diff options
Diffstat (limited to 'src/math/__cosl.c')
| -rw-r--r-- | src/math/__cosl.c | 37 |
1 files changed, 34 insertions, 3 deletions
diff --git a/src/math/__cosl.c b/src/math/__cosl.c index 9d325768..fa522ddd 100644 --- a/src/math/__cosl.c +++ b/src/math/__cosl.c @@ -1,4 +1,5 @@ /* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */ +/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. @@ -14,7 +15,8 @@ #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 __cos.c. See __cos.c for most comments. */ @@ -43,7 +45,6 @@ */ static const long double C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */ - static const double C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ @@ -51,13 +52,43 @@ C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */ +#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))))) +#elif LDBL_MANT_DIG == 113 +/* + * ld128 version of __cos.c. See __cos.c for most comments. + */ +/* + * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: + * |cos(x) - c(x))| < 2**-122.0 + * + * 113-bit precision requires more care than 64-bit precision, since + * simple methods give a minimax polynomial with coefficient for x^2 + * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See + * above for more details. + */ +static const long double +C1 = 0.04166666666666666666666666666666658424671L, +C2 = -0.001388888888888888888888888888863490893732L, +C3 = 0.00002480158730158730158730158600795304914210L, +C4 = -0.2755731922398589065255474947078934284324e-6L, +C5 = 0.2087675698786809897659225313136400793948e-8L, +C6 = -0.1147074559772972315817149986812031204775e-10L, +C7 = 0.4779477332386808976875457937252120293400e-13L; +static const double +C8 = -0.1561920696721507929516718307820958119868e-15, +C9 = 0.4110317413744594971475941557607804508039e-18, +C10 = -0.8896592467191938803288521958313920156409e-21, +C11 = 0.1601061435794535138244346256065192782581e-23; +#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \ + z*(C8+z*(C9+z*(C10+z*C11))))))))))) +#endif long double __cosl(long double x, long double y) { long double hz,z,r,w; z = x*x; - r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))); + r = POLY(z); hz = 0.5*z; w = 1.0-hz; return w + (((1.0-w)-hz) + (z*r-x*y)); |