cosmopolitan/libc/tinymath/kcosl.c
Justine Tunney 957c61cbbf
Release Cosmopolitan v3.3
This change upgrades to GCC 12.3 and GNU binutils 2.42. The GNU linker
appears to have changed things so that only a single de-duplicated str
table is present in the binary, and it gets placed wherever the linker
wants, regardless of what the linker script says. To cope with that we
need to stop using .ident to embed licenses. As such, this change does
significant work to revamp how third party licenses are defined in the
codebase, using `.section .notice,"aR",@progbits`.

This new GCC 12.3 toolchain has support for GNU indirect functions. It
lets us support __target_clones__ for the first time. This is used for
optimizing the performance of libc string functions such as strlen and
friends so far on x86, by ensuring AVX systems favor a second codepath
that uses VEX encoding. It shaves some latency off certain operations.
It's a useful feature to have for scientific computing for the reasons
explained by the test/libcxx/openmp_test.cc example which compiles for
fifteen different microarchitectures. Thanks to the upgrades, it's now
also possible to use newer instruction sets, such as AVX512FP16, VNNI.

Cosmo now uses the %gs register on x86 by default for TLS. Doing it is
helpful for any program that links `cosmo_dlopen()`. Such programs had
to recompile their binaries at startup to change the TLS instructions.
That's not great, since it means every page in the executable needs to
be faulted. The work of rewriting TLS-related x86 opcodes, is moved to
fixupobj.com instead. This is great news for MacOS x86 users, since we
previously needed to morph the binary every time for that platform but
now that's no longer necessary. The only platforms where we need fixup
of TLS x86 opcodes at runtime are now Windows, OpenBSD, and NetBSD. On
Windows we morph TLS to point deeper into the TIB, based on a TlsAlloc
assignment, and on OpenBSD/NetBSD we morph %gs back into %fs since the
kernels do not allow us to specify a value for the %gs register.

OpenBSD users are now required to use APE Loader to run Cosmo binaries
and assimilation is no longer possible. OpenBSD kernel needs to change
to allow programs to specify a value for the %gs register, or it needs
to stop marking executable pages loaded by the kernel as mimmutable().

This release fixes __constructor__, .ctor, .init_array, and lastly the
.preinit_array so they behave the exact same way as glibc.

We no longer use hex constants to define math.h symbols like M_PI.
2024-02-20 13:27:59 -08:00

127 lines
6.5 KiB
C

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ Musl Libc │
│ Copyright © 2005-2014 Rich Felker, et al. │
│ │
│ Permission is hereby granted, free of charge, to any person obtaining │
│ a copy of this software and associated documentation files (the │
│ "Software"), to deal in the Software without restriction, including │
│ without limitation the rights to use, copy, modify, merge, publish, │
│ distribute, sublicense, and/or sell copies of the Software, and to │
│ permit persons to whom the Software is furnished to do so, subject to │
│ the following conditions: │
│ │
│ The above copyright notice and this permission notice shall be │
│ included in all copies or substantial portions of the Software. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/kernel.internal.h"
__static_yoink("musl_libc_notice");
__static_yoink("fdlibm_notice");
__static_yoink("freebsd_libm_notice");
/* 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.
* ====================================================
*/
#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