/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
+/* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */
/*
* ====================================================
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
#include "libm.h"
-#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#if LDBL_MANT_DIG == 64
/*
* ld80 version of __tan.c. See __tan.c for most comments.
*/
*
* 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 */
T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
+#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
+ w * (T25 + w * (T29 + w * T33)))))))
+#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
+ w * (T27 + w * T31))))))
+#elif LDBL_MANT_DIG == 113
+/*
+ * ld128 version of __tan.c. See __tan.c for most comments.
+ */
+/*
+ * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37]
+ * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37)
+ *
+ * See __cosl.c for more details about the polynomial.
+ */
+static const long double
+T3 = 0x1.5555555555555555555555555553p-2L,
+T5 = 0x1.1111111111111111111111111eb5p-3L,
+T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L,
+T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L,
+T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L,
+T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L,
+T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L,
+T17 = 0x1.355824803674477dfcf726649efep-11L,
+T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L,
+T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L,
+T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L,
+T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L,
+T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L,
+T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L,
+T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L,
+T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L,
+T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L,
+T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L,
+pio4 = 0x1.921fb54442d18469898cc51701b8p-1L,
+pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L;
+static const double
+T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */
+T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */
+T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */
+T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */
+T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */
+T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */
+T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */
+T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */
+T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */
+T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */
+#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \
+ w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 + \
+ w * (T45 + w * (T49 + w * (T53 + w * T57)))))))))))))
+#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \
+ w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 + \
+ w * (T47 + w * (T51 + w * T55))))))))))))
+#endif
-long double __tanl(long double x, long double y, int iy) {
+long double __tanl(long double x, long double y, int odd) {
long double z, r, v, w, s, a, t;
- long double osign;
- int i;
+ int big, sign;
- 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) {
+ big = fabsl(x) >= 0.67434;
+ if (big) {
+ sign = 0;
if (x < 0) {
+ sign = 1;
x = -x;
y = -y;
}
- z = pio4 - x;
- w = pio4lo - y;
- x = z + w;
+ x = (pio4 - x) + (pio4lo - y);
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))))));
+ r = RPOLY(w);
+ v = z * VPOLY(w);
s = z * x;
- r = y + z * (s * (r + v) + y);
- r += T3 * s;
+ r = y + z * (s * (r + v) + y) + T3 * s;
w = x + r;
- if (i == 1) {
- v = (long double)iy;
- return osign * (v - 2.0 * (x - (w * w / (w + v) - r)));
+ if (big) {
+ s = 1 - 2*odd;
+ v = s - 2.0 * (x + (r - w * w / (w + s)));
+ return sign ? -v : v;
}
- if (iy == 1)
+ if (!odd)
return w;
-
/*
* if allow error up to 2 ulp, simply return
* -1.0 / (x+r) here