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[PATCH] PowerPC: Trigonometric optimizations for POWER
- From: Adhemerval Zanella <azanella at linux dot vnet dot ibm dot com>
- To: "GNU C. Library" <libc-alpha at sourceware dot org>
- Date: Tue, 09 Aug 2011 14:46:37 -0300
- Subject: [PATCH] PowerPC: Trigonometric optimizations for POWER
- References: <4E36F78A.50403@linux.vnet.ibm.com> <1312308652.7676.186.camel@localhost.localdomain>
These POWER optimizations remove most of the FP->INT conversions in
hypot/hypotf and sinf/cosf on POWER making the computation done with
FP operations instead. This eliminates Load-Hit-Store (LHS) stalls,
increasing performance of hypot/hypotf (by about 100% on POWER7 and
12% on POWER6) and sinf/cosf (by 80% on POWER7 and 30% on POWER6).
2011-08-01 Adhemerval Zanella <azanella@linux.vnet.ibm.com>
* sysdeps/powerpc/fpu/e_hypot.c: New file: hypot optimized for POWER.
* sysdeps/powerpc/fpu/e_hypotf.c: New file: hypotf optimized for POWER.
* sysdeps/powerpc/fpu/e_rem_pio2f.c: New file: optimized for POWER.
* sysdeps/powerpc/fpu/k_rem_pio2f.c: Likewise.
* sysdeps/powerpc/fpu/k_cosf.c: Likewise.
* sysdeps/powerpc/fpu/k_sinf.c: Likewise.
* sysdeps/powerpc/fpu/s_cosf.c: Likewise.
* sysdeps/powerpc/fpu/s_sinf.c: Likewise.
* sysdeps/powerpc/fpu/s_scalbnf.c: Likewise.
* sysdeps/powerpc/fpu/s_float_bitwise.h: new file: bitwise operation over
floats optimized for POWER7.
diff --git a/sysdeps/powerpc/fpu/e_hypot.c b/sysdeps/powerpc/fpu/e_hypot.c
new file mode 100644
index 0000000..22bd563
--- /dev/null
+++ b/sysdeps/powerpc/fpu/e_hypot.c
@@ -0,0 +1,117 @@
+/* Pythagorean addition using doubles
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double two60 = 1.152921504606847e+18;
+static const double two500 = 3.2733906078961419e+150;
+static const double two600 = 4.149515568880993e+180;
+static const double two1022 = 4.49423283715579e+307;
+static const double twoM500 = 3.054936363499605e-151;
+static const double twoM600 = 4.616489308892868e-128;
+static const double pdnum = 2.225073858507201e-308;
+
+/* __ieee754_hypot(x,y)
+ *
+ * This a FP only version without any FP->INT conversion.
+ * It is similar to default C version, making appropriates
+ * overflow and underflows checks as well scaling when it
+ * is needed.
+ */
+
+#ifdef _ARCH_PWR7
+/* POWER7 isinf and isnan optimization are fast. */
+# define TEST_INF_NAN(x, y) \
+ if (isinf(x) || isinf(y)) \
+ return INFINITY; \
+ if (isnan(x) || isnan(y)) \
+ return NAN;
+# else
+/* For POWER6 and below isinf/isnan triggers LHS and PLT calls are
+ * costly (especially for POWER6). */
+# define GET_TW0_HIGH_WORD(d1,d2,i1,i2) \
+ do { \
+ ieee_double_shape_type gh_u1; \
+ ieee_double_shape_type gh_u2; \
+ gh_u1.value = (d1); \
+ gh_u2.value = (d2); \
+ (i1) = gh_u1.parts.msw; \
+ (i2) = gh_u2.parts.msw; \
+ } while (0)
+
+# define TEST_INF_NAN(x, y) \
+ do { \
+ int32_t hx, hy; \
+ GET_TW0_HIGH_WORD(x, y, hx, hy); \
+ if (hy > hx) { \
+ uint32_t ht = hx; hx = hy; hy = ht; \
+ } \
+ if (hx >= 0x7ff00000) { \
+ if (hx == 0x7ff00000 || hy == 0x7ff00000) \
+ return INFINITY; \
+ return NAN; \
+ } \
+ } while (0)
+
+#endif
+
+
+double
+__ieee754_hypot (double x, double y)
+{
+ x = fabs (x);
+ y = fabs (y);
+
+ TEST_INF_NAN (x, y);
+
+ if (y > x)
+ {
+ double t = x;
+ x = y;
+ y = t;
+ }
+ if (y == 0.0 || (x / y) > two60)
+ {
+ return x + y;
+ }
+ if (x > two500)
+ {
+ x *= twoM600;
+ y *= twoM600;
