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  • src/libcfa/math

    r43f8fd8 r53a6c2a  
    1010// Created On       : Mon Apr 18 23:37:04 2016
    1111// Last Modified By : Peter A. Buhr
    12 // Last Modified On : Mon Aug  7 07:51:15 2017
    13 // Update Count     : 108
     12// Last Modified On : Fri Jul  7 09:34:15 2017
     13// Update Count     : 61
    1414//
    1515
    1616#pragma once
    1717
    18 #include <math.h>
    19 #include <complex.h>
    20 
    21 //---------------------- General ----------------------
    22 
    23 static inline float ?%?( float x, float y ) { return fmodf( x, y ); }
    24 static inline float fmod( float x, float y ) { return fmodf( x, y ); }
    25 static inline double ?%?( double x, double y ) { return fmod( x, y ); }
     18extern "C" {
     19#include <math.h>                                                                               // fpclassify, isfinite, isnormal, isnan, isinf
     20} // extern "C"
     21
     22float ?%?( float, float );
     23float fmod( float, float );
     24double ?%?( double, double );
    2625// extern "C" { double fmod( double, double ); }
    27 static inline long double ?%?( long double x, long double y ) { return fmodl( x, y ); }
    28 static inline long double fmod( long double x, long double y ) { return fmodl( x, y ); }
    29 
    30 static inline float remainder( float x, float y ) { return remainderf( x, y ); }
     26long double ?%?( long double, long double );
     27long double fmod( long double, long double );
     28
     29float remainder( float, float );
    3130// extern "C" { double remainder( double, double ); }
    32 static inline long double remainder( long double x, long double y ) { return remainderl( x, y ); }
    33 
    34 static inline float remquo( float x, float y, int * quo ) { return remquof( x, y, quo ); }
    35 // extern "C" { double remquo( double x, double y, int * quo ); }
    36 static inline long double remquo( long double x, long double y, int * quo ) { return remquol( x, y, quo ); }
    37 static inline [ int, float ] remquo( float x, float y ) { int quo; x = remquof( x, y, &quo ); return [ quo, x ]; }
    38 static inline [ int, double ] remquo( double x, double y ) { int quo; x = remquo( x, y, &quo ); return [ quo, x ]; }
    39 static inline [ int, long double ] remquo( long double x, long double y ) { int quo; x = remquol( x, y, &quo ); return [ quo, x ]; }
    40 
    41 static inline [ float, float ] div( float x, float y ) { y = modff( x / y, &x ); return [ x, y ]; }
    42 static inline [ double, double ] div( double x, double y ) { y = modf( x / y, &x ); return [ x, y ]; }
    43 static inline [ long double, long double ] div( long double x, long double y ) { y = modfl( x / y, &x ); return [ x, y ]; }
    44 
    45 static inline float fma( float x, float y, float z ) { return fmaf( x, y, z ); }
     31long double remainder( long double, long double );
     32
     33[ int, float ] remquo( float, float );
     34float remquo( float, float, int * );
     35[ int, double ] remquo( double, double );
     36// extern "C" { double remquo( double, double, int * ); }
     37[ int, long double ] remquo( long double, long double );
     38long double remquo( long double, long double, int * );
     39
     40[ int, float ] div( float, float );                                             // alternative name for remquo
     41float div( float, float, int * );
     42[ int, double ] div( double, double );
     43// extern "C" { double div( double, double, int * ); }
     44[ int, long double ] div( long double, long double );
     45long double div( long double, long double, int * );
     46
     47float fma( float, float, float );
    4648// extern "C" { double fma( double, double, double ); }
    47 static inline long double fma( long double x, long double y, long double z ) { return fmal( x, y, z ); }
    48 
    49 static inline float fdim( float x, float y ) { return fdimf( x, y ); }
     49long double fma( long double, long double, long double );
     50
     51float fdim( float, float );
    5052// extern "C" { double fdim( double, double ); }
    51 static inline long double fdim( long double x, long double y ) { return fdiml( x, y ); }
    52 
    53 static inline float nan( const char * tag ) { return nanf( tag ); }
     53long double fdim( long double, long double );
     54
     55float nan( const char * );
    5456// extern "C" { double nan( const char * ); }
    55 static inline long double nan( const char * tag ) { return nanl( tag ); }
