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2d3b0a687b
patch to fix half-cycle trigonometric functions
Paul Zimmermann, a MPFR developer, contacted me about large errors in
the half-cycle trigonometric functions. I've have investigated these
issues and developed the attached patch. The float, double, and ld80
(long double) changes have been tested.
Caveat emptor: The ld128 changes have not been compiled. The ld128
changes have not been tested. I do not have access to a system that
uses ld128 floating point.
Here is an itemized list of changes:
* lib/msun/src/math_private.h:
. Add fast floor macros to compute the integer part of |x| for
0 <= |x| 01xp(N-1), where N is the precision of the type of x.
These macros are used in the half-cycle trigonometric functions
(e.g., sinpi(x)).
. The FFLOOR80 macros is used with the Intel 80-bit extended double
functions. This macors corrects an off-by-one error, which led to
enormous error for |x| > 0x1p32.
* lib/msun/src/s_cospif.c:
* lib/msun/src/s_cospi.c:
* lib/msun/ld80/s_cospil.c:
. Update Copyright years.
. Use FFLOOR*() macro to get integer part of |x|.
. Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs
to determine if the integral value of |x| is even or odd to choose
+1 or -1. If |x| >= 0x1pN, always return +1.
* lib/msun/src/s_sinpif.c:
* lib/msun/src/s_sinpi.c:
* lib/msun/ld80/s_sinpil.c:
. Update Copyright years.
. Use FFLOOR*() macro to get integer part of |x|.
* lib/msun/src/s_tanpif.c:
* lib/msun/src/s_tanpi.c:
* lib/msun/ld80/s_tanpil.c:
. Update Copyright years.
. For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN.
. Use FFLOOR*() to get integer part of |x|. Need to determine if the
integer part is even or odd. This is used to set +-0 for |x|
integral
and +-inf for (n+1/2).
. For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or
odd
integer to select +0 or -0. For |x| >= 0x1pN, it is always an even
integer, select 0.
. Note, tanpi[fl](x) is an odd function, so one needs to consider
tanpi[fl](-|x|) = - tanpi[fl](|x|).
* lib/msun/ld128/s_cospil.c:
* lib/msun/ld128/s_sinpil.c:
* lib/msun/ld128/s_tanpil.c:
. Update Copyright years.
. These routines use an FFLOOR128 macros, which likely should be
replaced by a bit twiddling algorithm.
. The same considerations above are applied to 0x1p112 <= |x| <
0x1p113,
and |x| >= 0x1p113 cases.
. Note, even and odd determination used fmodl(x,2.), which is likely
slow.
PR: 272742
MFC after: 1 week
134 lines
3.6 KiB
C
134 lines
3.6 KiB
C
/*-
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* Copyright (c) 2017, 2023 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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/*
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* See ../src/s_tanpi.c for implementation details.
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*/
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#ifdef __i386__
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#include <ieeefp.h>
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#endif
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#include <stdint.h>
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#include "fpmath.h"
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#include "math.h"
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#include "math_private.h"
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static const double
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pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
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pi_lo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
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static inline long double
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__kernel_tanpil(long double x)
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{
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long double hi, lo, t;
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if (x < 0.25) {
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hi = (float)x;
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lo = x - hi;
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lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
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hi *= pi_hi;
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_2sumF(hi, lo);
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t = __kernel_tanl(hi, lo, -1);
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} else if (x > 0.25) {
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x = 0.5 - x;
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hi = (float)x;
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lo = x - hi;
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lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
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hi *= pi_hi;
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_2sumF(hi, lo);
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t = - __kernel_tanl(hi, lo, 1);
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} else
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t = 1;
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return (t);
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}
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volatile static const double vzero = 0;
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long double
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tanpil(long double x)
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{
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long double ax, hi, lo, odd, t;
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uint64_t lx, m;
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uint32_t j0;
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uint16_t hx, ix;
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EXTRACT_LDBL80_WORDS(hx, lx, x);
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ix = hx & 0x7fff;
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INSERT_LDBL80_WORDS(ax, ix, lx);
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ENTERI();
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if (ix < 0x3fff) { /* |x| < 1 */
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if (ix < 0x3ffe) { /* |x| < 0.5 */
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if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
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if (x == 0)
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RETURNI(x);
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INSERT_LDBL80_WORDS(hi, hx,
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lx & 0xffffffff00000000ull);
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hi *= 0x1p63L;
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lo = x * 0x1p63L - hi;
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t = (pi_lo + pi_hi) * lo + pi_lo * hi +
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pi_hi * hi;
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RETURNI(t * 0x1p-63L);
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}
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t = __kernel_tanpil(ax);
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} else if (ax == 0.5)
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t = 1 / vzero;
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else
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t = -__kernel_tanpil(1 - ax);
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RETURNI((hx & 0x8000) ? -t : t);
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}
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if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
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FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
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odd = (uint64_t)x & 1 ? -1 : 1;
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ax -= x;
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EXTRACT_LDBL80_WORDS(ix, lx, ax);
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if (ix < 0x3ffe) /* |x| < 0.5 */
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t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
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else if (ax == 0.5L)
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t = odd / vzero;
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else
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t = -__kernel_tanpil(1 - ax);
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RETURNI((hx & 0x8000) ? -t : t);
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}
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/* x = +-inf or nan. */
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if (ix >= 0x7fff)
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RETURNI(vzero / vzero);
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/*
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* For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
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* or odd integer to set t = +0 or -0.
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* For |x| >= 0x1p64, it is always an even integer, so t = 0.
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*/
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t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
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RETURNI((hx & 0x8000) ? -t : t);
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}
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