path: root/baseline/source/fmref/wcclibm.c

#include "math_private.h"
#include "wcclibm.h"



/* e_rem_pio2f.c -- float version of e_rem_pio2.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
#endif

/* __ieee754_rem_pio2f(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __kernel_rem_pio2f()
 */

/* This array is like the one in e_rem_pio2.c, but the numbers are
   single precision and the last 8 bits are forced to 0.  */
#ifdef __STDC__
static const int32_t fmref_npio2_hw[] = {
#else
static int32_t fmref_npio2_hw[] = {
#endif
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
0x4242c700, 0x42490f00
};

/*
 * invpio2:  24 bits of 2/pi
 * pio2_1:   first  17 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 17 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  17 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

#ifdef __STDC__
static const float
#else
static float
#endif
/* zero =  0.0000000000e+00f, /\* 0x00000000 *\/ */
/* half =  5.0000000000e-01f, /\* 0x3f000000 *\/ */
/* two8 =  2.5600000000e+02f, /\* 0x43800000 *\/ */
fmref_invpio2 =  6.3661980629e-01f, /* 0x3f22f984 */
fmref_pio2_1  =  1.5707855225e+00f, /* 0x3fc90f80 */
fmref_pio2_1t =  1.0804334124e-05f, /* 0x37354443 */
fmref_pio2_2  =  1.0804273188e-05f, /* 0x37354400 */
fmref_pio2_2t =  6.0770999344e-11f, /* 0x2e85a308 */
fmref_pio2_3  =  6.0770943833e-11f, /* 0x2e85a300 */
fmref_pio2_3t =  6.1232342629e-17f; /* 0x248d3132 */

#ifdef __STDC__
	int32_t fmref___ieee754_rem_pio2f(float x, float *y)
#else
	int32_t fmref___ieee754_rem_pio2f(x,y)
	float x,y[];
#endif
{
	float z,w,t,r,fn;
	int32_t i,j,n,ix,hx;

	GET_FLOAT_WORD(hx,x);
	ix = hx&0x7fffffff;
	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
	    {y[0] = x; y[1] = 0; return 0;}
	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
	    if(hx>0) {
		z = x - fmref_pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z - fmref_pio2_1t;
		    y[1] = (z-y[0])-fmref_pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z -= fmref_pio2_2;
		    y[0] = z - fmref_pio2_2t;
		    y[1] = (z-y[0])-fmref_pio2_2t;
		}
		return 1;
	    } else {	/* negative x */
		z = x + fmref_pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z + fmref_pio2_1t;
		    y[1] = (z-y[0])+fmref_pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z += fmref_pio2_2;
		    y[0] = z + fmref_pio2_2t;
		    y[1] = (z-y[0])+fmref_pio2_2t;
		}
		return -1;
	    }
	}
	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
	    t  = fabsf(x);
	    n  = (int32_t) (t*fmref_invpio2+fmref_half);
	    fn = (float)n;
	    r  = t-fn*fmref_pio2_1;
	    w  = fn*fmref_pio2_1t;	/* 1st round good to 40 bit */
	    if(n<32&&(int32_t)(ix&0xffffff00)!=fmref_npio2_hw[n-1]) {
		y[0] = r-w;	/* quick check no cancellation */
	    } else {
	        u_int32_t high;
	        j  = ix>>23;
	        y[0] = r-w;
		GET_FLOAT_WORD(high,y[0]);
	        i = j-((high>>23)&0xff);
	        if(i>8) {  /* 2nd iteration needed, good to 57 */
		    t  = r;
		    w  = fn*fmref_pio2_2;
		    r  = t-w;
		    w  = fn*fmref_pio2_2t-((t-r)-w);
		    y[0] = r-w;
		    GET_FLOAT_WORD(high,y[0]);
		    i = j-((high>>23)&0xff);
		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */
		        t  = r;	/* will cover all possible cases */
		        w  = fn*fmref_pio2_3;
		        r  = t-w;
		        w  = fn*fmref_pio2_3t-((t-r)-w);
		        y[0] = r-w;
		    }
		}
	    }
	    y[1] = (r-y[0])-w;
	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
	    else	 return n;
	}
    /*
     * all other (large) arguments
     */
	if(ix>=0x7f800000) {		/* x is inf or NaN */
	    y[0]=y[1]=x-x; return 0;
	}

	y[0]=y[1]=x-x; /* dummy initialization */
	return 0; /* doesn't happen for our input */
}

/* k_cosf.c -- float version of k_cos.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $";
#endif


