diff options
Diffstat (limited to 'src/math/__tanl.c')
| -rw-r--r-- | src/math/__tanl.c | 118 |
1 files changed, 118 insertions, 0 deletions
diff --git a/src/math/__tanl.c b/src/math/__tanl.c new file mode 100644 index 00000000..f842543e --- /dev/null +++ b/src/math/__tanl.c @@ -0,0 +1,118 @@ +/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */ +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include "libm.h" + +#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 +/* + * ld80 version of __tan.c. See __tan.c for most comments. + */ +/* + * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] + * |tan(x)/x - t(x)| < 2**-71.9 + * + * See __cosl.c for more details about the polynomial. + */ + +/* Long double constants are slow on these arches, and broken on i386. */ +static const volatile double +T3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ +T3lo = 1.8350121769317163e-17, /* 0x15280000000000.0p-108 */ +T5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ +T5lo = 1.3051083651294260e-17, /* 0x1e180000000000.0p-109 */ +T7hi = 0.053968253968250494, /* 0x1ba1ba1ba1b827.0p-57 */ +T7lo = 3.1509625637859973e-18, /* 0x1d100000000000.0p-111 */ +pio4_hi = 0.78539816339744828, /* 0x1921fb54442d18.0p-53 */ +pio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ +pio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ +pio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ +#define T3 ((long double)T3hi + T3lo) +#define T5 ((long double)T5hi + T5lo) +#define T7 ((long double)T7hi + T7lo) +#define pio4 ((long double)pio4_hi + pio4_lo) +#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) + +#if 0 +static const long double +T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ +T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ +T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ +pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ +pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ +#endif + +static const double +T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ +T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ +T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ +T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ +T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ +T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ +T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ +T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ +T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ +T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ +T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ +T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ +T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ + +long double __tanl(long double x, long double y, int iy) { + long double z, r, v, w, s, a, t; + long double osign; + int i; + + iy = iy == 1 ? -1 : 1; /* XXX recover original interface */ + // FIXME: this is wrong, use copysign, signbit or union bithack + osign = x >= 0 ? 1.0 : -1.0; /* XXX slow, probably wrong for -0 */ + if (fabsl(x) >= 0.67434) { + if (x < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + i = 1; + } else + i = 0; + z = x * x; + w = z * z; + r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + + w * (T25 + w * (T29 + w * T33)))))); + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + + w * (T27 + w * T31)))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T3 * s; + w = x + r; + if (i == 1) { + v = (long double)iy; + return osign * (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + z = w; + z = z + 0x1p32 - 0x1p32; + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + t = t + 0x1p32 - 0x1p32; + s = 1.0 + t * z; + return t + a * (s + t * v); +} +#endif |