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From fdd895c45c52241f786cf4e29ccc45c240b1acb5 Mon Sep 17 00:00:00 2001
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From: Tulio Magno Quites Machado Filho <tuliom@linux.vnet.ibm.com>
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Date: Mon, 27 Jun 2016 16:03:10 -0300
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Subject: [PATCH] powerpc: Add a POWER8-optimized version of expf()
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This implementation is based on the one already used at
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sysdeps/x86_64/fpu/e_expf.S.
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This implementation improves the performance by ~14% on average in synthetic
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benchmarks at the cost of decreasing accuracy to 1 ULP.
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(cherry picked from commit 35da2541c382d1d4b7c9a15049a3cd1c7a6863a3)
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---
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 ChangeLog                                          |  11 +
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 sysdeps/powerpc/fpu/libm-test-ulps                 |   2 +
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 sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile   |   3 +-
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 .../powerpc64/fpu/multiarch/e_expf-power8.S        |  26 ++
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 .../powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c |  24 ++
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 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c   |  31 +++
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 sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S      | 303 +++++++++++++++++++++
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 7 files changed, 399 insertions(+), 1 deletion(-)
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 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
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 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
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 create mode 100644 sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
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 create mode 100644 sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S
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diff --git a/ChangeLog b/ChangeLog
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index af5f694..6cb2578 100644
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diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
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index 0e3eac7..331763e 100644
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--- a/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
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+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/Makefile
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@@ -24,7 +24,8 @@ libm-sysdep_routines += s_isnan-power7 s_isnan-power6x s_isnan-power6 \
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                        s_modff-power5+ s_modff-ppc64 e_hypot-ppc64 \
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                        e_hypot-power7 e_hypotf-ppc64 e_hypotf-power7 \
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                        s_isnan-power8 s_isinf-power8 s_finite-power8 \
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-                       s_llrint-power8 s_llround-power8
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+                       s_llrint-power8 s_llround-power8 \
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+                       e_expf-power8 e_expf-ppc64
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 CFLAGS-s_logbf-power7.c = -mcpu=power7
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 CFLAGS-s_logbl-power7.c = -mcpu=power7
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diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
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new file mode 100644
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index 0000000..02eff24
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--- /dev/null
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+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-power8.S
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@@ -0,0 +1,26 @@
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+/* __ieee754_expf() POWER8 version.
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+   Copyright (C) 2016 Free Software Foundation, Inc.
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+   This file is part of the GNU C Library.
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+
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+   The GNU C Library is free software; you can redistribute it and/or
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+   modify it under the terms of the GNU Lesser General Public
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+   License as published by the Free Software Foundation; either
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+   version 2.1 of the License, or (at your option) any later version.
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+
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+   The GNU C Library is distributed in the hope that it will be useful,
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+   but WITHOUT ANY WARRANTY; without even the implied warranty of
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+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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+   Lesser General Public License for more details.
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+
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+   You should have received a copy of the GNU Lesser General Public
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+   License along with the GNU C Library; if not, see
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+   <http://www.gnu.org/licenses/>.  */
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+
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+#include <sysdep.h>
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+
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+#undef strong_alias
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+#define strong_alias(a, b)
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+
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+#define __ieee754_expf __ieee754_expf_power8
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+
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+#include <sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S>
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diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
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new file mode 100644
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index 0000000..40f9e3a
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--- /dev/null
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+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf-ppc64.c
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@@ -0,0 +1,24 @@
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+/* __ieee_expf() PowerPC64 version.
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+   Copyright (C) 2016 Free Software Foundation, Inc.
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+   This file is part of the GNU C Library.
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+
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+   The GNU C Library is free software; you can redistribute it and/or
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+   modify it under the terms of the GNU Lesser General Public
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+   License as published by the Free Software Foundation; either
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+   version 2.1 of the License, or (at your option) any later version.
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+
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+   The GNU C Library is distributed in the hope that it will be useful,
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+   but WITHOUT ANY WARRANTY; without even the implied warranty of
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+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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+   Lesser General Public License for more details.
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+
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+   You should have received a copy of the GNU Lesser General Public
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+   License along with the GNU C Library; if not, see
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+   <http://www.gnu.org/licenses/>.  */
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+
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+#undef strong_alias
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+#define strong_alias(a, b)
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+
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+#define __ieee754_expf __ieee754_expf_ppc64
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+
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+#include <sysdeps/ieee754/flt-32/e_expf.c>
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diff --git a/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
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new file mode 100644
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index 0000000..1d9a8c6
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--- /dev/null
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+++ b/sysdeps/powerpc/powerpc64/fpu/multiarch/e_expf.c
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@@ -0,0 +1,31 @@
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+/* Multiple versions of ieee754_expf.
