From e3aa1d5d0d457203bfefccb61a665eaffed7822f Mon Sep 17 00:00:00 2001 From: drepper Date: Tue, 17 Apr 2001 06:47:52 +0000 Subject: [PATCH] tan implementation for 128-bit long double. --- sysdeps/ieee754/ldbl-128/k_tanl.c | 147 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 147 insertions(+) create mode 100644 sysdeps/ieee754/ldbl-128/k_tanl.c diff --git a/sysdeps/ieee754/ldbl-128/k_tanl.c b/sysdeps/ieee754/ldbl-128/k_tanl.c new file mode 100644 index 0000000000..3d8e0342e8 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/k_tanl.c @@ -0,0 +1,147 @@ +/* + * ==================================================== + * 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 +*/ + +/* __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))) + */ + +#include "math.h" +#include "math_private.h" +#ifdef __STDC__ +static const long double +#else +static long double +#endif + one = 1.0L, + 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 */ + + +#ifdef __STDC__ +long double +__kernel_tanl (long double x, long double y, int iy) +#else +long double +__kernel_tanl (x, y, iy) + long double x, y; + int iy; +#endif +{ + long double z, r, v, w, s; + int32_t ix, sign; + ieee854_long_double_shape_type u, u1; + + u.value = x; + ix = u.parts32.w0 & 0x7fffffff; + if (ix < 0x3fc60000) /* x < 2**-57 */ + { + if ((int) x == 0) + { /* generate inexact */ + if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3 + | (iy + 1)) == 0) + return one / fabs (x); + else + return (iy == 1) ? x : -one / x; + } + } + if (ix >= 0x3ffe5942) /* |x| >= 0.6743316650390625 */ + { + if ((u.parts32.w0 & 0x80000000) != 0) + { + 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 (ix >= 0x3ffe5942) + { + 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.value = w; + u1.parts32.w2 = 0; + u1.parts32.w3 = 0; + v = r - (u1.value - x); /* u1+v = r+x */ + z = -1.0 / w; + u.value = z; + u.parts32.w2 = 0; + u.parts32.w3 = 0; + s = 1.0 + u.value * u1.value; + return u.value + z * (s + u.value * v); + } +} -- 2.11.0