#ifdef __STDC__
static const float 
#else
static float 
#endif
/* one =  1.0000000000e+00, /\* 0x3f800000 *\/ */
fmref_C1  =  4.1666667908e-02f, /* 0x3d2aaaab */
fmref_C2  = -1.3888889225e-03f, /* 0xbab60b61 */
fmref_C3  =  2.4801587642e-05f, /* 0x37d00d01 */
fmref_C4  = -2.7557314297e-07f, /* 0xb493f27c */
fmref_C5  =  2.0875723372e-09f, /* 0x310f74f6 */
fmref_C6  = -1.1359647598e-11f; /* 0xad47d74e */

#ifdef __STDC__
	float fmref___kernel_cosf(float x, float y)
#else
	float fmref___kernel_cosf(x, y)
	float x,y;
#endif
{
	float a,hz,z,r,qx;
	int32_t ix;
	GET_FLOAT_WORD(ix,x);
	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
	if(ix<0x32000000) {			/* if x < 2**27 */
	    if(((int)x)==0) return fmref_one;		/* generate inexact */
	}
	z  = x*x;
	r  = z*(fmref_C1+z*(fmref_C2+z*(fmref_C3+z*(fmref_C4+z*(fmref_C5+z*fmref_C6)))));
	if(ix < 0x3e99999a) 			/* if |x| < 0.3 */ 
	    return fmref_one - ((float)0.5f*z - (z*r - x*y));
	else {
	    if(ix > 0x3f480000) {		/* x > 0.78125 */
		qx = (float)0.28125f;
	    } else {
	        SET_FLOAT_WORD(qx,ix-0x01000000);	/* x/4 */
	    }
	    hz = (float)0.5f*z-qx;
	    a  = fmref_one-qx;
	    return a - (hz - (z*r-x*y));
	}
}

/* k_sinf.c -- float version of k_sin.c
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $";
#endif


#ifdef __STDC__
static const float 
#else
static float 
#endif
/* half =  5.0000000000e-01f,/\* 0x3f000000 *\/ */
fmref_S1  = -1.6666667163e-01f, /* 0xbe2aaaab */
fmref_S2  =  8.3333337680e-03f, /* 0x3c088889 */
fmref_S3  = -1.9841270114e-04f, /* 0xb9500d01 */
fmref_S4  =  2.7557314297e-06f, /* 0x3638ef1b */
fmref_S5  = -2.5050759689e-08f, /* 0xb2d72f34 */
fmref_S6  =  1.5896910177e-10f; /* 0x2f2ec9d3 */

#ifdef __STDC__
	float fmref___kernel_sinf(float x, float y, int iy)
#else
	float fmref___kernel_sinf(x, y, iy)
	float x,y; int iy;		/* iy=0 if y is zero */
#endif
{
	float z,r,v;
	int32_t ix;
	GET_FLOAT_WORD(ix,x);
	ix &= 0x7fffffff;			/* high word of x */
	if(ix<0x32000000)			/* |x| < 2**-27 */
	   {if((int)x==0) return x;}		/* generate inexact */
	z	=  x*x;
	v	=  z*x;
	r	=  fmref_S2+z*(fmref_S3+z*(fmref_S4+z*(fmref_S5+z*fmref_S6)));
	if(iy==0) return x+v*(fmref_S1+z*r);
	else      return x-((z*(fmref_half*y-v*r)-y)-v*fmref_S1);
}
/* s_atanf.c -- float version of s_atan.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $";
#endif


#ifdef __STDC__
static const float fmref_atanhi[] = {
#else
static float fmref_atanhi[] = {
#endif
  4.6364760399e-01f, /* atan(0.5)hi 0x3eed6338 */
  7.8539812565e-01f, /* atan(1.0)hi 0x3f490fda */
  9.8279368877e-01f, /* atan(1.5)hi 0x3f7b985e */
  1.5707962513e+00f, /* atan(inf)hi 0x3fc90fda */
};

#ifdef __STDC__
static const float fmref_atanlo[] = {
#else
static float fmref_atanlo[] = {
#endif
  5.0121582440e-09f, /* atan(0.5)lo 0x31ac3769 */
  3.7748947079e-08f, /* atan(1.0)lo 0x33222168 */
  3.4473217170e-08f, /* atan(1.5)lo 0x33140fb4 */
  7.5497894159e-08f, /* atan(inf)lo 0x33a22168 */
};

#ifdef __STDC__
static const float fmref_aT[] = {
#else
static float fmref_aT[] = {
#endif
  3.3333334327e-01f, /* 0x3eaaaaaa */
 -2.0000000298e-01f, /* 0xbe4ccccd */
  1.4285714924e-01f, /* 0x3e124925 */
 -1.1111110449e-01f, /* 0xbde38e38 */
  9.0908870101e-02f, /* 0x3dba2e6e */
 -7.6918758452e-02f, /* 0xbd9d8795 */
  6.6610731184e-02f, /* 0x3d886b35 */
 -5.8335702866e-02f, /* 0xbd6ef16b */
  4.9768779427e-02f, /* 0x3d4bda59 */
 -3.6531571299e-02f, /* 0xbd15a221 */
  1.6285819933e-02f, /* 0x3c8569d7 */
};

