Commit 7d7c2c1e authored by cshapiro's avatar cshapiro
Browse files

Retrieve the constituent words of a double through a union instead of

casts and pointer arithmetic.  This code now compiles correctly on GCC
version 4 without disabling the default assumption of strict aliasing
rules.  Also, remove lots of dead code associated with parts of fdlibm
that have not been imported into the runtime.
parent 0104cad3
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+12 −23
Original line number Diff line number Diff line
@@ -23,11 +23,7 @@
/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
 */
#ifdef __STDC__
static const int two_over_pi[] = {
#else
static int two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 
@@ -41,11 +37,7 @@ static int two_over_pi[] = {
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 
};

#ifdef __STDC__
static const int npio2_hw[] = {
#else
static int npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
@@ -64,11 +56,7 @@ static int npio2_hw[] = {
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

#ifdef __STDC__
static const double 
#else
static double 
#endif
zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
@@ -80,18 +68,15 @@ pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

#ifdef __STDC__
int __ieee754_rem_pio2(double x, double *y)
#else
	int __ieee754_rem_pio2(x,y)
	double x,y[];
#endif
{
	double z,w,t,r,fn;
	double tx[3];
	int e0,i,j,nx,n,ix,hx;
	union { int i[2]; double d; } ux,uy0,uz;

	hx = __HI(x);		/* high word of x */
	ux.d = x;
	hx = ux.i[HIWORD];		/* high word of x */
	ix = hx&0x7fffffff;
	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
	    {y[0] = x; y[1] = 0; return 0;}
@@ -131,14 +116,16 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
	    } else {
	        j  = ix>>20;
	        y[0] = r-w; 
	        i = j-(((__HI(y[0]))>>20)&0x7ff);
	        uy0.d = y[0];
		i = j-((uy0.i[HIWORD]>>20)&0x7ff);
	        if(i>16) {  /* 2nd iteration needed, good to 118 */
		    t  = r;
		    w  = fn*pio2_2;	
		    r  = t-w;
		    w  = fn*pio2_2t-((t-r)-w);	
		    y[0] = r-w;
		    i = j-(((__HI(y[0]))>>20)&0x7ff);
		    uy0.d = y[0];
		    i = j-((uy0.i[HIWORD]>>20)&0x7ff);
		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
		    	t  = r;	/* will cover all possible cases */
		    	w  = fn*pio2_3;	
@@ -159,9 +146,11 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
	    y[0]=y[1]=x-x; return 0;
	}
    /* set z = scalbn(|x|,ilogb(x)-23) */
	__LO(z) = __LO(x);
	ux.d = x;
	uz.i[LOWORD] = ux.i[LOWORD];
	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
	__HI(z) = ix - (e0<<20);
	uz.i[HIWORD] = ix - (e0<<20);
	z = uz.d;
	for(i=0;i<2;i++) {
		tx[i] = (double)((int)(z));
		z     = (z-tx[i])*two24;
+8 −181
Original line number Diff line number Diff line
@@ -20,197 +20,24 @@
#endif

#ifdef __LITTLE_ENDIAN
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
#define __HIp(x) *(1+(int*)x)
#define __LOp(x) *(int*)x
enum { HIWORD = 1, LOWORD = 0 };
#else
#define __HI(x) *(int*)&x
#define __LO(x) *(1+(int*)&x)
#define __HIp(x) *(int*)x
#define __LOp(x) *(1+(int*)x)
enum { HIWORD = 0, LOWORD = 1 };
#endif

#ifdef __STDC__
#define	__P(p)	p
#else
#define	__P(p)	()
#endif

/*
 * ANSI/POSIX
 */

extern int signgam;

#define	MAXFLOAT	((float)3.40282346638528860e+38)

enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};

#define _LIB_VERSION_TYPE enum fdversion
#define _LIB_VERSION _fdlib_version  

/* if global variable _LIB_VERSION is not desirable, one may 
 * change the following to be a constant by: 
 *	#define _LIB_VERSION_TYPE const enum version
 * In that case, after one initializes the value _LIB_VERSION (see
 * s_lib_version.c) during compile time, it cannot be modified
 * in the middle of a program
 */ 
extern  _LIB_VERSION_TYPE  _LIB_VERSION;

#define _IEEE_  fdlibm_ieee
#define _SVID_  fdlibm_svid
#define _XOPEN_ fdlibm_xopen
#define _POSIX_ fdlibm_posix

struct exception {
	int type;
	char *name;
	double arg1;
	double arg2;
	double retval;
};

#define	HUGE		MAXFLOAT

/* 
 * set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
 * (one may replace the following line by "#include <values.h>")
 */

#define X_TLOSS		1.41484755040568800000e+16 

#define	DOMAIN		1
#define	SING		2
#define	OVERFLOW	3
#define	UNDERFLOW	4
#define	TLOSS		5
#define	PLOSS		6