+ return sqrt (x * x + y * y) / twoM600;
+ }
+ if (y < twoM500)
+ {
+ if (y <= pdnum)
+ {
+ x *= two1022;
+ y *= two1022;
+ return sqrt (x * x + y * y) / two1022;
+ }
+ else
+ {
+ x *= two600;
+ y *= two600;
+ return sqrt (x * x + y * y) / two600;
+ }
+ }
+ return sqrt (x * x + y * y);
+}
diff --git a/sysdeps/powerpc/fpu/e_hypotf.c b/sysdeps/powerpc/fpu/e_hypotf.c
new file mode 100644
index 0000000..3e6c597
--- /dev/null
+++ b/sysdeps/powerpc/fpu/e_hypotf.c
@@ -0,0 +1,118 @@
+/* Pythagorean addition using floats
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include "math.h"
+#include "math_private.h"
+
+
+static const float two30 = 1.0737418e09;
+static const float two50 = 1.1259000e15;
+static const float two60 = 1.1529221e18;
+static const float two126 = 8.5070592e+37;
+static const float twoM50 = 8.8817842e-16;
+static const float twoM60 = 6.7762644e-21;
+static const float pdnum = 1.1754939e-38;
+
+
+/* __ieee754_hypotf(x,y)
+ *
+ * This a FP only version without any FP->INT conversion.
+ * It is similar to default C version, making appropriates
+ * overflow and underflows checks as well scaling when it
+ * is needed.
+ */
+
+#ifdef _ARCH_PWR7
+/* POWER7 isinf and isnan optimizations are fast. */
+# define TEST_INF_NAN(x, y) \
+ if (isinff(x) || isinff(y)) \
+ return INFINITY; \
+ if (isnanf(x) || isnanf(y)) \
+ return NAN;
+# else
+/* For POWER6 and below isinf/isnan triggers LHS and PLT calls are
+ * costly (especially for POWER6). */
+# define GET_TWO_FLOAT_WORD(f1,f2,i1,i2) \
+ do { \
+ ieee_float_shape_type gf_u1; \
+ ieee_float_shape_type gf_u2; \
+ gf_u1.value = (f1); \
+ gf_u2.value = (f2); \
+ (i1) = gf_u1.word; \
+ (i2) = gf_u2.word; \
+ } while (0)
+
+# define TEST_INF_NAN(x, y) \
+ do { \
+ int32_t hx, hy; \
+ GET_TWO_FLOAT_WORD(x, y, hx, hy); \
+ if (hy > hx) { \
+ uint32_t ht = hx; hx = hy; hy = ht; \
+ } \
+ if (hx >= 0x7f800000) { \
+ if (hx == 0x7f800000 || hy == 0x7f800000) \
+ return INFINITY; \
+ return NAN; \
+ } \
+ } while (0)
+#endif
+
+
+float
+__ieee754_hypotf (float x, float y)
+{
+ x = fabsf (x);
+ y = fabsf (y);
+
+ TEST_INF_NAN (x, y);
+
+ if (y > x)
+ {
+ float t = y;
+ y = x;
+ x = t;
+ }
+ if (y == 0.0 || (x / y) > two30)
+ {
+ return x + y;
+ }
+ if (x > two50)
+ {
+ x *= twoM60;
+ y *= twoM60;
+ return sqrtf (x * x + y * y) / twoM60;
+ }
+ if (y < twoM50)
+ {
+ if (y <= pdnum)
+ {
+ x *= two126;
+ y *= two126;
+ return sqrtf (x * x + y * y) / two126;
+ }
+ else
+ {
+ x *= two60;
+ y *= two60;
+ return sqrtf (x * x + y * y) / two60;
+ }
+ }
+ return sqrtf (x * x + y * y);
+}
diff --git a/sysdeps/powerpc/fpu/e_rem_pio2f.c b/sysdeps/powerpc/fpu/e_rem_pio2f.c
new file mode 100644
index 0000000..4744895
--- /dev/null
+++ b/sysdeps/powerpc/fpu/e_rem_pio2f.c
@@ -0,0 +1,190 @@
+/* e_rem_pio2f.c -- float version of e_rem_pio2.c
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <math.h>
+
+#include "math_private.h"
+#include "s_float_bitwise.h"
+
+/* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */
+int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx);
+
+/* __ieee754_rem_pio2f(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ */
+
+static const float npio2_hw[] = {
+ 1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00,
+ 7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01,
+ 1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01,
+ 2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01,
+ 2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01,
