Changeset 95bda0a for libcfa/src/math.hfa

Timestamp:

Oct 8, 2022, 4:29:32 PM (19 months ago)

Author:

Peter A. Buhr <pabuhr@…>

Branches:

ADT, ast-experimental, master

Children:

301071a, affb51b

Parents:

b2ddaf3

Message:

add attribute always_inline to many CFA-library cover-routines to force inlining

File:

• libcfa/src/math.hfa (modified) (6 diffs)

libcfa/src/math.hfa

@@ -10 +10 @@
 // Created On       : Mon Apr 18 23:37:04 2016
 // Last Modified By : Peter A. Buhr
-// Last Modified On : Thu Apr 15 11:47:56 2021
-// Update Count     : 132
+// Last Modified On : Sat Oct  8 08:40:42 2022
+// Update Count     : 136
 //
 
@@ -26 +26 @@
 //---------------------- General ----------------------
 
-static inline {
+static inline __attribute__((always_inline)) {
         float ?%?( float x, float y ) { return fmodf( x, y ); }
         float fmod( float x, float y ) { return fmodf( x, y ); }
@@ -64 +64 @@
 //---------------------- Exponential ----------------------
 
-static inline {
+static inline __attribute__((always_inline)) {
         float exp( float x ) { return expf( x ); }
         // extern "C" { double exp( double ); }
@@ -93 +93 @@
 //---------------------- Logarithm ----------------------
 
-static inline {
+static inline __attribute__((always_inline)) {
         float log( float x ) { return logf( x ); }
         // extern "C" { double log( double ); }
@@ -148 +148 @@
 } // distribution
 
