144 lines
5.3 KiB
C
144 lines
5.3 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
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/* origin: FreeBSD /usr/src/lib/msun/ld128/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 "libc/math/libm.h"
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#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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#if LDBL_MANT_DIG == 64
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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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#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
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w * (T25 + w * (T29 + w * T33)))))))
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#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
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w * (T27 + w * T31))))))
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#elif LDBL_MANT_DIG == 113
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/*
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* ld128 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 ~[-3.37e-36, 1.982e-37]
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* |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
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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 = 0x1.5555555555555555555555555553p-2L,
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T5 = 0x1.1111111111111111111111111eb5p-3L,
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T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
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T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
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T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
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T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
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T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
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T17 = 0x1.355824803674477dfcf726649efep-11L,
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T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
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T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
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T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
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T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
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T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
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T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
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T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
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T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
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T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
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T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
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pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
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pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
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static const double
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T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
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T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
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T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
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T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
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T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
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T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
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T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
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T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
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T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
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T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
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#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
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w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 + \
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w * (T45 + w * (T49 + w * (T53 + w * T57)))))))))))))
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#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
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w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 + \
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w * (T47 + w * (T51 + w * T55))))))))))))
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#endif
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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 = RPOLY(w);
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v = z * VPOLY(w);
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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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