     57long double nan( const char * );
    5658
    5759//---------------------- Exponential ----------------------
    5860
    59 static inline float exp( float x ) { return expf( x ); }
     61float exp( float );
    6062// extern "C" { double exp( double ); }
    61 static inline long double exp( long double x ) { return expl( x ); }
    62 static inline float _Complex exp( float _Complex x ) { return cexpf( x ); }
    63 static inline double _Complex exp( double _Complex x ) { return cexp( x ); }
    64 static inline long double _Complex exp( long double _Complex x ) { return cexpl( x ); }
    65 
    66 static inline float exp2( float x ) { return exp2f( x ); }
     63long double exp( long double );
     64float _Complex exp( float _Complex );
     65double _Complex exp( double _Complex );
     66long double _Complex exp( long double _Complex );
     67
     68float exp2( float );
    6769// extern "C" { double exp2( double ); }
    68 static inline long double exp2( long double x ) { return exp2l( x ); }
    69 //static inline float _Complex exp2( float _Complex x ) { return cexp2f( x ); }
    70 //static inline double _Complex exp2( double _Complex x ) { return cexp2( x ); }
    71 //static inline long double _Complex exp2( long double _Complex x ) { return cexp2l( x ); }
    72 
    73 static inline float expm1( float x ) { return expm1f( x ); }
     70long double exp2( long double );
     71// float _Complex exp2( float _Complex );
     72// double _Complex exp2( double _Complex );
     73// long double _Complex exp2( long double _Complex );
     74
     75float expm1( float );
    7476// extern "C" { double expm1( double ); }
    75 static inline long double expm1( long double x ) { return expm1l( x ); }
    76 
    77 static inline float pow( float x, float y ) { return powf( x, y ); }
     77long double expm1( long double );
     78
     79float log( float );
     80// extern "C" { double log( double ); }
     81long double log( long double );
     82float _Complex log( float _Complex );
     83double _Complex log( double _Complex );
     84long double _Complex log( long double _Complex );
     85
     86float log2( float );
     87// extern "C" { double log2( double ); }
     88long double log2( long double );
     89// float _Complex log2( float _Complex );
     90// double _Complex log2( double _Complex );
     91// long double _Complex log2( long double _Complex );
     92
     93float log10( float );
     94// extern "C" { double log10( double ); }
     95long double log10( long double );
     96// float _Complex log10( float _Complex );
     97// double _Complex log10( double _Complex );
     98// long double _Complex log10( long double _Complex );
     99
     100float log1p( float );
     101// extern "C" { double log1p( double ); }
     102long double log1p( long double );
     103
     104int ilogb( float );
     105// extern "C" { int ilogb( double ); }
     106int ilogb( long double );
     107
     108float logb( float );
     109// extern "C" { double logb( double ); }
     110long double logb( long double );
     111
     112//---------------------- Power ----------------------
     113
     114float sqrt( float );
     115// extern "C" { double sqrt( double ); }
     116long double sqrt( long double );
     117float _Complex sqrt( float _Complex );
     118double _Complex sqrt( double _Complex );
     119long double _Complex sqrt( long double _Complex );
     120
     121float cbrt( float );
     122// extern "C" { double cbrt( double ); }
     123long double cbrt( long double );
     124
     125float hypot( float, float );
     126// extern "C" { double hypot( double, double ); }
     127long double hypot( long double, long double );
     128
     129float pow( float, float );
    78130// extern "C" { double pow( double, double ); }
    79 static inline long double pow( long double x, long double y ) { return powl( x, y ); }
    80 static inline float _Complex pow( float _Complex x, float _Complex y ) { return cpowf( x, y ); }
    81 static inline double _Complex pow( double _Complex x, double _Complex y ) { return cpow( x, y ); }
    82 static inline long double _Complex pow( long double _Complex x, long double _Complex y ) { return cpowl( x, y ); }
    83 
    84 //---------------------- Logarithm ----------------------
    85 
    86 static inline float log( float x ) { return logf( x ); }
    87 // extern "C" { double log( double ); }
    88 static inline long double log( long double x ) { return logl( x ); }
