# GCC libquadmath

## Short Contents

- Introduction
- 1 Typedef and constants
- 2 Math Library Routines
- 3 I/O Library Routines
- GNU Free Documentation License
- 4 Reporting Bugs

## Table of Contents

- Introduction
- 1 Typedef and constants
- 2 Math Library Routines
- 3 I/O Library Routines
  - 3.1 `strtoflt128` — Convert from string
  - 3.2 `quadmath_snprintf` — Convert to string
- GNU Free Documentation License
  - ADDENDUM: How to use this License for your documents
- 4 Reporting Bugs

Next: Typedef and constants, Up: (dir)

## Introduction

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

Next: Math Library Routines, Previous: Top, Up: Top

## 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

Next: I/O Library Routines, Previous: Typedef and constants, Up: Top

## 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
`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
`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
`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 simulataneously
`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

Next: GNU Free Documentation License, Previous: Math Library Routines, Up: Top

## 3 I/O Library Routines

Next: quadmath_snprintf, Up: 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;
                }

Previous: strtoflt128, Up: I/O Library Routines

### 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;
                  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;
                }

Next: Reporting Bugs, Previous: I/O Library Routines, Up: Top

## GNU Free Documentation License

Version 1.3, 3 November 2008

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## 4 Reporting Bugs

Bugs in the GCC Quad-Precision Math Library implementation should be reported via http://gcc.gnu.org/bugs.html.