From db97a804d67dfa6ab8d8fb3665e71882b09a32e4 Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Thu, 18 Aug 2011 09:25:37 -0500 Subject: Trigonometric optimizations for POWER cpus 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). --- ChangeLog | 14 ++ sysdeps/powerpc/fpu/e_hypot.c | 117 +++++++++++++++ sysdeps/powerpc/fpu/e_hypotf.c | 118 +++++++++++++++ sysdeps/powerpc/fpu/e_rem_pio2f.c | 189 +++++++++++++++++++++++ sysdeps/powerpc/fpu/k_cosf.c | 65 ++++++++ sysdeps/powerpc/fpu/k_rem_pio2f.c | 274 ++++++++++++++++++++++++++++++++++ sysdeps/powerpc/fpu/k_sinf.c | 53 +++++++ sysdeps/powerpc/fpu/s_cosf.c | 71 +++++++++ sysdeps/powerpc/fpu/s_float_bitwise.h | 112 ++++++++++++++ sysdeps/powerpc/fpu/s_sinf.c | 70 +++++++++ 10 files changed, 1083 insertions(+) create mode 100644 sysdeps/powerpc/fpu/e_hypot.c create mode 100644 sysdeps/powerpc/fpu/e_hypotf.c create mode 100644 sysdeps/powerpc/fpu/e_rem_pio2f.c create mode 100644 sysdeps/powerpc/fpu/k_cosf.c create mode 100644 sysdeps/powerpc/fpu/k_rem_pio2f.c create mode 100644 sysdeps/powerpc/fpu/k_sinf.c create mode 100644 sysdeps/powerpc/fpu/s_cosf.c create mode 100644 sysdeps/powerpc/fpu/s_float_bitwise.h create mode 100644 sysdeps/powerpc/fpu/s_sinf.c diff --git a/ChangeLog b/ChangeLog index debb8846ab..afdd8833ff 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,17 @@ +2011-08-01 Adhemerval Zanella + + * 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. + 2011-06-30 Ryan S. Arnold * nptl/sysdeps/unix/sysv/linux/aio_misc.h diff --git a/sysdeps/powerpc/fpu/e_hypot.c b/sysdeps/powerpc/fpu/e_hypot.c new file mode 100644 index 0000000000..f5300ef226 --- /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 , 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 0000000000..0476498f8c --- /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 , 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 0000000000..24ac936a22 --- /dev/null +++ b/sysdeps/powerpc/fpu/e_rem_pio2f.c @@ -0,0 +1,189 @@ +/* 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 , 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 + +#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 0000000000..bef54dc4d3 --- /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 , 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 0000000000..a94ca1380b --- /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 , 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 + +#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 0000000000..df16e1c8cb --- /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 , 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 0000000000..71e24dc50a --- /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 , 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 +#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 0000000000..06b4f2a76e --- /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 , 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 0000000000..d482ccff93 --- /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 , 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 +#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) -- cgit 1.4.1