@@ -1,7 +1,6 @@
/* Compute sine and cosine of argument.
- Copyright (C) 1997-2017 Free Software Foundation, Inc.
+ Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
- Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@@ -29,53 +28,239 @@
# define SINCOSF_FUNC SINCOSF
#endif
-void
-SINCOSF_FUNC (float x, float *sinx, float *cosx)
+/* Chebyshev constants for sin & cos, range -PI/4 - PI/4. */
+static const double C0 = -0x1.ffffffffe98ae000p-2;
+static const double C1 = 0x1.55555545c50c7000p-5;
+static const double C2 = -0x1.6c16b348b6874000p-10;
+static const double C3 = 0x1.a00eb9ac43cc0000p-16;
+static const double C4 = -0x1.23c97dd8844d7000p-22;
+static const double CC0 = -0x1.fffffff5cc6fd000p-2;
+static const double CC1 = 0x1.55514b178dac5000p-5;
+static const double S0 = -0x1.5555555551cd9000p-3;
+static const double S1 = 0x1.1111110c2688b000p-7;
+static const double S2 = -0x1.a019f8b4bd1f9000p-13;
+static const double S3 = 0x1.71d7264e6b5b4000p-19;
+static const double S4 = -0x1.a947e1674b58a000p-26;
+static const double SS0 = -0x1.555555543d49d000p-3;
+static const double SS1 = 0x1.110f475cec8c5000p-7;
+static const double SMALL = 0x1.0000000000000000p-50;
+static const double inv_PI_4 = 0x1.45f306dc9c883000p+0;
+static const double PI_2_hi = -0x1.921fb54400000000p+0;
+static const double PI_2_lo = -0x1.0b4611a626332000p-34;
+
+#define FLOAT_EXPONENT_SHIFT 23
+#define FLOAT_EXPONENT_BIAS 127
+
+static const double pio2_table[] = {
+ 0 * M_PI_2,
+ 1 * M_PI_2,
+ 2 * M_PI_2,
+ 3 * M_PI_2,
+ 4 * M_PI_2,
+ 5 * M_PI_2,
+ 6 * M_PI_2,
+ 7 * M_PI_2,
+ 8 * M_PI_2,
+ 9 * M_PI_2,
+ 10 * M_PI_2
+};
+
+static const double invpio4_table[] = {
+ 0x0.0000000000000000p+0,
+ 0x1.45f306c000000000p+0,
+ 0x1.c9c882a000000000p-28,
+ 0x1.4fe13a8000000000p-58,
+ 0x1.f47d4d0000000000p-85,
+ 0x1.bb81b6c000000000p-112,
+ 0x1.4acc9e0000000000p-142,
+ 0x1.0e4107c000000000p-169,
+ 0x1.ca2c756000000000p-196,
+ 0x1.bd778ac000000000p-224,
+ 0x1.b7246e0000000000p-255,
+ 0x1.d2126e8000000000p-282,
+ 0x1.7003248000000000p-310,
+ 0x1.77504e8000000000p-338,
+ 0x1.921cfe0000000000p-367,
+ 0x1.deb1cb0000000000p-395,
+ 0x1.29a73e0000000000p-423,
+ 0x1.d1046be000000000p-448,
+ 0x1.4baed10000000000p-477,
+ 0x1.09d338e000000000p-504,
+ 0x1.35a2f80000000000p-538,
+ 0x1.f904e64000000000p-561,
+ 0x1.d639830000000000p-591,
+ 0x1.4ce7d24000000000p-617,
+ 0x1.908bf16000000000p-644
+};
+
+static const int ones[] = { +1, -1 };
+
+static inline void
+reduced (const double theta, const unsigned long n, float *const sinx,
+ float *const cosx, const unsigned long signbit)
{
- int32_t ix;
+ double sx, cx, theta2;
+ /* We are operating on |x|, so we need to add back the original
+ * signbit for sinf. */
+ int sign_sin, sign_cos;
+ sign_sin = ones[((n >> 2) & 1) ^ signbit];
+ sign_cos = ones[((n + 2) >> 2) & 1];
+ theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for sin and cos:
+ * x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).