+ 3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01,
+ 3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01,
+ 4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01
+};
+
+
+static const float zero = 0.0000000000e+00;
+static const float two8 = 2.5600000000e+02;
+
+static const float half = 5.0000000000e-01;
+static const float invpio2 = 6.3661980629e-01;
+static const float pio2_1 = 1.5707855225e+00;
+static const float pio2_1t = 1.0804334124e-05;
+static const float pio2_2 = 1.0804273188e-05;
+static const float pio2_2t = 6.0770999344e-11;
+static const float pio2_3 = 6.0770943833e-11;
+static const float pio2_3t = 6.1232342629e-17;
+
+static const float pio4 = 7.8539801e-01;
+static const float pio3_4 = 2.3561945e+00;
+static const float pio2_24b = 1.5707951e+00;
+static const float pio2_2e7 = 2.0106054e+02;
+
+
+int32_t
+__ieee754_rem_pio2f (float x, float *y)
+{
+ float ax, z, n, r, w, t, e0;
+ float tx[3];
+ int32_t i, nx;
+
+ ax = __builtin_fabsf (x);
+ if (ax <= pio4)
+ {
+ y[0] = x;
+ y[1] = 0;
+ return 0;
+ }
+ if (ax < pio3_4)
+ {
+ if (x > 0)
+ {
+ z = x - pio2_1;
+ if (!__float_and_test28 (ax, pio2_24b))
+ {
+ y[0] = z - pio2_1t;
+ y[1] = (z - y[0]) - pio2_1t;
+ }
+ else
+ {
+ z -= pio2_2;
+ y[0] = z - pio2_2t;
+ y[1] = (z - y[0]) - pio2_2t;
+ }
+ return 1;
+ }
+ else
+ {
+ z = x + pio2_1;
+ if (!__float_and_test28 (ax, pio2_24b))
+ {
+ y[0] = z + pio2_1t;
+ y[1] = (z - y[0]) + pio2_1t;
+ }
+ else
+ {
+ z += pio2_2;
+ y[0] = z + pio2_2t;
+ y[1] = (z - y[0]) + pio2_2t;
+ }
+ return -1;
+ }
+ }
+ if (ax <= pio2_2e7)
+ {
+ n = floorf (ax * invpio2 + half);
+ i = (int32_t) n;
+ r = ax - n * pio2_1;
+ w = n * pio2_1t; /* 1st round good to 40 bit */
+ if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1]))
+ {
+ y[0] = r - w;
+ }
+ else
+ {
+ float i, j;
+ j = __float_and8 (ax);
+ y[0] = r - w;
+ i = __float_and8 (y[0]);
+ if (j / i > 256.0 || j / i < 3.9062500e-3)
+ { /* 2nd iterations needed, good to 57 */
+ t = r;
+ w = n * pio2_2;
+ r = t - w;
+ w = n * pio2_2t - ((t - r) - w);
+ y[0] = r - w;
+ i = __float_and8 (y[0]);
+ if (j / i > 33554432 || j / i < 2.9802322e-8)
+ { /* 3rd iteration needed, 74 bits acc */
+ t = r;
+ w = n * pio2_3;
+ r = t - w;
+ w = n * pio2_3t - ((t - r) - w);
+ y[0] = r - w;
+ }
+ }
+ }
+ y[1] = (r - y[0]) - w;
+ if (x < 0)
+ {
+ y[0] = -y[0];
+ y[1] = -y[1];
+ return -i;
+ }
+ else
+ {
+ return i;
+ }
+ }
+
+ /* all other (large) arguments */
+ if (isnanf (x) || isinff (x))
+ {
+ y[0] = y[1] = x - x;
+ return 0;
+ }
+
+ /* set z = scalbn(|x|,ilogb(x)-7) */
+ e0 = __float_and8 (ax / 128.0);
+ z = ax / e0;
+
+ tx[0] = floorf (z);
+ z = (z - tx[0]) * two8;
+ tx[1] = floorf (z);
+ z = (z - tx[1]) * two8;
+ tx[2] = floorf (z);
+
+ nx = 3;
+ while (tx[nx - 1] == zero)
+ nx--;
+
+ i = __fp_kernel_rem_pio2f (tx, y, e0, nx);
+ if (x < 0)
+ {
+ y[0] = -y[0];
+ y[1] = -y[1];
+ return -i;
+ }
+ return i;
+}
+
diff --git a/sysdeps/powerpc/fpu/k_cosf.c b/sysdeps/powerpc/fpu/k_cosf.c
new file mode 100644
index 0000000..cb0e34e
--- /dev/null
+++ b/sysdeps/powerpc/fpu/k_cosf.c
@@ -0,0 +1,65 @@
+/* k_cosf.c -- float version of k_cos.c
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include "math.h"
+#include "math_private.h"
+
+static const float twom27 = 7.4505806e-09;
+static const float dot3 = 3.0000001e-01;
+static const float dot78125 = 7.8125000e-01;
+
+static const float one = 1.0000000000e+00;
