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      4 Copyright (C) 2010-2013 Free Software Foundation, Inc.
      5 
      6      Permission is granted to copy, distribute and/or modify this
      7      document under the terms of the GNU Free Documentation License,
      8      Version 1.2 or any later version published by the Free Software
      9      Foundation; with no Invariant Sections, with the Front-Cover Texts
     10      being "A GNU Manual," and with the Back-Cover Texts as in (a)
     11      below.  A copy of the license is included in the section entitled
     12      "GNU Free Documentation License."
     13 
     14      (a) The FSF's Back-Cover Text is: "You have the freedom to copy
     15      and modify this GNU manual.
     16 
     17 INFO-DIR-SECTION GNU Libraries
     18 START-INFO-DIR-ENTRY
     19 * libquadmath: (libquadmath).                  GCC Quad-Precision Math Library
     20 END-INFO-DIR-ENTRY
     21 
     22    This manual documents the GCC Quad-Precision Math Library API.
     23 
     24    Published by the Free Software Foundation 51 Franklin Street, Fifth
     25 Floor Boston, MA 02110-1301 USA
     26 
     27    Copyright (C) 2010-2013 Free Software Foundation, Inc.
     28 
     29      Permission is granted to copy, distribute and/or modify this
     30      document under the terms of the GNU Free Documentation License,
     31      Version 1.2 or any later version published by the Free Software
     32      Foundation; with no Invariant Sections, with the Front-Cover Texts
     33      being "A GNU Manual," and with the Back-Cover Texts as in (a)
     34      below.  A copy of the license is included in the section entitled
     35      "GNU Free Documentation License."
     36 
     37      (a) The FSF's Back-Cover Text is: "You have the freedom to copy
     38      and modify this GNU manual.
     39 
     40 
     41 File: libquadmath.info,  Node: Top,  Next: Typedef and constants,  Up: (dir)
     42 
     43 Introduction
     44 ************
     45 
     46 This manual documents the usage of libquadmath, the GCC Quad-Precision
     47 Math Library Application Programming Interface (API).
     48 
     49 * Menu:
     50 
     51 * Typedef and constants::      Defined data types and constants
     52 * Math Library Routines::      The Libquadmath math runtime application
     53                                programming interface.
     54 * I/O Library Routines::       The Libquadmath I/O runtime application
     55                                programming interface.
     56 * GNU Free Documentation License::
     57                                How you can copy and share this manual.
     58 * Reporting Bugs::             How to report bugs in GCC Libquadmath.
     59 
     60 
     61 File: libquadmath.info,  Node: Typedef and constants,  Next: Math Library Routines,  Prev: Top,  Up: Top
     62 
     63 1 Typedef and constants
     64 ***********************
     65 
     66 The following data type has been defined via `typedef'.
     67 
     68 `__complex128': `__float128'-based complex number
     69 
     70    The following macros are defined, which give the numeric limits of
     71 the `__float128' data type.
     72 
     73 `FLT128_MAX': largest finite number
     74 
     75 `FLT128_MIN': smallest positive number with full precision
     76 
     77 `FLT128_EPSILON': difference between 1 and the next larger
     78      representable number
     79 
     80 `FLT128_DENORM_MIN': smallest positive denormalized number
     81 
     82 `FLT128_MANT_DIG': number of digits in the mantissa (bit precision)
     83 
     84 `FLT128_MIN_EXP': maximal negative exponent
     85 
     86 `FLT128_MAX_EXP': maximal positive exponent
     87 
     88 `FLT128_DIG': number of decimal digits in the mantissa
     89 
     90 `FLT128_MIN_10_EXP': maximal negative decimal exponent
     91 
     92 `FLT128_MAX_10_EXP': maximal positive decimal exponent
     93 
     94    The following mathematical constants of type `__float128' are
     95 defined.
