mirror of
https://github.com/jart/cosmopolitan.git
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3a8e01a77a
Somehow or another, I previously had missed `BUILD.mk` files. In the process I found a few straggler cases where the modeline was different from the file, including one very involved manual fix where a file had been treated like it was ts=2 and ts=8 on separate occasions. The commit history in the PR shows the gory details; the BUILD.mk was automated, everything else was mostly manual.
522 lines
17 KiB
C
522 lines
17 KiB
C
/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
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│ vi: set noet ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi │
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╞══════════════════════════════════════════════════════════════════════════════╡
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│ Copyright 2023 Justine Alexandra Roberts Tunney │
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│ │
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│ Permission to use, copy, modify, and/or distribute this software for │
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│ any purpose with or without fee is hereby granted, provided that the │
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│ above copyright notice and this permission notice appear in all copies. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL │
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│ WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED │
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│ WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE │
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│ AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL │
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│ DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR │
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│ PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER │
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│ TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR │
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│ PERFORMANCE OF THIS SOFTWARE. │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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#include "libc/tinymath/internal.h"
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asm(".ident\t\"\\n\\n\
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OpenBSD libm (ISC License)\\n\
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Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/*
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* Exponential function, long double precision
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, expl();
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*
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* y = expl( x );
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*
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*
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* DESCRIPTION:
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*
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* Returns e (2.71828...) raised to the x power.
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*
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* Range reduction is accomplished by separating the argument
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* into an integer k and fraction f such that
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*
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* x k f
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* e = 2 e.
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*
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* A Pade' form of degree 5/6 is used to approximate exp(f) - 1
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* in the basic range [-0.5 ln 2, 0.5 ln 2].
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE +-10000 50000 1.12e-19 2.81e-20
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*
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*
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* Error amplification in the exponential function can be
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* a serious matter. The error propagation involves
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* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
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* which shows that a 1 lsb error in representing X produces
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* a relative error of X times 1 lsb in the function.
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* While the routine gives an accurate result for arguments
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* that are exactly represented by a long double precision
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* computer number, the result contains amplified roundoff
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* error for large arguments not exactly represented.
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* exp underflow x < MINLOG 0.0
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* exp overflow x > MAXLOG MAXNUM
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*
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*/
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static const long double P[3] = {
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1.2617719307481059087798E-4L,
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3.0299440770744196129956E-2L,
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9.9999999999999999991025E-1L,
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};
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static const long double Q[4] = {
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3.0019850513866445504159E-6L,
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2.5244834034968410419224E-3L,
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2.2726554820815502876593E-1L,
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2.0000000000000000000897E0L,
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};
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static const long double
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LN2HI = 6.9314575195312500000000E-1L,
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LN2LO = 1.4286068203094172321215E-6L,
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LOG2E = 1.4426950408889634073599E0L;
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/**
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* Returns 𝑒ˣ.
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*/
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long double expl(long double x)
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{
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long double px, xx;
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int k;
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if (isnan(x))
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return x;
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if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
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return x * 0x1p16383L;
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if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
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return -0x1p-16445L/x;
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/* Express e**x = e**f 2**k
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* = e**(f + k ln(2))
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*/
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px = floorl(LOG2E * x + 0.5);
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k = px;
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x -= px * LN2HI;
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x -= px * LN2LO;
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/* rational approximation of the fractional part:
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* e**x = 1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
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*/
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xx = x * x;
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px = x * __polevll(xx, P, 2);
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x = px/(__polevll(xx, Q, 3) - px);
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x = 1.0 + 2.0 * x;
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return scalbnl(x, k);
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}
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#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
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#include "libc/tinymath/freebsd.internal.h"
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asm(".ident\t\"\\n\\n\
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FreeBSD libm (BSD-2 License)\\n\
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Copyright (c) 2005-2011, Bruce D. Evans, Steven G. Kargl, David Schultz.\"");
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asm(".ident\t\"\\n\\n\
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fdlibm (fdlibm license)\\n\
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Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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asm(".include \"libc/disclaimer.inc\"");
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// clang-format off
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/*-
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* SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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*
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* Copyright (c) 2009-2013 Steven G. Kargl
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice unmodified, this list of conditions, and the following
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* disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Optimized by Bruce D. Evans.
