path: root/baseline/source/susan/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.  */
static const int32_t susan_npio2_hw[] = {
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)
 */

static const float
/* zero =  0.0000000000e+00f, /\* 0x00000000 *\/ */
/* half =  5.0000000000e-01f, /\* 0x3f000000 *\/ */
/* two8 =  2.5600000000e+02f, /\* 0x43800000 *\/ */
susan_invpio2 =  6.3661980629e-01f, /* 0x3f22f984 */
susan_pio2_1  =  1.5707855225e+00f, /* 0x3fc90f80 */
susan_pio2_1t =  1.0804334124e-05f, /* 0x37354443 */
susan_pio2_2  =  1.0804273188e-05f, /* 0x37354400 */
susan_pio2_2t =  6.0770999344e-11f, /* 0x2e85a308 */
susan_pio2_3  =  6.0770943833e-11f, /* 0x2e85a300 */
susan_pio2_3t =  6.1232342629e-17f; /* 0x248d3132 */

int32_t susan___ieee754_rem_pio2f(float x, float *y)
{
	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 - susan_pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z - susan_pio2_1t;
		    y[1] = (z-y[0])-susan_pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z -= susan_pio2_2;
		    y[0] = z - susan_pio2_2t;
		    y[1] = (z-y[0])-susan_pio2_2t;
		}
		return 1;
	    } else {	/* negative x */
		z = x + susan_pio2_1;
		if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
		    y[0] = z + susan_pio2_1t;
		    y[1] = (z-y[0])+susan_pio2_1t;
		} else {		/* near pi/2, use 24+24+24 bit pi */
		    z += susan_pio2_2;
		    y[0] = z + susan_pio2_2t;
		    y[1] = (z-y[0])+susan_pio2_2t;
		}
		return -1;
	    }
	}
	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
	    t  = fabsf(x);
	    n  = (int32_t) (t*susan_invpio2+susan_half);
	    fn = (float)n;
	    r  = t-fn*susan_pio2_1;
	    w  = fn*susan_pio2_1t;	/* 1st round good to 40 bit */
	    if(n<32&&(int32_t)(ix&0xffffff00)!=susan_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*susan_pio2_2;
		    r  = t-w;
		    w  = fn*susan_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*susan_pio2_3;
		    	r  = t-w;
		    	w  = fn*susan_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; return 0; /* dummy initialisation */
	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


static const float 
/* one =  1.0000000000e+00, /\* 0x3f800000 *\/ */
susan_C1  =  4.1666667908e-02f, /* 0x3d2aaaab */
susan_C2  = -1.3888889225e-03f, /* 0xbab60b61 */
susan_C3  =  2.4801587642e-05f, /* 0x37d00d01 */
susan_C4  = -2.7557314297e-07f, /* 0xb493f27c */
susan_C5  =  2.0875723372e-09f, /* 0x310f74f6 */
susan_C6  = -1.1359647598e-11f; /* 0xad47d74e */

float susan___kernel_cosf(float x, float y)
{
	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 susan_one;		/* generate inexact */
	}
	z  = x*x;
	r  = z*(susan_C1+z*(susan_C2+z*(susan_C3+z*(susan_C4+z*(susan_C5+z*susan_C6)))));
	if(ix < 0x3e99999a) 			/* if |x| < 0.3 */ 
	    return susan_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  = susan_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


static const float 
/* half =  5.0000000000e-01f,/\* 0x3f000000 *\/ */
susan_S1  = -1.6666667163e-01f, /* 0xbe2aaaab */
susan_S2  =  8.3333337680e-03f, /* 0x3c088889 */
susan_S3  = -1.9841270114e-04f, /* 0xb9500d01 */
susan_S4  =  2.7557314297e-06f, /* 0x3638ef1b */
susan_S5  = -2.5050759689e-08f, /* 0xb2d72f34 */
susan_S6  =  1.5896910177e-10f; /* 0x2f2ec9d3 */

float susan___kernel_sinf(float x, float y, int iy)
{
	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	=  susan_S2+z*(susan_S3+z*(susan_S4+z*(susan_S5+z*susan_S6)));
	if(iy==0) return x+v*(susan_S1+z*r);
	else      return x-((z*(susan_half*y-v*r)-y)-v*susan_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


static const float susan_atanhi[] = {
  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 */
};

static const float susan_atanlo[] = {
  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 */
};

static const float susan_aT[] = {
  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 */
};

float susan___atanf(float x)
{
	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  susan_atanhi[3]+susan_atanlo[3];
	    else     return -susan_atanhi[3]-susan_atanlo[3];
	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
		if(susan_huge+x>susan_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-susan_one)/((float)2.0f+x); 
	    } else {			/* 11/16<=|x|< 19/16 */
		id = 1; x  = (x-susan_one)/(x+susan_one); 
	    }
	} else {
	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
		id = 2; x  = (x-(float)1.5f)/(susan_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*(susan_aT[0]+w*(susan_aT[2]+w*(susan_aT[4]+w*(susan_aT[6]+w*(susan_aT[8]+w*susan_aT[10])))));
	s2 = w*(susan_aT[1]+w*(susan_aT[3]+w*(susan_aT[5]+w*(susan_aT[7]+w*susan_aT[9]))));
	if (id<0) return x - x*(s1+s2);
	else {
	    z = susan_atanhi[id] - ((x*(s1+s2) - susan_atanlo[id]) - x);
	    return (hx<0)? -z:z;
	}
}

/* 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.
 * ====================================================
 */

float susan___cosf(float x)
{
	float y[2],z=0.0f;
	int32_t n,ix;

	GET_FLOAT_WORD(ix,x);

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

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

    /* argument reduction needed */
	else {
	    n = susan___ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  susan___kernel_cosf(y[0],y[1]);
		case 1: return -susan___kernel_sinf(y[0],y[1],1);
		case 2: return -susan___kernel_cosf(y[0],y[1]);
		default:
		        return  susan___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.
 * ====================================================
 */

float susan___sinf(float x)
{
	float y[2],z=0.0;
	int32_t n, ix;

	GET_FLOAT_WORD(ix,x);

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

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

    /* argument reduction needed */
	else {
	    n = susan___ieee754_rem_pio2f(x,y);
	    switch(n&3) {
		case 0: return  susan___kernel_sinf(y[0],y[1],1);
		case 1: return  susan___kernel_cosf(y[0],y[1]);
		case 2: return -susan___kernel_sinf(y[0],y[1],1);
		default:
			return -susan___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.
 */


float susan___fabsf(float x)
{
	u_int32_t ix;
	GET_FLOAT_WORD(ix,x);
	SET_FLOAT_WORD(x,ix&0x7fffffff);
        return x;
}