-//---------------------- Trigonometric ----------------------
-
-static inline {
-        float sin( float x ) { return sinf( x ); }
-        // extern "C" { double sin( double ); }
-        long double sin( long double x ) { return sinl( x ); }
-        float _Complex sin( float _Complex x ) { return csinf( x ); }
-        double _Complex sin( double _Complex x ) { return csin( x ); }
-        long double _Complex sin( long double _Complex x ) { return csinl( x ); }
-
-        float cos( float x ) { return cosf( x ); }
-        // extern "C" { double cos( double ); }
-        long double cos( long double x ) { return cosl( x ); }
-        float _Complex cos( float _Complex x ) { return ccosf( x ); }
-        double _Complex cos( double _Complex x ) { return ccos( x ); }
-        long double _Complex cos( long double _Complex x ) { return ccosl( x ); }
-
-        float tan( float x ) { return tanf( x ); }
-        // extern "C" { double tan( double ); }
-        long double tan( long double x ) { return tanl( x ); }
-        float _Complex tan( float _Complex x ) { return ctanf( x ); }
-        double _Complex tan( double _Complex x ) { return ctan( x ); }
-        long double _Complex tan( long double _Complex x ) { return ctanl( x ); }
-
-        float asin( float x ) { return asinf( x ); }
-        // extern "C" { double asin( double ); }
-        long double asin( long double x ) { return asinl( x ); }
-        float _Complex asin( float _Complex x ) { return casinf( x ); }
-        double _Complex asin( double _Complex x ) { return casin( x ); }
-        long double _Complex asin( long double _Complex x ) { return casinl( x ); }
-
-        float acos( float x ) { return acosf( x ); }
-        // extern "C" { double acos( double ); }
-        long double acos( long double x ) { return acosl( x ); }
-        float _Complex acos( float _Complex x ) { return cacosf( x ); }
-        double _Complex acos( double _Complex x ) { return cacos( x ); }
-        long double _Complex acos( long double _Complex x ) { return cacosl( x ); }
-
-        float atan( float x ) { return atanf( x ); }
-        // extern "C" { double atan( double ); }
-        long double atan( long double x ) { return atanl( x ); }
-        float _Complex atan( float _Complex x ) { return catanf( x ); }
-        double _Complex atan( double _Complex x ) { return catan( x ); }
-        long double _Complex atan( long double _Complex x ) { return catanl( x ); }
-
-        float atan2( float x, float y ) { return atan2f( x, y ); }
-        // extern "C" { double atan2( double, double ); }
-        long double atan2( long double x, long double y ) { return atan2l( x, y ); }
-
-        // alternative name for atan2
-        float atan( float x, float y ) { return atan2f( x, y ); }
-        double atan( double x, double y ) { return atan2( x, y ); }
-        long double atan( long double x, long double y ) { return atan2l( x, y ); }
-} // distribution
-
-//---------------------- Hyperbolic ----------------------
-
-static inline {
-        float sinh( float x ) { return sinhf( x ); }
-        // extern "C" { double sinh( double ); }
-        long double sinh( long double x ) { return sinhl( x ); }
-        float _Complex sinh( float _Complex x ) { return csinhf( x ); }
-        double _Complex sinh( double _Complex x ) { return csinh( x ); }
-        long double _Complex sinh( long double _Complex x ) { return csinhl( x ); }
-
-        float cosh( float x ) { return coshf( x ); }
-        // extern "C" { double cosh( double ); }
-        long double cosh( long double x ) { return coshl( x ); }
-        float _Complex cosh( float _Complex x ) { return ccoshf( x ); }
-        double _Complex cosh( double _Complex x ) { return ccosh( x ); }
-        long double _Complex cosh( long double _Complex x ) { return ccoshl( x ); }
-
-        float tanh( float x ) { return tanhf( x ); }
-        // extern "C" { double tanh( double ); }
-        long double tanh( long double x ) { return tanhl( x ); }
-        float _Complex tanh( float _Complex x ) { return ctanhf( x ); }
-        double _Complex tanh( double _Complex x ) { return ctanh( x ); }
-        long double _Complex tanh( long double _Complex x ) { return ctanhl( x ); }
-
-        float asinh( float x ) { return asinhf( x ); }
-        // extern "C" { double asinh( double ); }
-        long double asinh( long double x ) { return asinhl( x ); }
-        float _Complex asinh( float _Complex x ) { return casinhf( x ); }
-        double _Complex asinh( double _Complex x ) { return casinh( x ); }
-        long double _Complex asinh( long double _Complex x ) { return casinhl( x ); }
-
-        float acosh( float x ) { return acoshf( x ); }
-        // extern "C" { double acosh( double ); }
-        long double acosh( long double x ) { return acoshl( x ); }
-        float _Complex acosh( float _Complex x ) { return cacoshf( x ); }
-        double _Complex acosh( double _Complex x ) { return cacosh( x ); }
-        long double _Complex acosh( long double _Complex x ) { return cacoshl( x ); }
-
-        float atanh( float x ) { return atanhf( x ); }
-        // extern "C" { double atanh( double ); }
-        long double atanh( long double x ) { return atanhl( x ); }
-        float _Complex atanh( float _Complex x ) { return catanhf( x ); }
-        double _Complex atanh( double _Complex x ) { return catanh( x ); }
-        long double _Complex atanh( long double _Complex x ) { return catanhl( x ); }
-} // distribution
-
-//---------------------- Error / Gamma ----------------------