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*/
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/*
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* ld128 version of s_expl.c. See ../ld80/s_expl.c for most comments.
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*/
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/* XXX Prevent compilers from erroneously constant folding these: */
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static const volatile long double
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huge = 0x1p10000L,
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tiny = 0x1p-10000L;
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static const long double
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twom10000 = 0x1p-10000L;
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static const long double
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/* log(2**16384 - 0.5) rounded towards zero: */
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/* log(2**16384 - 0.5 + 1) rounded towards zero for expm1l() is the same: */
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o_threshold = 11356.523406294143949491931077970763428L,
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/* log(2**(-16381-64-1)) rounded towards zero: */
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u_threshold = -11433.462743336297878837243843452621503L;
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static const double
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/*
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* ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
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* have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
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* bits zero so that multiplication of it by n is exact.
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*/
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INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
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L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
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static const long double
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/* 0x1.62e42fefa39ef35793c768000000p-8 */
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L1 = 5.41521234812457272982212595914567508e-3L;
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/*
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* XXX values in hex in comments have been lost (or were never present)
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* from here.
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*/
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static const long double
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/*
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* Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
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* |exp(x) - p(x)| < 2**-124.9
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* (0.002708 is ln2/(2*INTERVALS) rounded up a little).
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*
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* XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits.
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*/
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A2 = 0.5,
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A3 = 1.66666666666666666666666666651085500e-1L,
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A4 = 4.16666666666666666666666666425885320e-2L,
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A5 = 8.33333333333333333334522877160175842e-3L,
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A6 = 1.38888888888888888889971139751596836e-3L;
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static const double
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A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */
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A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */
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A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */
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A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */
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/**
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* Returns 𝑒ˣ.
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*/
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long double
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expl(long double x)
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{
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union IEEEl2bits u;
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long double hi, lo, t, twopk;
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int k;
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uint16_t hx, ix;
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DOPRINT_START(&x);
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/* Filter out exceptional cases. */
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u.e = x;
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hx = u.xbits.expsign;
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ix = hx & 0x7fff;
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if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
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if (ix == BIAS + LDBL_MAX_EXP) {
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if (hx & 0x8000) /* x is -Inf or -NaN */
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RETURNP(-1 / x);
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RETURNP(x + x); /* x is +Inf or +NaN */
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}
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if (x > o_threshold)
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RETURNP(huge * huge);
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if (x < u_threshold)
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RETURNP(tiny * tiny);
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} else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */
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RETURN2P(1, x); /* 1 with inexact iff x != 0 */
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}
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ENTERI();
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twopk = 1;
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__k_expl(x, &hi, &lo, &k);
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t = SUM2P(hi, lo);
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/* Scale by 2**k. */
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/*
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* XXX sparc64 multiplication was so slow that scalbnl() is faster,
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* but performance on aarch64 and riscv hasn't yet been quantified.
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*/
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if (k >= LDBL_MIN_EXP) {
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if (k == LDBL_MAX_EXP)
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RETURNI(t * 2 * 0x1p16383L);
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SET_LDBL_EXPSIGN(twopk, BIAS + k);
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RETURNI(t * twopk);
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} else {
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SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000);
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RETURNI(t * twopk * twom10000);
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}
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}
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/*
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* Our T1 and T2 are chosen to be approximately the points where method
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* A and method B have the same accuracy. Tang's T1 and T2 are the
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* points where method A's accuracy changes by a full bit. For Tang,
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* this drop in accuracy makes method A immediately less accurate than
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* method B, but our larger INTERVALS makes method A 2 bits more
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* accurate so it remains the most accurate method significantly
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* closer to the origin despite losing the full bit in our extended
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* range for it.
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*
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* Split the interval [T1, T2] into two intervals [T1, T3] and [T3, T2].
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* Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear
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* in both subintervals, so set T3 = 2**-5, which places the condition
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* into the [T1, T3] interval.
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*
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* XXX we now do this more to (partially) balance the number of terms
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* in the C and D polys than to avoid checking the condition in both
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* intervals.
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*
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* XXX these micro-optimizations are excessive.