+ * 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ sx = S3 + theta2 * S4; /* S3+x^2*S4. */
+ sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
+ sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
+ sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
+ /* x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ sx = theta + theta * theta2 * sx;
- /* High word of x. */
- GET_FLOAT_WORD (ix, x);
+ cx = C3 + theta2 * C4; /* C3+x^2*C4. */
+ cx = C2 + theta2 * cx; /* C2+x^2*(C3+x^2*C4). */
+ cx = C1 + theta2 * cx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
+ cx = C0 + theta2 * cx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
+ /* 1.0 + x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ cx = 1.0 + theta2 * cx;
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if (ix <= 0x3f490fd8)
+ /* Add in the signbit and assign the result. */
+ if ((n & 2) == 0)
{
- *sinx = __kernel_sinf (x, 0.0, 0);
- *cosx = __kernel_cosf (x, 0.0);
- }
- else if (ix>=0x7f800000)
- {
- /* sin(Inf or NaN) is NaN */
- *sinx = *cosx = x - x;
- if (ix == 0x7f800000)
- __set_errno (EDOM);
+ *sinx = sign_sin * sx;
+ *cosx = sign_cos * cx;
}
else
{
- /* Argument reduction needed. */
- float y[2];
- int n;
+ *sinx = sign_sin * cx;
+ *cosx = sign_cos * sx;
+ }
+}
- n = __ieee754_rem_pio2f (x, y);
- switch (n & 3)
+void
+SINCOSF_FUNC (float x, float *sinx, float *cosx)
+{
+ double cx;
+ double theta = x;
+ double abstheta = fabs (theta);
+ /* if |x|< Pi/4. */
+ if (abstheta < M_PI_4)
+ {
+ if (abstheta >= +0.03125) /* |x| >= 2^-5. */
+ {
+ double theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for sin and cos. */
+ cx = C3 + theta2 * C4;
+ cx = C2 + theta2 * cx;
+ cx = C1 + theta2 * cx;
+ cx = C0 + theta2 * cx;
+ cx = 1.0 + theta2 * cx;
+ *cosx = cx;
+ cx = S3 + theta2 * S4;
+ cx = S2 + theta2 * cx;
+ cx = S1 + theta2 * cx;
+ cx = S0 + theta2 * cx;
+ cx = theta + theta * theta2 * cx;
+ *sinx = cx;
+ }
+ else if (abstheta >= 0x1p-27) /* |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). */
+ double theta2 = theta * theta;
+ cx = CC0 + theta * theta2 * CC1;
+ cx = 1.0 + theta2 * cx;
+ *cosx = cx;
+ cx = SS0 + theta2 * SS1;
+ cx = theta + theta * theta2 * cx;
+ *sinx = cx;
+ }
+ else
+ {
+ /* Handle some special cases. */
+ if (theta)
+ *sinx = theta - (theta * SMALL);
+ else
+ *sinx = theta;
+ *cosx = 1.0 - abstheta;
+ }
+ }
+ else /* |x| >= Pi/4. */
+ {
+ unsigned long signbit = (x < 0);
+ if (abstheta < 9 * M_PI_4) /* |x| < 9*Pi/4. */
+ {
+ unsigned long n = (abstheta * inv_PI_4) + 1;
+ theta = abstheta - pio2_table[n / 2];
+ reduced (theta, n, sinx, cosx, signbit);
+ }
+ else if (abstheta < INFINITY)
+ {
+ if (abstheta < 8388608.0) /* |x| < 2^23. */
+ {
+ unsigned long n = floor (abstheta * inv_PI_4) + 1.0;
+ double x = floor (n / 2.0);
+ theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+ /* Argument reduction needed. */
+ reduced (theta, n, sinx, cosx, signbit);
+ }
+ else /* |x| >= 2^23. */
+ {
+ x = fabs (x);
+ int32_t exponent;
+ GET_FLOAT_WORD (exponent, x);
+ exponent =
+ (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+ exponent += 3;
+ exponent = (exponent * (0x100000000 / 28 + 1)) >> 32;
+ 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;
+ unsigned long 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 (e, l + 1, sinx, cosx, signbit);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ reduced (e, l + 1, sinx, cosx, signbit);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ reduced (e, l + 1, sinx, cosx, signbit);
