ÿØÿà JFIF    ÿÛ „  ( %!1"%)+...383-7(-.+  -%%--------+------------/----------------------------ÿÀ  ¶" ÿÄ     ÿÄ @    !1AQaq‘¡"±ÁÑð2’BRráS‚ñ3b¢CT²Ò #cÿÄ    ÿÄ '   1!AQ2a"‘±#ÿÚ   ? ò(/p‘—–¢·,M|¯G»R£üešT. ôŸEoCFñ‡ 4ÔkåóxR|µÁ¨ÓDà!Ç´µ˜‡p ÍQ‹§!þž^õWsŒy  åÁ§$á«%ºq˜™JyyË0y«^Ϗ -3ÃÏËÈ£Æ\P’ä„s&•‹Üs üô'àWt¹pñCp$bÚF`·7.^)¾!)ÒÙ˜–ÅÏš^h¾ø³·ìe±ŒaeÖ—Í,e=B}Jéߦ$$½—šÙÜCC¯¶è8β–Åkèwx LÉngT±æ¹£Ócœ¿Í/©Éÿ ‰ÚCÒ­mq;Tt¶–}0"zÖPcd1š­¤tˆ„ÐÓâqú[™öUCŠ2޿د­É(¸ßúçšmW,Ò ºf‹Ån™ÄLêÁ8üÁkÁ€L¥ÍuJ1œôrÂSŒÓöt!7EUíïb)AËi¬â-ÙHk8òÁiXYwÅ)O^"ÇØriÛô{»wRUKÙÏÚlÓ¬€‚’שT ] ªb—ÊîKC^×M“xùäñz¬zJ× {4[¹M'IÆeH1LCWÕ]œûº WDæà°OÅ‚¹c²ÞuA–rL`HšpCez‡V’— Ž‚Ë„–ñ­'µR0ÕÖ=À:±G»C\nÆÉ5*¢ †3šhQ4ýÒi$Õ1"Ü]¢p-q3zcQ$ªö¨¥æf›‘»´ÝÚHá„e²JÇ–iÊ:·à¬Øc5Åk»Laª*wi [0Ówk ¦a¦0Õ²ÅÅ‚T¸’³q:Æ<¹ú Ò˜Æ}2VE•Ð€p¡Ô3Úº …h³^LJºçì¥Ánó|˜ÖˆÎˆ+« ¦dø‘Mº–d\ªDðÛ„Ì×LÝ——Ð9Ç|•FèçVm™¨€™3õS–9Äå¢<̉Ìm¢±`·º˜&Z²ž Ë®D«¶»6™‰©­HÈ Àá«h­i³04æ’hxœi3ï¨(ÓL·†‹¶ËpŒ ƒÜÒ? :õdsÀ –3æÓ·Üjâ¬9—]8n¼&]I F£¼…ì–—Œ0v°LǐÅfÛ2TÖ’aµ˜N@ÖBSÏ^à´4-±°b×nÈÈœÆD=KdŒø…ÄÈK,›ÖR§fjü$^ÔÎ!„6^ s:Üun\ôkCÞò÷<—Lúl Í›G¹ÀPá¼Nc¡šÒ…ÙWͳœ±vÊáЄ×9‹P‰cEØ‘™›µŸP<×g1 º©Ø¬wiÁ^l5× I/';Ë+´Z‡ÓÄFÕp[Èð’ HÄ ó 9¬Dl4“é±Ï”V=^Hð;žLädÉa‚°Ë,#/Ž~²BÔÛ QãñQtIeórVB,ÏÂf‹4#Îœc‹É3ZIÖ Œ¢¥·üxa‡Ãçè„jŠ[5 Ä!U?,3žÎ×…ðdÓ÷háŠA‰ìÄ4÷ÃÜZÃE{‰®+W\ZÍE[‰»µk»MÝ­`¢©†˜ÃV‹-f¢¡†¢a«eŠ%«Y¨©q%jâd,Ôq`) ¤¦…šˆ ¦E>0Ùb²t–Ÿ  ÷jsÏ‚Ò’KÈcø(é›;k(’#ôŒQ ™C> õ³M9óºÆµ¤çâ;uÀ)5>RÔ¸fÓ~Ȧ—’-$fe«"FâUˆÊwµPÏu w+"åÉó¨6s™Û9(À¨ù©hE°½†n`m~“@©›p!Vkhµ Á1šbEqqÊ@ºèl›2 –Yã%‘‚hÛ{a¶‡ÅÞM²¬çL34®Çl]®‹ŽØŒm'RÜe35æöˆ­Á­ cP9šeÁköo´L³Ì=p8]”‡B¶,šº|ɏdzXˆØk*ÇÚ{#ñ‰pã(€¶‡9ý'šÜ³½¯kƒ†Â’ëSOƒ•Å®H6+a¢µˆ‹Y¨b˜b+XˆÖ!°u!¢"µˆˆn2ˆ Å0Ä`Å Ô®c(ÓÜGº•Ä»Œ âWî%q.áÐÄ÷î%umÍ£+ÜQ,Vn¦-GphU¸¢X­&,Gt ·K¢ÅÅ·¥RÄÊÉbKn N­R2g$VµÕó Qr#–ÓZUÏð0ÎtÙÀœz ëöo“Îk¯n„T°"SÞ+³/…€½"ižãO%Í%&Δâ‘ËØ´IˆÓ°Ë‰ÞM3.™yçÁzit›`4C`k¢¼á!álÄï sÂ[×!¤l¾æo"ƒIÔ'@ªu)3›ô®“@Z à¾] üœ'‡4¸PÞkÁ-qÄH‰ÓÍBd´ÿ —¹°ÄA&ÊUC„öz‚‚RæŠtf¬>˜ÑidšEçÑL÷áý¡V±h§­c¿¥¨ƒ@g¼…Ýö^ÞËc.ž„æ“I[ ª+·zÐÒÚ,½Ð»¶€C›7jk$๖€Ž¾ÅÙpp¶ÍþéΤ ½ØÎŒq ñpæžÅ¥#Øâ49ÃÂK^MYV“,¶Éz_òæ:…;Õ«¦I3âJ£¤û5$7Èxün\â]Êe¯(Ÿ&Ž‹¶2<6Ćf× æ¢ƱqWı[(ÙÂŽç‚T7¨@ÈÉÍß‚ïÙ"&3TYlGŽ†)†#5ŠA©^T2ÆÁ†)©†©†¤yGXÁ†©"†)©¼ÅV WS†#©]R–r‹q5ÕbâWþBh¯u+ªÅÄ×ü„nÑ^êkªÁj‰jeœWˆÕÕ`µDµ2Ì+Ä µDµµ5Ô{¤Þ0RF’H÷AÛ<ÊÁ§ ƈæ0Ñ£ê4 öÚµ[¬/1²€â<-¬šö²r×0o×w ´xÐÒË„ g01¬„åEM蛇Ã\6µE›‘fÙO k÷CºnÓ1`iîÒ² áÂ!ÑLÄÿ ³¬\õ*:M=Ç»c‹2[‰ØsÕLò\ŒK L^™üÄN\¶#» Ç\……ßïIœÉ$¸ÎñÍ®ÔHÇ Ûí/´>Li”„†g^$ 7NÍÑÑ2M2ªNg=k½Ð}Ÿl6‡ —JWˆ”ÞéT·+µ¦üÂFè¢Vs6ýÆ4»2+2IÝ9ô9®ÇGÙÇ1+Ä8;*Õ§ž½D*îÑWÚçá3Ma¤·ˆ¥t}š²Ü…Q+Æüµ8HíS”üxGéÁˆ¦Ël„éÈ 5 µÄƒ6äÜ(kIš¯S†fÖ&¸®×v|Äyˆ*禌Éù@7-®Ä[]ÎÖ¿ê`º…=:…žJVnݳvðÖKE¼‚ »mà ÷f®:Ë ™–4rð¡4` ܹçž~‹C=œ…¾Ïj|VDtK.ƒ"9 Ï ­–éXá³6WÒïIL-Ї Ç usr/include/bits/mathcalls.h000064400000031454152670302200012066 0ustar00/* Prototype declarations for math functions; helper file for . Copyright (C) 1996-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU C Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU C Library; if not, see . */ /* NOTE: Because of the special way this file is used by , this file must NOT be protected from multiple inclusion as header files usually are. This file provides prototype declarations for the math functions. Most