+static const float C1 = 4.1666667908e-02;
+static const float C2 = -1.3888889225e-03;
+static const float C3 = 2.4801587642e-05;
+static const float C4 = -2.7557314297e-07;
+static const float C5 = 2.0875723372e-09;
+static const float C6 = -1.1359647598e-11;
+
+float
+__kernel_cosf (float x, float y)
+{
+ float a, hz, z, r, qx;
+ float ix;
+ ix = __builtin_fabsf (x);
+ if (ix < twom27)
+ { /* |x| < 2**-27 */
+ if (x == 0.0)
+ return one;
+ }
+ z = x * x;
+ r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
+ if (ix < dot3) /* if |x| < 0.3 */
+ return one - ((float) 0.5 * z - (z * r - x * y));
+ else
+ {
+ if (ix > dot78125)
+ { /* x > 0.78125 */
+ qx = (float) 0.28125;
+ }
+ else
+ {
+ qx = ix / 4.0;
+ }
+ hz = (float) 0.5 *z - qx;
+ a = one - qx;
+ return a - (hz - (z * r - x * y));
+ }
+}
diff --git a/sysdeps/powerpc/fpu/k_rem_pio2f.c b/sysdeps/powerpc/fpu/k_rem_pio2f.c
new file mode 100644
index 0000000..9635340
--- /dev/null
+++ b/sysdeps/powerpc/fpu/k_rem_pio2f.c
@@ -0,0 +1,274 @@
+/* k_rem_pio2f.c -- float version of e_rem_pio2.c
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <math.h>
+
+#include "math_private.h"
+#include "s_float_bitwise.h"
+
+
+static const float two_over_pi[] = {
+ 1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,
+ 7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,
+ 2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,
+ 2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,
+ 2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,
+ 6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,
+ 2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,
+ 2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,
+ 1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,
+ 6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,
+ 6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,
+ 9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,
+ 2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,
+ 1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,
+ 2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,
+ 4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,
+ 2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,
+ 1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,
+ 5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,
+ 1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,
+ 1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,
+ 1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,
+ 3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,
+ 2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,
+ 2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,
+ 9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,
+ 1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,
+ 3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,
+ 7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,
+ 1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,
+ 1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,
+ 2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,
+ 6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,
+ 1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,
+ 1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,
+ 3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,
+ 8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,
+ 2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,
+ 2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,
