@@ -19,22 +19,13 @@
#include <stdint.h>
#include <math.h>
#include "math_config.h"
+#include <sincosf_poly.h>
/* 2PI * 2^-64. */
static const double pi63 = 0x1.921FB54442D18p-62;
/* PI / 4. */
static const double pio4 = 0x1.921FB54442D18p-1;
-/* The constants and polynomials for sine and cosine. */
-typedef struct
-{
- double sign[4]; /* Sign of sine in quadrants 0..3. */
- double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
- double hpi; /* PI / 2. */
- double c0, c1, c2, c3, c4; /* Cosine polynomial. */
- double s1, s2, s3; /* Sine polynomial. */
-} sincos_t;
-
/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */
extern const sincos_t __sincosf_table[2] attribute_hidden;
@@ -48,66 +39,6 @@ abstop12 (float x)
return (asuint (x) >> 20) & 0x7ff;
}
-/* Compute the sine and cosine of inputs X and X2 (X squared), using the
- polynomial P and store the results in SINP and COSP. N is the quadrant,
- if odd the cosine and sine polynomials are swapped. */
-static inline void
-sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
- float *cosp)
-{
- double x3, x4, x5, x6, s, c, c1, c2, s1;
-
- x4 = x2 * x2;
- x3 = x2 * x;
- c2 = p->c3 + x2 * p->c4;
- s1 = p->s2 + x2 * p->s3;
-
- /* Swap sin/cos result based on quadrant. */
- float *tmp = (n & 1 ? cosp : sinp);
- cosp = (n & 1 ? sinp : cosp);
- sinp = tmp;
-
- c1 = p->c0 + x2 * p->c1;
- x5 = x3 * x2;
- x6 = x4 * x2;
-
- s = x + x3 * p->s1;
- c = c1 + x4 * p->c2;
-
- *sinp = s + x5 * s1;
- *cosp = c + x6 * c2;
-}
-
-/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
- N is the quadrant, and if odd the cosine polynomial is used. */
-static inline float
-sinf_poly (double x, double x2, const sincos_t *p, int n)
-{
- double x3, x4, x6, x7, s, c, c1, c2, s1;
-
- if ((n & 1) == 0)
- {
- x3 = x * x2;
- s1 = p->s2 + x2 * p->s3;
-
- x7 = x3 * x2;
- s = x + x3 * p->s1;
-
- return s + x7 * s1;
- }
- else
- {
- x4 = x2 * x2;
- c2 = p->c3 + x2 * p->c4;
- c1 = p->c0 + x2 * p->c1;
-
- x6 = x4 * x2;
- c = c1 + x4 * p->c2;
-
- return c + x6 * c2;
- }
-}
-
/* Fast range reduction using single multiply-subtract. Return the modulo of
X as a value between -PI/4 and PI/4 and store the quadrant in NP.
The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double
new file mode 100644
@@ -0,0 +1,87 @@
+/* Used by sinf, cosf and sincosf functions.
