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authorH.J. Lu <hjl.tools@gmail.com>2017-08-16 08:43:35 -0700
committerH.J. Lu <hjl.tools@gmail.com>2017-08-16 08:46:05 -0700
commit6d5f5b16bc4bd3945e138509d7986a5231ab5ee6 (patch)
treeadbaec0e7ea9b1ba01b4cff58431e25bd3d0d091
parentce3e7f4136a9f5943328c74511542834ca05811b (diff)
downloadtermbaud-hjl/fma/2.26.tar.gz
termbaud-hjl/fma/2.26.tar.xz
termbaud-hjl/fma/2.26.zip
x86-64: Optimize e_expf with FMA [BZ #21912]hjl/fma/2.26
FMA optimized e_expf improves performance by more than 50% on Skylake. [BZ #21912] * sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines): Add e_expf-fma. * sysdeps/x86_64/fpu/multiarch/e_expf-fma.S: New file. * sysdeps/x86_64/fpu/multiarch/e_expf.c: Likewise. * sysdeps/x86_64/fpu/multiarch/ifunc-fma.h: Likewise. (cherry picked from commit 24a2e6588d2e0c91b4003878b0625d4a9360e8f3)
-rw-r--r--sysdeps/x86_64/fpu/multiarch/Makefile3
-rw-r--r--sysdeps/x86_64/fpu/multiarch/e_expf-fma.S182
-rw-r--r--sysdeps/x86_64/fpu/multiarch/e_expf.c26
-rw-r--r--sysdeps/x86_64/fpu/multiarch/ifunc-fma.h34
4 files changed, 245 insertions, 0 deletions
diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
index e9e4f7c7451..41e94b2337b 100644
--- a/sysdeps/x86_64/fpu/multiarch/Makefile
+++ b/sysdeps/x86_64/fpu/multiarch/Makefile
@@ -31,6 +31,9 @@ CFLAGS-slowpow-fma.c = -mfma -mavx2
CFLAGS-s_sin-fma.c = -mfma -mavx2
CFLAGS-s_tan-fma.c = -mfma -mavx2
+# e_expf-fma.S implements both FMA and SSE2 versions of e_expf.
+libm-sysdep_routines += e_expf-fma
+
libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
diff --git a/sysdeps/x86_64/fpu/multiarch/e_expf-fma.S b/sysdeps/x86_64/fpu/multiarch/e_expf-fma.S
new file mode 100644
index 00000000000..43140deced9
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/e_expf-fma.S
@@ -0,0 +1,182 @@
+/* FMA/AVX2 version of IEEE 754 expf.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <sysdep.h>
+
+/* Short algorithm description:
+
+ Let K = 64 (table size).
+ e^x = 2^(x/log(2)) = 2^n * T[j] * (1 + P(y))
+ where
+ x = m*log(2)/K + y, y in [0.0..log(2)/K]
+ m = n*K + j, m,n,j - signed integer, j in [0..K-1]
+ values of 2^(j/K) are tabulated as T[j].
+
+ P(y) is a minimax polynomial approximation of expf(x)-1
+ on small interval [0.0..log(2)/K].
