x86-64: Optimize e_expf with FMA [BZ #21912]

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.

4 files changed, 245 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
index 9daf2cf205..1b61795aff 100644
--- a/sysdeps/x86_64/fpu/multiarch/Makefile
+++ b/sysdeps/x86_64/fpu/multiarch/Makefile
@@ -35,6 +35,9 @@ 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 0000000000..43140deced
--- /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 0000000000..864d5f9b21
--- /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 0000000000..383c41ffb1
--- /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);
+}