diff options
Diffstat (limited to 'libc-top-half/musl/src/math/__cosl.c')
| -rw-r--r-- | libc-top-half/musl/src/math/__cosl.c | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/__cosl.c b/libc-top-half/musl/src/math/__cosl.c new file mode 100644 index 0000000..fa522dd --- /dev/null +++ b/libc-top-half/musl/src/math/__cosl.c @@ -0,0 +1,96 @@ +/* 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. + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * 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_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 +#if LDBL_MANT_DIG == 64 +/* + * ld80 version of __cos.c. See __cos.c for most comments. + */ +/* + * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]: + * |cos(x) - c(x)| < 2**-75.1 + * + * The coefficients of c(x) were generated by a pari-gp script using + * a Remez algorithm that searches for the best higher coefficients + * after rounding leading coefficients to a specified precision. + * + * Simpler methods like Chebyshev or basic Remez barely suffice for + * cos() in 64-bit precision, because we want the coefficient of x^2 + * to be precisely -0.5 so that multiplying by it is exact, and plain + * rounding of the coefficients of a good polynomial approximation only + * gives this up to about 64-bit precision. Plain rounding also gives + * a mediocre approximation for the coefficient of x^4, but a rounding + * error of 0.5 ulps for this coefficient would only contribute ~0.01 + * ulps to the final error, so this is unimportant. Rounding errors in + * higher coefficients are even less important. + * + * In fact, coefficients above the x^4 one only need to have 53-bit + * precision, and this is more efficient. We get this optimization + * almost for free from the complications needed to search for the best + * higher coefficients. + */ +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 */ +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 = POLY(z); + hz = 0.5*z; + w = 1.0-hz; + return w + (((1.0-w)-hz) + (z*r-x*y)); +} +#endif |