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+   Copyright (C) 2016 Free Software Foundation, Inc.
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+   This file is part of the GNU C Library.
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+
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+   The GNU C Library is free software; you can redistribute it and/or
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+   modify it under the terms of the GNU Lesser General Public
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+   License as published by the Free Software Foundation; either
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+   version 2.1 of the License, or (at your option) any later version.
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+
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+   The GNU C Library is distributed in the hope that it will be useful,
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+   but WITHOUT ANY WARRANTY; without even the implied warranty of
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+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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+   Lesser General Public License for more details.
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+
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+   You should have received a copy of the GNU Lesser General Public
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+   License along with the GNU C Library; if not, see
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+   <http://www.gnu.org/licenses/>.  */
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+
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+#include <math.h>
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+#include <math_ldbl_opt.h>
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+#include "init-arch.h"
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+
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+extern __typeof (__ieee754_expf) __ieee754_expf_ppc64 attribute_hidden;
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+extern __typeof (__ieee754_expf) __ieee754_expf_power8 attribute_hidden;
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+
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+libc_ifunc (__ieee754_expf,
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+	    (hwcap2 & PPC_FEATURE2_ARCH_2_07)
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+	    ? __ieee754_expf_power8
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+	    : __ieee754_expf_ppc64);
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+
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+strong_alias (__ieee754_expf, __expf_finite)
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diff --git a/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S
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new file mode 100644
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index 0000000..a5e68bb
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--- /dev/null
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+++ b/sysdeps/powerpc/powerpc64/power8/fpu/e_expf.S
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@@ -0,0 +1,303 @@
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+/* Optimized expf().  PowerPC64/POWER8 version.
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+   Copyright (C) 2016 Free Software Foundation, Inc.
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+   This file is part of the GNU C Library.
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+
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+   The GNU C Library is free software; you can redistribute it and/or
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+   modify it under the terms of the GNU Lesser General Public
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+   License as published by the Free Software Foundation; either
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+   version 2.1 of the License, or (at your option) any later version.
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+
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+   The GNU C Library is distributed in the hope that it will be useful,
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+   but WITHOUT ANY WARRANTY; without even the implied warranty of
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+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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+   Lesser General Public License for more details.
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+
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+   You should have received a copy of the GNU Lesser General Public
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+   License along with the GNU C Library; if not, see
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+   <http://www.gnu.org/licenses/>.  */
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+
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+#include <sysdep.h>
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+
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+/* Short algorithm description:
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+ *
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+ *  Let K = 64 (table size).
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+ *       e^x  = 2^(x/log(2)) = 2^n * T[j] * (1 + P(y))
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+ *  where:
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+ *       x = m*log(2)/K + y,    y in [0.0..log(2)/K]
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+ *       m = n*K + j,           m,n,j - signed integer, j in [0..K-1]
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+ *       values of 2^(j/K) are tabulated as T[j].
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+ *
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+ *       P(y) is a minimax polynomial approximation of expf(y)-1
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+ *       on small interval [0.0..log(2)/K].
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+ *
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+ *       P(y) = P3*y*y*y*y + P2*y*y*y + P1*y*y + P0*y, calculated as
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+ *       z = y*y;    P(y) = (P3*z + P1)*z + (P2*z + P0)*y
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+ *
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+ * Special cases:
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+ *  expf(NaN) = NaN