+
+ P(y) = P3*y*y*y*y + P2*y*y*y + P1*y*y + P0*y, calculated as
+ z = y*y; P(y) = (P3*z + P1)*z + (P2*z + P0)*y
+
+ Special cases:
+ expf(NaN) = NaN
+ expf(+INF) = +INF
+ expf(-INF) = 0
+ expf(x) = 1 for subnormals
+ for finite argument, only expf(0)=1 is exact
+ expf(x) overflows if x>88.7228317260742190
+ expf(x) underflows if x<-103.972076416015620
+ */
+
+ .section .text.fma,"ax",@progbits
+ENTRY(__ieee754_expf_fma)
+ /* Input: single precision x in %xmm0 */
+ vcvtss2sd %xmm0, %xmm0, %xmm1 /* Convert x to double precision */
+ vmovd %xmm0, %ecx /* Copy x */
+ vmovsd L(DP_KLN2)(%rip), %xmm2 /* DP K/log(2) */
+ vfmadd213sd L(DP_RD)(%rip), %xmm1, %xmm2 /* DP x*K/log(2)+RD */
+ vmovsd L(DP_P2)(%rip), %xmm3 /* DP P2 */
+ movl %ecx, %eax /* x */
+ andl $0x7fffffff, %ecx /* |x| */
+ lea L(DP_T)(%rip), %rsi /* address of table T[j] */
+ vmovsd L(DP_P3)(%rip), %xmm4 /* DP P3 */
+
+ cmpl $0x42ad496b, %ecx /* |x|<125*log(2) ? */
+ jae L(special_paths_fma)
+
+ /* Here if |x|<125*log(2) */
+ cmpl $0x31800000, %ecx /* |x|<2^(-28) ? */
+ jb L(small_arg_fma)
+
+ /* Main path: here if 2^(-28)<=|x|<125*log(2) */
+ /* %xmm2 = SP x*K/log(2)+RS */
+ vmovd %xmm2, %eax
+ vsubsd L(DP_RD)(%rip), %xmm2, %xmm2 /* DP t=round(x*K/log(2)) */
+ movl %eax, %edx /* n*K+j with trash */
+ andl $0x3f, %eax /* bits of j */
+ vmovsd (%rsi,%rax,8), %xmm5 /* T[j] */
+ andl $0xffffffc0, %edx /* bits of n */
+
+ vfmadd132sd L(DP_NLN2K)(%rip), %xmm1, %xmm2 /* DP y=x-t*log(2)/K */
+ vmulsd %xmm2, %xmm2, %xmm6 /* DP z=y*y */
+
+
+ vfmadd213sd L(DP_P1)(%rip), %xmm6, %xmm4 /* DP P3*z + P1 */
+ vfmadd213sd L(DP_P0)(%rip), %xmm6, %xmm3 /* DP P2*z+P0 */
+
+ addl $0x1fc0, %edx /* bits of n + SP exponent bias */
+ shll $17, %edx /* SP 2^n */
+ vmovd %edx, %xmm1 /* SP 2^n */
+
+ vmulsd %xmm6, %xmm4, %xmm4 /* DP (P3*z+P1)*z */
+
+ vfmadd213sd %xmm4, %xmm3, %xmm2 /* DP P(Y) (P2*z+P0)*y */
+ vfmadd213sd %xmm5, %xmm5, %xmm2 /* DP T[j]*(P(y)+1) */
+ vcvtsd2ss %xmm2, %xmm2, %xmm0 /* SP T[j]*(P(y)+1) */
+ vmulss %xmm1, %xmm0, %xmm0 /* SP result=2^n*(T[j]*(P(y)+1)) */
+ ret
+
+ .p2align 4
+L(small_arg_fma):
+ /* Here if 0<=|x|<2^(-28) */
+ vaddss L(SP_ONE)(%rip), %xmm0, %xmm0 /* 1.0 + x */
+ /* Return 1.0 with inexact raised, except for x==0 */
+ ret
+
+ .p2align 4
+L(special_paths_fma):
+ /* Here if 125*log(2)<=|x| */
+ shrl $31, %eax /* Get sign bit of x, and depending on it: */
+ lea L(SP_RANGE)(%rip), %rdx /* load over/underflow bound */
+ cmpl (%rdx,%rax,4), %ecx /* |x|<under/overflow bound ? */
+ jbe L(near_under_or_overflow_fma)
+
+ /* Here if |x|>under/overflow bound */
+ cmpl $0x7f800000, %ecx /* |x| is finite ? */
+ jae L(arg_inf_or_nan_fma)
+
+ /* Here if |x|>under/overflow bound, and x is finite */
+ testl %eax, %eax /* sign of x nonzero ? */
+ je L(res_overflow_fma)
+
+ /* Here if -inf<x<underflow bound (x<0) */
+ vmovss L(SP_SMALL)(%rip), %xmm0/* load small value 2^(-100) */
+ vmulss %xmm0, %xmm0, %xmm0 /* Return underflowed result (zero or subnormal) */
+ ret
+
+ .p2align 4
+L(res_overflow_fma):
+ /* Here if overflow bound<x<inf (x>0) */
+ vmovss L(SP_LARGE)(%rip), %xmm0/* load large value 2^100 */
+ vmulss %xmm0, %xmm0, %xmm0 /* Return overflowed result (Inf or max normal) */