     96 
     97 `M_Eq': the constant e (Euler's number)
     98 
     99 `M_LOG2Eq': binary logarithm of 2
    100 
    101 `M_LOG10Eq': common, decimal logarithm of 2
    102 
    103 `M_LN2q': natural logarithm of 2
    104 
    105 `M_LN10q': natural logarithm of 10
    106 
    107 `M_PIq': pi
    108 
    109 `M_PI_2q': pi divided by two
    110 
    111 `M_PI_4q': pi divided by four
    112 
    113 `M_1_PIq': one over pi
    114 
    115 `M_2_PIq': one over two pi
    116 
    117 `M_2_SQRTPIq': two over square root of pi
    118 
    119 `M_SQRT2q': square root of 2
    120 
    121 `M_SQRT1_2q': one over square root of 2
    122 
    123 
    124 File: libquadmath.info,  Node: Math Library Routines,  Next: I/O Library Routines,  Prev: Typedef and constants,  Up: Top
    125 
    126 2 Math Library Routines
    127 ***********************
    128 
    129 The following mathematical functions are available:
    130 
    131 `acosq': arc cosine function
    132 
    133 `acoshq': inverse hyperbolic cosine function
    134 
    135 `asinq': arc sine function
    136 
    137 `asinhq': inverse hyperbolic sine function
    138 
    139 `atanq': arc tangent function
    140 
    141 `atanhq': inverse hyperbolic tangent function
    142 
    143 `atan2q': arc tangent function
    144 
    145 `cbrtq': cube root function
    146 
    147 `ceilq': ceiling value function
    148 
    149 `copysignq': copy sign of a number
    150 
    151 `coshq': hyperbolic cosine function
    152 
    153 `cosq': cosine function
    154 
    155 `erfq': error function
    156 
    157 `erfcq': complementary error function
    158 
    159 `expq': exponential function
    160 
    161 `expm1q': exponential minus 1 function
    162 
    163 `fabsq': absolute value function
    164 
    165 `fdimq': positive difference function
    166 
    167 `finiteq': check finiteness of value
    168 
    169 `floorq': floor value function
    170 
    171 `fmaq': fused multiply and add
    172 
    173 `fmaxq': determine maximum of two values
    174 
    175 `fminq': determine minimum of two values
    176 
    177 `fmodq': remainder value function
    178 
    179 `frexpq': extract mantissa and exponent
    180 
    181 `hypotq': Eucledian distance function
    182 
    183 `ilogbq': get exponent of the value
    184 
    185 `isinfq': check for infinity
    186 
    187 `isnanq': check for not a number
    188 
    189 `j0q': Bessel function of the first kind, first order
    190 
    191 `j1q': Bessel function of the first kind, second order
    192 
    193 `jnq': Bessel function of the first kind, N-th order
    194 
    195 `ldexpq': load exponent of the value
    196 
    197 `lgammaq': logarithmic gamma function
    198 
    199 `llrintq': round to nearest integer value
    200 
    201 `llroundq': round to nearest integer value away from zero
    202 
    203 `logq': natural logarithm function
    204 
    205 `log10q': base 10 logarithm function
    206 
    207 `log1pq': compute natural logarithm of the value plus one
    208 
    209 `log2q': base 2 logarithm function
    210 
    211 `lrintq': round to nearest integer value
    212 
    213 `lroundq': round to nearest integer value away from zero
    214 
    215 `modfq': decompose the floating-point number
    216 
    217 `nanq': return quiet NaN
    218 
    219 `nearbyintq': round to nearest integer
    220 
    221 `nextafterq': next representable floating-point number
    222 
    223 `powq': power function
    224 
    225 `remainderq': remainder function
    226 
    227 `remquoq': remainder and part of quotient
    228 
    229 `rintq': round-to-nearest integral value
    230 
    231 `roundq': round-to-nearest integral value, return `__float128'
    232 
    233 `scalblnq': compute exponent using `FLT_RADIX'
    234 
    235 `scalbnq': compute exponent using `FLT_RADIX'
    236 
    237 `signbitq': return sign bit
    238 
    239 `sincosq': calculate sine and cosine simulataneously
    240 
    241 `sinhq': hyperbolic sine function
    242 
    243 `sinq': sine function
    244 
    245 `sqrtq': square root function
    246 
    247 `tanq': tangent function
    248 
    249 `tanhq': hyperbolic tangent function
    250 
    251 `tgammaq': true gamma function
    252 