-
-static inline {
-        float erf( float x ) { return erff( x ); }
-        // extern "C" { double erf( double ); }
-        long double erf( long double x ) { return erfl( x ); }
-        // float _Complex erf( float _Complex );
-        // double _Complex erf( double _Complex );
-        // long double _Complex erf( long double _Complex );
-
-        float erfc( float x ) { return erfcf( x ); }
-        // extern "C" { double erfc( double ); }
-        long double erfc( long double x ) { return erfcl( x ); }
-        // float _Complex erfc( float _Complex );
-        // double _Complex erfc( double _Complex );
-        // long double _Complex erfc( long double _Complex );
-
-        float lgamma( float x ) { return lgammaf( x ); }
-        // extern "C" { double lgamma( double ); }
-        long double lgamma( long double x ) { return lgammal( x ); }
-        float lgamma( float x, int * sign ) { return lgammaf_r( x, sign ); }
-        double lgamma( double x, int * sign ) { return lgamma_r( x, sign ); }
-        long double lgamma( long double x, int * sign ) { return lgammal_r( x, sign ); }
-
-        float tgamma( float x ) { return tgammaf( x ); }
-        // extern "C" { double tgamma( double ); }
-        long double tgamma( long double x ) { return tgammal( x ); }
-} // distribution
-
-//---------------------- Nearest Integer ----------------------
-
-static inline {
-        signed char floor( signed char n, signed char align ) { return n / align * align; }
-        unsigned char floor( unsigned char n, unsigned char align ) { return n / align * align; }
-        short int floor( short int n, short int align ) { return n / align * align; }
-        unsigned short int floor( unsigned short int n, unsigned short int align ) { return n / align * align; }
-        int floor( int n, int align ) { return n / align * align; }
-        unsigned int floor( unsigned int n, unsigned int align ) { return n / align * align; }
-        long int floor( long int n, long int align ) { return n / align * align; }
-        unsigned long int floor( unsigned long int n, unsigned long int align ) { return n / align * align; }
-        long long int floor( long long int n, long long int align ) { return n / align * align; }
-        unsigned long long int floor( unsigned long long int n, unsigned long long int align ) { return n / align * align; }
-
-        // forall( T | { T ?/?( T, T ); T ?*?( T, T ); } )
-        // T floor( T n, T align ) { return n / align * align; }
-
-        signed char ceiling_div( signed char n, char align ) { return (n + (align - 1)) / align; }
-        unsigned char ceiling_div( unsigned char n, unsigned char align ) { return (n + (align - 1)) / align; }
-        short int ceiling_div( short int n, short int align ) { return (n + (align - 1)) / align; }
-        unsigned short int ceiling_div( unsigned short int n, unsigned short int align ) { return (n + (align - 1)) / align; }
-        int ceiling_div( int n, int align ) { return (n + (align - 1)) / align; }
-        unsigned int ceiling_div( unsigned int n, unsigned int align ) { return (n + (align - 1)) / align; }
-        long int ceiling_div( long int n, long int align ) { return (n + (align - 1)) / align; }
-        unsigned long int ceiling_div( unsigned long int n, unsigned long int align ) { return (n + (align - 1)) / align; }
-        long long int ceiling_div( long long int n, long long int align ) { return (n + (align - 1)) / align; }
-        unsigned long long int ceiling_div( unsigned long long int n, unsigned long long int align ) { return (n + (align - 1)) / align; }
-
-        // forall( T | { T ?+?( T, T ); T ?-?( T, T ); T ?%?( T, T ); } )
-        // T ceiling_div( T n, T align ) { verify( is_pow2( align ) );return (n + (align - 1)) / align; }
-
-        // gcc notices the div/mod pair and saves both so only one div.
-        signed char ceiling( signed char n, signed char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned char ceiling( unsigned char n, unsigned char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        short int ceiling( short int n, short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned short int ceiling( unsigned short int n, unsigned short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        int ceiling( int n, int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned int ceiling( unsigned int n, unsigned int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        long int ceiling( long int n, long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned long int ceiling( unsigned long int n, unsigned long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0) , align); }
-        long long int ceiling( long long int n, long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-        unsigned long long int ceiling( unsigned long long int n, unsigned long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
-
-        // forall( T | { void ?{}( T &, one_t ); T ?+?( T, T ); T ?-?( T, T ); T ?/?( T, T ); } )
-        // T ceiling( T n, T align ) { return return floor( n + (n % align != 0 ? align - 1 : 0), align ); *}
-
-        float floor( float x ) { return floorf( x ); }
-        // extern "C" { double floor( double ); }
-        long double floor( long double x ) { return floorl( x ); }
-
-        float ceil( float x ) { return ceilf( x ); }
-        // extern "C" { double ceil( double ); }
-        long double ceil( long double x ) { return ceill( x ); }
-
-        float trunc( float x ) { return truncf( x ); }