    89 static inline float _Complex log( float _Complex x ) { return clogf( x ); }
    90 static inline double _Complex log( double _Complex x ) { return clog( x ); }
    91 static inline long double _Complex log( long double _Complex x ) { return clogl( x ); }
    92 
    93 static inline float log2( float x ) { return log2f( x ); }
    94 // extern "C" { double log2( double ); }
    95 static inline long double log2( long double x ) { return log2l( x ); }
    96 // static inline float _Complex log2( float _Complex x ) { return clog2f( x ); }
    97 // static inline double _Complex log2( double _Complex x ) { return clog2( x ); }
    98 // static inline long double _Complex log2( long double _Complex x ) { return clog2l( x ); }
    99 
    100 static inline float log10( float x ) { return log10f( x ); }
    101 // extern "C" { double log10( double ); }
    102 static inline long double log10( long double x ) { return log10l( x ); }
    103 // static inline float _Complex log10( float _Complex x ) { return clog10f( x ); }
    104 // static inline double _Complex log10( double _Complex x ) { return clog10( x ); }
    105 // static inline long double _Complex log10( long double _Complex x ) { return clog10l( x ); }
    106 
    107 static inline float log1p( float x ) { return log1pf( x ); }
    108 // extern "C" { double log1p( double ); }
    109 static inline long double log1p( long double x ) { return log1pl( x ); }
    110 
    111 static inline int ilogb( float x ) { return ilogbf( x ); }
    112 // extern "C" { int ilogb( double ); }
    113 static inline int ilogb( long double x ) { return ilogbl( x ); }
    114 
    115 static inline float logb( float x ) { return logbf( x ); }
    116 // extern "C" { double logb( double ); }
    117 static inline long double logb( long double x ) { return logbl( x ); }
    118 
    119 static inline float sqrt( float x ) { return sqrtf( x ); }
    120 // extern "C" { double sqrt( double ); }
    121 static inline long double sqrt( long double x ) { return sqrtl( x ); }
    122 static inline float _Complex sqrt( float _Complex x ) { return csqrtf( x ); }
    123 static inline double _Complex sqrt( double _Complex x ) { return csqrt( x ); }
    124 static inline long double _Complex sqrt( long double _Complex x ) { return csqrtl( x ); }
    125 
    126 static inline float cbrt( float x ) { return cbrtf( x ); }
    127 // extern "C" { double cbrt( double ); }
    128 static inline long double cbrt( long double x ) { return cbrtl( x ); }
    129 
    130 static inline float hypot( float x, float y ) { return hypotf( x, y ); }
    131 // extern "C" { double hypot( double, double ); }
    132 static inline long double hypot( long double x, long double y ) { return hypotl( x, y ); }
     131long double pow( long double, long double );
     132float _Complex pow( float _Complex, float _Complex );
     133double _Complex pow( double _Complex, double _Complex );
     134long double _Complex pow( long double _Complex, long double _Complex );
    133135
    134136//---------------------- Trigonometric ----------------------
    135137
    136 static inline float sin( float x ) { return sinf( x ); }
     138float sin( float );
    137139// extern "C" { double sin( double ); }
    138 static inline long double sin( long double x ) { return sinl( x ); }
    139 static inline float _Complex sin( float _Complex x ) { return csinf( x ); }
    140 static inline double _Complex sin( double _Complex x ) { return csin( x ); }
    141 static inline long double _Complex sin( long double _Complex x ) { return csinl( x ); }
    142 
    143 static inline float cos( float x ) { return cosf( x ); }
     140long double sin( long double );
     141float _Complex sin( float _Complex );
     142double _Complex sin( double _Complex );
     143long double _Complex sin( long double _Complex );
     144
     145float cos( float );
    144146// extern "C" { double cos( double ); }
    145 static inline long double cos( long double x ) { return cosl( x ); }
    146 static inline float _Complex cos( float _Complex x ) { return ccosf( x ); }
    147 static inline double _Complex cos( double _Complex x ) { return ccos( x ); }
    148 static inline long double _Complex cos( long double _Complex x ) { return ccosl( x ); }
    149 
    150 static inline float tan( float x ) { return tanf( x ); }
     147long double cos( long double );
     148float _Complex cos( float _Complex );
     149double _Complex cos( double _Complex );
     150long double _Complex cos( long double _Complex );
     151
     152float tan( float );