+ Copyright (C) 2018 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/>. */
+
+/* The constants and polynomials for sine and cosine. */
+typedef struct
+{
+ double sign[4]; /* Sign of sine in quadrants 0..3. */
+ double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
+ double hpi; /* PI / 2. */
+ double c0, c1, c2, c3, c4; /* Cosine polynomial. */
+ double s1, s2, s3; /* Sine polynomial. */
+} sincos_t;
+
+/* Compute the sine and cosine of inputs X and X2 (X squared), using the
+ polynomial P and store the results in SINP and COSP. N is the quadrant,
+ if odd the cosine and sine polynomials are swapped. */
+static inline void
+sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
+ float *cosp)
+{
+ double x3, x4, x5, x6, s, c, c1, c2, s1;
+
+ x4 = x2 * x2;
+ x3 = x2 * x;
+ c2 = p->c3 + x2 * p->c4;
+ s1 = p->s2 + x2 * p->s3;
+
+ /* Swap sin/cos result based on quadrant. */
+ float *tmp = (n & 1 ? cosp : sinp);
+ cosp = (n & 1 ? sinp : cosp);
+ sinp = tmp;
+
+ c1 = p->c0 + x2 * p->c1;
+ x5 = x3 * x2;
+ x6 = x4 * x2;
+
+ s = x + x3 * p->s1;
+ c = c1 + x4 * p->c2;
+
+ *sinp = s + x5 * s1;
+ *cosp = c + x6 * c2;
+}
+
+/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
+ N is the quadrant, and if odd the cosine polynomial is used. */
+static inline float
+sinf_poly (double x, double x2, const sincos_t *p, int n)
+{
+ double x3, x4, x6, x7, s, c, c1, c2, s1;
+
+ if ((n & 1) == 0)
+ {
+ x3 = x * x2;
+ s1 = p->s2 + x2 * p->s3;
+
+ x7 = x3 * x2;
+ s = x + x3 * p->s1;
+
+ return s + x7 * s1;
+ }
+ else
+ {
+ x4 = x2 * x2;
+ c2 = p->c3 + x2 * p->c4;
+ c1 = p->c0 + x2 * p->c1;
+
+ x6 = x4 * x2;
+ c = c1 + x4 * p->c2;
+
+ return c + x6 * c2;
+ }
+}
new file mode 100644
@@ -0,0 +1,68 @@
+/* Compute sine and cosine of argument.
+ Copyright (C) 2018 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 <stdint.h>
+#include <math.h>
+#include <sysdeps/ieee754/flt-32/math_config.h>
+#include <s_sincosf.h>
+
+/* The constants and polynomials for sine and cosine. The 2nd entry
+ computes -cos (x) rather than cos (x) to get negation for free. */
+const sincos_t __sincosf_table[2] =
+{
+ {
+ { 1.0, -1.0, -1.0, 1.0 },
+#if TOINT_INTRINSICS
+ 0x1.45F306DC9C883p-1,
+#else
+ 0x1.45F306DC9C883p+23,
+#endif
+ 0x1.921FB54442D18p0,
+ 0x1p0,
+ -0x1.ffffffd0c621cp-2,
+ { -0x1.555545995a603p-3, 0x1.55553e1068f19p-5 },
+ { 0x1.1107605230bc4p-7, -0x1.6c087e89a359dp-10 },
+ { -0x1.994eb3774cf24p-13, 0x1.99343027bf8c3p-16 }
+ },
+ {
+ { 1.0, -1.0, -1.0, 1.0 },
+#if TOINT_INTRINSICS
+ 0x1.45F306DC9C883p-1,
+#else
+ 0x1.45F306DC9C883p+23,
+#endif
+ 0x1.921FB54442D18p0,
+ -0x1p0,
+ 0x1.ffffffd0c621cp-2,
+ { -0x1.555545995a603p-3, -0x1.55553e1068f19p-5 },
+ { 0x1.1107605230bc4p-7, 0x1.6c087e89a359dp-10 },
+ { -0x1.994eb3774cf24p-13, -0x1.99343027bf8c3p-16 }
+ }
+};
+
+/* Table with 4/PI to 192 bit precision. To avoid unaligned accesses
+ only 8 new bits are added per entry, making the table 4 times larger. */
+const uint32_t __inv_pio4[24] =
+{
+ 0xa2, 0xa2f9, 0xa2f983, 0xa2f9836e,
+ 0xf9836e4e, 0x836e4e44, 0x6e4e4415, 0x4e441529,
+ 0x441529fc, 0x1529fc27, 0x29fc2757, 0xfc2757d1,
+ 0x2757d1f5, 0x57d1f534, 0xd1f534dd, 0xf534ddc0,
+ 0x34ddc0db, 0xddc0db62, 0xc0db6295, 0xdb629599,
+ 0x6295993c, 0x95993c43, 0x993c4390, 0x3c439041
+};
new file mode 100644
@@ -0,0 +1,111 @@
+/* Used by sinf, cosf and sincosf functions. X86-64 version.