functions are declared using the macro: __MATHCALL (NAME,[_r], (ARGS...)); This means there is a function `NAME' returning `double' and a function `NAMEf' returning `float'. Each place `_Mdouble_' appears in the prototype, that is actually `double' in the prototype for `NAME' and `float' in the prototype for `NAMEf'. Reentrant variant functions are called `NAME_r' and `NAMEf_r'. Functions returning other types like `int' are declared using the macro: __MATHDECL (TYPE, NAME,[_r], (ARGS...)); This is just like __MATHCALL but for a function returning `TYPE' instead of `_Mdouble_'. In all of these cases, there is still both a `NAME' and a `NAMEf' that takes `float' arguments. Note that there must be no whitespace before the argument passed for NAME, to make token pasting work with -traditional. */ #ifndef _MATH_H # error "Never include directly; include instead." #endif /* Trigonometric functions. */ /* Arc cosine of X. */ __MATHCALL (acos,, (_Mdouble_ __x)); /* Arc sine of X. */ __MATHCALL (asin,, (_Mdouble_ __x)); /* Arc tangent of X. */ __MATHCALL (atan,, (_Mdouble_ __x)); /* Arc tangent of Y/X. */ __MATHCALL (atan2,, (_Mdouble_ __y, _Mdouble_ __x)); /* Cosine of X. */ __MATHCALL_VEC (cos,, (_Mdouble_ __x)); /* Sine of X. */ __MATHCALL_VEC (sin,, (_Mdouble_ __x)); /* Tangent of X. */ __MATHCALL (tan,, (_Mdouble_ __x)); /* Hyperbolic functions. */ /* Hyperbolic cosine of X. */ __MATHCALL (cosh,, (_Mdouble_ __x)); /* Hyperbolic sine of X. */ __MATHCALL (sinh,, (_Mdouble_ __x)); /* Hyperbolic tangent of X. */ __MATHCALL (tanh,, (_Mdouble_ __x)); #ifdef __USE_GNU /* Cosine and sine of X. */ __MATHDECL_VEC (void,sincos,, (_Mdouble_ __x, _Mdouble_ *__sinx, _Mdouble_ *__cosx)); #endif #if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 /* Hyperbolic arc cosine of X. */ __MATHCALL (acosh,, (_Mdouble_ __x)); /* Hyperbolic arc sine of X. */ __MATHCALL (asinh,, (_Mdouble_ __x)); /* Hyperbolic arc tangent of X. */ __MATHCALL (atanh,, (_Mdouble_ __x)); #endif /* Exponential and logarithmic functions. */ /* Exponential function of X. */ __MATHCALL_VEC (exp,, (_Mdouble_ __x)); /* Break VALUE into a normalized fraction and an integral power of 2. */ __MATHCALL (frexp,, (_Mdouble_ __x, int *__exponent)); /* X times (two to the EXP power). */ __MATHCALL (ldexp,, (_Mdouble_ __x, int __exponent)); /* Natural logarithm of X. */ __MATHCALL_VEC (log,, (_Mdouble_ __x)); /* Base-ten logarithm of X. */ __MATHCALL (log10,, (_Mdouble_ __x)); /* Break VALUE into integral and fractional parts. */ __MATHCALL (modf,, (_Mdouble_ __x, _Mdouble_ *__iptr)) __nonnull ((2)); #if __GLIBC_USE (IEC_60559_FUNCS_EXT) /* Compute exponent to base ten. */ __MATHCALL (exp10,, (_Mdouble_ __x)); #endif #if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 /* Return exp(X) - 1. */ __MATHCALL (expm1,, (_Mdouble_ __x)); /* Return log(1 + X). */ __MATHCALL (log1p,, (_Mdouble_ __x)); /* Return