The GCC Quad-Precision Math Library

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

Copyright \begin{matrix}c \\ ◯ \end{matrix} 2010-2019 Free Software Foundation, Inc. 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.

Short Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Typedef and constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Math Library Routines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 I/O Library Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 GNU Free Documentation License . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 Reporting Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Typedef and constants . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Math Library Routines. . . . . . . . . . . . . . . . . . . . . . . . . 5 3 I/O Library Routines. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 strtoflt128 — Convert from string . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 quadmath_snprintf — Convert to string . . . . . . . . . . . . . . . . . . . . . . . 9

GNU Free Documentation License. . . . . . . . . . . . . . . 11

ADDENDUM: How to use this License for your documents . . . . . . . . . 18

4 Reporting Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Introduction 1

Introduction

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

1 Typedef and constants

The following data type has been defined via typedef.

__complex128: __float128-based complex number

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

FLT128_MAX: largest finite number FLT128_MIN: smallest positive number with full precision FLT128_EPSILON: difference between 1 and the next larger

representable number

FLT128_DENORM_MIN: smallest positive denormalized number FLT128_MANT_DIG: number of digits in the mantissa (bit precision) FLT128_MIN_EXP: maximal negative exponent FLT128_MAX_EXP: maximal positive exponent FLT128_DIG: number of decimal digits in the mantissa FLT128_MIN_10_EXP: maximal negative decimal exponent FLT128_MAX_10_EXP: maximal positive decimal exponent

The following mathematical constants of type __float128 are defined.

M_Eq: the constant e (Euler’s number) M_LOG2Eq: binary logarithm of 2 M_LOG10Eq: common, decimal logarithm of 2 M_LN2q: natural logarithm of 2 M_LN10q: natural logarithm of 10

M_PIq: pi

M_PI_2q: pi divided by two M_PI_4q: pi divided by four M_1_PIq: one over pi M_2_PIq: one over two pi M_2_SQRTPIq: two over square root of pi M_SQRT2q: square root of 2 M_SQRT1_2q: one over square root of 2

2 Math Library Routines

The following mathematical functions are available:

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

real value clogq: complex natural logarithm clog10q: complex base 10 logarithm conjq: complex conjugate function cpowq: complex power function cprojq: project into Riemann Sphere csinq: complex sine function csinhq: complex hyperbolic sine function csqrtq: complex square root ctanq: complex tangent function ctanhq: complex hyperbolic tangent function

3 I/O Library Routines

3.1 strtoflt128 — Convert from string

The function strtoflt128 converts a string into a __float128 number.

Syntax  __float128 strtoflt128 (const char *s, char **sp)

Arguments:

s  input string
sp  the address of the next character in the string

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

Example

                  #include <quadmath.h>
                  int main ()
                  {
                    __float128 r;
                    r = strtoflt128 ("1.2345678", NULL);
                    return 0;
                  }

3.2 quadmath_snprintf — Convert to string

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

Syntax  int quadmath_snprintf (char *s, size_t size, const char *format,
          ...)

Arguments:

s  output string
size  byte size of the string, including tailing NUL
format  conversion specifier string

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

Example

                  #include <quadmath.h>
                  #include <stdlib.h>
                  #include <stdio.h>
                  int main ()
                  {
                    __float128 r;
                    int prec = 20;

10 GCC libquadmath

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;
}

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Chapter 4: Reporting Bugs 19

4 Reporting Bugs

Bugs in the GCC Quad-Precision Math Library implementation should be reported via

https://gcc.gnu.org/bugs/.