diff options
Diffstat (limited to 'gnulib/lib/tanl.c')
| m--------- | gnulib | 0 | ||||
| -rw-r--r-- | gnulib/lib/tanl.c | 235 |
2 files changed, 235 insertions, 0 deletions
diff --git a/gnulib b/gnulib deleted file mode 160000 -Subproject 443bc5ffcf7429e557f4a371b0661abe98ddbc1 diff --git a/gnulib/lib/tanl.c b/gnulib/lib/tanl.c new file mode 100644 index 0000000..e5efb06 --- /dev/null +++ b/gnulib/lib/tanl.c @@ -0,0 +1,235 @@ +/* s_tanl.c -- long double version of s_tan.c. + * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. + */ + +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +#include <config.h> + +/* Specification. */ +#include <math.h> + +#if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE + +long double +tanl (long double x) +{ + return tan (x); +} + +#else + +/* tanl(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tanl ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2l ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +# include "trigl.h" + +/* + * ==================================================== + * 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 contributed by + Stephen L. Moshier <moshier@na-net.ornl.gov> +*/ + +/* __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^-57, 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))) + */ + + +static const long double + pio4hi = 7.8539816339744830961566084581987569936977E-1L, + pio4lo = 2.1679525325309452561992610065108379921906E-35L, + + /* 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 */ + + +static long double +kernel_tanl (long double x, long double y, int iy) +{ + long double z, r, v, w, s, u, u1; + int invert = 0, sign; + + sign = 1; + if (x < 0) + { + x = -x; + y = -y; + sign = -1; + } + + if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* x < 2**-57 */ + { + if ((int) x == 0) + { /* generate inexact */ + if (iy == -1 && x == 0.0) + return 1.0L / fabs (x); + else + return (iy == 1) ? x : -1.0L / x; + } + } + if (x >= 0.6743316650390625) /* |x| >= 0.6743316650390625 */ + { + invert = 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 (invert) + { + v = (long double) iy; + w = (v - 2.0 * (x - (w * w / (w + v) - r))); + if (sign < 0) + w = -w; + return w; + } + if (iy == 1) + return w; + else + { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + u1 = (double) w; + v = r - (u1 - x); + z = -1.0 / w; + u = (double) z; + s = 1.0 + u * u1; + return u + z * (s + u * v); + } +} + +long double +tanl (long double x) +{ + long double y[2], z = 0.0L; + int n; + + /* tanl(NaN) is NaN */ + if (isnanl (x)) + return x; + + /* |x| ~< pi/4 */ + if (x >= -0.7853981633974483096156608458198757210492 && + x <= 0.7853981633974483096156608458198757210492) + return kernel_tanl (x, z, 1); + + /* tanl(Inf) is NaN, tanl(0) is 0 */ + else if (x + x == x) + return x - x; /* NaN */ + + /* argument reduction needed */ + else + { + n = ieee754_rem_pio2l (x, y); + /* 1 -- n even, -1 -- n odd */ + return kernel_tanl (y[0], y[1], 1 - ((n & 1) << 1)); + } +} + +#endif + +#if 0 +int +main (void) +{ + printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492)); + printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492)); + printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 *3)); + printf ("%.16Lg\n", tanl (-0.7853981633974483096156608458198757210492 *31)); + printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 / 2)); + printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 3/2)); + printf ("%.16Lg\n", tanl (0.7853981633974483096156608458198757210492 * 5/2)); +} +#endif |