summaryrefslogtreecommitdiff
path: root/usr/src/libm/src/Q/atanl.c
diff options
context:
space:
mode:
Diffstat (limited to 'usr/src/libm/src/Q/atanl.c')
-rw-r--r--usr/src/libm/src/Q/atanl.c208
1 files changed, 208 insertions, 0 deletions
diff --git a/usr/src/libm/src/Q/atanl.c b/usr/src/libm/src/Q/atanl.c
new file mode 100644
index 0000000..9e77162
--- /dev/null
+++ b/usr/src/libm/src/Q/atanl.c
@@ -0,0 +1,208 @@
+/*
+ * 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 2006 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#pragma ident "@(#)atanl.c 1.12 06/01/31 SMI"
+
+#pragma weak atanl = __atanl
+
+/*
+ * atanl(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
+ * Here poly1 and poly2 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
+ * 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_atanl_hi[j] + (_TBL_atanl_lo[j] + poly2(s) )
+ *
+ * Note. |s| <= 1.5384615385e-02 = 1/65. Maxium occurs at x = 1.03125
+ *
+ */
+
+#include "libm.h"
+
+extern const long double _TBL_atanl_hi[], _TBL_atanl_lo[];
+static const long double
+ one = 1.0L,
+ p1 = -3.333333333333333333333333333331344526118e-0001L,
+ p2 = 1.999999999999999999999999989931277668570e-0001L,
+ p3 = -1.428571428571428571428553606221309530901e-0001L,
+ p4 = 1.111111111111111111095219842737139747418e-0001L,
+ p5 = -9.090909090909090825503603835248061123323e-0002L,
+ p6 = 7.692307692307664052130743214708925258904e-0002L,
+ p7 = -6.666666666660213835187713228363717388266e-0002L,
+ p8 = 5.882352940152439399097283359608661949504e-0002L,
+ p9 = -5.263157780447533993046614040509529668487e-0002L,
+ p10 = 4.761895816878184933175855990886788439447e-0002L,
+ p11 = -4.347345005832274022681019724553538135922e-0002L,
+ p12 = 3.983031914579635037502589204647752042736e-0002L,
+ p13 = -3.348206704469830575196657749413894897554e-0002L,
+ q1 = -3.333333333333333333333333333195273650186e-0001L,
+ q2 = 1.999999999999999999999988146114392615808e-0001L,
+ q3 = -1.428571428571428571057630319435467111253e-0001L,
+ q4 = 1.111111111111105373263048208994541544098e-0001L,
+ q5 = -9.090909090421834209167373258681021816441e-0002L,
+ q6 = 7.692305377813692706850171767150701644539e-0002L,
+ q7 = -6.660896644393861499914731734305717901330e-0002L,
+ pio2hi = 1.570796326794896619231321691639751398740e+0000L,
+ pio2lo = 4.335905065061890512398522013021675984381e-0035L;
+
+#define i0 0
+#define i1 3
+
+long double
+atanl(long double x) {
+ long double y, z, r, p, s;
+ int *px = (int *) &x, *py = (int *) &y;
+ int ix, iy, sign, j;
+
+ ix = px[i0];
+ sign = ix & 0x80000000;
+ ix ^= sign;
+
+ /* for |x| < 1/8 */
+ if (ix < 0x3ffc0000) {
+ if (ix < 0x3feb0000) { /* when |x| < 2**(-prec/6-2) */
+ if (ix < 0x3fc50000) { /* if |x| < 2**(-prec/2-2) */
+ s = one;
+ *(3 - i0 + (int *) &s) = -1; /* s = 1-ulp */
+ *(1 + (int *) &s) = -1;
+ *(2 + (int *) &s) = -1;
+ *(i0 + (int *) &s) -= 1;
+ if ((int) (s * x) < 1)
+ return (x); /* raise inexact */
+ }
+ z = x * x;
+ if (ix < 0x3fe20000) { /* if |x| < 2**(-prec/4-1) */
+ return (x + (x * z) * p1);
+ } else { /* if |x| < 2**(-prec/6-2) */
+ return (x + (x * z) * (p1 + z * p2));
+ }
+ }
+ z = x * x;
+ return (x + (x * z) * (p1 + z * (p2 + z * (p3 + z * (p4 +
+ z * (p5 + z * (p6 + z * (p7 + z * (p8 + z * (p9 +
+ z * (p10 + z * (p11 + z * (p12 + z * p13)))))))))))));
+ }
+
+ /* for |x| >= 8.0 */
+ if (ix >= 0x40020000) {
+ px[i0] = ix;
+ if (ix < 0x40050400) { /* x < 65 */
+ r = one / x;
+ z = r * r;
+ /*
+ * poly1
+ */
+ y = r * (one + z * (p1 + z * (p2 + z * (p3 +
+ z * (p4 + z * (p5 + z * (p6 + z * (p7 +
+ z * (p8 + z * (p9 + z * (p10 + z * (p11 +
+ z * (p12 + z * p13)))))))))))));
+ y -= pio2lo;
+ } else if (ix < 0x40260000) { /* x < 2**(prec/3+2) */
+ r = one / x;
+ z = r * r;
+ /*
+ * poly2
+ */
+ y = r * (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
+ z * (q5 + z * (q6 + z * q7)))))));
+ y -= pio2lo;
+ } else if (ix < 0x40720000) { /* x < 2**(prec+2) */
+ y = one / x - pio2lo;
+ } else if (ix < 0x7fff0000) { /* x < inf */
+ y = -pio2lo;
+ } else { /* x is inf or NaN */
+ if (((ix - 0x7fff0000) | px[1] | px[2] | px[i1]) != 0)
+ return (x - x);
+ y = -pio2lo;
+ }
+
+ if (sign == 0)
+ return (pio2hi - y);
+ else
+ return (y - pio2hi);
+ }
+
+ /* now x is between 1/8 and 8 */
+ px[i0] = ix;
+ iy = (ix + 0x00000800) & 0x7ffff000;
+ py[i0] = iy;
+ py[1] = py[2] = py[i1] = 0;
+ j = (iy - 0x3ffc0000) >> 12;
+
+ if (sign == 0)
+ s = (x - y) / (one + x * y);
+ else
+ s = (y - x) / (one + x * y);
+ z = s * s;
+ if (ix == iy)
+ p = s * (one + z * (q1 + z * (q2 + z * (q3 + z * q4))));
+ else
+ p = s * (one + z * (q1 + z * (q2 + z * (q3 + z * (q4 +
+ z * (q5 + z * (q6 + z * q7)))))));
+ if (sign == 0) {
+ r = p + _TBL_atanl_lo[j];
+ return (r + _TBL_atanl_hi[j]);
+ } else {
+ r = p - _TBL_atanl_lo[j];
+ return (r - _TBL_atanl_hi[j]);
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-29 02:23:32 +0000