+ }
+ }
+ }
+ }
+ else
{
- case 0:
- *sinx = __kernel_sinf (y[0], y[1], 1);
- *cosx = __kernel_cosf (y[0], y[1]);
- break;
- case 1:
- *sinx = __kernel_cosf (y[0], y[1]);
- *cosx = -__kernel_sinf (y[0], y[1], 1);
- break;
- case 2:
- *sinx = -__kernel_sinf (y[0], y[1], 1);
- *cosx = -__kernel_cosf (y[0], y[1]);
- break;
- default:
- *sinx = -__kernel_cosf (y[0], y[1]);
- *cosx = __kernel_sinf (y[0], y[1], 1);
- break;
+ int32_t ix;
+ /* High word of x. */
+ GET_FLOAT_WORD (ix, abstheta);
+ /* sin/cos(Inf or NaN) is NaN. */
+ *sinx = *cosx = x - x;
+ if (ix == 0x7f800000)
+ __set_errno (EDOM);
}
}
}
@@ -29,6 +29,7 @@ libm-sysdep_routines += s_llround-power6x \
e_expf-power8 e_expf-ppc64 \
s_sinf-ppc64 s_sinf-power8 \
s_cosf-ppc64 s_cosf-power8 \
+ s_sincosf-ppc64 s_sincosf-power8 \
$(sysdep_calls:s_%=m_%)
CFLAGS-s_logbf-power7.c = -mcpu=power7
@@ -38,6 +39,7 @@ CFLAGS-s_modf-power5+.c = -mcpu=power5+
CFLAGS-s_modff-power5+.c = -mcpu=power5+
CFLAGS-e_hypot-power7.c = -mcpu=power7
CFLAGS-e_hypotf-power7.c = -mcpu=power7
+CFLAGS-s_sincosf-power8.c = -mcpu=power8
# These files quiet sNaNs in a way that is optimized away without
# -fsignaling-nans.
new file mode 100644
@@ -0,0 +1,26 @@
+/* sincosf(). PowerPC64/POWER8 version.
+ 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 <sysdep.h>
+
+#undef weak_alias
+#define weak_alias(a,b)
+
+#define __sincosf __sincosf_power8
+
+#include <sysdeps/ieee754/flt-32/s_sincosf.c>
new file mode 100644
@@ -0,0 +1,26 @@
+/* sincosf(). PowerPC64 default version.
+ 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 <sysdep.h>
+
+#undef weak_alias
+#define weak_alias(a, b)
+
+#define __sincosf __sincosf_ppc64
+
+#include <sysdeps/ieee754/flt-32/s_sincosf.c>
new file mode 100644
@@ -0,0 +1,31 @@
+/* Multiple versions of sincosf.
+ 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 <math.h>
+#include <shlib-compat.h>
+#include "init-arch.h"
+
+extern __typeof (__sincosf) __sincosf_ppc64 attribute_hidden;
+extern __typeof (__sincosf) __sincosf_power8 attribute_hidden;
+
+libc_ifunc (__sincosf,
+ (hwcap2 & PPC_FEATURE2_ARCH_2_07)
+ ? __sincosf_power8
+ : __sincosf_ppc64);
+
+weak_alias (__sincosf, sincosf)
This implementation is based on optimized sinf and cosf versions of x86_64 and powerpc. Tested on x86_64 and powerpc64le. 2017-10-09 Paul Clarke <pc@us.ibm.com> Rajalakshmi Srinivasaraghavan <raji@linux.vnet.ibm.com> * sysdeps/ieee754/flt-32/s_sincosf.c: New generic implementation. * sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile [$(subdir) = math] (libm-sysdep_routines): Add s_sincosf-power8 and s_sincosf-ppc64. * sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf-power8.c: New file. * sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf-ppc64.c: Likewise. * sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf.c: Likewise. --- sysdeps/ieee754/flt-32/s_sincosf.c | 265 +++++++++++++++++---- sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile | 2 + .../powerpc64/fpu/multiarch/s_sincosf-power8.c | 26 ++ .../powerpc64/fpu/multiarch/s_sincosf-ppc64.c | 26 ++ .../powerpc/powerpc64/fpu/multiarch/s_sincosf.c | 31 +++ 5 files changed, 310 insertions(+), 40 deletions(-) create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf-power8.c create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf-ppc64.c create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/s_sincosf.c