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*/
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static const double
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T1 = -0.1659, /* ~-30.625/128 * log(2) */
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T2 = 0.1659, /* ~30.625/128 * log(2) */
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T3 = 0.03125;
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/*
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* Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]:
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* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03
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*
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* XXX none of the long double C or D coeffs except C10 is correctly printed.
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* If you re-print their values in %.35Le format, the result is always
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* different. For example, the last 2 digits in C3 should be 59, not 67.
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* 67 is apparently from rounding an extra-precision value to 36 decimal
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* places.
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*/
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static const long double
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C3 = 1.66666666666666666666666666666666667e-1L,
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C4 = 4.16666666666666666666666666666666645e-2L,
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C5 = 8.33333333333333333333333333333371638e-3L,
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C6 = 1.38888888888888888888888888891188658e-3L,
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C7 = 1.98412698412698412698412697235950394e-4L,
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C8 = 2.48015873015873015873015112487849040e-5L,
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C9 = 2.75573192239858906525606685484412005e-6L,
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C10 = 2.75573192239858906612966093057020362e-7L,
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C11 = 2.50521083854417203619031960151253944e-8L,
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C12 = 2.08767569878679576457272282566520649e-9L,
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C13 = 1.60590438367252471783548748824255707e-10L;
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/*
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* XXX this has 1 more coeff than needed.
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* XXX can start the double coeffs but not the double mults at C10.
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* With my coeffs (C10-C17 double; s = best_s):
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* Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]:
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* |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
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*/
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static const double
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C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */
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C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */
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C16 = 4.7793721460260450e-14, /* 0x1.ae7cd18a18eacp-45 */
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C17 = 2.8074757356658877e-15, /* 0x1.949992a1937d9p-49 */
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C18 = 1.4760610323699476e-16; /* 0x1.545b43aabfbcdp-53 */
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/*
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* Domain [0.03125, 0.1659], range ~[-2.7676e-37, -1.0367e-38]:
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* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-121.44
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*/
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static const long double
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D3 = 1.66666666666666666666666666666682245e-1L,
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D4 = 4.16666666666666666666666666634228324e-2L,
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D5 = 8.33333333333333333333333364022244481e-3L,
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D6 = 1.38888888888888888888887138722762072e-3L,
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D7 = 1.98412698412698412699085805424661471e-4L,
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D8 = 2.48015873015873015687993712101479612e-5L,
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D9 = 2.75573192239858944101036288338208042e-6L,
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D10 = 2.75573192239853161148064676533754048e-7L,
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D11 = 2.50521083855084570046480450935267433e-8L,
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D12 = 2.08767569819738524488686318024854942e-9L,
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D13 = 1.60590442297008495301927448122499313e-10L;
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/*
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* XXX this has 1 more coeff than needed.
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* XXX can start the double coeffs but not the double mults at D11.
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* With my coeffs (D11-D16 double):
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* Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]:
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* |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
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*/
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static const double
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D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */
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D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */
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D16 = 4.7628892832607741e-14, /* 0x1.ad00Dfe41feccp-45 */
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D17 = 3.0524857220358650e-15; /* 0x1.D7e8d886Df921p-49 */
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/**
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* Returns 𝑒ˣ-1.
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*/
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long double
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expm1l(long double x)
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{
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union IEEEl2bits u, v;
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long double hx2_hi, hx2_lo, q, r, r1, t, twomk, twopk, x_hi;
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long double x_lo, x2;
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double dr, dx, fn, r2;
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int k, n, n2;
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uint16_t hx, ix;
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DOPRINT_START(&x);
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/* Filter out exceptional cases. */
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u.e = x;
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hx = u.xbits.expsign;
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ix = hx & 0x7fff;
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if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */
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if (ix == BIAS + LDBL_MAX_EXP) {
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if (hx & 0x8000) /* x is -Inf or -NaN */
|
|
RETURNP(-1 / x - 1);
|
|
RETURNP(x + x); /* x is +Inf or +NaN */
|
|
}
|
|
if (x > o_threshold)
|
|
RETURNP(huge * huge);
|
|
/*
|
|
* expm1l() never underflows, but it must avoid
|
|
* unrepresentable large negative exponents. We used a
|
|
* much smaller threshold for large |x| above than in
|
|
* expl() so as to handle not so large negative exponents
|
|
* in the same way as large ones here.