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+ *  expf(+INF) = +INF
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+ *  expf(-INF) = 0
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+ *  expf(x) = 1 for subnormals
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+ *  for finite argument, only expf(0)=1 is exact
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+ *  expf(x) overflows if x>88.7228317260742190
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+ *  expf(x) underflows if x<-103.972076416015620
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+ */
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+
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+#define C1 0x42ad496b		/* Single precision 125*log(2).  */
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+#define C2 0x31800000		/* Single precision 2^(-28).  */
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+#define SP_INF 0x7f800000	/* Single precision Inf.  */
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+#define SP_EXP_BIAS 0x1fc0	/* Single precision exponent bias.  */
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+
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+#define DATA_OFFSET r9
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+
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+/* Implements the function
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+
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+   float [fp1] expf (float [fp1] x)  */
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+
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+	.machine power8
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+EALIGN(__ieee754_expf, 4, 0)
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+	addis	DATA_OFFSET,r2,.Lanchor@toc@ha
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+	addi	DATA_OFFSET,DATA_OFFSET,.Lanchor@toc@l
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+
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+	xscvdpspn v0,v1
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+	mfvsrd	r8,v0		/* r8 = x  */
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+	lfd	fp2,(.KLN2-.Lanchor)(DATA_OFFSET)
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+	lfd	fp3,(.P2-.Lanchor)(DATA_OFFSET)
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+	rldicl	r3,r8,32,33	/* r3 = |x|  */
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+	lis	r4,C1@ha	/* r4 = 125*log(2)  */
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+	ori	r4,r4,C1@l
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+	cmpw	r3,r4
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+	lfd	fp5,(.P3-.Lanchor)(DATA_OFFSET)
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+	lfd	fp4,(.RS-.Lanchor)(DATA_OFFSET)
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+	fmadd	fp2,fp1,fp2,fp4	/* fp2 = x * K/log(2) + (2^23 + 2^22)  */
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+	bge	L(special_paths)	/* |x| >= 125*log(2) ?  */
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+
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+	lis	r4,C2@ha
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+	ori	r4,r4,C2@l
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+	cmpw	r3,r4
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+	blt	L(small_args)	/* |x| < 2^(-28) ?  */
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+
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+	/* Main path: here if 2^(-28) <= |x| < 125*log(2) */
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+	frsp	fp6,fp2
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+	xscvdpsp v2,v2
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+	mfvsrd	r8,v2
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+	mr	r3,r8			/* r3 = m  */
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+	rldicl	r8,r8,32,58		/* r8 = j  */
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+	lfs	fp4,(.SP_RS-.Lanchor)(DATA_OFFSET)
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+	fsubs	fp2,fp6,fp4		/* fp2 = m = x * K/log(2)  */
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+	srdi	r3,r3,32
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+	clrrwi	r3,r3,6			/* r3 = n  */
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+	lfd	fp6,(.NLN2K-.Lanchor)(DATA_OFFSET)
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+	fmadd	fp0,fp2,fp6,fp1		/* fp0 = y = x - m*log(2)/K  */
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+	fmul	fp2,fp0,fp0		/* fp2 = z = y^2  */
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+	lfd	fp4,(.P1-.Lanchor)(DATA_OFFSET)
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+	lfd	fp6,(.P0-.Lanchor)(DATA_OFFSET)
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+	lis	r4,SP_EXP_BIAS@ha
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+	ori	r4,r4,SP_EXP_BIAS@l
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+	add	r3,r3,r4
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+	rldic	r3,r3,49,1		/* r3 = 2^n  */
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+	fmadd	fp4,fp5,fp2,fp4		/* fp4 = P3 * z + P1  */
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+	fmadd	fp6,fp3,fp2,fp6		/* fp6 = P2 * z + P0  */
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+	mtvsrd	v1,r3
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+	xscvspdp v1,v1
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+	fmul	fp4,fp4,fp2		/* fp4 = (P3 * z + P1)*z  */
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+	fmadd	fp0,fp0,fp6,fp4		/* fp0 = P(y)  */
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+	sldi	r8,r8,3			/* Access doublewords from T[j].  */
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+	addi	r6,DATA_OFFSET,(.Ttable-.Lanchor)
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+	lfdx	fp3,r6,r8
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+	fmadd	fp0,fp0,fp3,fp3		/* fp0 = T[j] * (1 + P(y))  */
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+	fmul	fp1,fp1,fp0		/* fp1 = 2^n * T[j] * (1 + P(y))  */
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+	frsp	fp1,fp1
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+	blr
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+
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+	.align	4
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+/* x is either underflow, overflow, infinite or NaN.  */
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+L(special_paths):
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+	srdi	r8,r8,32
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+	rlwinm	r8,r8,3,29,29		/* r8 = 0, if x positive.