+ Copyright (C) 2018 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/>. */
+
+typedef double v2df_t __attribute__ ((vector_size (2 * sizeof (double))));
+
+#ifdef __SSE2_MATH__
+typedef float v4sf_t __attribute__ ((vector_size (4 * sizeof (float))));
+
+static inline void
+v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
+{
+ v4sf_t v4sf = __builtin_ia32_cvtpd2ps (v2df);
+ *f0p = v4sf[0];
+ *f1p = v4sf[1];
+}
+#else
+static inline void
+v2df_to_sf (v2df_t v2df, float *f0p, float *f1p)
+{
+ *f0p = (float) v2df[0];
+ *f1p = (float) v2df[1];
+}
+#endif
+
+/* The constants and polynomials for sine and cosine. */
+typedef struct
+{
+ double sign[4]; /* Sign of sine in quadrants 0..3. */
+ double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */
+ double hpi; /* PI / 2. */
+ /* Cosine polynomial: c0, c1, c2, c3, c4.
+ Sine polynomial: s1, s2, s3. */
+ double c0, c1;
+ v2df_t s1c2, s2c3, s3c4;
+} sincos_t;
+
+/* Compute the sine and cosine of inputs X and X2 (X squared), using the
+ polynomial P and store the results in SINP and COSP. N is the quadrant,
+ if odd the cosine and sine polynomials are swapped. */
+static inline void
+sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,
+ float *cosp)
+{
+ v2df_t vx2x2 = { x2, x2 };
+ v2df_t vxx2 = { x, x2 };
+ v2df_t vx3x4, vs1c2;
+
+ vx3x4 = vx2x2 * vxx2;
+ vs1c2 = p->s2c3 + vx2x2 * p->s3c4;
+
+ /* Swap sin/cos result based on quadrant. */
+ if (n & 1)
+ {
+ float *tmp = cosp;
+ cosp = sinp;
+ sinp = tmp;
+ }
+
+ double c1 = p->c0 + x2 * p->c1;
+ v2df_t vxc1 = { x, c1 };
+ v2df_t vx5x6 = vx3x4 * vx2x2;
+
+ v2df_t vsincos = vxc1 + vx3x4 * p->s1c2;
+ vsincos = vsincos + vx5x6 * vs1c2;
+ v2df_to_sf (vsincos, sinp, cosp);
+}
+
+/* Return the sine of inputs X and X2 (X squared) using the polynomial P.
+ N is the quadrant, and if odd the cosine polynomial is used. */
+static inline float
+sinf_poly (double x, double x2, const sincos_t *p, int n)
+{
+ double x3, x4, x6, x7, s, c, c1, c2, s1;
+
+ if ((n & 1) == 0)
+ {
+ x3 = x * x2;
+ s1 = p->s2c3[0] + x2 * p->s3c4[0];
+
+ x7 = x3 * x2;
+ s = x + x3 * p->s1c2[0];
+
+ return s + x7 * s1;
+ }
+ else
+ {
+ x4 = x2 * x2;
+ c2 = p->s2c3[1] + x2 * p->s3c4[1];
+ c1 = p->c0 + x2 * p->c1;
+
+ x6 = x4 * x2;
+ c = c1 + x4 * p->s1c2[1];
+
+ return c + x6 * c2;
+ }
+}
@@ -1,271 +1,2 @@
-/* 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>
-
#define SINCOSF __sincosf_fma
-
-#ifndef SINCOSF
-# define SINCOSF_FUNC __sincosf
-#else
-# define SINCOSF_FUNC SINCOSF
-#endif
-
-/* PI/2 with 98 bits of accuracy. */
-static const double PI_2_hi = 0x1.921fb544p+0;
-static const double PI_2_lo = 0x1.0b4611a626332p-34;
-
-static const double SMALL = 0x1p-50; /* 2^-50. */
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
-
-#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
-};
-
-static const double invpio4_table[] = {
- 0x0p+0,
- 0x1.45f306cp+0,
- 0x1.c9c882ap-28,
- 0x1.4fe13a8p-58,
- 0x1.f47d4dp-85,
- 0x1.bb81b6cp-112,
- 0x1.4acc9ep-142,
- 0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* 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
+#include <sysdeps/ieee754/flt-32/s_sincosf.c>