|
|
*/
|
|
if (hx & 0x8000) /* x <= -128 */
|
|
RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */
|
|
}
|
|
|
|
ENTERI();
|
|
|
|
if (T1 < x && x < T2) {
|
|
x2 = x * x;
|
|
dx = x;
|
|
|
|
if (x < T3) {
|
|
if (ix < BIAS - 113) { /* |x| < 0x1p-113 */
|
|
/* x (rounded) with inexact if x != 0: */
|
|
RETURNPI(x == 0 ? x :
|
|
(0x1p200 * x + fabsl(x)) * 0x1p-200);
|
|
}
|
|
q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 +
|
|
x * (C7 + x * (C8 + x * (C9 + x * (C10 +
|
|
x * (C11 + x * (C12 + x * (C13 +
|
|
dx * (C14 + dx * (C15 + dx * (C16 +
|
|
dx * (C17 + dx * C18))))))))))))));
|
|
} else {
|
|
q = x * x2 * D3 + x2 * x2 * (D4 + x * (D5 + x * (D6 +
|
|
x * (D7 + x * (D8 + x * (D9 + x * (D10 +
|
|
x * (D11 + x * (D12 + x * (D13 +
|
|
dx * (D14 + dx * (D15 + dx * (D16 +
|
|
dx * D17)))))))))))));
|
|
}
|
|
|
|
x_hi = (float)x;
|
|
x_lo = x - x_hi;
|
|
hx2_hi = x_hi * x_hi / 2;
|
|
hx2_lo = x_lo * (x + x_hi) / 2;
|
|
if (ix >= BIAS - 7)
|
|
RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q);
|
|
else
|
|
RETURN2PI(x, hx2_lo + q + hx2_hi);
|
|
}
|
|
|
|
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
|
|
fn = rnint((double)x * INV_L);
|
|
n = irint(fn);
|
|
n2 = (unsigned)n % INTERVALS;
|
|
k = n >> LOG2_INTERVALS;
|
|
r1 = x - fn * L1;
|
|
r2 = fn * -L2;
|
|
r = r1 + r2;
|
|
|
|
/* Prepare scale factor. */
|
|
v.e = 1;
|
|
v.xbits.expsign = BIAS + k;
|
|
twopk = v.e;
|
|
|
|
/*
|
|
* Evaluate lower terms of
|
|
* expl(endpoint[n2] + r1 + r2) = kExplData[n2] * expl(r1 + r2).
|
|
*/
|
|
dr = r;
|
|
q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
|
|
dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
|
|
|
|
t = kExplData[n2].lo + kExplData[n2].hi;
|
|
|
|
if (k == 0) {
|
|
t = SUM2P(kExplData[n2].hi - 1, kExplData[n2].lo * (r1 + 1) + t * q +
|
|
kExplData[n2].hi * r1);
|
|
RETURNI(t);
|
|
}
|
|
if (k == -1) {
|
|
t = SUM2P(kExplData[n2].hi - 2, kExplData[n2].lo * (r1 + 1) + t * q +
|
|
kExplData[n2].hi * r1);
|
|
RETURNI(t / 2);
|
|
}
|
|
if (k < -7) {
|
|
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo + t * (q + r1));
|
|
RETURNI(t * twopk - 1);
|
|
}
|
|
if (k > 2 * LDBL_MANT_DIG - 1) {
|
|
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo + t * (q + r1));
|
|
if (k == LDBL_MAX_EXP)
|
|
RETURNI(t * 2 * 0x1p16383L - 1);
|
|
RETURNI(t * twopk - 1);
|
|
}
|
|
|
|
v.xbits.expsign = BIAS - k;
|
|
twomk = v.e;
|
|
|
|
if (k > LDBL_MANT_DIG - 1)
|
|
t = SUM2P(kExplData[n2].hi, kExplData[n2].lo - twomk + t * (q + r1));
|
|
else
|
|
t = SUM2P(kExplData[n2].hi - twomk, kExplData[n2].lo + t * (q + r1));
|
|
RETURNI(t * twopk);
|
|
}
|
|
|
|
#endif
|