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+					   r8 = 4, otherwise.  */
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+	addi	r6,DATA_OFFSET,(.SPRANGE-.Lanchor)
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+	lwzx	r4,r6,r8		/* r4 = .SPRANGE[signbit(x)]  */
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+	cmpw	r3,r4
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+	/* |x| <= .SPRANGE[signbit(x)]  */
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+	ble	L(near_under_or_overflow)
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+
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+	lis	r4,SP_INF@ha
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+	ori	r4,r4,SP_INF@l
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+	cmpw	r3,r4
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+	bge	L(arg_inf_or_nan)	/* |x| > Infinite ?  */
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+
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+	addi	r6,DATA_OFFSET,(.SPLARGE_SMALL-.Lanchor)
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+	lfsx	fp1,r6,r8
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+	fmuls	fp1,fp1,fp1
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+	blr
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+
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+
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+	.align	4
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+L(small_args):
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+	/* expf(x) = 1.0, where |x| < |2^(-28)|  */
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+	lfs	fp2,(.SPone-.Lanchor)(DATA_OFFSET)
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+	fadds	fp1,fp1,fp2
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+	blr
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+
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+
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+	.align	4
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+L(arg_inf_or_nan:)
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+	bne	L(arg_nan)
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+
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+	/* expf(+INF) = +INF
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+	   expf(-INF) = 0  */
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+	addi	r6,DATA_OFFSET,(.INF_ZERO-.Lanchor)
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+	lfsx	fp1,r6,r8
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+	blr
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+
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+
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+	.align	4
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+L(arg_nan):
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+	/* expf(NaN) = NaN  */
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+	fadd	fp1,fp1,fp1
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+	frsp	fp1,fp1
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+	blr
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+
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+	.align	4
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+L(near_under_or_overflow):
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+	frsp	fp6,fp2
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+	xscvdpsp v2,v2
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+	mfvsrd	r8,v2
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+	mr	r3,r8			/* r3 = m  */
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+	rldicl	r8,r8,32,58		/* r8 = j  */
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+	lfs	fp4,(.SP_RS-.Lanchor)(DATA_OFFSET)
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+	fsubs	fp2,fp6,fp4		/* fp2 = m = x * K/log(2)  */
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+	srdi	r3,r3,32
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+	clrrwi	r3,r3,6			/* r3 = n  */
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+	lfd	fp6,(.NLN2K-.Lanchor)(DATA_OFFSET)
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+	fmadd	fp0,fp2,fp6,fp1		/* fp0 = y = x - m*log(2)/K  */
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+	fmul	fp2,fp0,fp0		/* fp2 = z = y^2  */
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+	lfd	fp4,(.P1-.Lanchor)(DATA_OFFSET)
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+	lfd	fp6,(.P0-.Lanchor)(DATA_OFFSET)
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+	ld	r4,(.DP_EXP_BIAS-.Lanchor)(DATA_OFFSET)
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+	add	r3,r3,r4
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+	rldic	r3,r3,46,1		/* r3 = 2  */
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+	fmadd	fp4,fp5,fp2,fp4		/* fp4 = P3 * z + P1  */
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+	fmadd	fp6,fp3,fp2,fp6		/* fp6 = P2 * z + P0  */
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+	mtvsrd	v1,r3
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+	fmul	fp4,fp4,fp2		/* fp4 = (P3*z + P1)*z  */
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+	fmadd	fp0,fp0,fp6,fp4		/* fp0 = P(y)  */
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+	sldi	r8,r8,3			/* Access doublewords from T[j].  */
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+	addi	r6,DATA_OFFSET,(.Ttable-.Lanchor)
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+	lfdx	fp3,r6,r8
