lib quad math

7/16/2019 Lib Quad Math

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The GCC Quad-Precision Math Library



Published by the Free Sotware Foundation51 Franklin Street, Fith FloorBoston, MA 02110-1301, USA

Copyright c 2010-2013 Free Sotware Foundation, Inc.

Permission is granted to copy, distribute and/or modiy this document underthe terms o the GNU Free Documentation License, Version 1.2 or any laterversion published by the Free Sotware Foundation; with no Invariant Sections,with the Front-Cover Texts being “A GNU Manual,” and with the Back-CoverTexts as in (a) below. A copy o the license is included in the section entitled“GNU Free Documentation License.”

(a) The FSF’s Back-Cover Text is: “You have the reedom to copy and modiythis GNU manual.



i

Short Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 Typedef and constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32 Math Library Routines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 I/O Library Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

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

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



iii

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1 Typedef and constants . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Math Library Routines . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 I/O Library Routines . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 strtoflt128 — Convert rom string . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 quadmath_snprintf — Convert to string . . . . . . . . . . . . . . . . . . . . . . . 9

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

11ADDENDUM: How to use this License or your documents . . . . . . . . . 18

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



Introduction 1

Introduction

This manual documents the usage o libquadmath, the GCC Quad-Precision Math LibraryApplication Programming Interace (API).



Chapter 1: Typede and constants 3

1 Typedef and constants

The ollowing data type has been dened via typedef.

__complex128: __float128-based complex numberThe ollowing macros are dened, which give the numeric limits o the __float128 data

type.

FLT128_MAX: largest nite numberFLT128_MIN: smallest positive number with ull precisionFLT128_EPSILON: diference between 1 and the next larger

representable number

FLT128_DENORM_MIN: smallest positive denormalized numberFLT128_MANT_DIG: number o digits in the mantissa (bit precision)FLT128_MIN_EXP: maximal negative exponentFLT128_MAX_EXP: maximal positive exponentFLT128_DIG: number o decimal digits in the mantissaFLT128_MIN_10_EXP: maximal negative decimal exponentFLT128_MAX_10_EXP: maximal positive decimal exponent

The ollowing mathematical constants o type __float128 are dened.

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

M_PI_2q : pi divided by twoM_PI_4q : pi divided by ourM_1_PIq : one over piM_2_PIq : one over two piM_2_SQRTPIq : two over square root o piM_SQRT2q : square root o 2M_SQRT1_2q : one over square root o 2



Chapter 2: Math Library Routines 5

2 Math Library Routines

The ollowing mathematical unctions are available:

acosq : arc cosine unctionacoshq : inverse hyperbolic cosine unctionasinq : arc sine unctionasinhq : inverse hyperbolic sine unctionatanq : arc tangent unctionatanhq : inverse hyperbolic tangent unctionatan2q : arc tangent unctioncbrtq : cube root unctionceilq : ceiling value unction

copysignq : copy sign o a numbercoshq : hyperbolic cosine unctioncosq : cosine unctionerfq : error unctionerfcq : complementary error unctionexpq : exponential unctionexpm1q : exponential minus 1 unction



6 GCC libquadmath

fabsq : absolute value unctionfdimq : positive diference unctionfiniteq : check niteness o valuefloorq : oor value unctionfmaq : used multiply and addfmaxq : determine maximum o two valuesfminq : determine minimum o two valuesfmodq : remainder value unctionfrexpq : extract mantissa and exponenthypotq : Eucledian distance unctionilogbq : get exponent o the valueisinfq : check or innityisnanq : check or not a numberj0q : Bessel unction o the rst kind, rst orderj1q : Bessel unction o the rst kind, second order

jnq : Bessel unction o the rst kind, n-th orderldexpq : load exponent o the valuelgammaq : logarithmic gamma unctionllrintq : round to nearest integer valuellroundq : round to nearest integer value away rom zerologq : natural logarithm unctionlog10q : base 10 logarithm unctionlog1pq : compute natural logarithm o the value plus onelog2q : base 2 logarithm unction



Chapter 2: Math Library Routines 7

lrintq : round to nearest integer valuelroundq : round to nearest integer value away rom zero

modfq : decompose the oating-point numbernanq : return quiet NaNnearbyintq : round to nearest integernextafterq : next representable oating-point numberpowq : power unctionremainderq : remainder unctionremquoq : remainder and part o quotientrintq : round-to-nearest integral valueroundq : round-to-nearest integral value, return __float128

scalblnq : compute exponent using FLT_RADIX

scalbnq : compute exponent using FLT_RADIX

signbitq : return sign bitsincosq : calculate sine and cosine simulataneously

sinhq : hyperbolic sine unctionsinq : sine unctionsqrtq : square root unctiontanq : tangent unctiontanhq : hyperbolic tangent unctiontgammaq : true gamma unctiontruncq : round to integer, towards zeroy0q : Bessel unction o the second kind, rst ordery1q : Bessel unction o the second kind, second orderynq : Bessel unction o the second kind, n-th ordercabsq complex absolute value unctioncargq : calculate the argument

cimagq imaginary part o complex numbercrealq : real part o complex numbercacoshq : complex arc hyperbolic cosine unctioncacosq : complex arc cosine unctioncasinhq : complex arc hyperbolic sine unctioncasinq : complex arc sine unctioncatanhq : complex arc hyperbolic tangent unctioncatanq : complex arc tangent unctionccosq complex cosine unction:ccoshq : complex hyperbolic cosine unctioncexpq : complex exponential unctioncexpiq : computes the exponential unction o “i” times a

real value



8 GCC libquadmath

clogq : complex natural logarithmclog10q : complex base 10 logarithmconjq : complex conjugate unctioncpowq : complex power unctioncprojq : project into Riemann Spherecsinq : complex sine unctioncsinhq : complex hyperbolic sine unctioncsqrtq : complex square rootctanq : complex tangent unctionctanhq : complex hyperbolic tangent unction



Chapter 3: I/O Library Routines 9

3 I/O Library Routines

3.1 strtoflt128 — Convert from string

The unction strtoflt128 converts a string into a __float128 number.

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

Arguments :s input stringsp the address o the next character in the string

The argument sp contains, i not NULL, the address o the next character ol-lowing the parts o 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 unction quadmath_snprintf converts a __float128 oating-point number into astring. It is a specialized alternative to snprintf, where the ormat string is restricted

to a single conversion specier with Q modier and conversion specier e, E, f, F, g, G, a orA, with no extra characters beore or ater the conversion specier. The %m$ or *m$ stylemust not be used in the ormat.

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

...)

Arguments :s output stringsize byte size o the string, including tailing NULformat conversion specier string

Note On some targets when supported by the C library hooks are installed or printf

amily o unctions, 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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18 GCC libquadmath

ADDENDUM: How to use this License for your documents

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Chapter 4: Reporting Bugs 19

4 Reporting Bugs

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

http://gcc.gnu.org/bugs/

http://gcc.gnu.org/bugs/

lib quad math

Documents

math library routinesthe

decimal logarithm

square root of pim

smallest positive number

hyperbolic cosine functioncosq

arc cosine functionacoshq

number of decimal digits

natural logarithm