-        // extern "C" { double trunc( double ); }
-        long double trunc( long double x ) { return truncl( x ); }
-
-        float rint( float x ) { return rintf( x ); }
-        // extern "C" { double rint( double x ); }
-        long double rint( long double x ) { return rintl( x ); }
-        long int rint( float x ) { return lrintf( x ); }
-        long int rint( double x ) { return lrint( x ); }
-        long int rint( long double x ) { return lrintl( x ); }
-        long long int rint( float x ) { return llrintf( x ); }
-        long long int rint( double x ) { return llrint( x ); }
-        long long int rint( long double x ) { return llrintl( x ); }
-
-        long int lrint( float x ) { return lrintf( x ); }
-        // extern "C" { long int lrint( double ); }
-        long int lrint( long double x ) { return lrintl( x ); }
-        long long int llrint( float x ) { return llrintf( x ); }
-        // extern "C" { long long int llrint( double ); }
-        long long int llrint( long double x ) { return llrintl( x ); }
-
-        float nearbyint( float x ) { return nearbyintf( x ); }
-        // extern "C" { double nearbyint( double ); }
-        long double nearbyint( long double x ) { return nearbyintl( x ); }
-
-        float round( float x ) { return roundf( x ); }
-        // extern "C" { double round( double x ); }
-        long double round( long double x ) { return roundl( x ); }
-        long int round( float x ) { return lroundf( x ); }
-        long int round( double x ) { return lround( x ); }
-        long int round( long double x ) { return lroundl( x ); }
-        long long int round( float x ) { return llroundf( x ); }
-        long long int round( double x ) { return llround( x ); }
-        long long int round( long double x ) { return llroundl( x ); }
-
-        long int lround( float x ) { return lroundf( x ); }
-        // extern "C" { long int lround( double ); }
-        long int lround( long double x ) { return lroundl( x ); }
-        long long int llround( float x ) { return llroundf( x ); }
-        // extern "C" { long long int llround( double ); }
-        long long int llround( long double x ) { return llroundl( x ); }
-} // distribution
-
-//---------------------- Manipulation ----------------------
-
-static inline {
-        float copysign( float x, float y ) { return copysignf( x, y ); }
-        // extern "C" { double copysign( double, double ); }
-        long double copysign( long double x, long double y ) { return copysignl( x, y ); }
-
-        float frexp( float x, int * ip ) { return frexpf( x, ip ); }
-        // extern "C" { double frexp( double, int * ); }
-        long double frexp( long double x, int * ip ) { return frexpl( x, ip ); }
-
-        float ldexp( float x, int exp2 ) { return ldexpf( x, exp2 ); }
-        // extern "C" { double ldexp( double, int ); }
-        long double ldexp( long double x, int exp2 ) { return ldexpl( x, exp2 ); }
-
-        [ float, float ] modf( float x ) { float i; x = modff( x, &i ); return [ i, x ]; }
-        float modf( float x, float * i ) { return modff( x, i ); }
-        [ double, double ] modf( double x ) { double i; x = modf( x, &i ); return [ i, x ]; }
-        // extern "C" { double modf( double, double * ); }
-        [ long double, long double ] modf( long double x ) { long double i; x = modfl( x, &i ); return [ i, x ]; }
-        long double modf( long double x, long double * i ) { return modfl( x, i ); }
-
-        float nextafter( float x, float y ) { return nextafterf( x, y ); }
-        // extern "C" { double nextafter( double, double ); }
-        long double nextafter( long double x, long double y ) { return nextafterl( x, y ); }
-
-        float nexttoward( float x, long double y ) { return nexttowardf( x, y ); }
-        // extern "C" { double nexttoward( double, long double ); }
-        long double nexttoward( long double x, long double y ) { return nexttowardl( x, y ); }
-
-        float scalbn( float x, int exp ) { return scalbnf( x, exp ); }
-        // extern "C" { double scalbn( double, int ); }
-        long double scalbn( long double x, int exp ) { return scalbnl( x, exp ); }
-        float scalbn( float x, long int exp ) { return scalblnf( x, exp ); }
-        double scalbn( double x, long int exp ) { return scalbln( x, exp ); }
-        long double scalbn( long double x, long int exp ) { return scalblnl( x, exp ); }
-
-        float scalbln( float x, long int exp ) { return scalblnf( x, exp ); }
-        // extern "C" { double scalbln( double, long int ); }
-        long double scalbln( long double x, long int exp ) { return scalblnl( x, exp ); }
-} // distribution
-
-//---------------------------------------
-
-static inline {
-        forall( T | { void ?{}( T &, one_t ); T ?+?( T, T ); T ?-?( T, T );T ?*?( T, T ); } )
-        T lerp( T x, T y, T a ) { return x * ((T){1} - a) + y * a; }
-
-        forall( T | { void ?{}( T &, zero_t ); void ?{}( T &, one_t ); int ?<?( T, T ); } )
-        T step( T edge, T x ) { return x < edge ? (T){0} : (T){1}; }
-
-        forall( T | { void ?{}( T &, int ); T clamp( T, T, T ); T ?-?( T, T ); T ?*?( T, T ); T ?/?( T, T ); } )
-        T smoothstep( T edge0, T edge1, T x ) { T t = clamp( (x - edge0) / (edge1 - edge0), (T){0}, (T){1} ); return t * t * ((T){3} - (T){2} * t); }
-} // distribution
-
-static inline unsigned long long log2_u32_32(unsigned long long val) {
+static inline unsigned long long log2_u32_32( unsigned long long val ) {
         enum {
                 TABLE_BITS = 6,
@@ -520 +238 @@
 }
 
