1d5ba3bb5a
* use unsigned arithmetics on the representation * store arg reduction quotient in unsigned (so n%2 would work like n&1) * use different convention to pass the arg reduction bit to __tan (this argument used to be 1 for even and -1 for odd reduction which meant obscure bithacks, the new n&1 is cleaner) * raise inexact and underflow flags correctly for small x (tanl(x) may still raise spurious underflow for small but normal x) (this exception raising code increases codesize a bit, similar fixes are needed in many other places, it may worth investigating at some point if the inexact and underflow flags are worth raising correctly as this is not strictly required by the standard) * tanf manual reduction optimization is kept for now * tanl code path is cleaned up to follow similar logic to tan and tanf
93 lines
3 KiB
C
93 lines
3 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
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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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#include "libm.h"
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#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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/*
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* ld80 version of __tan.c. See __tan.c for most comments.
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*/
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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 __cosl.c for more details about the polynomial.
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*/
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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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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 __tanl(long double x, long double y, int odd) {
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long double z, r, v, w, s, a, t;
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int big, sign;
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big = fabsl(x) >= 0.67434;
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if (big) {
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sign = 0;
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if (x < 0) {
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sign = 1;
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x = -x;
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y = -y;
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}
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x = (pio4 - x) + (pio4lo - y);
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y = 0.0;
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}
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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) + T3 * s;
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w = x + r;
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if (big) {
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s = 1 - 2*odd;
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v = s - 2.0 * (x + (r - w * w / (w + s)));
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return sign ? -v : v;
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}
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if (!odd)
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return w;
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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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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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#endif
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