the base 2 signed integral exponent of X. */ __MATHCALL (logb,, (_Mdouble_ __x)); #endif #ifdef __USE_ISOC99 /* Compute base-2 exponential of X. */ __MATHCALL (exp2,, (_Mdouble_ __x)); /* Compute base-2 logarithm of X. */ __MATHCALL (log2,, (_Mdouble_ __x)); #endif /* Power functions. */ /* Return X to the Y power. */ __MATHCALL_VEC (pow,, (_Mdouble_ __x, _Mdouble_ __y)); /* Return the square root of X. */ __MATHCALL (sqrt,, (_Mdouble_ __x)); #if defined __USE_XOPEN || defined __USE_ISOC99 /* Return `sqrt(X*X + Y*Y)'. */ __MATHCALL (hypot,, (_Mdouble_ __x, _Mdouble_ __y)); #endif #if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 /* Return the cube root of X. */ __MATHCALL (cbrt,, (_Mdouble_ __x)); #endif /* Nearest integer, absolute value, and remainder functions. */ /* Smallest integral value not less than X. */ __MATHCALLX (ceil,, (_Mdouble_ __x), (__const__)); /* Absolute value of X. */ __MATHCALLX (fabs,, (_Mdouble_ __x), (__const__)); /* Largest integer not greater than X. */ __MATHCALLX (floor,, (_Mdouble_ __x), (__const__)); /* Floating-point modulo remainder of X/Y. */ __MATHCALL (fmod,, (_Mdouble_ __x, _Mdouble_ __y)); #ifdef __USE_MISC # if ((!defined __cplusplus \ || __cplusplus < 201103L /* isinf conflicts with C++11. */ \ || __MATH_DECLARING_DOUBLE == 0)) /* isinff or isinfl don't. */ \ && !__MATH_DECLARING_FLOATN /* Return 0 if VALUE is finite or NaN, +1 if it is +Infinity, -1 if it is -Infinity. */ __MATHDECL_1 (int,isinf,, (_Mdouble_ __value)) __attribute__ ((__const__)); # endif # if !__MATH_DECLARING_FLOATN /* Return nonzero if VALUE is finite and not NaN. */ __MATHDECL_1 (int,finite,, (_Mdouble_ __value)) __attribute__ ((__const__)); /* Return the remainder of X/Y. */ __MATHCALL (drem,, (_Mdouble_ __x, _Mdouble_ __y)); /* Return the fractional part of X after dividing out `ilogb (X)'. */ __MATHCALL (significand,, (_Mdouble_ __x)); # endif #endif /* Use misc. */ #ifdef __USE_ISOC99 /* Return X with its signed changed to Y's. */ __MATHCALLX (copysign,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); #endif #ifdef __USE_ISOC99 /* Return representation of qNaN for double type. */ __MATHCALL (nan,, (const char *__tagb)); #endif #if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K) # if ((!defined __cplusplus \ || __cplusplus < 201103L /* isnan conflicts with C++11. */ \ || __MATH_DECLARING_DOUBLE == 0)) /* isnanf or isnanl don't. */ \ && !__MATH_DECLARING_FLOATN /* Return nonzero if VALUE is not a number. */ __MATHDECL_1 (int,isnan,, (_Mdouble_ __value)) __attribute__ ((__const__)); # endif #endif #if defined __USE_MISC || (defined __USE_XOPEN && __MATH_DECLARING_DOUBLE) /* Bessel functions. */ __MATHCALL (j0,, (_Mdouble_)); __MATHCALL (j1,, (_Mdouble_)); __MATHCALL (jn,, (int, _Mdouble_)); __MATHCALL (y0,, (_Mdouble_)); __MATHCALL (y1,, (_Mdouble_)); __MATHCALL (yn,, (int, _Mdouble_)); #endif #if defined __USE_XOPEN || defined __USE_ISOC99 /* Error and gamma functions. */ __MATHCALL (erf,, (_Mdouble_)); __MATHCALL (erfc,, (_Mdouble_)); __MATHCALL (lgamma,, (_Mdouble_)); #endif #ifdef __USE_ISOC99 /* True gamma function. */ __MATHCALL (tgamma,, (_Mdouble_)); #endif #if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K) # if !