+//---------------------- Trigonometric ----------------------
+
+static inline __attribute__((always_inline)) {
+        float sin( float x ) { return sinf( x ); }
+        // extern "C" { double sin( double ); }
+        long double sin( long double x ) { return sinl( x ); }
+        float _Complex sin( float _Complex x ) { return csinf( x ); }
+        double _Complex sin( double _Complex x ) { return csin( x ); }
+        long double _Complex sin( long double _Complex x ) { return csinl( x ); }
+
+        float cos( float x ) { return cosf( x ); }
+        // extern "C" { double cos( double ); }
+        long double cos( long double x ) { return cosl( x ); }
+        float _Complex cos( float _Complex x ) { return ccosf( x ); }
+        double _Complex cos( double _Complex x ) { return ccos( x ); }
+        long double _Complex cos( long double _Complex x ) { return ccosl( x ); }
+
+        float tan( float x ) { return tanf( x ); }
+        // extern "C" { double tan( double ); }
+        long double tan( long double x ) { return tanl( x ); }
+        float _Complex tan( float _Complex x ) { return ctanf( x ); }
+        double _Complex tan( double _Complex x ) { return ctan( x ); }
+        long double _Complex tan( long double _Complex x ) { return ctanl( x ); }
+
+        float asin( float x ) { return asinf( x ); }
+        // extern "C" { double asin( double ); }
+        long double asin( long double x ) { return asinl( x ); }
+        float _Complex asin( float _Complex x ) { return casinf( x ); }
+        double _Complex asin( double _Complex x ) { return casin( x ); }
+        long double _Complex asin( long double _Complex x ) { return casinl( x ); }
+
+        float acos( float x ) { return acosf( x ); }
+        // extern "C" { double acos( double ); }
+        long double acos( long double x ) { return acosl( x ); }
+        float _Complex acos( float _Complex x ) { return cacosf( x ); }
+        double _Complex acos( double _Complex x ) { return cacos( x ); }
+        long double _Complex acos( long double _Complex x ) { return cacosl( x ); }
+
+        float atan( float x ) { return atanf( x ); }
+        // extern "C" { double atan( double ); }
+        long double atan( long double x ) { return atanl( x ); }
+        float _Complex atan( float _Complex x ) { return catanf( x ); }
+        double _Complex atan( double _Complex x ) { return catan( x ); }
+        long double _Complex atan( long double _Complex x ) { return catanl( x ); }
+
+        float atan2( float x, float y ) { return atan2f( x, y ); }
+        // extern "C" { double atan2( double, double ); }
+        long double atan2( long double x, long double y ) { return atan2l( x, y ); }
+
+        // alternative name for atan2
+        float atan( float x, float y ) { return atan2f( x, y ); }
+        double atan( double x, double y ) { return atan2( x, y ); }
+        long double atan( long double x, long double y ) { return atan2l( x, y ); }
+} // distribution
+
+//---------------------- Hyperbolic ----------------------
+
+static inline __attribute__((always_inline)) {
+        float sinh( float x ) { return sinhf( x ); }
+        // extern "C" { double sinh( double ); }
+        long double sinh( long double x ) { return sinhl( x ); }
+        float _Complex sinh( float _Complex x ) { return csinhf( x ); }
+        double _Complex sinh( double _Complex x ) { return csinh( x ); }
+        long double _Complex sinh( long double _Complex x ) { return csinhl( x ); }
+
+        float cosh( float x ) { return coshf( x ); }
+        // extern "C" { double cosh( double ); }
+        long double cosh( long double x ) { return coshl( x ); }
+        float _Complex cosh( float _Complex x ) { return ccoshf( x ); }
+        double _Complex cosh( double _Complex x ) { return ccosh( x ); }
+        long double _Complex cosh( long double _Complex x ) { return ccoshl( x ); }
+
+        float tanh( float x ) { return tanhf( x ); }
+        // extern "C" { double tanh( double ); }
+        long double tanh( long double x ) { return tanhl( x ); }
+        float _Complex tanh( float _Complex x ) { return ctanhf( x ); }
+        double _Complex tanh( double _Complex x ) { return ctanh( x ); }
