dce5f3abed
Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle
trignometric functions cospi, sinpi, and tanpi. The attached
patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited
testing on the cospi and sinpi reveal a max ULP less than 0.89;
while tanpi is more problematic with a max ULP less than 2.01
in the interval [0,0.5]. The algorithms used in these functions
are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c.
Note. I no longer have access to a system with ld128 and
adequate support to compile and test the ld128 implementations
of these functions. Given the almost complete lack of input from
others on improvements to libm, I doubt that anyone cares. If
someone does care, the ld128 files contain a number of FIXME comments,
and in particular, while the polynomial coefficients are given
I did not update the polynomial algorithms to properly use the
coefficients.
PR: 218514
MFC after: 2 weeks
140 lines
3.5 KiB
C
140 lines
3.5 KiB
C
/*-
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* Copyright (c) 2017 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, 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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RETURNI((ax - ax) / (ax - ax));
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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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/* Determine integer part of ax. */
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j0 = ix - 0x3fff + 1;
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if (j0 < 32) {
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lx = (lx >> 32) << 32;
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lx &= ~(((lx << 32)-1) >> j0);
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} else {
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m = (uint64_t)-1 >> (j0 + 1);
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if (lx & m) lx &= ~m;
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}
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INSERT_LDBL80_WORDS(x, ix, lx);
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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 = ax == 0 ? 0 : __kernel_tanpil(ax);
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else if (ax == 0.5)
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RETURNI((ax - ax) / (ax - ax));
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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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* |x| >= 0x1p63 is always an integer, so return +-0.
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*/
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RETURNI(copysignl(0, x));
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}
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