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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.
*/
#pragma weak atanf = __atanf
/* INDENT OFF */
/*
* float atanf(float x);
* Table look-up algorithm
* By K.C. Ng, March 9, 1989
*
* Algorithm.
*
* The algorithm is based on atan(x)=atan(y)+atan((x-y)/(1+x*y)).
* We use poly1(x) to approximate atan(x) for x in [0,1/8] with
* error (relative)
* |(atan(x)-poly1(x))/x|<= 2^-115.94 long double
* |(atan(x)-poly1(x))/x|<= 2^-58.85 double
* |(atan(x)-poly1(x))/x|<= 2^-25.53 float
* and use poly2(x) to approximate atan(x) for x in [0,1/65] with
* error (absolute)
* |atan(x)-poly2(x)|<= 2^-122.15 long double
* |atan(x)-poly2(x)|<= 2^-64.79 double
* |atan(x)-poly2(x)|<= 2^-35.36 float
* and use poly3(x) to approximate atan(x) for x in [1/8,7/16] with
* error (relative, on for single precision)
* |(atan(x)-poly1(x))/x|<= 2^-25.53 float
*
* Here poly1-3 are odd polynomial with the following form:
* x + x^3*(a1+x^2*(a2+...))
*
* (0). Purge off Inf and NaN and 0
* (1). Reduce x to positive by atan(x) = -atan(-x).
* (2). For x <= 1/8, use
* (2.1) if x < 2^(-prec/2-2), atan(x) = x with inexact
* (2.2) Otherwise
* atan(x) = poly1(x)
* (3). For x >= 8 then
* (3.1) if x >= 2^(prec+2), atan(x) = atan(inf) - pio2lo
* (3.2) if x >= 2^(prec/3+2), atan(x) = atan(inf) - 1/x
* (3.3) if x > 65, atan(x) = atan(inf) - poly2(1/x)
* (3.4) Otherwise, atan(x) = atan(inf) - poly1(1/x)
*
* (4). Now x is in (0.125, 8)
* Find y that match x to 4.5 bit after binary (easy).
* If iy is the high word of y, then
* single : j = (iy - 0x3e000000) >> 19
* (single is modified to (iy-0x3f000000)>>19)
* double : j = (iy - 0x3fc00000) >> 16
* quad : j = (iy - 0x3ffc0000) >> 12
*
* Let s = (x-y)/(1+x*y). Then
* atan(x) = atan(y) + poly1(s)
* = _TBL_r_atan_hi[j] + (_TBL_r_atan_lo[j] + poly2(s) )
*
* Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
*
*/
#include "libm.h"
extern const float _TBL_r_atan_hi[], _TBL_r_atan_lo[];
static const float
big = 1.0e37F,
one = 1.0F,
p1 = -3.333185951111688247225368498733544672172e-0001F,
p2 = 1.969352894213455405211341983203180636021e-0001F,
q1 = -3.332921964095646819563419704110132937456e-0001F,
a1 = -3.333323465223893614063523351509338934592e-0001F,
a2 = 1.999425625935277805494082274808174062403e-0001F,
a3 = -1.417547090509737780085769846290301788559e-0001F,
a4 = 1.016250813871991983097273733227432685084e-0001F,
a5 = -5.137023693688358515753093811791755221805e-0002F,
pio2hi = 1.570796371e+0000F,
pio2lo = -4.371139000e-0008F;
/* INDENT ON */
float
atanf(float xx) {
float x, y, z, r, p, s;
volatile double dummy;
int ix, iy, sign, j;
x = xx;
ix = *(int *) &x;
sign = ix & 0x80000000;
ix ^= sign;
/* for |x| < 1/8 */
if (ix < 0x3e000000) {
if (ix < 0x38800000) { /* if |x| < 2**(-prec/2-2) */
dummy = big + x; /* get inexact flag if x != 0 */
#ifdef lint
dummy = dummy;
#endif
return (x);
}
z = x * x;
if (ix < 0x3c000000) { /* if |x| < 2**(-prec/4-1) */
x = x + (x * z) * p1;
return (x);
} else {
x = x + (x * z) * (p1 + z * p2);
return (x);
}
}
/* for |x| >= 8.0 */
if (ix >= 0x41000000) {
*(int *) &x = ix;
if (ix < 0x42820000) { /* x < 65 */
r = one / x;
z = r * r;
y = r * (one + z * (p1 + z * p2)); /* poly1 */
y -= pio2lo;
} else if (ix < 0x44800000) { /* x < 2**(prec/3+2) */
r = one / x;
z = r * r;
y = r * (one + z * q1); /* poly2 */
y -= pio2lo;
} else if (ix < 0x4c800000) { /* x < 2**(prec+2) */
y = one / x - pio2lo;
} else if (ix < 0x7f800000) { /* x < inf */
y = -pio2lo;
} else { /* x is inf or NaN */
if (ix > 0x7f800000) {
return (x * x); /* - -> * for Cheetah */
}
y = -pio2lo;
}
if (sign == 0)
x = pio2hi - y;
else
x = y - pio2hi;
return (x);
}
/* now x is between 1/8 and 8 */
if (ix < 0x3f000000) { /* between 1/8 and 1/2 */
z = x * x;
x = x + (x * z) * (a1 + z * (a2 + z * (a3 + z * (a4 +
z * a5))));
return (x);
}
*(int *) &x = ix;
iy = (ix + 0x00040000) & 0x7ff80000;
*(int *) &y = iy;
j = (iy - 0x3f000000) >> 19;
if (ix == iy)
p = x - y; /* p=0.0 */
else {
if (sign == 0)
s = (x - y) / (one + x * y);
else
s = (y - x) / (one + x * y);
z = s * s;
p = s * (one + z * q1);
}
if (sign == 0) {
r = p + _TBL_r_atan_lo[j];
x = r + _TBL_r_atan_hi[j];
} else {
r = p - _TBL_r_atan_lo[j];
x = r - _TBL_r_atan_hi[j];
}
return (x);
}
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