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Diffstat (limited to 'sysdeps/ieee754/ldbl-96/k_tanl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/k_tanl.c | 152 |
1 files changed, 0 insertions, 152 deletions
diff --git a/sysdeps/ieee754/ldbl-96/k_tanl.c b/sysdeps/ieee754/ldbl-96/k_tanl.c deleted file mode 100644 index f8641d5ce4..0000000000 --- a/sysdeps/ieee754/ldbl-96/k_tanl.c +++ /dev/null @@ -1,152 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* - Long double expansions are - Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> - and are incorporated herein by permission of the author. The author - reserves the right to distribute this material elsewhere under different - copying permissions. These modifications are distributed here under - the following terms: - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, see - <http://www.gnu.org/licenses/>. */ - -/* __kernel_tanl( x, y, k ) - * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input k indicates whether tan (if k=1) or - * -1/tan (if k= -1) is returned. - * - * Algorithm - * 1. Since tan(-x) = -tan(x), we need only to consider positive x. - * 2. if x < 2^-33, return x with inexact if x!=0. - * 3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2) - * on [0,0.67433]. - * - * Note: tan(x+y) = tan(x) + tan'(x)*y - * ~ tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing tan(x+y), let - * r = x^3 * R(x^2) - * then - * tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y)) - * - * 4. For x in [0.67433,pi/4], let y = pi/4 - x, then - * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) - * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) - */ - -#include <float.h> -#include <math.h> -#include <math_private.h> -#include <libc-diag.h> - -static const long double - one = 1.0L, - pio4hi = 0xc.90fdaa22168c235p-4L, - pio4lo = -0x3.b399d747f23e32ecp-68L, - - /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) - 0 <= x <= 0.6743316650390625 - Peak relative error 8.0e-36 */ - TH = 3.333333333333333333333333333333333333333E-1L, - T0 = -1.813014711743583437742363284336855889393E7L, - T1 = 1.320767960008972224312740075083259247618E6L, - T2 = -2.626775478255838182468651821863299023956E4L, - T3 = 1.764573356488504935415411383687150199315E2L, - T4 = -3.333267763822178690794678978979803526092E-1L, - - U0 = -1.359761033807687578306772463253710042010E8L, - U1 = 6.494370630656893175666729313065113194784E7L, - U2 = -4.180787672237927475505536849168729386782E6L, - U3 = 8.031643765106170040139966622980914621521E4L, - U4 = -5.323131271912475695157127875560667378597E2L; - /* 1.000000000000000000000000000000000000000E0 */ - - -long double -__kernel_tanl (long double x, long double y, int iy) -{ - long double z, r, v, w, s; - long double absx = fabsl (x); - int sign; - - if (absx < 0x1p-33) - { - if ((int) x == 0) - { /* generate inexact */ - if (x == 0 && iy == -1) - return one / fabsl (x); - else if (iy == 1) - { - math_check_force_underflow_nonneg (absx); - return x; - } - else - return -one / x; - } - } - if (absx >= 0.6743316650390625L) - { - if (signbit (x)) - { - x = -x; - y = -y; - sign = -1; - } - else - sign = 1; - z = pio4hi - x; - w = pio4lo - y; - x = z + w; - y = 0.0; - } - z = x * x; - r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4))); - v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z)))); - r = r / v; - - s = z * x; - r = y + z * (s * r + y); - r += TH * s; - w = x + r; - if (absx >= 0.6743316650390625L) - { - v = (long double) iy; - w = (v - 2.0 * (x - (w * w / (w + v) - r))); - /* SIGN is set for arguments that reach this code, but not - otherwise, resulting in warnings that it may be used - uninitialized although in the cases where it is used it has - always been set. */ - DIAG_PUSH_NEEDS_COMMENT; - DIAG_IGNORE_NEEDS_COMMENT (4.8, "-Wmaybe-uninitialized"); - if (sign < 0) - w = -w; - DIAG_POP_NEEDS_COMMENT; - return w; - } - if (iy == 1) - return w; - else - return -1.0 / (x + r); -} |