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/* $OpenBSD: k_tanl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */ |
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/* From: @(#)k_tan.c 1.5 04/04/22 SMI */ |
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/* |
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* ==================================================== |
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* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. |
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. |
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* |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* |
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* ld80 version of k_tan.c. See ../k_tan.c for most comments. |
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*/ |
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#include <math.h> |
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#include "math_private.h" |
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/* |
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* Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] |
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* |tan(x)/x - t(x)| < 2**-71.9 |
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* |
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* See k_cosl.c for more details about the polynomial. |
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*/ |
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#if defined(__amd64__) || defined(__i386__) |
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/* Long double constants are slow on these arches, and broken on i386. */ |
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static const volatile double |
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T3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ |
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T3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */ |
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T5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ |
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T5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */ |
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T7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */ |
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T7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */ |
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pio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */ |
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pio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ |
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pio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ |
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pio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ |
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#define T3 ((long double)T3hi + T3lo) |
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#define T5 ((long double)T5hi + T5lo) |
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#define T7 ((long double)T7hi + T7lo) |
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#define pio4 ((long double)pio4_hi + pio4_lo) |
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#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) |
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#else |
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static const long double |
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T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ |
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T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ |
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T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ |
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pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ |
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pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ |
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#endif |
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static const double |
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T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ |
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T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ |
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T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ |
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T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ |
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T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ |
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T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ |
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T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ |
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T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ |
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T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ |
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T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ |
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T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ |
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T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ |
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T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ |
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long double |
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__kernel_tanl(long double x, long double y, int iy) { |
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long double z, r, v, w, s; |
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long double osign; |
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int i; |
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iy = (iy == 1 ? -1 : 1); /* XXX recover original interface */ |
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osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for -0 */ |
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if (fabsl(x) >= 0.67434) { |
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if (x < 0) { |
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x = -x; |
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y = -y; |
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} |
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z = pio4 - x; |
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w = pio4lo - y; |
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x = z + w; |
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y = 0.0; |
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i = 1; |
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} else |
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i = 0; |
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z = x * x; |
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w = z * z; |
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r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + |
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w * (T25 + w * (T29 + w * T33)))))); |
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v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + |
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w * (T27 + w * T31)))))); |
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s = z * x; |
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r = y + z * (s * (r + v) + y); |
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r += T3 * s; |
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w = x + r; |
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if (i == 1) { |
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v = (long double) iy; |
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return osign * |
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(v - 2.0 * (x - (w * w / (w + v) - r))); |
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} |
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if (iy == 1) |
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return w; |
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else { |
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/* |
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* if allow error up to 2 ulp, simply return |
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* -1.0 / (x+r) here |
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*/ |
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/* compute -1.0 / (x+r) accurately */ |
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long double a, t; |
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z = w; |
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z = z + 0x1p32 - 0x1p32; |
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v = r - (z - x); /* z+v = r+x */ |
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t = a = -1.0 / w; /* a = -1.0/w */ |
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t = t + 0x1p32 - 0x1p32; |
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s = 1.0 + t * z; |
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return t + a * (s + t * v); |
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} |
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} |