/* #ifdef __STDC__ */
/* 	static const float  */
/* #else */
/* 	static float  */
/* #endif */
/* one   = 1.0, */
/* huge   = 1.0e30; */

#ifdef __STDC__
	float fmref___atanf(float x)
#else
	float fmref___atanf(x)
	float x;
#endif
{
	float w,s1,s2,z;
	int32_t ix,hx,id;

	GET_FLOAT_WORD(hx,x);
	ix = hx&0x7fffffff;
	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
	    if(ix>0x7f800000)
		return x+x;		/* NaN */
	    if(hx>0) return  fmref_atanhi[3]+fmref_atanlo[3];
	    else     return -fmref_atanhi[3]-fmref_atanlo[3];
	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
		if(fmref_huge+x>fmref_one) return x;	/* raise inexact */
	    }
	    id = -1;
	} else {
	x = fabsf(x);
	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
		id = 0; x = ((float)2.0f*x-fmref_one)/((float)2.0f+x); 
	    } else {			/* 11/16<=|x|< 19/16 */
		id = 1; x  = (x-fmref_one)/(x+fmref_one); 
	    }
	} else {
	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
		id = 2; x  = (x-(float)1.5f)/(fmref_one+(float)1.5f*x);
	    } else {			/* 2.4375 <= |x| < 2^66 */
		id = 3; x  = -(float)1.0f/x;
	    }
	}}
    /* end of argument reduction */
	z = x*x;
	w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
	s1 = z*(fmref_aT[0]+w*(fmref_aT[2]+w*(fmref_aT[4]+w*(fmref_aT[6]+w*(fmref_aT[8]+w*fmref_aT[10])))));
	s2 = w*(fmref_aT[1]+w*(fmref_aT[3]+w*(fmref_aT[5]+w*(fmref_aT[7]+w*fmref_aT[9]))));
	if (id<0) return x - x*(s1+s2);
	else {
	    z = fmref_atanhi[id] - ((x*(s1+s2) - fmref_atanlo[id]) - x);
	    return (hx<0)? -z:z;
	}
}
//weak_alias (__atanf, atanf)

/* s_cosf.c -- float version of s_cos.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* #ifdef __STDC__ */
/* static const float one=1.0; */
/* #else */
/* static float one=1.0; */
/* #endif */

#ifdef __STDC__
	float fmref___cosf(float x)
#else
	float fmref___cosf(x)
	float x;
#endif
{
	float y[2],z=0.0f;
	int32_t n,ix;

	GET_FLOAT_WORD(ix,x);

    /* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3f490fd8) return fmref___kernel_cosf(x,z);

    /* cos(Inf or NaN) is NaN */
	else if (ix>=0x7f800000) return x-x;

    /* argument reduction needed */
	else {
	    n = fmref___ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  fmref___kernel_cosf(y[0],y[1]);
		case 1: return -fmref___kernel_sinf(y[0],y[1],1);
		case 2: return -fmref___kernel_cosf(y[0],y[1]);
		default:
		        return  fmref___kernel_sinf(y[0],y[1],1);
	    }
	}
}

/* s_sinf.c -- float version of s_sin.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

 #ifdef __STDC__
	float fmref___sinf(float x)
#else
	float fmref___sinf(x)
	float x;
#endif
{
	float y[2],z=0.0;
	int32_t n, ix;

	GET_FLOAT_WORD(ix,x);

    /* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3f490fd8) return fmref___kernel_sinf(x,z,0);

    /* sin(Inf or NaN) is NaN */
	else if (ix>=0x7f800000) return x-x;

    /* argument reduction needed */
	else {
	    n = fmref___ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  fmref___kernel_sinf(y[0],y[1],1);
		case 1: return  fmref___kernel_cosf(y[0],y[1]);
		case 2: return -fmref___kernel_sinf(y[0],y[1],1);
		default:
			return -fmref___kernel_cosf(y[0],y[1]);
	    }
	}
}

/* s_fabsf.c -- float version of s_fabs.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/*
 * fabsf(x) returns the absolute value of x.
 */


#ifdef __STDC__
	float fmref___fabsf(float x)
#else
	float fmref___fabsf(x)
	float x;
#endif
{
	u_int32_t ix;
	GET_FLOAT_WORD(ix,x);
	SET_FLOAT_WORD(x,ix&0x7fffffff);
        return x;
}