    151153// extern "C" { double tan( double ); }
    152 static inline long double tan( long double x ) { return tanl( x ); }
    153 static inline float _Complex tan( float _Complex x ) { return ctanf( x ); }
    154 static inline double _Complex tan( double _Complex x ) { return ctan( x ); }
    155 static inline long double _Complex tan( long double _Complex x ) { return ctanl( x ); }
    156 
    157 static inline float asin( float x ) { return asinf( x ); }
     154long double tan( long double );
     155float _Complex tan( float _Complex );
     156double _Complex tan( double _Complex );
     157long double _Complex tan( long double _Complex );
     158
     159float asin( float );
    158160// extern "C" { double asin( double ); }
    159 static inline long double asin( long double x ) { return asinl( x ); }
    160 static inline float _Complex asin( float _Complex x ) { return casinf( x ); }
    161 static inline double _Complex asin( double _Complex x ) { return casin( x ); }
    162 static inline long double _Complex asin( long double _Complex x ) { return casinl( x ); }
    163 
    164 static inline float acos( float x ) { return acosf( x ); }
     161long double asin( long double );
     162float _Complex asin( float _Complex );
     163double _Complex asin( double _Complex );
     164long double _Complex asin( long double _Complex );
     165
     166float acos( float );
    165167// extern "C" { double acos( double ); }
    166 static inline long double acos( long double x ) { return acosl( x ); }
    167 static inline float _Complex acos( float _Complex x ) { return cacosf( x ); }
    168 static inline double _Complex acos( double _Complex x ) { return cacos( x ); }
    169 static inline long double _Complex acos( long double _Complex x ) { return cacosl( x ); }
    170 
    171 static inline float atan( float x ) { return atanf( x ); }
     168long double acos( long double );
     169float _Complex acos( float _Complex );
     170double _Complex acos( double _Complex );
     171long double _Complex acos( long double _Complex );
     172
     173float atan( float );
    172174// extern "C" { double atan( double ); }
    173 static inline long double atan( long double x ) { return atanl( x ); }
    174 static inline float _Complex atan( float _Complex x ) { return catanf( x ); }
    175 static inline double _Complex atan( double _Complex x ) { return catan( x ); }
    176 static inline long double _Complex atan( long double _Complex x ) { return catanl( x ); }
    177 
    178 static inline float atan2( float x, float y ) { return atan2f( x, y ); }
     175long double atan( long double );
     176float _Complex atan( float _Complex );
     177double _Complex atan( double _Complex );
     178long double _Complex atan( long double _Complex );
     179
     180float atan2( float, float );
    179181// extern "C" { double atan2( double, double ); }
    180 static inline long double atan2( long double x, long double y ) { return atan2l( x, y ); }
    181 
    182 // alternative name for atan2
    183 static inline float atan( float x, float y ) { return atan2f( x, y ); }
    184 static inline double atan( double x, double y ) { return atan2( x, y ); }
    185 static inline long double atan( long double x, long double y ) { return atan2l( x, y ); }
     182long double atan2( long double, long double );
     183
     184float atan( float, float );                                                             // alternative name for atan2
     185double atan( double, double );
     186long double atan( long double, long double );
    186187
    187188//---------------------- Hyperbolic ----------------------
    188189
    189 static inline float sinh( float x ) { return sinhf( x ); }
     190float sinh( float );
    190191// extern "C" { double sinh( double ); }
    191 static inline long double sinh( long double x ) { return sinhl( x ); }
    192 static inline float _Complex sinh( float _Complex x ) { return csinhf( x ); }
    193 static inline double _Complex sinh( double _Complex x ) { return csinh( x ); }
    194 static inline long double _Complex sinh( long double _Complex x ) { return csinhl( x ); }
    195 
    196 static inline float cosh( float x ) { return coshf( x ); }
     192long double sinh( long double );
     193float _Complex sinh( float _Complex );
     194double _Complex sinh( double _Complex );
     195long double _Complex sinh( long double _Complex );
     196
     197float cosh( float );
    197198// extern "C" { double cosh( double ); }
