[PATCH] x86-64: Optimize e_expf with FMA [BZ #21912]
H.J. Lu
hjl.tools@gmail.com
Wed Aug 16 15:33:00 GMT 2017
On Wed, Aug 16, 2017 at 7:04 AM, Carlos O'Donell <carlos@redhat.com> wrote:
> On 08/16/2017 09:34 AM, H.J. Lu wrote:
>> FMA optimized e_expf improves performance by more than 50% on Skylake.
>>
>> Any comments?
>
> Exactly how much of e_expf-fma.S do you need to achieve that 50% speedup?
>
> How does this algorithm compare to what is already implemented for e_expf?
>
> My questions are basically leading to this:
>
> (a) Can we write a generic e_expf in C with the special cases written
> in C, and...
>
> (b) Is there a core kernel computation that we can then implement in assembly?
>
>> H.J.
>> [BZ #21912]
>> * sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
>> Add and 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.
>> ---
>> sysdeps/x86_64/fpu/multiarch/Makefile | 2 +
>> sysdeps/x86_64/fpu/multiarch/e_expf-fma.S | 182 ++++++++++++++++++++++++++++++
>> sysdeps/x86_64/fpu/multiarch/e_expf.c | 26 +++++
>> sysdeps/x86_64/fpu/multiarch/ifunc-fma.h | 34 ++++++
>> 4 files changed, 244 insertions(+)
>> create mode 100644 sysdeps/x86_64/fpu/multiarch/e_expf-fma.S
>> create mode 100644 sysdeps/x86_64/fpu/multiarch/e_expf.c
>> create mode 100644 sysdeps/x86_64/fpu/multiarch/ifunc-fma.h
>>
>> diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
>> index 9daf2cf205..20dd44a7ff 100644
>> --- a/sysdeps/x86_64/fpu/multiarch/Makefile
>> +++ b/sysdeps/x86_64/fpu/multiarch/Makefile
>> @@ -35,6 +35,8 @@ CFLAGS-slowpow-fma.c = -mfma -mavx2
>> CFLAGS-s_sin-fma.c = -mfma -mavx2
>> CFLAGS-s_tan-fma.c = -mfma -mavx2
>>
>> +libm-sysdep_routines += e_expf-fma
>> +
>
> Add a comment explaining why this is a distinct line from the ones below.
Done.
>> 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..e081186667
>> --- /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
>> + */
>
> Use GNU-style comments please.
Done.
>> +
>> + .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)
>
> OK.
>
>> 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);
>> +}
>
> OK.
Here is the updated patch I am checking in.
Thanks.
--
H.J.
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