/*

** $Id: lnum.h,v ... $

** Internal Number model

** See Copyright Notice in lua.h

*/

#ifndef lnum_h

#define lnum_h

#include <math.h>

#include "lobject.h"

/*

** The luai_num* macros define the primitive operations over 'lua_Number's

** (not 'lua_Integer's, not 'lua_Complex').

*/

#define luai_numadd(a,b) ((a)+(b))

#define luai_numsub(a,b) ((a)-(b))

#define luai_nummul(a,b) ((a)*(b))

#define luai_numdiv(a,b) ((a)/(b))

#define luai_nummod(a,b) ((a) - _LF(floor)((a)/(b))*(b))

#define luai_numpow(a,b) (_LF(pow)(a,b))

#define luai_numunm(a) (-(a))

#define luai_numeq(a,b) ((a)==(b))

#define luai_numlt(a,b) ((a)<(b))

#define luai_numle(a,b) ((a)<=(b))

/*

* If '-ffast-math' is used, there are no NaNs or Infs. We shouldn't pretend

* there is.

*/

#ifdef __FAST_MATH__

# define luai_numisnan(a) (0) /* has no concept of NANs */

#elif (defined __STDC_VERSION__) && (__STDC_VERSION__ >= 199901L)

# define luai_numisnan(a) isnan(a) /* same regardless of number size */

#else

# define luai_numisnan(a) (!luai_numeq((a), (a)))

#endif

#ifdef LUA_TINT

int try_addint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_subint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_mulint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_divint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_modint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_powint( lua_Integer *r, lua_Integer ib, lua_Integer ic );

int try_unmint( lua_Integer *r, lua_Integer ib );

#endif

#ifdef LNUM_COMPLEX

static inline lua_Complex luai_vectunm( lua_Complex a ) { return -a; }

static inline lua_Complex luai_vectadd( lua_Complex a, lua_Complex b ) { return a+b; }

static inline lua_Complex luai_vectsub( lua_Complex a, lua_Complex b ) { return a-b; }

static inline lua_Complex luai_vectmul( lua_Complex a, lua_Complex b ) { return a*b; }

static inline lua_Complex luai_vectdiv( lua_Complex a, lua_Complex b ) { return a/b; }

/*

* Complex power

*

* C99 'cpow' gives inaccurate results for many common cases s.a. (1i)^2 ->

* -1+1.2246467991474e-16i (OS X 10.4, gcc 4.0.1 build 5367)

*

* [(a+bi)^(c+di)] = (r^c) * exp(-d*t) * cos(c*t + d*ln(r)) +

* = (r^c) * exp(-d*t) * sin(c*t + d*ln(r)) *i

* r = sqrt(a^2+b^2), t = arctan( b/a )

*

* Reference: <http://home.att.net/~srschmitt/complexnumbers.html>

* Could also be calculated using: x^y = exp(ln(x)*y)

*

* Note: Defined here (and not in .c) so 'lmathlib.c' can share the

* implementation.

*/

static inline

lua_Complex luai_vectpow( lua_Complex a, lua_Complex b )

{

lua_Number ar= _LF(creal)(a), ai= _LF(cimag)(a);

lua_Number br= _LF(creal)(b), bi= _LF(cimag)(b);

if (ai==0 && bi==0) { /* a^c (real) */

return luai_numpow( ar, br );

}

int br_int= (int)br;

if ( ai!=0 && bi==0 && br_int==br && br_int!=0 && br_int!=INT_MIN ) {

/* (a+bi)^N, N = { +-1,+-2, ... +-INT_MAX }

*/

lua_Number k= luai_numpow( _LF(sqrt) (ar*ar + ai*ai), br );

lua_Number cos_z, sin_z;

/* Situation depends upon c (N) in the following manner:

*

* N%4==0 => cos(c*t)=1, sin(c*t)=0

* (N*sign(b))%4==1 or (N*sign(b))%4==-3 => cos(c*t)=0, sin(c*t)=1

* N%4==2 or N%4==-2 => cos(c*t)=-1, sin(c*t)=0

* (N*sign(b))%4==-1 or (N*sign(b))%4==3 => cos(c*t)=0, sin(c*t)=-1

*/

int br_int_abs = br_int<0 ? -br_int:br_int;

switch( (br_int_abs%4) * (br_int<0 ? -1:1) * (ai<0 ? -1:1) ) {

case 0: cos_z=1, sin_z=0; break;

case 2: case -2: cos_z=-1, sin_z=0; break;

case 1: case -3: cos_z=0, sin_z=1; break;

case 3: case -1: cos_z=0, sin_z=-1; break;

default: lua_assert(0); return 0;

}

return k*cos_z + (k*sin_z)*I;

}

return _LF(cpow) ( a, b );

}

#endif

LUAI_FUNC int luaO_str2d (const char *s, lua_Number *res1, lua_Integer *res2);

LUAI_FUNC void luaO_num2buf( char *s, const TValue *o );

LUAI_FUNC int /*bool*/ tt_integer_valued( const TValue *o, lua_Integer *ref );

#endif