97 lines
3.8 KiB
C
97 lines
3.8 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */
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/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */
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/*
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* ====================================================
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* Copyright (C) 1993 by 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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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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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 __cos.c. See __cos.c for most comments.
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*/
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/*
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* Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]:
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* |cos(x) - c(x)| < 2**-75.1
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*
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* The coefficients of c(x) were generated by a pari-gp script using
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* a Remez algorithm that searches for the best higher coefficients
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* after rounding leading coefficients to a specified precision.
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*
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* Simpler methods like Chebyshev or basic Remez barely suffice for
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* cos() in 64-bit precision, because we want the coefficient of x^2
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* to be precisely -0.5 so that multiplying by it is exact, and plain
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* rounding of the coefficients of a good polynomial approximation only
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* gives this up to about 64-bit precision. Plain rounding also gives
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* a mediocre approximation for the coefficient of x^4, but a rounding
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* error of 0.5 ulps for this coefficient would only contribute ~0.01
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* ulps to the final error, so this is unimportant. Rounding errors in
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* higher coefficients are even less important.
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*
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* In fact, coefficients above the x^4 one only need to have 53-bit
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* precision, and this is more efficient. We get this optimization
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* almost for free from the complications needed to search for the best
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* higher coefficients.
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*/
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static const long double
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C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
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static const double
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C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
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C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
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C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
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C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
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C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
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C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */
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#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7)))))))
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#elif LDBL_MANT_DIG == 113
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/*
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* ld128 version of __cos.c. See __cos.c for most comments.
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*/
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/*
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* Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
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* |cos(x) - c(x))| < 2**-122.0
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*
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* 113-bit precision requires more care than 64-bit precision, since
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* simple methods give a minimax polynomial with coefficient for x^2
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* that is 1 ulp below 0.5, but we want it to be precisely 0.5. See
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* above for more details.
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*/
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static const long double
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C1 = 0.04166666666666666666666666666666658424671L,
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C2 = -0.001388888888888888888888888888863490893732L,
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C3 = 0.00002480158730158730158730158600795304914210L,
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C4 = -0.2755731922398589065255474947078934284324e-6L,
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C5 = 0.2087675698786809897659225313136400793948e-8L,
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C6 = -0.1147074559772972315817149986812031204775e-10L,
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C7 = 0.4779477332386808976875457937252120293400e-13L;
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static const double
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C8 = -0.1561920696721507929516718307820958119868e-15,
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C9 = 0.4110317413744594971475941557607804508039e-18,
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C10 = -0.8896592467191938803288521958313920156409e-21,
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C11 = 0.1601061435794535138244346256065192782581e-23;
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#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \
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z*(C8+z*(C9+z*(C10+z*C11)))))))))))
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#endif
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long double __cosl(long double x, long double y)
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{
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long double hz,z,r,w;
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z = x*x;
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r = POLY(z);
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hz = 0.5*z;
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w = 1.0-hz;
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return w + (((1.0-w)-hz) + (z*r-x*y));
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}
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#endif
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