+ ret
+
+ .p2align 4
+L(arg_inf_or_nan_fma):
+ /* Here if |x| is Inf or NAN */
+ jne L(arg_nan_fma) /* |x| is Inf ? */
+
+ /* Here if |x| is Inf */
+ lea L(SP_INF_0)(%rip), %rdx /* depending on sign of x: */
+ vmovss (%rdx,%rax,4), %xmm0 /* return zero or Inf */
+ ret
+
+ .p2align 4
+L(arg_nan_fma):
+ /* Here if |x| is NaN */
+ vaddss %xmm0, %xmm0, %xmm0 /* Return x+x (raise invalid) */
+ ret
+
+ .p2align 4
+L(near_under_or_overflow_fma):
+ /* Here if 125*log(2)<=|x|<under/overflow bound */
+ vmovd %xmm2, %eax /* bits of n*K+j with trash */
+ vsubsd L(DP_RD)(%rip), %xmm2, %xmm2 /* DP t=round(x*K/log(2)) */
+ movl %eax, %edx /* n*K+j with trash */
+ andl $0x3f, %eax /* bits of j */
+ vmulsd L(DP_NLN2K)(%rip),%xmm2, %xmm2/* DP -t*log(2)/K */
+ andl $0xffffffc0, %edx /* bits of n */
+ vaddsd %xmm1, %xmm2, %xmm0 /* DP y=x-t*log(2)/K */
+ vmulsd %xmm0, %xmm0, %xmm2 /* DP z=y*y */
+ addl $0xffc0, %edx /* bits of n + DP exponent bias */
+ vfmadd213sd L(DP_P0)(%rip), %xmm2, %xmm3/* DP P2*z+P0 */
+ shlq $46, %rdx /* DP 2^n */
+ vfmadd213sd L(DP_P1)(%rip), %xmm2, %xmm4/* DP P3*z+P1 */
+ vmovq %rdx, %xmm1 /* DP 2^n */
+ vmulsd %xmm2, %xmm4, %xmm4 /* DP (P3*z+P1)*z */
+ vfmadd213sd %xmm4, %xmm3, %xmm0 /* DP (P2*z+P0)*y */
+ vmovsd (%rsi,%rax,8), %xmm2
+ vfmadd213sd %xmm2, %xmm2, %xmm0 /* DP T[j]*(P(y)+1) */
+ vmulsd %xmm1, %xmm0, %xmm0 /* DP result=2^n*(T[j]*(P(y)+1)) */
+ vcvtsd2ss %xmm0, %xmm0, %xmm0 /* convert result to single precision */
+ ret
+END(__ieee754_expf_fma)
+
+ .section .rodata.cst8,"aM",@progbits,8
+ .p2align 3
+L(DP_RD): /* double precision 2^52+2^51 */
+ .long 0x00000000, 0x43380000
+ .type L(DP_RD), @object
+ ASM_SIZE_DIRECTIVE(L(DP_RD))
+
+#define __ieee754_expf __ieee754_expf_sse2
+
+#undef strong_alias
+#define strong_alias(ignored1, ignored2)
+
+#include <sysdeps/x86_64/fpu/e_expf.S>
diff --git a/sysdeps/x86_64/fpu/multiarch/e_expf.c b/sysdeps/x86_64/fpu/multiarch/e_expf.c
new file mode 100644
index 00000000000..864d5f9b21a
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/e_expf.c
@@ -0,0 +1,26 @@
+/* Multiple versions of IEEE 754 expf.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+extern double __redirect_ieee754_expf (double);
+
+#define SYMBOL_NAME ieee754_expf
+#include "ifunc-fma.h"
+
+libc_ifunc_redirected (__redirect_ieee754_expf, __ieee754_expf,
+ IFUNC_SELECTOR ());
+strong_alias (__ieee754_expf, __expf_finite)
diff --git a/sysdeps/x86_64/fpu/multiarch/ifunc-fma.h b/sysdeps/x86_64/fpu/multiarch/ifunc-fma.h
new file mode 100644
index 00000000000..383c41ffb17
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/ifunc-fma.h
@@ -0,0 +1,34 @@
+/* Common definition for ifunc selections optimized with AVX2/FMA.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+#include <init-arch.h>
+
+extern __typeof (REDIRECT_NAME) OPTIMIZE (sse2) attribute_hidden;
+extern __typeof (REDIRECT_NAME) OPTIMIZE (fma) attribute_hidden;
+
+static inline void *
+IFUNC_SELECTOR (void)
+{
+ const struct cpu_features* cpu_features = __get_cpu_features ();
+
+ if (CPU_FEATURES_ARCH_P (cpu_features, FMA_Usable)
+ && CPU_FEATURES_ARCH_P (cpu_features, AVX2_Usable))
+ return OPTIMIZE (fma);
+
+ return OPTIMIZE (sse2);
+}