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+/* Compute sine and cosine of argument optimized with vector.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <errno.h>
+#include <math.h>
+#include <math_private.h>
+#include <x86intrin.h>
+#include <libm-alias-float.h>
+#include "s_sincosf.h"
+
+#define SINCOSF __sincosf_fma
+
+#ifndef SINCOSF
+# define SINCOSF_FUNC __sincosf
+#else
+# define SINCOSF_FUNC SINCOSF
+#endif
+
+/* Chebyshev constants for sin and cos, range -PI/4 - PI/4. */
+static const __v2df V0 = { -0x1.5555555551cd9p-3, -0x1.ffffffffe98aep-2};
+static const __v2df V1 = { 0x1.1111110c2688bp-7, 0x1.55555545c50c7p-5 };
+static const __v2df V2 = { -0x1.a019f8b4bd1f9p-13, -0x1.6c16b348b6874p-10 };
+static const __v2df V3 = { 0x1.71d7264e6b5b4p-19, 0x1.a00eb9ac43ccp-16 };
+static const __v2df V4 = { -0x1.a947e1674b58ap-26, -0x1.23c97dd8844d7p-22 };
+
+/* Chebyshev constants for sin and cos, range 2^-27 - 2^-5. */
+static const __v2df VC0 = { -0x1.555555543d49dp-3, -0x1.fffffff5cc6fdp-2 };
+static const __v2df VC1 = { 0x1.110f475cec8c5p-7, 0x1.55514b178dac5p-5 };
+
+static const __v2df v2ones = { 1.0, 1.0 };
+
+/* Compute the sine and cosine values using Chebyshev polynomials where
+ THETA is the range reduced absolute value of the input
+ and it is less than Pi/4,
+ N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+ whether a sine or cosine approximation is more accurate and
+ SIGNBIT is used to add the correct sign after the Chebyshev
+ polynomial is computed. */
+static void
+reduced_sincos (const double theta, const unsigned int n,
+ const unsigned int signbit, float *sinx, float *cosx)
+{
+ __v2df v2x, v2sx, v2cx;
+ const __v2df v2theta = { theta, theta };
+ const __v2df v2theta2 = v2theta * v2theta;
+ /* Here sinf() and cosf() are calculated using sin Chebyshev polynomial:
+ x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ v2x = V3 + v2theta2 * V4; /* S3+x^2*S4. */
+ v2x = V2 + v2theta2 * v2x; /* S2+x^2*(S3+x^2*S4). */
+ v2x = V1 + v2theta2 * v2x; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
+ v2x = V0 + v2theta2 * v2x; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
+ v2x = v2theta2 * v2x;
+ v2cx = v2ones + v2x;
+ v2sx = v2theta + v2theta * v2x;
+ /* We are operating on |x|, so we need to add back the original
+ signbit for sinf. */
+ /* Determine positive or negative primary interval. */
+ /* Are we in the primary interval of sin or cos? */
+ if ((n & 2) == 0)
+ {
+ const __v2df v2sign =
+ {
+ ones[((n >> 2) & 1) ^ signbit],
+ ones[((n + 2) >> 2) & 1]
+ };
+ v2cx[0] = v2sx[0];
+ v2cx *= v2sign;
+ __v4sf v4sx = _mm_cvtpd_ps (v2cx);
+ *sinx = v4sx[0];
+ *cosx = v4sx[1];
+ }
+ else
+ {
+ const __v2df v2sign =
+ {
+ ones[((n + 2) >> 2) & 1],
+ ones[((n >> 2) & 1) ^ signbit]
+ };
+ v2cx[0] = v2sx[0];
+ v2cx *= v2sign;
+ __v4sf v4sx = _mm_cvtpd_ps (v2cx);
+ *sinx = v4sx[1];
+ *cosx = v4sx[0];
+ }
+}
+
+void
+SINCOSF_FUNC (float x, float *sinx, float *cosx)
+{
+ double theta = x;
+ double abstheta = fabs (theta);
+ uint32_t ix, xi;
+ GET_FLOAT_WORD (xi, x);