+        long double _Complex tanh( long double _Complex x ) { return ctanhl( x ); }
+
+        float asinh( float x ) { return asinhf( x ); }
+        // extern "C" { double asinh( double ); }
+        long double asinh( long double x ) { return asinhl( x ); }
+        float _Complex asinh( float _Complex x ) { return casinhf( x ); }
+        double _Complex asinh( double _Complex x ) { return casinh( x ); }
+        long double _Complex asinh( long double _Complex x ) { return casinhl( x ); }
+
+        float acosh( float x ) { return acoshf( x ); }
+        // extern "C" { double acosh( double ); }
+        long double acosh( long double x ) { return acoshl( x ); }
+        float _Complex acosh( float _Complex x ) { return cacoshf( x ); }
+        double _Complex acosh( double _Complex x ) { return cacosh( x ); }
+        long double _Complex acosh( long double _Complex x ) { return cacoshl( x ); }
+
+        float atanh( float x ) { return atanhf( x ); }
+        // extern "C" { double atanh( double ); }
+        long double atanh( long double x ) { return atanhl( x ); }
+        float _Complex atanh( float _Complex x ) { return catanhf( x ); }
+        double _Complex atanh( double _Complex x ) { return catanh( x ); }
+        long double _Complex atanh( long double _Complex x ) { return catanhl( x ); }
+} // distribution
+
+//---------------------- Error / Gamma ----------------------
+
+static inline __attribute__((always_inline)) {
+        float erf( float x ) { return erff( x ); }
+        // extern "C" { double erf( double ); }
+        long double erf( long double x ) { return erfl( x ); }
+        // float _Complex erf( float _Complex );
+        // double _Complex erf( double _Complex );
+        // long double _Complex erf( long double _Complex );
+
+        float erfc( float x ) { return erfcf( x ); }
+        // extern "C" { double erfc( double ); }
+        long double erfc( long double x ) { return erfcl( x ); }
+        // float _Complex erfc( float _Complex );
+        // double _Complex erfc( double _Complex );
+        // long double _Complex erfc( long double _Complex );
+
+        float lgamma( float x ) { return lgammaf( x ); }
+        // extern "C" { double lgamma( double ); }
+        long double lgamma( long double x ) { return lgammal( x ); }
+        float lgamma( float x, int * sign ) { return lgammaf_r( x, sign ); }
+        double lgamma( double x, int * sign ) { return lgamma_r( x, sign ); }
+        long double lgamma( long double x, int * sign ) { return lgammal_r( x, sign ); }
+
+        float tgamma( float x ) { return tgammaf( x ); }
+        // extern "C" { double tgamma( double ); }
+        long double tgamma( long double x ) { return tgammal( x ); }
+} // distribution
+
+//---------------------- Nearest Integer ----------------------
+
+inline __attribute__((always_inline)) static {
+        signed char floor( signed char n, signed char align ) { return n / align * align; }
+        unsigned char floor( unsigned char n, unsigned char align ) { return n / align * align; }
+        short int floor( short int n, short int align ) { return n / align * align; }
+        unsigned short int floor( unsigned short int n, unsigned short int align ) { return n / align * align; }
+        int floor( int n, int align ) { return n / align * align; }
+        unsigned int floor( unsigned int n, unsigned int align ) { return n / align * align; }
+        long int floor( long int n, long int align ) { return n / align * align; }
+        unsigned long int floor( unsigned long int n, unsigned long int align ) { return n / align * align; }
+        long long int floor( long long int n, long long int align ) { return n / align * align; }
+        unsigned long long int floor( unsigned long long int n, unsigned long long int align ) { return n / align * align; }
+
+        // forall( T | { T ?/?( T, T ); T ?*?( T, T ); } )
+        // T floor( T n, T align ) { return n / align * align; }
+
+        signed char ceiling_div( signed char n, char align ) { return (n + (align - 1)) / align; }
+        unsigned char ceiling_div( unsigned char n, unsigned char align ) { return (n + (align - 1)) / align; }