    198 static inline long double cosh( long double x ) { return coshl( x ); }
    199 static inline float _Complex cosh( float _Complex x ) { return ccoshf( x ); }
    200 static inline double _Complex cosh( double _Complex x ) { return ccosh( x ); }
    201 static inline long double _Complex cosh( long double _Complex x ) { return ccoshl( x ); }
    202 
    203 static inline float tanh( float x ) { return tanhf( x ); }
     199long double cosh( long double );
     200float _Complex cosh( float _Complex );
     201double _Complex cosh( double _Complex );
     202long double _Complex cosh( long double _Complex );
     203
     204float tanh( float );
    204205// extern "C" { double tanh( double ); }
    205 static inline long double tanh( long double x ) { return tanhl( x ); }
    206 static inline float _Complex tanh( float _Complex x ) { return ctanhf( x ); }
    207 static inline double _Complex tanh( double _Complex x ) { return ctanh( x ); }
    208 static inline long double _Complex tanh( long double _Complex x ) { return ctanhl( x ); }
    209 
    210 static inline float asinh( float x ) { return asinhf( x ); }
     206long double tanh( long double );
     207float _Complex tanh( float _Complex );
     208double _Complex tanh( double _Complex );
     209long double _Complex tanh( long double _Complex );
     210
     211float asinh( float );
    211212// extern "C" { double asinh( double ); }
    212 static inline long double asinh( long double x ) { return asinhl( x ); }
    213 static inline float _Complex asinh( float _Complex x ) { return casinhf( x ); }
    214 static inline double _Complex asinh( double _Complex x ) { return casinh( x ); }
    215 static inline long double _Complex asinh( long double _Complex x ) { return casinhl( x ); }
    216 
    217 static inline float acosh( float x ) { return acoshf( x ); }
     213long double asinh( long double );
     214float _Complex asinh( float _Complex );
     215double _Complex asinh( double _Complex );
     216long double _Complex asinh( long double _Complex );
     217
     218float acosh( float );
    218219// extern "C" { double acosh( double ); }
    219 static inline long double acosh( long double x ) { return acoshl( x ); }
    220 static inline float _Complex acosh( float _Complex x ) { return cacoshf( x ); }
    221 static inline double _Complex acosh( double _Complex x ) { return cacosh( x ); }
    222 static inline long double _Complex acosh( long double _Complex x ) { return cacoshl( x ); }
    223 
    224 static inline float atanh( float x ) { return atanhf( x ); }
     220long double acosh( long double );
     221float _Complex acosh( float _Complex );
     222double _Complex acosh( double _Complex );
     223long double _Complex acosh( long double _Complex );
     224
     225float atanh( float );
    225226// extern "C" { double atanh( double ); }
    226 static inline long double atanh( long double x ) { return atanhl( x ); }
    227 static inline float _Complex atanh( float _Complex x ) { return catanhf( x ); }
    228 static inline double _Complex atanh( double _Complex x ) { return catanh( x ); }
    229 static inline long double _Complex atanh( long double _Complex x ) { return catanhl( x ); }
     227long double atanh( long double );
     228float _Complex atanh( float _Complex );
     229double _Complex atanh( double _Complex );
     230long double _Complex atanh( long double _Complex );
    230231
    231232//---------------------- Error / Gamma ----------------------
    232233
    233 static inline float erf( float x ) { return erff( x ); }
     234float erf( float );
    234235// extern "C" { double erf( double ); }
    235 static inline long double erf( long double x ) { return erfl( x ); }
     236long double erf( long double );
    236237// float _Complex erf( float _Complex );
    237238// double _Complex erf( double _Complex );
    238239// long double _Complex erf( long double _Complex );
    239240
    240 static inline float erfc( float x ) { return erfcf( x ); }
     241float erfc( float );
    241242// extern "C" { double erfc( double ); }
    242 static inline long double erfc( long double x ) { return erfcl( x ); }
     243long double erfc( long double );
    243244// float _Complex erfc( float _Complex );
    244245// double _Complex erfc( double _Complex );
    245246// long double _Complex erfc( long double _Complex );
    246247
    247 static inline float lgamma( float x ) { return lgammaf( x ); }
     248float lgamma( float );
    248249// extern "C" { double lgamma( double ); }