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+	fmadd	fp0,fp0,fp3,fp3		/* fp0 = T[j] * (1 + T[j])  */
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+	fmul	fp1,fp1,fp0		/* fp1 = 2^n * T[j] * (1 + T[j])  */
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+	frsp	fp1,fp1
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+	blr
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+END(__ieee754_expf)
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+
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+	.section .rodata, "a",@progbits
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+.Lanchor:
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+	.balign	8
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+/* Table T[j] = 2^(j/K).  Double precision.  */
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+.Ttable:
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+	.8byte	0x3ff0000000000000
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+	.8byte	0x3ff02c9a3e778061
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+	.8byte	0x3ff059b0d3158574
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+	.8byte	0x3ff0874518759bc8
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+	.8byte	0x3ff0b5586cf9890f
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+	.8byte	0x3ff0e3ec32d3d1a2
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+	.8byte	0x3ff11301d0125b51
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+	.8byte	0x3ff1429aaea92de0
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+	.8byte	0x3ff172b83c7d517b
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+	.8byte	0x3ff1a35beb6fcb75
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+	.8byte	0x3ff1d4873168b9aa
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+	.8byte	0x3ff2063b88628cd6
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+	.8byte	0x3ff2387a6e756238
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+	.8byte	0x3ff26b4565e27cdd
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+	.8byte	0x3ff29e9df51fdee1
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+	.8byte	0x3ff2d285a6e4030b
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+	.8byte	0x3ff306fe0a31b715
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+	.8byte	0x3ff33c08b26416ff
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+	.8byte	0x3ff371a7373aa9cb
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+	.8byte	0x3ff3a7db34e59ff7
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+	.8byte	0x3ff3dea64c123422
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+	.8byte	0x3ff4160a21f72e2a
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+	.8byte	0x3ff44e086061892d
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+	.8byte	0x3ff486a2b5c13cd0
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+	.8byte	0x3ff4bfdad5362a27
00db10
+	.8byte	0x3ff4f9b2769d2ca7
00db10
+	.8byte	0x3ff5342b569d4f82
00db10
+	.8byte	0x3ff56f4736b527da
00db10
+	.8byte	0x3ff5ab07dd485429
00db10
+	.8byte	0x3ff5e76f15ad2148
00db10
+	.8byte	0x3ff6247eb03a5585
00db10
+	.8byte	0x3ff6623882552225
00db10
+	.8byte	0x3ff6a09e667f3bcd
00db10
+	.8byte	0x3ff6dfb23c651a2f
00db10
+	.8byte	0x3ff71f75e8ec5f74
00db10
+	.8byte	0x3ff75feb564267c9
00db10
+	.8byte	0x3ff7a11473eb0187
00db10
+	.8byte	0x3ff7e2f336cf4e62
00db10
+	.8byte	0x3ff82589994cce13
00db10
+	.8byte	0x3ff868d99b4492ed
00db10
+	.8byte	0x3ff8ace5422aa0db
00db10
+	.8byte	0x3ff8f1ae99157736
00db10
+	.8byte	0x3ff93737b0cdc5e5
00db10
+	.8byte	0x3ff97d829fde4e50
00db10
+	.8byte	0x3ff9c49182a3f090
00db10
+	.8byte	0x3ffa0c667b5de565
00db10
+	.8byte	0x3ffa5503b23e255d
00db10
+	.8byte	0x3ffa9e6b5579fdbf
00db10
+	.8byte	0x3ffae89f995ad3ad
00db10
+	.8byte	0x3ffb33a2b84f15fb
00db10
+	.8byte	0x3ffb7f76f2fb5e47
00db10
+	.8byte	0x3ffbcc1e904bc1d2
00db10
+	.8byte	0x3ffc199bdd85529c
00db10
+	.8byte	0x3ffc67f12e57d14b
00db10
+	.8byte	0x3ffcb720dcef9069
00db10
+	.8byte	0x3ffd072d4a07897c
00db10
+	.8byte	0x3ffd5818dcfba487
00db10
+	.8byte	0x3ffda9e603db3285
00db10
+	.8byte	0x3ffdfc97337b9b5f
00db10
+	.8byte	0x3ffe502ee78b3ff6
00db10
+	.8byte	0x3ffea4afa2a490da
00db10
+	.8byte	0x3ffefa1bee615a27
00db10
+	.8byte	0x3fff50765b6e4540
00db10
+	.8byte	0x3fffa7c1819e90d8
00db10
+
00db10
+.KLN2:
00db10
+	.8byte	0x40571547652b82fe	/* Double precision K/log(2).  */
00db10
+
00db10
+/* Double precision polynomial coefficients.  */
00db10
+.P0:
00db10
+	.8byte	0x3fefffffffffe7c6
00db10
+.P1:
00db10
+	.8byte	0x3fe00000008d6118
00db10
+.P2:
00db10
+	.8byte	0x3fc55550da752d4f
00db10
+.P3:
00db10
+	.8byte	0x3fa56420eb78fa85
00db10
+
00db10
+.RS:
00db10
+	.8byte	0x4168000000000000	/* Double precision 2^23 + 2^22.  */
00db10
+.NLN2K:
00db10
+	.8byte	0xbf862e42fefa39ef	/* Double precision -log(2)/K.  */
00db10
+.DP_EXP_BIAS:
00db10
+	.8byte	0x000000000000ffc0	/* Double precision exponent bias.  */
00db10
+
00db10
+	.balign	4
00db10
+.SPone:
00db10
+	.4byte	0x3f800000	/* Single precision 1.0.  */
00db10
+.SP_RS:
00db10
+	.4byte	0x4b400000	/* Single precision 2^23 + 2^22.  */
00db10
+
00db10
+.SPRANGE: /* Single precision overflow/underflow bounds.  */
00db10
+	.4byte	0x42b17217	/* if x>this bound, then result overflows.  */
00db10
+	.4byte	0x42cff1b4	/* if x
00db10
+
00db10
+.SPLARGE_SMALL:
00db10
+	.4byte	0x71800000	/* 2^100.  */
00db10
+	.4byte	0x0d800000	/* 2^-100.  */
00db10
+
00db10
+.INF_ZERO:
00db10
+	.4byte	0x7f800000	/* Single precision Inf.  */
00db10
+	.4byte	0		/* Single precision zero.  */
00db10
+
00db10
+strong_alias (__ieee754_expf, __expf_finite)
00db10
-- 
00db10
2.1.0
00db10