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/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#include <sys/isa_defs.h>
#include "libm_inlines.h"
#ifdef _LITTLE_ENDIAN
#define HI(x) *(1+(int*)x)
#define LO(x) *(unsigned*)x
#else
#define HI(x) *(int*)x
#define LO(x) *(1+(unsigned*)x)
#endif
#ifdef __RESTRICT
#define restrict _Restrict
#else
#define restrict
#endif
void
__vatan(int n, double * restrict x, int stridex, double * restrict y, int stridey)
{
double f, z, ans = 0.0L, ansu, ansl, tmp, poly, conup, conlo, dummy;
double f1, ans1, ansu1, ansl1, tmp1, poly1, conup1, conlo1;
double f2, ans2, ansu2, ansl2, tmp2, poly2, conup2, conlo2;
int index, sign, intf, intflo, intz, argcount;
int index1, sign1 = 0;
int index2, sign2 = 0;
double *yaddr,*yaddr1 = 0,*yaddr2 = 0;
extern const double __vlibm_TBL_atan1[];
extern double fabs(double);
/* Power series atan(x) = x + p1*x**3 + p2*x**5 + p3*x**7
* Error = -3.08254E-18 On the interval |x| < 1/64 */
/* define dummy names for readability. Use parray to help compiler optimize loads */
#define p3 parray[0]
#define p2 parray[1]
#define p1 parray[2]
static const double parray[] = {
-1.428029046844299722E-01, /* p[3] */
1.999999917247000615E-01, /* p[2] */
-3.333333333329292858E-01, /* p[1] */
1.0, /* not used for p[0], though */
-1.0, /* used to flip sign of answer */
};
if (n <= 0) return; /* if no. of elements is 0 or neg, do nothing */
do
{
LOOP0:
f = fabs(*x); /* fetch argument */
intf = HI(x); /* upper half of x, as integer */
intflo = LO(x); /* lower half of x, as integer */
sign = intf & 0x80000000; /* sign of argument */
intf = intf & ~0x80000000; /* abs(upper argument) */
if ((intf > 0x43600000) || (intf < 0x3e300000)) /* filter out special cases */
{
if ( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0)))
{
ans = f - f; /* return NaN if x=NaN*/
}
else if (intf < 0x3e300000) /* avoid underflow for small arg */
{
dummy = 1.0e37 + f;
dummy = dummy;
ans = f;
}
else if (intf > 0x43600000) /* avoid underflow for big arg */
{
index = 2;
ans = __vlibm_TBL_atan1[index] + __vlibm_TBL_atan1[index+1];/* pi/2 up + pi/2 low */
}
*y = (sign) ? -ans: ans; /* store answer, with sign bit */
x += stridex;
y += stridey;
argcount = 0; /* initialize argcount */
if (--n <=0) break; /* we are done */
goto LOOP0; /* otherwise, examine next arg */
}
index = 0; /* points to 0,0 in table */
if (intf > 0x40500000) /* if (|x| > 64 */
{ f = -1.0/f;
index = 2; /* point to pi/2 upper, lower */
}
else if (intf >= 0x3f900000) /* if |x| >= (1/64)... */
{
intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
HI(&z) = intz; /* store as a double (z) */
LO(&z) = 0; /* ...lower */
f = (f - z)/(1.0 + f*z); /* get reduced argument */
index = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
index = index + 4; /* skip over 0,0,pi/2,pi/2 */
}
yaddr = y; /* address to store this answer */
x += stridex; /* point to next arg */
y += stridey; /* point to next result */
argcount = 1; /* we now have 1 good argument */
if (--n <=0)
{
f1 = 0.0; /* put dummy values in args 1,2 */
f2 = 0.0;
index1 = 0;
index2 = 0;
goto UNROLL3; /* finish up with 1 good arg */
}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
LOOP1:
f1 = fabs(*x); /* fetch argument */
intf = HI(x); /* upper half of x, as integer */
intflo = LO(x); /* lower half of x, as integer */
sign1 = intf & 0x80000000; /* sign of argument */
intf = intf & ~0x80000000; /* abs(upper argument) */
if ((intf > 0x43600000) || (intf < 0x3e300000)) /* filter out special cases */
{
if ( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0)))
{
ans = f1 - f1; /* return NaN if x=NaN*/
}
else if (intf < 0x3e300000) /* avoid underflow for small arg */
{
dummy = 1.0e37 + f1;
dummy = dummy;
ans = f1;
}
else if (intf > 0x43600000) /* avoid underflow for big arg */
{
index1 = 2;
ans = __vlibm_TBL_atan1[index1] + __vlibm_TBL_atan1[index1+1];/* pi/2 up + pi/2 low */
}
*y = (sign1) ? -ans: ans; /* store answer, with sign bit */
x += stridex;
y += stridey;
argcount = 1; /* we still have 1 good arg */
if (--n <=0)
{
f1 = 0.0; /* put dummy values in args 1,2 */