    253 `truncq': round to integer, towards zero
    254 
    255 `y0q': Bessel function of the second kind, first order
    256 
    257 `y1q': Bessel function of the second kind, second order
    258 
    259 `ynq': Bessel function of the second kind, N-th order
    260 
    261 `cabsq' complex absolute value function
    262 
    263 `cargq': calculate the argument
    264 
    265 `cimagq' imaginary part of complex number
    266 
    267 `crealq': real part of complex number
    268 
    269 `cacoshq': complex arc hyperbolic cosine function
    270 
    271 `cacosq': complex arc cosine function
    272 
    273 `casinhq': complex arc hyperbolic sine function
    274 
    275 `casinq': complex arc sine function
    276 
    277 `catanhq': complex arc hyperbolic tangent function
    278 
    279 `catanq': complex arc tangent function
    280 
    281 `ccosq' complex cosine function:
    282 
    283 `ccoshq': complex hyperbolic cosine function
    284 
    285 `cexpq': complex exponential function
    286 
    287 `cexpiq': computes the exponential function of "i" times a
    288      real value
    289 
    290 `clogq': complex natural logarithm
    291 
    292 `clog10q': complex base 10 logarithm
    293 
    294 `conjq': complex conjugate function
    295 
    296 `cpowq': complex power function
    297 
    298 `cprojq': project into Riemann Sphere
    299 
    300 `csinq': complex sine function
    301 
    302 `csinhq': complex hyperbolic sine function
    303 
    304 `csqrtq': complex square root
    305 
    306 `ctanq': complex tangent function
    307 
    308 `ctanhq': complex hyperbolic tangent function
    309 
    310 
    311 File: libquadmath.info,  Node: I/O Library Routines,  Next: GNU Free Documentation License,  Prev: Math Library Routines,  Up: Top
    312 
    313 3 I/O Library Routines
    314 **********************
    315 
    316 * Menu:
    317 
    318 * `strtoflt128':          strtoflt128,          Convert from string
    319 * `quadmath_snprintf':    quadmath_snprintf,    Convert to string
    320 
    321 
    322 File: libquadmath.info,  Node: strtoflt128,  Next: quadmath_snprintf,  Up: I/O Library Routines
    323 
    324 3.1 `strtoflt128' -- Convert from string
    325 ========================================
    326 
    327 The function `strtoflt128' converts a string into a `__float128' number.
    328 
    329 Syntax
    330      `__float128 strtoflt128 (const char *s, char **sp)'
    331 
    332 _Arguments_:
    333      S          input string
    334      SP         the address of the next character in the string
    335 
    336      The argument SP contains, if not `NULL', the address of the next
    337      character following the parts of the string, which have been read.
    338 
    339 Example
    340           #include <quadmath.h>
    341 
    342           int main ()
    343           {
    344             __float128 r;
    345 
    346             r = strtoflt128 ("1.2345678", NULL);
    347 
    348             return 0;
    349           }
    350 
    351 
    352 File: libquadmath.info,  Node: quadmath_snprintf,  Prev: strtoflt128,  Up: I/O Library Routines
    353 
    354 3.2 `quadmath_snprintf' -- Convert to string
    355 ============================================
    356 
    357 The function `quadmath_snprintf' converts a `__float128' floating-point
    358 number into a string.  It is a specialized alternative to `snprintf',
    359 where the format string is restricted to a single conversion specifier
    360 with `Q' modifier and conversion specifier `e', `E', `f', `F', `g',
    361 `G', `a' or `A', with no extra characters before or after the
    362 conversion specifier.  The `%m$' or `*m$' style must not be used in the
    363 format.
    364 
    365 Syntax
    366      `int quadmath_snprintf (char *s, size_t size, const char *format,
    367      ...)'
    368 
    369 _Arguments_:
    370      S          output string
    371      SIZE       byte size of the string, including tailing NUL
    372      FORMAT     conversion specifier string
    373 
    374 Note
    375      On some targets when supported by the C library hooks are installed
    376      for `printf' family of functions, so that `printf ("%Qe", 1.2Q);'
    377      etc. works too.