+ 1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,
+ 1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,
+ 9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,
+ 1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,
+ 2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,
+ 1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,
+ 7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,
+ 6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,
+ 2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,
+ 9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,
+ 1.40000000e+02, 1.07000000e+02
+};
+
+
+static const float PIo2[] = {
+ 1.5703125000e+00, /* 0x3fc90000 */
+ 4.5776367188e-04, /* 0x39f00000 */
+ 2.5987625122e-05, /* 0x37da0000 */
+ 7.5437128544e-08, /* 0x33a20000 */
+ 6.0026650317e-11, /* 0x2e840000 */
+ 7.3896444519e-13, /* 0x2b500000 */
+ 5.3845816694e-15, /* 0x27c20000 */
+ 5.6378512969e-18, /* 0x22d00000 */
+ 8.3009228831e-20, /* 0x1fc40000 */
+ 3.2756352257e-22, /* 0x1bc60000 */
+ 6.3331015649e-25, /* 0x17440000 */
+};
+
+
+static const float zero = 0.0000000000e+00;
+static const float one = 1.0000000000;
+static const float twon8 = 3.9062500000e-03;
+static const float two8 = 2.5600000000e+02;
+
+
+int32_t
+__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)
+{
+ int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;
+ float z, fw, f[20], fq[20], q[20];
+
+ /* initialize jk */
+ jp = jk = 9;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ jx = nx - 1;
+ exp = __float_get_exp (e0) - 127;
+ jv = (exp - 3) / 8;
+ if (jv < 0)
+ jv = 0;
+ q0 = exp - 8 * (jv + 1);
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */
+ j = jv - jx;
+ m = jx + jk;
+ for (i = 0; i <= m; i++, j++)
+ f[i] = (j < 0) ? zero : two_over_pi[j];
+
+ /* compute q[0],q[1],...q[jk] */
+ for (i = 0; i <= jk; i++)
+ {
+ for (j = 0, fw = 0.0; j <= jx; j++)
+ fw += x[j] * f[jx + i - j];
+ q[i] = fw;
+ }
+
+ jz = jk;
+recompute:
+ /* distill q[] into iq[] reversingly */
+ for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
+ {
+ fw = truncf (twon8 * z);
+ iq[i] = (int32_t) (z - two8 * fw);
+ z = q[j - 1] + fw;
+ }
+
+ /* compute n */
+ z = __scalbnf (z, q0); /* actual value of z */
+ z -= 8.0 * floorf (z * 0.125); /* trim off integer >= 8 */
+ n = (int32_t) z;
+ z -= truncf (z);
+ ih = 0;
+ if (q0 > 0)
+ { /* need iq[jz-1] to determine n */
+ i = (iq[jz - 1] >> (8 - q0));
+ n += i;
+ iq[jz - 1] -= i << (8 - q0);
+ ih = iq[jz - 1] >> (7 - q0);
+ }
+ else if (q0 == 0)
+ ih = iq[jz - 1] >> 8;
+ else if (z >= 0.5)
+ ih = 2;
+
+ if (ih > 0)
+ { /* q > 0.5 */
+ n += 1;
+ carry = 0;
+ for (i = 0; i < jz; i++)
+ { /* compute 1-q */
+ j = iq[i];
+ if (carry == 0)
+ {
+ if (j != 0)
+ {
+ carry = 1;
+ iq[i] = 0x100 - j;
+ }
+ }
+ else
+ iq[i] = 0xff - j;
+ }
+ if (q0 > 0)
+ { /* rare case: chance is 1 in 12 */
+ switch (q0)
+ {
+ case 1:
+ iq[jz - 1] &= 0x7f;
+ break;
+ case 2:
+ iq[jz - 1] &= 0x3f;
+ break;
+ }
+ }
+ if (ih == 2)
+ {
+ z = one - z;
+ if (carry != 0)
+ z -= __scalbnf (one, q0);
+ }
+ }
+
+ /* check if recomputation is needed */
+ if (z == zero)
+ {
+ j = 0;
+ for (i = jz - 1; i >= jk; i--)
+ j |= iq[i];
+ if (j == 0)
+ { /* need recomputation */
+ for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
+
+ for (i = jz + 1; i <= jz + k; i++)
+ { /* add q[jz+1] to q[jz+k] */
+ f[jx + i] = two_over_pi[jv + i];
+ for (j = 0, fw = 0.0; j <= jx; j++)