/*
 * ANSI/POSIX
 */
extern double acos __P((double));
extern double asin __P((double));
extern double atan __P((double));
extern double atan2 __P((double, double));
extern double cos __P((double));
extern double sin __P((double));
extern double tan __P((double));

extern double cosh __P((double));
extern double sinh __P((double));
extern double tanh __P((double));
extern double fabs(double);
extern double floor(double);

extern double exp __P((double));
extern double frexp __P((double, int *));
extern double ldexp __P((double, int));
extern double log __P((double));
extern double log10 __P((double));
extern double modf __P((double, double *));

extern double pow __P((double, double));
extern double sqrt __P((double));

extern double ceil __P((double));
extern double fabs __P((double));
extern double floor __P((double));
extern double fmod __P((double, double));

extern double erf __P((double));
extern double erfc __P((double));
extern double gamma __P((double));
extern double hypot __P((double, double));
extern int isnan __P((double));
extern int finite __P((double));
extern double j0 __P((double));
extern double j1 __P((double));
extern double jn __P((int, double));
extern double lgamma __P((double));
extern double y0 __P((double));
extern double y1 __P((double));
extern double yn __P((int, double));

extern double acosh __P((double));
extern double asinh __P((double));
extern double atanh __P((double));
extern double cbrt __P((double));
extern double logb __P((double));
extern double nextafter __P((double, double));
extern double remainder __P((double, double));
#ifdef _SCALB_INT
extern double scalb __P((double, int));
#else
extern double scalb __P((double, double));
#endif

extern int matherr __P((struct exception *));

/*
 * IEEE Test Vector
 */
extern double significand __P((double));
/* ieee style elementary functions */
extern int    __ieee754_rem_pio2(double,double*);

/*
 * Functions callable from C, intended to support IEEE arithmetic.
 */
extern double copysign __P((double, double));
extern int ilogb __P((double));
extern double rint __P((double));
extern double scalbn __P((double, int));

/*
 * BSD math library entry points
 */
extern double expm1 __P((double));
extern double log1p __P((double));

/*
 * Reentrant version of gamma & lgamma; passes signgam back by reference
 * as the second argument; user must allocate space for signgam.
 */
#ifdef _REENTRANT
extern double gamma_r __P((double, int *));
extern double lgamma_r __P((double, int *));
#endif	/* _REENTRANT */

/* ieee style elementary functions */
extern double __ieee754_sqrt __P((double));			
extern double __ieee754_acos __P((double));			
extern double __ieee754_acosh __P((double));			
extern double __ieee754_log __P((double));			
extern double __ieee754_atanh __P((double));			
extern double __ieee754_asin __P((double));			
extern double __ieee754_atan2 __P((double,double));			
extern double __ieee754_exp __P((double));
extern double __ieee754_cosh __P((double));
extern double __ieee754_fmod __P((double,double));
extern double __ieee754_pow __P((double,double));
extern double __ieee754_lgamma_r __P((double,int *));
extern double __ieee754_gamma_r __P((double,int *));
extern double __ieee754_lgamma __P((double));
extern double __ieee754_gamma __P((double));
extern double __ieee754_log10 __P((double));
extern double __ieee754_sinh __P((double));
extern double __ieee754_hypot __P((double,double));
extern double __ieee754_j0 __P((double));
extern double __ieee754_j1 __P((double));
extern double __ieee754_y0 __P((double));
extern double __ieee754_y1 __P((double));
extern double __ieee754_jn __P((int,double));
extern double __ieee754_yn __P((int,double));
extern double __ieee754_remainder __P((double,double));
extern int    __ieee754_rem_pio2 __P((double,double*));
#ifdef _SCALB_INT
extern double __ieee754_scalb __P((double,int));
#else
extern double __ieee754_scalb __P((double,double));
#endif
extern double scalbn(double, int);

/* fdlibm kernel function */
extern double __kernel_standard __P((double,double,int));	
extern double __kernel_sin __P((double,double,int));
extern double __kernel_cos __P((double,double));
extern double __kernel_tan __P((double,double,int));
extern int    __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*));
extern int    __kernel_rem_pio2(double*,double*,int,int,int,const int*);
+1 −18
Original line number Diff line number Diff line
@@ -129,17 +129,9 @@

#include "fdlibm.h"

#ifdef __STDC__
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6}; 
#endif

#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
@@ -150,22 +142,13 @@ static double PIo2[] = {
  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};

#ifdef __STDC__
static const double			
#else
static double			
#endif
zero   = 0.0,
one    = 1.0,
two24   =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24  =  5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */

#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) 
#else
	int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) 	
	double x[], y[]; int e0,nx,prec; int ipio2[];
#endif
{
	int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
	double z,fw,f[20],fq[20],q[20];