    378 
    379 Example
    380           #include <quadmath.h>
    381           #include <stdlib.h>
    382           #include <stdio.h>
    383 
    384           int main ()
    385           {
    386             __float128 r;
    387             int prec = 20;
    388             int width = 46;
    389             char buf[128];
    390 
    391             r = 2.0q;
    392             r = sqrtq (r);
    393             int n = quadmath_snprintf (buf, sizeof buf, "%+-#*.20Qe", width, r);
    394             if ((size_t) n < sizeof buf)
    395               printf ("%s\n", buf);
    396               /* Prints: +1.41421356237309504880e+00 */
    397             quadmath_snprintf (buf, sizeof buf, "%Qa", r);
    398             if ((size_t) n < sizeof buf)
    399               printf ("%s\n", buf);
    400               /* Prints: 0x1.6a09e667f3bcc908b2fb1366ea96p+0 */
    401             n = quadmath_snprintf (NULL, 0, "%+-#46.*Qe", prec, r);
    402             if (n > -1)
    403               {
    404                 char *str = malloc (n + 1);
    405                 if (str)
    406                   {
    407                     quadmath_snprintf (str, n + 1, "%+-#46.*Qe", prec, r);
    408                     printf ("%s\n", str);
    409                     /* Prints: +1.41421356237309504880e+00 */
    410                   }
    411                 free (str);
    412               }
    413             return 0;
    414           }
    415 
    416 
    417 
    418 File: libquadmath.info,  Node: GNU Free Documentation License,  Next: Reporting Bugs,  Prev: I/O Library Routines,  Up: Top
    419 
    420 GNU Free Documentation License
    421 ******************************
    422 
    423                      Version 1.3, 3 November 2008
    424 
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    426      `http://fsf.org/'
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    663 
    664        K. For any section Entitled "Acknowledgements" or "Dedications",
    665           Preserve the Title of the section, and preserve in the
    666           section all the substance and tone of each of the contributor
    667           acknowledgements and/or dedications given therein.
    668 
    669        L. Preserve all the Invariant Sections of the Document,
    670           unaltered in their text and in their titles.  Section numbers
    671           or the equivalent are not considered part of the section
    672           titles.
    673 
    674        M. Delete any section Entitled "Endorsements".  Such a section
    675           may not be included in the Modified Version.
    676 
    677        N. Do not retitle any existing section to be Entitled
    678           "Endorsements" or to conflict in title with any Invariant
    679           Section.
    680 
    681        O. Preserve any Warranty Disclaimers.
    682 
    683      If the Modified Version includes new front-matter sections or
    684      appendices that qualify as Secondary Sections and contain no
    685      material copied from the Document, you may at your option
    686      designate some or all of these sections as invariant.  To do this,
    687      add their titles to the list of Invariant Sections in the Modified
    688      Version's license notice.  These titles must be distinct from any
    689      other section titles.
    690 
    691      You may add a section Entitled "Endorsements", provided it contains
    692      nothing but endorsements of your Modified Version by various
    693      parties--for example, statements of peer review or that the text
    694      has been approved by an organization as the authoritative
    695      definition of a standard.
    696 
    697      You may add a passage of up to five words as a Front-Cover Text,
    698      and a passage of up to 25 words as a Back-Cover Text, to the end
    699      of the list of Cover Texts in the Modified Version.  Only one
    700      passage of Front-Cover Text and one of Back-Cover Text may be
    701      added by (or through arrangements made by) any one entity.  If the
    702      Document already includes a cover text for the same cover,
    703      previously added by you or by arrangement made by the same entity
    704      you are acting on behalf of, you may not add another; but you may
    705      replace the old one, on explicit permission from the previous
    706      publisher that added the old one.
    707 
    708      The author(s) and publisher(s) of the Document do not by this
    709      License give permission to use their names for publicity for or to
    710      assert or imply endorsement of any Modified Version.
    711 
    712   5. COMBINING DOCUMENTS
    713 
    714      You may combine the Document with other documents released under
    715      this License, under the terms defined in section 4 above for
    716      modified versions, provided that you include in the combination
    717      all of the Invariant Sections of all of the original documents,
    718      unmodified, and list them all as Invariant Sections of your
    719      combined work in its license notice, and that you preserve all
    720      their Warranty Disclaimers.
    721 
    722      The combined work need only contain one copy of this License, and
    723      multiple identical Invariant Sections may be replaced with a single
    724      copy.  If there are multiple Invariant Sections with the same name
    725      but different contents, make the title of each such section unique
    726      by adding at the end of it, in parentheses, the name of the
    727      original author or publisher of that section if known, or else a
    728      unique number.  Make the same adjustment to the section titles in
    729      the list of Invariant Sections in the license notice of the
    730      combined work.