__MATH_DECLARING_FLOATN /* Obsolete alias for `lgamma'. */ __MATHCALL (gamma,, (_Mdouble_)); # endif #endif #ifdef __USE_MISC /* Reentrant version of lgamma. This function uses the global variable `signgam'. The reentrant version instead takes a pointer and stores the value through it. */ __MATHCALL (lgamma,_r, (_Mdouble_, int *__signgamp)); #endif #if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99 /* Return the integer nearest X in the direction of the prevailing rounding mode. */ __MATHCALL (rint,, (_Mdouble_ __x)); /* Return X + epsilon if X < Y, X - epsilon if X > Y. */ __MATHCALL (nextafter,, (_Mdouble_ __x, _Mdouble_ __y)); # if defined __USE_ISOC99 && !defined __LDBL_COMPAT && !__MATH_DECLARING_FLOATN __MATHCALL (nexttoward,, (_Mdouble_ __x, long double __y)); # endif # if __GLIBC_USE (IEC_60559_BFP_EXT) || __MATH_DECLARING_FLOATN /* Return X - epsilon. */ __MATHCALL (nextdown,, (_Mdouble_ __x)); /* Return X + epsilon. */ __MATHCALL (nextup,, (_Mdouble_ __x)); # endif /* Return the remainder of integer divison X / Y with infinite precision. */ __MATHCALL (remainder,, (_Mdouble_ __x, _Mdouble_ __y)); # ifdef __USE_ISOC99 /* Return X times (2 to the Nth power). */ __MATHCALL (scalbn,, (_Mdouble_ __x, int __n)); # endif /* Return the binary exponent of X, which must be nonzero. */ __MATHDECL (int,ilogb,, (_Mdouble_ __x)); #endif #if __GLIBC_USE (IEC_60559_BFP_EXT) || __MATH_DECLARING_FLOATN /* Like ilogb, but returning long int. */ __MATHDECL (long int, llogb,, (_Mdouble_ __x)); #endif #ifdef __USE_ISOC99 /* Return X times (2 to the Nth power). */ __MATHCALL (scalbln,, (_Mdouble_ __x, long int __n)); /* Round X to integral value in floating-point format using current rounding direction, but do not raise inexact exception. */ __MATHCALL (nearbyint,, (_Mdouble_ __x)); /* Round X to nearest integral value, rounding halfway cases away from zero. */ __MATHCALLX (round,, (_Mdouble_ __x), (__const__)); /* Round X to the integral value in floating-point format nearest but not larger in magnitude. */ __MATHCALLX (trunc,, (_Mdouble_ __x), (__const__)); /* Compute remainder of X and Y and put in *QUO a value with sign of x/y and magnitude congruent `mod 2^n' to the magnitude of the integral quotient x/y, with n >= 3. */ __MATHCALL (remquo,, (_Mdouble_ __x, _Mdouble_ __y, int *__quo)); /* Conversion functions. */ /* Round X to nearest integral value according to current rounding direction. */ __MATHDECL (long int,lrint,, (_Mdouble_ __x)); __extension__ __MATHDECL (long long int,llrint,, (_Mdouble_ __x)); /* Round X to nearest