+        short int ceiling_div( short int n, short int align ) { return (n + (align - 1)) / align; }
+        unsigned short int ceiling_div( unsigned short int n, unsigned short int align ) { return (n + (align - 1)) / align; }
+        int ceiling_div( int n, int align ) { return (n + (align - 1)) / align; }
+        unsigned int ceiling_div( unsigned int n, unsigned int align ) { return (n + (align - 1)) / align; }
+        long int ceiling_div( long int n, long int align ) { return (n + (align - 1)) / align; }
+        unsigned long int ceiling_div( unsigned long int n, unsigned long int align ) { return (n + (align - 1)) / align; }
+        long long int ceiling_div( long long int n, long long int align ) { return (n + (align - 1)) / align; }
+        unsigned long long int ceiling_div( unsigned long long int n, unsigned long long int align ) { return (n + (align - 1)) / align; }
+
+        // forall( T | { T ?+?( T, T ); T ?-?( T, T ); T ?%?( T, T ); } )
+        // T ceiling_div( T n, T align ) { verify( is_pow2( align ) );return (n + (align - 1)) / align; }
+
+        // gcc notices the div/mod pair and saves both so only one div.
+        signed char ceiling( signed char n, signed char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        unsigned char ceiling( unsigned char n, unsigned char align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        short int ceiling( short int n, short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        unsigned short int ceiling( unsigned short int n, unsigned short int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        int ceiling( int n, int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        unsigned int ceiling( unsigned int n, unsigned int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        long int ceiling( long int n, long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        unsigned long int ceiling( unsigned long int n, unsigned long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0) , align); }
+        long long int ceiling( long long int n, long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+        unsigned long long int ceiling( unsigned long long int n, unsigned long long int align ) { return floor( n + (n % align != 0 ? align - 1 : 0), align ); }
+
+        // forall( T | { void ?{}( T &, one_t ); T ?+?( T, T ); T ?-?( T, T ); T ?/?( T, T ); } )
+        // T ceiling( T n, T align ) { return return floor( n + (n % align != 0 ? align - 1 : 0), align ); *}
+
+        float floor( float x ) { return floorf( x ); }
+        // extern "C" { double floor( double ); }
+        long double floor( long double x ) { return floorl( x ); }
+
+        float ceil( float x ) { return ceilf( x ); }
+        // extern "C" { double ceil( double ); }
+        long double ceil( long double x ) { return ceill( x ); }
+
+        float trunc( float x ) { return truncf( x ); }
+        // extern "C" { double trunc( double ); }
+        long double trunc( long double x ) { return truncl( x ); }
+
+        float rint( float x ) { return rintf( x ); }
+        // extern "C" { double rint( double x ); }
+        long double rint( long double x ) { return rintl( x ); }
+        long int rint( float x ) { return lrintf( x ); }
+        long int rint( double x ) { return lrint( x ); }
+        long int rint( long double x ) { return lrintl( x ); }
+        long long int rint( float x ) { return llrintf( x ); }
+        long long int rint( double x ) { return llrint( x ); }
+        long long int rint( long double x ) { return llrintl( x ); }
+
+        long int lrint( float x ) { return lrintf( x ); }
+        // extern "C" { long int lrint( double ); }
+        long int lrint( long double x ) { return lrintl( x ); }
+        long long int llrint( float x ) { return llrintf( x ); }
+        // extern "C" { long long int llrint( double ); }
+        long long int llrint( long double x ) { return llrintl( x ); }
+
+        float nearbyint( float x ) { return nearbyintf( x ); }
+        // extern "C" { double nearbyint( double ); }
+        long double nearbyint( long double x ) { return nearbyintl( x ); }
+