    731 
    732      In the combination, you must combine any sections Entitled
    733      "History" in the various original documents, forming one section
    734      Entitled "History"; likewise combine any sections Entitled
    735      "Acknowledgements", and any sections Entitled "Dedications".  You
    736      must delete all sections Entitled "Endorsements."
    737 
    738   6. COLLECTIONS OF DOCUMENTS
    739 
    740      You may make a collection consisting of the Document and other
    741      documents released under this License, and replace the individual
    742      copies of this License in the various documents with a single copy
    743      that is included in the collection, provided that you follow the
    744      rules of this License for verbatim copying of each of the
    745      documents in all other respects.
    746 
    747      You may extract a single document from such a collection, and
    748      distribute it individually under this License, provided you insert
    749      a copy of this License into the extracted document, and follow
    750      this License in all other respects regarding verbatim copying of
    751      that document.
    752 
    753   7. AGGREGATION WITH INDEPENDENT WORKS
    754 
    755      A compilation of the Document or its derivatives with other
    756      separate and independent documents or works, in or on a volume of
    757      a storage or distribution medium, is called an "aggregate" if the
    758      copyright resulting from the compilation is not used to limit the
    759      legal rights of the compilation's users beyond what the individual
    760      works permit.  When the Document is included in an aggregate, this
    761      License does not apply to the other works in the aggregate which
    762      are not themselves derivative works of the Document.
    763 
    764      If the Cover Text requirement of section 3 is applicable to these
    765      copies of the Document, then if the Document is less than one half
    766      of the entire aggregate, the Document's Cover Texts may be placed
    767      on covers that bracket the Document within the aggregate, or the
    768      electronic equivalent of covers if the Document is in electronic
    769      form.  Otherwise they must appear on printed covers that bracket
    770      the whole aggregate.
    771 
    772   8. TRANSLATION
    773 
    774      Translation is considered a kind of modification, so you may
    775      distribute translations of the Document under the terms of section
    776      4.  Replacing Invariant Sections with translations requires special
    777      permission from their copyright holders, but you may include
    778      translations of some or all Invariant Sections in addition to the
    779      original versions of these Invariant Sections.  You may include a
    780      translation of this License, and all the license notices in the
    781      Document, and any Warranty Disclaimers, provided that you also
    782      include the original English version of this License and the
    783      original versions of those notices and disclaimers.  In case of a
    784      disagreement between the translation and the original version of
    785      this License or a notice or disclaimer, the original version will
    786      prevail.
    787 
    788      If a section in the Document is Entitled "Acknowledgements",
    789      "Dedications", or "History", the requirement (section 4) to
    790      Preserve its Title (section 1) will typically require changing the
    791      actual title.
    792 
    793   9. TERMINATION
    794 
    795      You may not copy, modify, sublicense, or distribute the Document
    796      except as expressly provided under this License.  Any attempt
    797      otherwise to copy, modify, sublicense, or distribute it is void,
    798      and will automatically terminate your rights under this License.
    799 
    800      However, if you cease all violation of this License, then your
    801      license from a particular copyright holder is reinstated (a)
    802      provisionally, unless and until the copyright holder explicitly
    803      and finally terminates your license, and (b) permanently, if the
    804      copyright holder fails to notify you of the violation by some
    805      reasonable means prior to 60 days after the cessation.
    806 
    807      Moreover, your license from a particular copyright holder is
    808      reinstated permanently if the copyright holder notifies you of the
    809      violation by some reasonable means, this is the first time you have
    810      received notice of violation of this License (for any work) from
    811      that copyright holder, and you cure the violation prior to 30 days
    812      after your receipt of the notice.
    813 
    814      Termination of your rights under this section does not terminate
    815      the licenses of parties who have received copies or rights from
    816      you under this License.  If your rights have been terminated and
    817      not permanently reinstated, receipt of a copy of some or all of
    818      the same material does not give you any rights to use it.