    249 static inline long double lgamma( long double x ) { return lgammal( x ); }
    250 static inline float lgamma( float x, int * sign ) { return lgammaf_r( x, sign ); }
    251 static inline double lgamma( double x, int * sign ) { return lgamma_r( x, sign ); }
    252 static inline long double lgamma( long double x, int * sign ) { return lgammal_r( x, sign ); }
    253 
    254 static inline float tgamma( float x ) { return tgammaf( x ); }
     250long double lgamma( long double );
     251float lgamma( float, int * );
     252double lgamma( double, int * );
     253long double lgamma( long double, int * );
     254
     255float tgamma( float );
    255256// extern "C" { double tgamma( double ); }
    256 static inline long double tgamma( long double x ) { return tgammal( x ); }
     257long double tgamma( long double );
    257258
    258259//---------------------- Nearest Integer ----------------------
    259260
    260 static inline float floor( float x ) { return floorf( x ); }
     261float floor( float );
    261262// extern "C" { double floor( double ); }
    262 static inline long double floor( long double x ) { return floorl( x ); }
    263 
    264 static inline float ceil( float x ) { return ceilf( x ); }
     263long double floor( long double );
     264
     265float ceil( float );
    265266// extern "C" { double ceil( double ); }
    266 static inline long double ceil( long double x ) { return ceill( x ); }
    267 
    268 static inline float trunc( float x ) { return truncf( x ); }
     267long double ceil( long double );
     268
     269float trunc( float );
    269270// extern "C" { double trunc( double ); }
    270 static inline long double trunc( long double x ) { return truncl( x ); }
    271 
    272 static inline float rint( float x ) { return rintf( x ); }
    273 // extern "C" { double rint( double x ); }
    274 static inline long double rint( long double x ) { return rintl( x ); }
    275 static inline long int rint( float x ) { return lrintf( x ); }
    276 static inline long int rint( double x ) { return lrint( x ); }
    277 static inline long int rint( long double x ) { return lrintl( x ); }
    278 static inline long long int rint( float x ) { return llrintf( x ); }
    279 static inline long long int rint( double x ) { return llrint( x ); }
    280 static inline long long int rint( long double x ) { return llrintl( x ); }
    281 
    282 static inline long int lrint( float x ) { return lrintf( x ); }
     271long double trunc( long double );
     272
     273float rint( float );
     274long double rint( long double );
     275long int rint( float );
     276long int rint( double );
     277long int rint( long double );
     278long long int rint( float );
     279long long int rint( double );
     280long long int rint( long double );
     281
     282long int lrint( float );
    283283// extern "C" { long int lrint( double ); }
    284 static inline long int lrint( long double x ) { return lrintl( x ); }
    285 static inline long long int llrint( float x ) { return llrintf( x ); }
     284long int lrint( long double );
     285long long int llrint( float );
    286286// extern "C" { long long int llrint( double ); }
    287 static inline long long int llrint( long double x ) { return llrintl( x ); }
    288 
    289 static inline float nearbyint( float x ) { return nearbyintf( x ); }
     287long long int llrint( long double );
     288
     289float nearbyint( float );
    290290// extern "C" { double nearbyint( double ); }
    291 static inline long double nearbyint( long double x ) { return nearbyintl( x ); }
    292 
    293 static inline float round( float x ) { return roundf( x ); }
    294 // extern "C" { double round( double x ); }
    295 static inline long double round( long double x ) { return roundl( x ); }
    296 static inline long int round( float x ) { return lroundf( x ); }
    297 static inline long int round( double x ) { return lround( x ); }
    298 static inline long int round( long double x ) { return lroundl( x ); }
    299 static inline long long int round( float x ) { return llroundf( x ); }
    300 static inline long long int round( double x ) { return llround( x ); }
    301 static inline long long int round( long double x ) { return llroundl( x ); }
    302 
    303 static inline long int lround( float x ) { return lroundf( x ); }
     291long double nearbyint( long double );
     292
     293float round( float );
     294long double round( long double );
     295long int round( float );