+        float round( float x ) { return roundf( x ); }
+        // extern "C" { double round( double x ); }
+        long double round( long double x ) { return roundl( x ); }
+        long int round( float x ) { return lroundf( x ); }
+        long int round( double x ) { return lround( x ); }
+        long int round( long double x ) { return lroundl( x ); }
+        long long int round( float x ) { return llroundf( x ); }
+        long long int round( double x ) { return llround( x ); }
+        long long int round( long double x ) { return llroundl( x ); }
+
+        long int lround( float x ) { return lroundf( x ); }
+        // extern "C" { long int lround( double ); }
+        long int lround( long double x ) { return lroundl( x ); }
+        long long int llround( float x ) { return llroundf( x ); }
+        // extern "C" { long long int llround( double ); }
+        long long int llround( long double x ) { return llroundl( x ); }
+} // distribution
+
+//---------------------- Manipulation ----------------------
+
+static inline __attribute__((always_inline)) {
+        float copysign( float x, float y ) { return copysignf( x, y ); }
+        // extern "C" { double copysign( double, double ); }
+        long double copysign( long double x, long double y ) { return copysignl( x, y ); }
+
+        float frexp( float x, int * ip ) { return frexpf( x, ip ); }
+        // extern "C" { double frexp( double, int * ); }
+        long double frexp( long double x, int * ip ) { return frexpl( x, ip ); }
+
+        float ldexp( float x, int exp2 ) { return ldexpf( x, exp2 ); }
+        // extern "C" { double ldexp( double, int ); }
+        long double ldexp( long double x, int exp2 ) { return ldexpl( x, exp2 ); }
+
+        [ float, float ] modf( float x ) { float i; x = modff( x, &i ); return [ i, x ]; }
+        float modf( float x, float * i ) { return modff( x, i ); }
+        [ double, double ] modf( double x ) { double i; x = modf( x, &i ); return [ i, x ]; }
+        // extern "C" { double modf( double, double * ); }
+        [ long double, long double ] modf( long double x ) { long double i; x = modfl( x, &i ); return [ i, x ]; }
+        long double modf( long double x, long double * i ) { return modfl( x, i ); }
+
+        float nextafter( float x, float y ) { return nextafterf( x, y ); }
+        // extern "C" { double nextafter( double, double ); }
+        long double nextafter( long double x, long double y ) { return nextafterl( x, y ); }
+
+        float nexttoward( float x, long double y ) { return nexttowardf( x, y ); }
+        // extern "C" { double nexttoward( double, long double ); }
+        long double nexttoward( long double x, long double y ) { return nexttowardl( x, y ); }
+
+        float scalbn( float x, int exp ) { return scalbnf( x, exp ); }
+        // extern "C" { double scalbn( double, int ); }
+        long double scalbn( long double x, int exp ) { return scalbnl( x, exp ); }
+        float scalbn( float x, long int exp ) { return scalblnf( x, exp ); }
+        double scalbn( double x, long int exp ) { return scalbln( x, exp ); }
+        long double scalbn( long double x, long int exp ) { return scalblnl( x, exp ); }
+
+        float scalbln( float x, long int exp ) { return scalblnf( x, exp ); }
+        // extern "C" { double scalbln( double, long int ); }
+        long double scalbln( long double x, long int exp ) { return scalblnl( x, exp ); }
+} // distribution
+
+//---------------------------------------
+
+static inline __attribute__((always_inline)) {
+        forall( T | { void ?{}( T &, one_t ); T ?+?( T, T ); T ?-?( T, T );T ?*?( T, T ); } )
+        T lerp( T x, T y, T a ) { return x * ((T){1} - a) + y * a; }
+
+        forall( T | { void ?{}( T &, zero_t ); void ?{}( T &, one_t ); int ?<?( T, T ); } )
+        T step( T edge, T x ) { return x < edge ? (T){0} : (T){1}; }
+
+        forall( T | { void ?{}( T &, int ); T clamp( T, T, T ); T ?-?( T, T ); T ?*?( T, T ); T ?/?( T, T ); } )
+        T smoothstep( T edge0, T edge1, T x ) { T t = clamp( (x - edge0) / (edge1 - edge0), (T){0}, (T){1} ); return t * t * ((T){3} - (T){2} * t); }
+} // distribution
+
 // Local Variables: //
 // mode: c //