integral value, rounding halfway cases away from zero. */ __MATHDECL (long int,lround,, (_Mdouble_ __x)); __extension__ __MATHDECL (long long int,llround,, (_Mdouble_ __x)); /* Return positive difference between X and Y. */ __MATHCALL (fdim,, (_Mdouble_ __x, _Mdouble_ __y)); /* Return maximum numeric value from X and Y. */ __MATHCALLX (fmax,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); /* Return minimum numeric value from X and Y. */ __MATHCALLX (fmin,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); /* Multiply-add function computed as a ternary operation. */ __MATHCALL (fma,, (_Mdouble_ __x, _Mdouble_ __y, _Mdouble_ __z)); #endif /* Use ISO C99. */ #if __GLIBC_USE (IEC_60559_BFP_EXT) || __MATH_DECLARING_FLOATN /* Round X to nearest integer value, rounding halfway cases to even. */ __MATHCALLX (roundeven,, (_Mdouble_ __x), (__const__)); /* Round X to nearest signed integer value, not raising inexact, with control of rounding direction and width of result. */ __MATHDECL (__intmax_t, fromfp,, (_Mdouble_ __x, int __round, unsigned int __width)); /* Round X to nearest unsigned integer value, not raising inexact, with control of rounding direction and width of result. */ __MATHDECL (__uintmax_t, ufromfp,, (_Mdouble_ __x, int __round, unsigned int __width)); /* Round X to nearest signed integer value, raising inexact for non-integers, with control of rounding direction and width of result. */ __MATHDECL (__intmax_t, fromfpx,, (_Mdouble_ __x, int __round, unsigned int __width)); /* Round X to nearest unsigned integer value, raising inexact for non-integers, with control of rounding direction and width of result. */ __MATHDECL (__uintmax_t, ufromfpx,, (_Mdouble_ __x, int __round, unsigned int __width)); /* Return value with maximum magnitude. */ __MATHCALLX (fmaxmag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); /* Return value with minimum magnitude. */ __MATHCALLX (fminmag,, (_Mdouble_ __x, _Mdouble_ __y), (__const__)); /* Total order operation. */ __MATHDECL_1 (int, totalorder,, (_Mdouble_ __x, _Mdouble_ __y)) __attribute__ ((__const__)); /* Total order operation on absolute values. */ __MATHDECL_1 (int, totalordermag,, (_Mdouble_ __x, _Mdouble_ __y)) __attribute__ ((__const__)); /* Canonicalize floating-point representation. */ __MATHDECL_1 (int, canonicalize,, (_Mdouble_ *__cx, const _Mdouble_ *__x)); /* Get NaN payload. */ __MATHCALL (getpayload,, (const _Mdouble_ *__x)); /* Set quiet NaN payload. */ __MATHDECL_1 (int, setpayload,, (_Mdouble_ *__x, _Mdouble_ __payload)); /* Set signaling NaN payload. */ __MATHDECL_1 (int, setpayloadsig,, (_Mdouble_ *__x, _Mdouble_ __payload)); #endif #if (defined __USE_MISC || (defined __USE_XOPEN_EXTENDED \ && __MATH_DECLARING_DOUBLE \ && !defined __USE_XOPEN2K8)) \ && !__MATH_DECLARING_FLOATN /* Return X times (2 to the Nth power). */ __MATHCALL (scalb,, (_Mdouble_ __x, _Mdouble_ __n)); #endif