+ fw += x[j] * f[jx + i - j];
+ q[i] = fw;
+ }
+ jz += k;
+ goto recompute;
+ }
+ }
+
+ /* chop off zero terms */
+ if (z == 0.0)
+ {
+ jz -= 1;
+ q0 -= 8;
+ while (iq[jz] == 0)
+ {
+ jz--;
+ q0 -= 8;
+ }
+ }
+ else
+ { /* break z into 8-bit if necessary */
+ z = __scalbnf (z, -q0);
+ if (z >= two8)
+ {
+ fw = truncf (twon8 * z);
+ iq[jz] = (int32_t) (z - two8 * fw);
+ jz += 1;
+ q0 += 8;
+ iq[jz] = (int32_t) fw;
+ }
+ else
+ iq[jz] = (int32_t) z;
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = __scalbnf (one, q0);
+ for (i = jz; i >= 0; i--)
+ {
+ q[i] = fw * (float) iq[i];
+ fw *= twon8;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for (i = jz; i >= 0; i--)
+ {
+ for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
+ fw += PIo2[k] * q[i + k];
+ fq[jz - i] = fw;
+ }
+
+ /* compress fq[] into y[] */
+ fw = 0.0;
+ for (i = jz; i >= 0; i--)
+ fw += fq[i];
+ y[0] = (ih == 0) ? fw : -fw;
+ fw = fq[0] - fw;
+ for (i = 1; i <= jz; i++)
+ fw += fq[i];
+ y[1] = (ih == 0) ? fw : -fw;
+
+ return n & 7;
+}
diff --git a/sysdeps/powerpc/fpu/k_sinf.c b/sysdeps/powerpc/fpu/k_sinf.c
new file mode 100644
index 0000000..f93a478
--- /dev/null
+++ b/sysdeps/powerpc/fpu/k_sinf.c
@@ -0,0 +1,53 @@
+/* k_sinf.c -- float version of k_sin.c
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include "math.h"
+#include "math_private.h"
+
+
+static const float twom27 = 7.4505806000e-09;
+static const float half = 5.0000000000e-01;
+static const float S1 = -1.6666667163e-01;
+static const float S2 = 8.3333337680e-03;
+static const float S3 = -1.9841270114e-04;
+static const float S4 = 2.7557314297e-06;
+static const float S5 = -2.5050759689e-08;
+static const float S6 = 1.5896910177e-10;
+
+
+float
+__kernel_sinf (float x, float y, int iy)
+{
+ float z, r, v;
+ float ix;
+ ix = __builtin_fabsf (x);
+ if (ix < twom27)
+ { /* |x| < 2**-27 */
+ if (x == 0.0)
+ return x;
+ }
+ z = x * x;
+ v = z * x;
+ r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
+ if (iy == 0)
+ return x + v * (S1 + z * r);
+ else
+ return x - ((z * (half * y - v * r) - y) - v * S1);
+}
diff --git a/sysdeps/powerpc/fpu/s_cosf.c b/sysdeps/powerpc/fpu/s_cosf.c
new file mode 100644
index 0000000..8b8778a
--- /dev/null
+++ b/sysdeps/powerpc/fpu/s_cosf.c
@@ -0,0 +1,71 @@
+/* s_cosf.c -- float version of s_cos.c.
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <errno.h>
+#include "math.h"
+#include "math_private.h"
+
+static const float one = 1.0;
+static const float pio4 = 7.8539801e-1;
+
+float
+__cosf (float x)
+{
+ float y[2], z = 0.0;
+ float ix;
+ int32_t n;
+
+ ix = __builtin_fabsf (x);
+
+ /* |x| ~< pi/4 */
+ if (ix <= pio4)
+ {
+ return __kernel_cosf (x, z);
+ /* cos(Inf or NaN) is NaN */
+ }
+ else if (isnanf (ix))
+ {
+ return x - x;
+ }
+ else if (isinff (ix))
+ {
+ __set_errno (EDOM);
+ return x - x;
+ }
+
+ /* argument reduction needed */
+ else
+ {
+ n = __ieee754_rem_pio2f (x, y);
+ switch (n & 3)
+ {
+ case 0:
+ return __kernel_cosf (y[0], y[1]);
+ case 1:
+ return -__kernel_sinf (y[0], y[1], 1);
+ case 2:
+ return -__kernel_cosf (y[0], y[1]);
+ default:
+ return __kernel_sinf (y[0], y[1], 1);
+ }
+ }
+}
+
+weak_alias (__cosf, cosf)
diff --git a/sysdeps/powerpc/fpu/s_float_bitwise.h b/sysdeps/powerpc/fpu/s_float_bitwise.h
new file mode 100644
index 0000000..c8b1d7a
--- /dev/null
+++ b/sysdeps/powerpc/fpu/s_float_bitwise.h
@@ -0,0 +1,112 @@
+/* Bitwise manipulation over float. Function prototypes.
