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/* $OpenBSD: s_sinl.c,v 1.2 2016/09/12 19:47:02 guenther Exp $ */ |
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/*- |
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* Copyright (c) 2007 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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* Compute sin(x) for x where x is reduced to y = x - k * pi / 2. |
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*/ |
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#include <sys/types.h> |
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#include <machine/ieee.h> |
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#include <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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#if LDBL_MANT_DIG == 64 |
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#define NX 3 |
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#define PREC 2 |
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#elif LDBL_MANT_DIG == 113 |
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#define NX 5 |
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#define PREC 3 |
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#else |
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#error "Unsupported long double format" |
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#endif |
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static const long double two24 = 1.67772160000000000000e+07L; |
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long double |
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sinl(long double x) |
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{ |
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union { |
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long double e; |
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struct ieee_ext bits; |
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} z; |
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int i, e0, s; |
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double xd[NX], yd[PREC]; |
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long double hi, lo; |
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z.e = x; |
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s = z.bits.ext_sign; |
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z.bits.ext_sign = 0; |
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/* If x = +-0 or x is a subnormal number, then sin(x) = x */ |
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✓✓ |
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if (z.bits.ext_exp == 0) |
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return (x); |
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/* If x = NaN or Inf, then sin(x) = NaN. */ |
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✗✓ |
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if (z.bits.ext_exp == 32767) |
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return ((x - x) / (x - x)); |
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/* Optimize the case where x is already within range. */ |
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✓✓ |
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if (z.e < M_PI_4) { |
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hi = __kernel_sinl(z.e, 0, 0); |
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return (s ? -hi : hi); |
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} |
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/* Split z.e into a 24-bit representation. */ |
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e0 = ilogbl(z.e) - 23; |
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z.e = scalbnl(z.e, -e0); |
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✓✓ |
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for (i = 0; i < NX; i++) { |
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xd[i] = (double)((int32_t)z.e); |
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z.e = (z.e - xd[i]) * two24; |
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} |
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/* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ |
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e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); |
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#if PREC == 2 |
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hi = (long double)yd[0] + yd[1]; |
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lo = yd[1] - (hi - yd[0]); |
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#else /* PREC == 3 */ |
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long double t; |
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t = (long double)yd[2] + yd[1]; |
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hi = t + yd[0]; |
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lo = yd[0] - (hi - t); |
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#endif |
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✗✓✓✗
✗ |
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switch (e0 & 3) { |
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case 0: |
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hi = __kernel_sinl(hi, lo, 1); |
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break; |
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case 1: |
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hi = __kernel_cosl(hi, lo); |
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break; |
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case 2: |
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hi = - __kernel_sinl(hi, lo, 1); |
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break; |
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case 3: |
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hi = - __kernel_cosl(hi, lo); |
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break; |
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} |
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return (s ? -hi : hi); |
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} |
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DEF_STD(sinl); |