#ifndef _TGMATH_H
#define _TGMATH_H
/*
the return types are only correct with gcc (__GNUC__)
otherwise they are long double or long double complex
the long double version of a function is never chosen when
sizeof(double) == sizeof(long double)
(but the return type is set correctly with gcc)
*/
#include <math.h>
#include <complex.h>
#define __IS_FP(x) !!((1?1:(x))/2)
#define __IS_CX(x) (__IS_FP(x) && sizeof(x) == sizeof((x)+I))
#define __IS_REAL(x) (__IS_FP(x) && 2*sizeof(x) == sizeof((x)+I))
#define __FLT(x) (__IS_REAL(x) && sizeof(x) == sizeof(float))
#define __LDBL(x) (__IS_REAL(x) && sizeof(x) == sizeof(long double) && sizeof(long double) != sizeof(double))
#define __FLTCX(x) (__IS_CX(x) && sizeof(x) == sizeof(float complex))
#define __DBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(double complex))
#define __LDBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(long double complex) && sizeof(long double) != sizeof(double))
/* return type */
#ifdef __GNUC__
/*
the conditional expression (that selects the right function
for evaluation) should be casted to the return type of the
selected function (otherwise the result type is determined
by the conversion rules applied to all the function return
types so it is long double or long double _Complex)
this cannot be done in c99 (c11 has _Generic that would help
but is not yet widely supported), so the typeof extension of
gcc is used and that ?: has special semantics when one of
the operands is a null pointer constant
unfortunately the standard is overly strict about the
definition of null pointer constants (current gcc does not
follow the standard but clang does) so we have to use a hack
to be able to tell integer and floating-point types apart:
both gcc and clang evaluate sizeof(void) to 1 even though it
is a constraint violation, we only use this on clang for now
*/
/* predicates that evaluate to integer constant expressions */
#ifdef __clang__
/* TODO: __c_IS_FP(1.0) is a constraint violation */
#define __c_IS_FP(x) (!(sizeof*(__typeof__(0?(int*)0:(void*)__IS_FP(x)))0-1))
#else
#define __c_IS_FP(x) __IS_FP(x)
#endif
#define __c_IS_CX(x) (__c_IS_FP(x) && sizeof(x) == sizeof((x)+I))
#define __c_FLTCX(x) (__c_IS_CX(x) && sizeof(x) == sizeof(float complex))
#define __c_DBLCX(x) (__c_IS_CX(x) && sizeof(x) == sizeof(double complex))
#define __c_LDBLCX(x) (__c_IS_CX(x) && sizeof(x) == sizeof(long double complex) && sizeof(long double) != sizeof(double))
/* if c then t else void */
#define __type1(c,t) __typeof__(*(0?(t*)0:(void*)!(c)))
/* if c then t1 else t2 */
#define __type2(c,t1,t2) __typeof__(*(0?(__type1(c,t1)*)0:(__type1(!(c),t2)*)0))
/* cast to double when x is integral, otherwise use typeof(x) */
#define __RETCAST(x) ( \
__type2(__c_IS_FP(x), __typeof__(x), double))
/* 2 args case, should work for complex types (cpow) */
#define __RETCAST_2(x, y) ( \
__type2(__c_IS_FP(x) && __c_IS_FP(y), \
__typeof__((x)+(y)), \
__typeof__((x)+(y)+1.0)))
/* 3 args case (fma only) */
#define __RETCAST_3(x, y, z) ( \