    819 
    820  10. FUTURE REVISIONS OF THIS LICENSE
    821 
    822      The Free Software Foundation may publish new, revised versions of
    823      the GNU Free Documentation License from time to time.  Such new
    824      versions will be similar in spirit to the present version, but may
    825      differ in detail to address new problems or concerns.  See
    826      `http://www.gnu.org/copyleft/'.
    827 
    828      Each version of the License is given a distinguishing version
    829      number.  If the Document specifies that a particular numbered
    830      version of this License "or any later version" applies to it, you
    831      have the option of following the terms and conditions either of
    832      that specified version or of any later version that has been
    833      published (not as a draft) by the Free Software Foundation.  If
    834      the Document does not specify a version number of this License,
    835      you may choose any version ever published (not as a draft) by the
    836      Free Software Foundation.  If the Document specifies that a proxy
    837      can decide which future versions of this License can be used, that
    838      proxy's public statement of acceptance of a version permanently
    839      authorizes you to choose that version for the Document.
    840 
    841  11. RELICENSING
    842 
    843      "Massive Multiauthor Collaboration Site" (or "MMC Site") means any
    844      World Wide Web server that publishes copyrightable works and also
    845      provides prominent facilities for anybody to edit those works.  A
    846      public wiki that anybody can edit is an example of such a server.
    847      A "Massive Multiauthor Collaboration" (or "MMC") contained in the
    848      site means any set of copyrightable works thus published on the MMC
    849      site.
    850 
    851      "CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0
    852      license published by Creative Commons Corporation, a not-for-profit
    853      corporation with a principal place of business in San Francisco,
    854      California, as well as future copyleft versions of that license
    855      published by that same organization.
    856 
    857      "Incorporate" means to publish or republish a Document, in whole or
    858      in part, as part of another Document.
    859 
    860      An MMC is "eligible for relicensing" if it is licensed under this
    861      License, and if all works that were first published under this
    862      License somewhere other than this MMC, and subsequently
    863      incorporated in whole or in part into the MMC, (1) had no cover
    864      texts or invariant sections, and (2) were thus incorporated prior
    865      to November 1, 2008.
    866 
    867      The operator of an MMC Site may republish an MMC contained in the
    868      site under CC-BY-SA on the same site at any time before August 1,
    869      2009, provided the MMC is eligible for relicensing.
    870 
    871 
    872 ADDENDUM: How to use this License for your documents
    873 ====================================================
    874 
    875 To use this License in a document you have written, include a copy of
    876 the License in the document and put the following copyright and license
    877 notices just after the title page:
    878 
    879        Copyright (C)  YEAR  YOUR NAME.
    880        Permission is granted to copy, distribute and/or modify this document
    881        under the terms of the GNU Free Documentation License, Version 1.3
    882        or any later version published by the Free Software Foundation;
    883        with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
    884        Texts.  A copy of the license is included in the section entitled ``GNU
    885        Free Documentation License''.
    886 
    887    If you have Invariant Sections, Front-Cover Texts and Back-Cover
    888 Texts, replace the "with...Texts." line with this:
    889 
    890          with the Invariant Sections being LIST THEIR TITLES, with
    891          the Front-Cover Texts being LIST, and with the Back-Cover Texts
    892          being LIST.
    893 
    894    If you have Invariant Sections without Cover Texts, or some other
    895 combination of the three, merge those two alternatives to suit the
    896 situation.
    897 
    898    If your document contains nontrivial examples of program code, we
    899 recommend releasing these examples in parallel under your choice of
    900 free software license, such as the GNU General Public License, to
    901 permit their use in free software.
    902 
    903 
    904 File: libquadmath.info,  Node: Reporting Bugs,  Prev: GNU Free Documentation License,  Up: Top
    905 
    906 4 Reporting Bugs
    907 ****************
    908 
    909 Bugs in the GCC Quad-Precision Math Library implementation should be
    910 reported via `http://gcc.gnu.org/bugs.html'.
    911 
    912 
    913 
    914 Tag Table:
    915 Node: Top1684
    916 Node: Typedef and constants2418
    917 Node: Math Library Routines3858
    918 Node: I/O Library Routines7663
    919 Node: strtoflt1287988
    920 Node: quadmath_snprintf8746
    921 Node: GNU Free Documentation License10954
    922 Node: Reporting Bugs36120
    923 
    924 End Tag Table
    925