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Diffstat (limited to 'usr/src/lib/libm/common/Q/atanl.c')
| -rw-r--r-- | usr/src/lib/libm/common/Q/atanl.c | 209 |
1 files changed, 209 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/Q/atanl.c b/usr/src/lib/libm/common/Q/atanl.c new file mode 100644 index 0000000000..10b6b71daf --- /dev/null +++ b/usr/src/lib/libm/common/Q/atanl.c @@ -0,0 +1,209 @@ +/* + * 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 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]); + } +} |