__type2(__c_IS_FP(x) && __c_IS_FP(y) && __c_IS_FP(z), \
__typeof__((x)+(y)+(z)), \
__typeof__((x)+(y)+(z)+1.0)))
/* drop complex from the type of x */
/* TODO: wrong when sizeof(long double)==sizeof(double) */
#define __RETCAST_REAL(x) ( \
__type2(sizeof(__RETCAST(x)0+I)==sizeof(float complex), float, \
__type2(sizeof(__RETCAST(x)0+I)==sizeof(double complex), double, \
long double)))
/* add complex to the type of x */
#define __RETCAST_CX(x) (__typeof__(__RETCAST(x)0+I))
#else
#define __RETCAST(x)
#define __RETCAST_2(x, y)
#define __RETCAST_3(x, y, z)
#define __RETCAST_REAL(x)
#define __RETCAST_CX(x)
#endif
/* function selection */
#define __tg_real_nocast(fun, x) ( \
__FLT(x) ? fun ## f (x) : \
__LDBL(x) ? fun ## l (x) : \
fun(x) )
#define __tg_real(fun, x) (__RETCAST(x)__tg_real_nocast(fun, x))
#define __tg_real_2_1(fun, x, y) (__RETCAST(x)( \
__FLT(x) ? fun ## f (x, y) : \
__LDBL(x) ? fun ## l (x, y) : \
fun(x, y) ))
#define __tg_real_2(fun, x, y) (__RETCAST_2(x, y)( \
__FLT(x) && __FLT(y) ? fun ## f (x, y) : \
__LDBL((x)+(y)) ? fun ## l (x, y) : \
fun(x, y) ))
#define __tg_complex(fun, x) (__RETCAST_CX(x)( \
__FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \
__LDBLCX((x)+I) ? fun ## l (x) : \
fun(x) ))
#define __tg_complex_retreal(fun, x) (__RETCAST_REAL(x)( \
__FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \
__LDBLCX((x)+I) ? fun ## l (x) : \
fun(x) ))
#define __tg_real_complex(fun, x) (__RETCAST(x)( \
__FLTCX(x) ? c ## fun ## f (x) : \
__DBLCX(x) ? c ## fun (x) : \
__LDBLCX(x) ? c ## fun ## l (x) : \
__FLT(x) ? fun ## f (x) : \
__LDBL(x) ? fun ## l (x) : \
fun(x) ))
/* special cases */
#define __tg_real_remquo(x, y, z) (__RETCAST_2(x, y)( \
__FLT(x) && __FLT(y) ? remquof(x, y, z) : \
__LDBL((x)+(y)) ? remquol(x, y, z) : \
remquo(x, y, z) ))
#define __tg_real_fma(x, y, z) (__RETCAST_3(x, y, z)( \
__FLT(x) && __FLT(y) && __FLT(z) ? fmaf(x, y, z) : \
__LDBL((x)+(y)+(z)) ? fmal(x, y, z) : \
fma(x, y, z) ))
#define __tg_real_complex_pow(x, y) (__RETCAST_2(x, y)( \
__FLTCX((x)+(y)) && __IS_FP(x) && __IS_FP(y) ? cpowf(x, y) : \
__FLTCX((x)+(y)) ? cpow(x, y) : \
__DBLCX((x)+(y)) ? cpow(x, y) : \
__LDBLCX((x)+(y)) ? cpowl(x, y) : \
__FLT(x) && __FLT(y) ? powf(x, y) : \
__LDBL((x)+(y)) ? powl(x, y) : \
pow(x, y) ))
#define __tg_real_complex_fabs(x) (__RETCAST_REAL(x)( \
__FLTCX(x) ? cabsf(x) : \
__DBLCX(x) ? cabs(x) : \
__LDBLCX(x) ? cabsl(x) : \
__FLT(x) ? fabsf(x) : \
__LDBL(x) ? fabsl(x) : \
fabs(x) ))
/* suppress any macros in math.h or complex.h */
#undef acos
#undef acosh
#undef asin
#undef asinh
#undef atan
#undef atan2
#undef atanh
#undef carg
#undef cbrt
#undef ceil
#undef cimag
#undef conj
#undef copysign
#undef cos
#undef cosh
#undef cproj
#undef creal
#undef erf
#undef erfc
#undef exp
#undef exp2
#undef expm1
#undef fabs
#undef fdim
#undef floor
#undef fma
#undef fmax
#undef fmin
#undef fmod
#undef frexp
#undef hypot
#undef ilogb
#undef ldexp
#undef lgamma
#undef llrint
#undef llround
#undef log
#undef log10
#undef log1p