f2 = 0.0;
index1 = 0;
index2 = 0;
goto UNROLL3; /* finish up with 1 good arg */
}
goto LOOP1; /* otherwise, examine next arg */
}
index1 = 0; /* points to 0,0 in table */
if (intf > 0x40500000) /* if (|x| > 64 */
{ f1 = -1.0/f1;
index1 = 2; /* point to pi/2 upper, lower */
}
else if (intf >= 0x3f900000) /* if |x| >= (1/64)... */
{
intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
HI(&z) = intz; /* store as a double (z) */
LO(&z) = 0; /* ...lower */
f1 = (f1 - z)/(1.0 + f1*z); /* get reduced argument */
index1 = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
index1 = index1 + 4; /* skip over 0,0,pi/2,pi/2 */
}
yaddr1 = y; /* address to store this answer */
x += stridex; /* point to next arg */
y += stridey; /* point to next result */
argcount = 2; /* we now have 2 good arguments */
if (--n <=0)
{
f2 = 0.0; /* put dummy value in arg 2 */
index2 = 0;
goto UNROLL3; /* finish up with 2 good args */
}
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
/*--------------------------------------------------------------------------*/
LOOP2:
f2 = fabs(*x); /* fetch argument */
intf = HI(x); /* upper half of x, as integer */
intflo = LO(x); /* lower half of x, as integer */
sign2 = intf & 0x80000000; /* sign of argument */
intf = intf & ~0x80000000; /* abs(upper argument) */
if ((intf > 0x43600000) || (intf < 0x3e300000)) /* filter out special cases */
{
if ( (intf > 0x7ff00000) || ((intf == 0x7ff00000) && (intflo !=0)))
{
ans = f2 - f2; /* return NaN if x=NaN*/
}
else if (intf < 0x3e300000) /* avoid underflow for small arg */
{
dummy = 1.0e37 + f2;
dummy = dummy;
ans = f2;
}
else if (intf > 0x43600000) /* avoid underflow for big arg */
{
index2 = 2;
ans = __vlibm_TBL_atan1[index2] + __vlibm_TBL_atan1[index2+1];/* pi/2 up + pi/2 low */
}
*y = (sign2) ? -ans: ans; /* store answer, with sign bit */
x += stridex;
y += stridey;
argcount = 2; /* we still have 2 good args */
if (--n <=0)
{
f2 = 0.0; /* put dummy value in arg 2 */
index2 = 0;
goto UNROLL3; /* finish up with 2 good args */
}
goto LOOP2; /* otherwise, examine next arg */
}
index2 = 0; /* points to 0,0 in table */
if (intf > 0x40500000) /* if (|x| > 64 */
{ f2 = -1.0/f2;
index2 = 2; /* point to pi/2 upper, lower */
}
else if (intf >= 0x3f900000) /* if |x| >= (1/64)... */
{
intz = (intf + 0x00008000) & 0x7fff0000;/* round arg, keep upper */
HI(&z) = intz; /* store as a double (z) */
LO(&z) = 0; /* ...lower */
f2 = (f2 - z)/(1.0 + f2*z); /* get reduced argument */
index2 = (intz - 0x3f900000) >> 15; /* (index >> 16) << 1) */
index2 = index2 + 4; /* skip over 0,0,pi/2,pi/2 */
}
yaddr2 = y; /* address to store this answer */
x += stridex; /* point to next arg */
y += stridey; /* point to next result */
argcount = 3; /* we now have 3 good arguments */
/* here is the 3 way unrolled section,
note, we may actually only have
1,2, or 3 'real' arguments at this point
*/
UNROLL3:
conup = __vlibm_TBL_atan1[index ]; /* upper table */
conup1 = __vlibm_TBL_atan1[index1]; /* upper table */
conup2 = __vlibm_TBL_atan1[index2]; /* upper table */
conlo = __vlibm_TBL_atan1[index +1]; /* lower table */
conlo1 = __vlibm_TBL_atan1[index1+1]; /* lower table */
conlo2 = __vlibm_TBL_atan1[index2+1]; /* lower table */
tmp = f *f ;
tmp1 = f1*f1;
tmp2 = f2*f2;
poly = f *((p3*tmp + p2)*tmp + p1)*tmp ;
poly1 = f1*((p3*tmp1 + p2)*tmp1 + p1)*tmp1;
poly2 = f2*((p3*tmp2 + p2)*tmp2 + p1)*tmp2;
ansu = conup + f ; /* compute atan(f) upper */
ansu1 = conup1 + f1; /* compute atan(f) upper */
ansu2 = conup2 + f2; /* compute atan(f) upper */
ansl = (((conup - ansu) + f) + poly) + conlo ;
ansl1 = (((conup1 - ansu1) + f1) + poly1) + conlo1;
ansl2 = (((conup2 - ansu2) + f2) + poly2) + conlo2;
ans = ansu + ansl ;
ans1 = ansu1 + ansl1;
ans2 = ansu2 + ansl2;
/* now check to see if these are 'real' or 'dummy' arguments BEFORE storing */
*yaddr = sign ? -ans: ans; /* this one is always good */
if (argcount < 3) break; /* end loop and finish up */
*yaddr1 = sign1 ? -ans1: ans1;
*yaddr2 = sign2 ? -ans2: ans2;
} while (--n > 0);
if (argcount == 2)
{ *yaddr1 = sign1 ? -ans1: ans1;
}
}
|