     296long int round( double );
     297long int round( long double );
     298long long int round( float );
     299long long int round( double );
     300long long int round( long double );
     301
     302long int lround( float );
    304303// extern "C" { long int lround( double ); }
    305 static inline long int lround( long double x ) { return lroundl( x ); }
    306 static inline long long int llround( float x ) { return llroundf( x ); }
     304long int lround( long double );
     305long long int llround( float );
    307306// extern "C" { long long int llround( double ); }
    308 static inline long long int llround( long double x ) { return llroundl( x ); }
     307long long int llround( long double );
    309308
    310309//---------------------- Manipulation ----------------------
    311310
    312 static inline float copysign( float x, float y ) { return copysignf( x, y ); }
     311float copysign( float, float );
    313312// extern "C" { double copysign( double, double ); }
    314 static inline long double copysign( long double x, long double y ) { return copysignl( x, y ); }
    315 
    316 static inline float frexp( float x, int * ip ) { return frexpf( x, ip ); }
     313long double copysign( long double, long double );
     314
     315float frexp( float, int * );
    317316// extern "C" { double frexp( double, int * ); }
    318 static inline long double frexp( long double x, int * ip ) { return frexpl( x, ip ); }
    319 
    320 static inline float ldexp( float x, int exp2 ) { return ldexpf( x, exp2 ); }
     317long double frexp( long double, int * );
     318
     319float ldexp( float, int );
    321320// extern "C" { double ldexp( double, int ); }
    322 static inline long double ldexp( long double x, int exp2 ) { return ldexpl( x, exp2 ); }
    323 
    324 static inline [ float, float ] modf( float x ) { float i; x = modff( x, &i ); return [ i, x ]; }
    325 static inline float modf( float x, float * i ) { return modff( x, i ); }
    326 static inline [ double, double ] modf( double x ) { double i; x = modf( x, &i ); return [ i, x ]; }
     321long double ldexp( long double, int );
     322
     323[ float, float ] modf( float );
     324float modf( float, float * );
     325[ double, double ] modf( double );
    327326// extern "C" { double modf( double, double * ); }
    328 static inline [ long double, long double ] modf( long double x ) { long double i; x = modfl( x, &i ); return [ i, x ]; }
    329 static inline long double modf( long double x, long double * i ) { return modfl( x, i ); }
    330 
    331 static inline float nextafter( float x, float y ) { return nextafterf( x, y ); }
     327[ long double, long double ] modf( long double );
     328long double modf( long double, long double * );
     329
     330float nextafter( float, float );
    332331// extern "C" { double nextafter( double, double ); }
    333 static inline long double nextafter( long double x, long double y ) { return nextafterl( x, y ); }
    334 
    335 static inline float nexttoward( float x, long double y ) { return nexttowardf( x, y ); }
     332long double nextafter( long double, long double );
     333
     334float nexttoward( float, long double );
    336335// extern "C" { double nexttoward( double, long double ); }
    337 static inline long double nexttoward( long double x, long double y ) { return nexttowardl( x, y ); }
    338 
    339 static inline float scalbn( float x, int exp ) { return scalbnf( x, exp ); }
     336long double nexttoward( long double, long double );
     337
     338float scalbn( float, int );
    340339// extern "C" { double scalbn( double, int ); }
    341 static inline long double scalbn( long double x, int exp ) { return scalbnl( x, exp ); }
    342 static inline float scalbn( float x, long int exp ) { return scalblnf( x, exp ); }
    343 static inline double scalbn( double x, long int exp ) { return scalbln( x, exp ); }
    344 static inline long double scalbn( long double x, long int exp ) { return scalblnl( x, exp ); }
    345 
    346 static inline float scalbln( float x, long int exp ) { return scalblnf( x, exp ); }
     340long double scalbn( long double, int );
     341
     342float scalbln( float, long int );
    347343// extern "C" { double scalbln( double, long int ); }
    348 static inline long double scalbln( long double x, long int exp ) { return scalblnl( x, exp ); }
     344long double scalbln( long double, long int );
    349345
    350346// Local Variables: //
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