+ /* |x| */
+ ix = xi & 0x7fffffff;
+ /* If |x|< Pi/4. */
+ if (ix < 0x3f490fdb)
+ {
+ if (ix >= 0x3d000000) /* |x| >= 2^-5. */
+ {
+ __v2df v2x, v2sx, v2cx;
+ const __v2df v2theta = { theta, theta };
+ const __v2df v2theta2 = v2theta * v2theta;
+ /* Chebyshev polynomial of the form for sin and cos. */
+ v2x = V3 + v2theta2 * V4;
+ v2x = V2 + v2theta2 * v2x;
+ v2x = V1 + v2theta2 * v2x;
+ v2x = V0 + v2theta2 * v2x;
+ v2x = v2theta2 * v2x;
+ v2cx = v2ones + v2x;
+ v2sx = v2theta + v2theta * v2x;
+ v2cx[0] = v2sx[0];
+ __v4sf v4sx = _mm_cvtpd_ps (v2cx);
+ *sinx = v4sx[0];
+ *cosx = v4sx[1];
+ }
+ else if (ix >= 0x32000000) /* |x| >= 2^-27. */
+ {
+ /* A simpler Chebyshev approximation is close enough for this range:
+ for sin: x+x^3*(SS0+x^2*SS1)
+ for cos: 1.0+x^2*(CC0+x^3*CC1). */
+ __v2df v2x, v2sx, v2cx;
+ const __v2df v2theta = { theta, theta };
+ const __v2df v2theta2 = v2theta * v2theta;
+ v2x = VC0 + v2theta * v2theta2 * VC1;
+ v2x = v2theta2 * v2x;
+ v2cx = v2ones + v2x;
+ v2sx = v2theta + v2theta * v2x;
+ v2cx[0] = v2sx[0];
+ __v4sf v4sx = _mm_cvtpd_ps (v2cx);
+ *sinx = v4sx[0];
+ *cosx = v4sx[1];
+ }
+ else
+ {
+ /* Handle some special cases. */
+ if (ix)
+ *sinx = theta - (theta * SMALL);
+ else
+ *sinx = theta;
+ *cosx = 1.0 - abstheta;
+ }
+ }
+ else /* |x| >= Pi/4. */
+ {
+ unsigned int signbit = xi >> 31;
+ if (ix < 0x40e231d6) /* |x| < 9*Pi/4. */
+ {
+ /* There are cases where FE_UPWARD rounding mode can
+ produce a result of abstheta * inv_PI_4 == 9,
+ where abstheta < 9pi/4, so the domain for
+ pio2_table must go to 5 (9 / 2 + 1). */
+ unsigned int n = (abstheta * inv_PI_4) + 1;
+ theta = abstheta - pio2_table[n / 2];
+ reduced_sincos (theta, n, signbit, sinx, cosx);
+ }
+ else if (ix < 0x7f800000)
+ {
+ if (ix < 0x4b000000) /* |x| < 2^23. */
+ {
+ unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
+ double x = n / 2;
+ theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
+ /* Argument reduction needed. */
+ reduced_sincos (theta, n, signbit, sinx, cosx);
+ }
+ else /* |x| >= 2^23. */
+ {
+ x = fabsf (x);
+ int exponent
+ = (ix >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+ exponent += 3;
+ exponent /= 28;
+ double a = invpio4_table[exponent] * x;
+ double b = invpio4_table[exponent + 1] * x;
+ double c = invpio4_table[exponent + 2] * x;
+ double d = invpio4_table[exponent + 3] * x;
+ uint64_t l = a;
+ l &= ~0x7;
+ a -= l;
+ double e = a + b;
+ l = e;
+ e = a - l;
+ if (l & 1)
+ {
+ e -= 1.0;
+ e += b;
+ e += c;
+ e += d;
+ e *= M_PI_4;
+ reduced_sincos (e, l + 1, signbit, sinx, cosx);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ reduced_sincos (e, l + 1, signbit, sinx, cosx);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ reduced_sincos (e, l + 1, signbit, sinx, cosx);
+ }
+ }
+ }
+ }
+ else
+ {
+ if (ix == 0x7f800000)
+ __set_errno (EDOM);
+ /* sin/cos(Inf or NaN) is NaN. */
+ *sinx = *cosx = x - x;
+ }
+ }
+}
+
+#ifndef SINCOSF
+libm_alias_float (__sincos, sincos)
+#endif
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