);
          /* Prints: +1.41421356237309504880e+00 */
        @}
      free (str);
    @}
  return 0;
@}
@end smallexample

@end table


@c ---------------------------------------------------------------------
@c GNU Free Documentation License
@c ---------------------------------------------------------------------

@include fdl.texi

@c ---------------------------------------------------------------------
@c Reporting Bugs
@c ---------------------------------------------------------------------

@c For BUGURL
@include libquadmath-vers.texi

@node Reporting Bugs
@chapter Reporting Bugs

Bugs in the GCC Quad-Precision Math Library implementation should be
reported via @value{BUGURL}.


@c ---------------------------------------------------------------------
@c Index
@c ---------------------------------------------------------------------

@c @node Index
@c @unnumbered Index
@c 
@c @printindex cp

@bye