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ 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, write to the Free
+ Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
+ 02111-1307 USA. */
+
+#ifndef _FLOAT_BITWISE_
+#define _FLOAT_BITWISE_ 1
+
+#include "math_private.h"
+
+/* Returns (int)(num & 0x7FFFFFF0 == value) */
+static inline
+int __float_and_test28 (float num, float value)
+{
+ float ret;
+#ifdef _ARCH_PWR7
+ vector int mask = (vector int) {
+ 0x7ffffffe, 0x00000000, 0x00000000, 0x0000000
+ };
+ __asm__ (
+ /* the 'f' constrain is use on mask because we just need
+ * to compare floats, not full vector */
+ "xxland %x0,%x1,%x2" : "=f" (ret) : "f" (num), "f" (mask)
+ );
+#else
+ int32_t inum;
+ GET_FLOAT_WORD(inum, num);
+ inum = (inum & 0x7ffffff0);
+ SET_FLOAT_WORD(ret, inum);
+#endif
+ return (ret == value);
+}
+
+/* Returns (int)(num & 0x7FFFFF00 == value) */
+static inline
+int __float_and_test24 (float num, float value)
+{
+ float ret;
+#ifdef _ARCH_PWR7
+ vector int mask = (vector int) {
+ 0x7fffffe0, 0x00000000, 0x00000000, 0x0000000
+ };
+ __asm__ (
+ "xxland %x0,%x1,%x2" : "=f" (ret) : "f" (num), "f" (mask)
+ );
+#else
+ int32_t inum;
+ GET_FLOAT_WORD(inum, num);
+ inum = (inum & 0x7fffff00);
+ SET_FLOAT_WORD(ret, inum);
+#endif
+ return (ret == value);
+}
+
+/* Returns (float)(num & 0x7F800000) */
+static inline
+float __float_and8 (float num)
+{
+ float ret;
+#ifdef _ARCH_PWR7
+ vector int mask = (vector int) {
+ 0x7ff00000, 0x00000000, 0x00000000, 0x00000000
+ };
+ __asm__ (
+ "xxland %x0,%x1,%x2" : "=f" (ret) : "f" (num), "f" (mask)
+ );
+#else
+ int32_t inum;
+ GET_FLOAT_WORD(inum, num);
+ inum = (inum & 0x7f800000);
+ SET_FLOAT_WORD(ret, inum);
+#endif
+ return ret;
+}
+
+/* Returns ((int32_t)(num & 0x7F800000) >> 23) */
+static inline
+int32_t __float_get_exp (float num)
+{
+ int32_t inum;
+#ifdef _ARCH_PWR7
+ float ret;
+ vector int mask = (vector int) {
+ 0x7ff00000, 0x00000000, 0x00000000, 0x00000000
+ };
+ __asm__ (
+ "xxland %x0,%x1,%x2" : "=f" (ret) : "f" (num), "f" (mask)
+ );
+ GET_FLOAT_WORD(inum, ret);
+#else
+ GET_FLOAT_WORD(inum, num);
+ inum = inum & 0x7f800000;
+#endif
+ return inum >> 23;
+}
+
+#endif /* s_float_bitwise.h */
diff --git a/sysdeps/powerpc/fpu/s_sinf.c b/sysdeps/powerpc/fpu/s_sinf.c
new file mode 100644
index 0000000..dd724aa
--- /dev/null
+++ b/sysdeps/powerpc/fpu/s_sinf.c
@@ -0,0 +1,70 @@
+/* s_sinf.c -- float version of s_sin.c.
+ Copyright (C) 2011 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+ Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Library General Public License as
+ published by the Free Software Foundation; either version 2 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
+ Library General Public License for more details.
+
+ You should have received a copy of the GNU Library General Public
+ License along with the GNU C Library; see the file COPYING.LIB. If not,
+ write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ Boston, MA 02111-1307, USA. */
+
+#include <errno.h>
+#include "math.h"
+#include "math_private.h"
+
+static const float pio4 = 7.8539801e-1;
+
+float
+__sinf (float x)
+{
+ float y[2], z = 0.0;
+ float ix;
+ int32_t n;
+
+ ix = __builtin_fabsf (x);
+
+ /* |x| ~< pi/4 */
+ if (ix <= pio4)
+ {
+ return __kernel_sinf (x, z, 0);
+ /* sin(Inf or NaN) is NaN */
+ }
+ else if (isnanf (ix))
+ {
+ return x - x;
+ }
+ else if (isinff (ix))
+ {
+ __set_errno (EDOM);
+ return x - x;
+ }
+
+ /* argument reduction needed */
+ else
+ {
+ n = __ieee754_rem_pio2f (x, y);
+ switch (n & 3)
+ {
+ case 0:
+ return __kernel_sinf (y[0], y[1], 1);
+ case 1:
+ return __kernel_cosf (y[0], y[1]);
+ case 2:
+ return -__kernel_sinf (y[0], y[1], 1);
+ default:
+ return -__kernel_cosf (y[0], y[1]);
+ }
+ }
+}
+
+weak_alias (__sinf, sinf)