#undef log2
#undef logb
#undef lrint
#undef lround
#undef nearbyint
#undef nextafter
#undef nexttoward
#undef pow
#undef remainder
#undef remquo
#undef rint
#undef round
#undef scalbln
#undef scalbn
#undef sin
#undef sinh
#undef sqrt
#undef tan
#undef tanh
#undef tgamma
#undef trunc
/* tg functions */
#define acos(x) __tg_real_complex(acos, (x))
#define acosh(x) __tg_real_complex(acosh, (x))
#define asin(x) __tg_real_complex(asin, (x))
#define asinh(x) __tg_real_complex(asinh, (x))
#define atan(x) __tg_real_complex(atan, (x))
#define atan2(x,y) __tg_real_2(atan2, (x), (y))
#define atanh(x) __tg_real_complex(atanh, (x))
#define carg(x) __tg_complex_retreal(carg, (x))
#define cbrt(x) __tg_real(cbrt, (x))
#define ceil(x) __tg_real(ceil, (x))
#define cimag(x) __tg_complex_retreal(cimag, (x))
#define conj(x) __tg_complex(conj, (x))
#define copysign(x,y) __tg_real_2(copysign, (x), (y))
#define cos(x) __tg_real_complex(cos, (x))
#define cosh(x) __tg_real_complex(cosh, (x))
#define cproj(x) __tg_complex(cproj, (x))
#define creal(x) __tg_complex_retreal(creal, (x))
#define erf(x) __tg_real(erf, (x))
#define erfc(x) __tg_real(erfc, (x))
#define exp(x) __tg_real_complex(exp, (x))
#define exp2(x) __tg_real(exp2, (x))
#define expm1(x) __tg_real(expm1, (x))
#define fabs(x) __tg_real_complex_fabs(x)
#define fdim(x,y) __tg_real_2(fdim, (x), (y))
#define floor(x) __tg_real(floor, (x))
#define fma(x,y,z) __tg_real_fma((x), (y), (z))
#define fmax(x,y) __tg_real_2(fmax, (x), (y))
#define fmin(x,y) __tg_real_2(fmin, (x), (y))
#define fmod(x,y) __tg_real_2(fmod, (x), (y))
#define frexp(x,y) __tg_real_2_1(frexp, (x), (y))
#define hypot(x,y) __tg_real_2(hypot, (x), (y))
#define ilogb(x) __tg_real_nocast(ilogb, (x))
#define ldexp(x,y) __tg_real_2_1(ldexp, (x), (y))
#define lgamma(x) __tg_real(lgamma, (x))
#define llrint(x) __tg_real_nocast(llrint, (x))
#define llround(x) __tg_real_nocast(llround, (x))
#define log(x) __tg_real_complex(log, (x))
#define log10(x) __tg_real(log10, (x))
#define log1p(x) __tg_real(log1p, (x))
#define log2(x) __tg_real(log2, (x))
#define logb(x) __tg_real(logb, (x))
#define lrint(x) __tg_real_nocast(lrint, (x))
#define lround(x) __tg_real_nocast(lround, (x))
#define nearbyint(x) __tg_real(nearbyint, (x))
#define nextafter(x,y) __tg_real_2(nextafter, (x), (y))
#define nexttoward(x,y) __tg_real_2(nexttoward, (x), (y))
#define pow(x,y) __tg_real_complex_pow((x), (y))
#define remainder(x,y) __tg_real_2(remainder, (x), (y))
#define remquo(x,y,z) __tg_real_remquo((x), (y), (z))
#define rint(x) __tg_real(rint, (x))
#define round(x) __tg_real(round, (x))
#define scalbln(x,y) __tg_real_2_1(scalbln, (x), (y))
#define scalbn(x,y) __tg_real_2_1(scalbn, (x), (y))
#define sin(x) __tg_real_complex(sin, (x))
#define sinh(x) __tg_real_complex(sinh, (x))
#define sqrt(x) __tg_real_complex(sqrt, (x))
#define tan(x) __tg_real_complex(tan, (x))
#define tanh(x) __tg_real_complex(tanh, (x))
#define tgamma(x) __tg_real(tgamma, (x))
#define trunc(x) __tg_real(trunc, (x))
#endif
