| Message ID | 20221018024901.3381469-5-goldstein.w.n@gmail.com |
|---|---|
| State | New |
| Headers | show |
| Series | [v1,1/7] x86: Optimize memchr-evex.S and implement with VMM headers | expand |
On Mon, Oct 17, 2022 at 7:49 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote: > > Optimization is: > 1. Cache latest result in "fast path" loop with `vmovdqu` instead of > `kunpckdq`. This helps if there are more than one matches. > > Code Size Changes: > strrchr-evex.S : +30 bytes (Same number of cache lines) > > Net perf changes: > > Reported as geometric mean of all improvements / regressions from N=10 > runs of the benchtests. Value as New Time / Old Time so < 1.0 is > improvement and 1.0 is regression. > > strrchr-evex.S : 0.932 (From cases with higher match frequency) > > Full results attached in email. > > Full check passes on x86-64. > --- > sysdeps/x86_64/multiarch/strrchr-evex.S | 371 +++++++++++++----------- > 1 file changed, 200 insertions(+), 171 deletions(-) > > diff --git a/sysdeps/x86_64/multiarch/strrchr-evex.S b/sysdeps/x86_64/multiarch/strrchr-evex.S > index 992b45fb47..45487dc87a 100644 > --- a/sysdeps/x86_64/multiarch/strrchr-evex.S > +++ b/sysdeps/x86_64/multiarch/strrchr-evex.S > @@ -26,25 +26,30 @@ > # define STRRCHR __strrchr_evex > # endif > > -# define VMOVU vmovdqu64 > -# define VMOVA vmovdqa64 > +# include "x86-evex256-vecs.h" > > # ifdef USE_AS_WCSRCHR > -# define SHIFT_REG esi > - > -# define kunpck kunpckbw > +# define RCX_M cl > +# define SHIFT_REG rcx > +# define VPCOMPRESS vpcompressd > +# define kunpck_2x kunpckbw > # define kmov_2x kmovd > # define maskz_2x ecx > # define maskm_2x eax > # define CHAR_SIZE 4 > # define VPMIN vpminud > # define VPTESTN vptestnmd > +# define VPTEST vptestmd > # define VPBROADCAST vpbroadcastd > +# define VPCMPEQ vpcmpeqd > # define VPCMP vpcmpd > -# else > -# define SHIFT_REG edi > > -# define kunpck kunpckdq > +# define USE_WIDE_CHAR > +# else > +# define RCX_M ecx > +# define SHIFT_REG rdi > +# define VPCOMPRESS vpcompressb > +# define kunpck_2x kunpckdq > # define kmov_2x kmovq > # define maskz_2x rcx > # define maskm_2x rax > @@ -52,58 +57,48 @@ > # define CHAR_SIZE 1 > # define VPMIN vpminub > # define VPTESTN vptestnmb > +# define VPTEST vptestmb > # define VPBROADCAST vpbroadcastb > +# define VPCMPEQ vpcmpeqb > # define VPCMP vpcmpb > # endif > > -# define XMMZERO xmm16 > -# define YMMZERO ymm16 > -# define YMMMATCH ymm17 > -# define YMMSAVE ymm18 > +# include "reg-macros.h" > > -# define YMM1 ymm19 > -# define YMM2 ymm20 > -# define YMM3 ymm21 > -# define YMM4 ymm22 > -# define YMM5 ymm23 > -# define YMM6 ymm24 > -# define YMM7 ymm25 > -# define YMM8 ymm26 > - > - > -# define VEC_SIZE 32 > +# define VMATCH VMM(0) > +# define CHAR_PER_VEC (VEC_SIZE / CHAR_SIZE) > # define PAGE_SIZE 4096 > - .section .text.evex, "ax", @progbits > -ENTRY(STRRCHR) > + > + .section SECTION(.text), "ax", @progbits > +ENTRY_P2ALIGN(STRRCHR, 6) > movl %edi, %eax > - /* Broadcast CHAR to YMMMATCH. */ > - VPBROADCAST %esi, %YMMMATCH > + /* Broadcast CHAR to VMATCH. */ > + VPBROADCAST %esi, %VMATCH > > andl $(PAGE_SIZE - 1), %eax > cmpl $(PAGE_SIZE - VEC_SIZE), %eax > jg L(cross_page_boundary) > > -L(page_cross_continue): > - VMOVU (%rdi), %YMM1 > - /* k0 has a 1 for each zero CHAR in YMM1. */ > - VPTESTN %YMM1, %YMM1, %k0 > - kmovd %k0, %ecx > - testl %ecx, %ecx > + VMOVU (%rdi), %VMM(1) > + /* k0 has a 1 for each zero CHAR in VEC(1). */ > + VPTESTN %VMM(1), %VMM(1), %k0 > + KMOV %k0, %VRSI > + test %VRSI, %VRSI > jz L(aligned_more) > /* fallthrough: zero CHAR in first VEC. */ > - > - /* K1 has a 1 for each search CHAR match in YMM1. */ > - VPCMP $0, %YMMMATCH, %YMM1, %k1 > - kmovd %k1, %eax > +L(page_cross_return): > + /* K1 has a 1 for each search CHAR match in VEC(1). */ > + VPCMPEQ %VMATCH, %VMM(1), %k1 > + KMOV %k1, %VRAX > /* Build mask up until first zero CHAR (used to mask of > potential search CHAR matches past the end of the string). > */ > - blsmskl %ecx, %ecx > - andl %ecx, %eax > + blsmsk %VRSI, %VRSI > + and %VRSI, %VRAX > jz L(ret0) > - /* Get last match (the `andl` removed any out of bounds > - matches). */ > - bsrl %eax, %eax > + /* Get last match (the `and` removed any out of bounds matches). > + */ > + bsr %VRAX, %VRAX > # ifdef USE_AS_WCSRCHR > leaq (%rdi, %rax, CHAR_SIZE), %rax > # else > @@ -116,22 +111,22 @@ L(ret0): > search path for earlier matches. */ > .p2align 4,, 6 > L(first_vec_x1): > - VPCMP $0, %YMMMATCH, %YMM2, %k1 > - kmovd %k1, %eax > - blsmskl %ecx, %ecx > + VPCMPEQ %VMATCH, %VMM(2), %k1 > + KMOV %k1, %VRAX > + blsmsk %VRCX, %VRCX > /* eax non-zero if search CHAR in range. */ > - andl %ecx, %eax > + and %VRCX, %VRAX > jnz L(first_vec_x1_return) > > - /* fallthrough: no match in YMM2 then need to check for earlier > - matches (in YMM1). */ > + /* fallthrough: no match in VEC(2) then need to check for > + earlier matches (in VEC(1)). */ > .p2align 4,, 4 > L(first_vec_x0_test): > - VPCMP $0, %YMMMATCH, %YMM1, %k1 > - kmovd %k1, %eax > - testl %eax, %eax > + VPCMPEQ %VMATCH, %VMM(1), %k1 > + KMOV %k1, %VRAX > + test %VRAX, %VRAX > jz L(ret1) > - bsrl %eax, %eax > + bsr %VRAX, %VRAX > # ifdef USE_AS_WCSRCHR > leaq (%rsi, %rax, CHAR_SIZE), %rax > # else > @@ -142,129 +137,144 @@ L(ret1): > > .p2align 4,, 10 > L(first_vec_x1_or_x2): > - VPCMP $0, %YMM3, %YMMMATCH, %k3 > - VPCMP $0, %YMM2, %YMMMATCH, %k2 > + VPCMPEQ %VMM(3), %VMATCH, %k3 > + VPCMPEQ %VMM(2), %VMATCH, %k2 > /* K2 and K3 have 1 for any search CHAR match. Test if any > - matches between either of them. Otherwise check YMM1. */ > - kortestd %k2, %k3 > + matches between either of them. Otherwise check VEC(1). */ > + KORTEST %k2, %k3 > jz L(first_vec_x0_test) > > - /* Guranteed that YMM2 and YMM3 are within range so merge the > - two bitmasks then get last result. */ > - kunpck %k2, %k3, %k3 > - kmovq %k3, %rax > - bsrq %rax, %rax > - leaq (VEC_SIZE)(%r8, %rax, CHAR_SIZE), %rax > + /* Guranteed that VEC(2) and VEC(3) are within range so merge > + the two bitmasks then get last result. */ > + kunpck_2x %k2, %k3, %k3 > + kmov_2x %k3, %maskm_2x > + bsr %maskm_2x, %maskm_2x > + leaq (VEC_SIZE * 1)(%r8, %rax, CHAR_SIZE), %rax > ret > > - .p2align 4,, 6 > + .p2align 4,, 7 > L(first_vec_x3): > - VPCMP $0, %YMMMATCH, %YMM4, %k1 > - kmovd %k1, %eax > - blsmskl %ecx, %ecx > - /* If no search CHAR match in range check YMM1/YMM2/YMM3. */ > - andl %ecx, %eax > + VPCMPEQ %VMATCH, %VMM(4), %k1 > + KMOV %k1, %VRAX > + blsmsk %VRCX, %VRCX > + /* If no search CHAR match in range check VEC(1)/VEC(2)/VEC(3). > + */ > + and %VRCX, %VRAX > jz L(first_vec_x1_or_x2) > - bsrl %eax, %eax > + bsr %VRAX, %VRAX > leaq (VEC_SIZE * 3)(%rdi, %rax, CHAR_SIZE), %rax > ret > > + > .p2align 4,, 6 > L(first_vec_x0_x1_test): > - VPCMP $0, %YMMMATCH, %YMM2, %k1 > - kmovd %k1, %eax > - /* Check YMM2 for last match first. If no match try YMM1. */ > - testl %eax, %eax > + VPCMPEQ %VMATCH, %VMM(2), %k1 > + KMOV %k1, %VRAX > + /* Check VEC(2) for last match first. If no match try VEC(1). > + */ > + test %VRAX, %VRAX > jz L(first_vec_x0_test) > .p2align 4,, 4 > L(first_vec_x1_return): > - bsrl %eax, %eax > + bsr %VRAX, %VRAX > leaq (VEC_SIZE)(%rdi, %rax, CHAR_SIZE), %rax > ret > > + > .p2align 4,, 10 > L(first_vec_x2): > - VPCMP $0, %YMMMATCH, %YMM3, %k1 > - kmovd %k1, %eax > - blsmskl %ecx, %ecx > - /* Check YMM3 for last match first. If no match try YMM2/YMM1. > - */ > - andl %ecx, %eax > + VPCMPEQ %VMATCH, %VMM(3), %k1 > + KMOV %k1, %VRAX > + blsmsk %VRCX, %VRCX > + /* Check VEC(3) for last match first. If no match try > + VEC(2)/VEC(1). */ > + and %VRCX, %VRAX > jz L(first_vec_x0_x1_test) > - bsrl %eax, %eax > + bsr %VRAX, %VRAX > leaq (VEC_SIZE * 2)(%rdi, %rax, CHAR_SIZE), %rax > ret > > > - .p2align 4 > + .p2align 4,, 12 > L(aligned_more): > - /* Need to keep original pointer incase YMM1 has last match. */ > +L(page_cross_continue): > + /* Need to keep original pointer incase VEC(1) has last match. > + */ > movq %rdi, %rsi > andq $-VEC_SIZE, %rdi > - VMOVU VEC_SIZE(%rdi), %YMM2 > - VPTESTN %YMM2, %YMM2, %k0 > - kmovd %k0, %ecx > - testl %ecx, %ecx > + > + VMOVU VEC_SIZE(%rdi), %VMM(2) > + VPTESTN %VMM(2), %VMM(2), %k0 > + KMOV %k0, %VRCX > + > + test %VRCX, %VRCX > jnz L(first_vec_x1) > > - VMOVU (VEC_SIZE * 2)(%rdi), %YMM3 > - VPTESTN %YMM3, %YMM3, %k0 > - kmovd %k0, %ecx > - testl %ecx, %ecx > + VMOVU (VEC_SIZE * 2)(%rdi), %VMM(3) > + VPTESTN %VMM(3), %VMM(3), %k0 > + KMOV %k0, %VRCX > + > + test %VRCX, %VRCX > jnz L(first_vec_x2) > > - VMOVU (VEC_SIZE * 3)(%rdi), %YMM4 > - VPTESTN %YMM4, %YMM4, %k0 > - kmovd %k0, %ecx > + VMOVU (VEC_SIZE * 3)(%rdi), %VMM(4) > + VPTESTN %VMM(4), %VMM(4), %k0 > + KMOV %k0, %VRCX > movq %rdi, %r8 > - testl %ecx, %ecx > + test %VRCX, %VRCX > jnz L(first_vec_x3) > > andq $-(VEC_SIZE * 2), %rdi > - .p2align 4 > + .p2align 4,, 10 > L(first_aligned_loop): > - /* Preserve YMM1, YMM2, YMM3, and YMM4 until we can gurantee > - they don't store a match. */ > - VMOVA (VEC_SIZE * 4)(%rdi), %YMM5 > - VMOVA (VEC_SIZE * 5)(%rdi), %YMM6 > + /* Preserve VEC(1), VEC(2), VEC(3), and VEC(4) until we can > + gurantee they don't store a match. */ > + VMOVA (VEC_SIZE * 4)(%rdi), %VMM(5) > + VMOVA (VEC_SIZE * 5)(%rdi), %VMM(6) > > - VPCMP $0, %YMM5, %YMMMATCH, %k2 > - vpxord %YMM6, %YMMMATCH, %YMM7 > + VPCMPEQ %VMM(5), %VMATCH, %k2 > + vpxord %VMM(6), %VMATCH, %VMM(7) > > - VPMIN %YMM5, %YMM6, %YMM8 > - VPMIN %YMM8, %YMM7, %YMM7 > + VPMIN %VMM(5), %VMM(6), %VMM(8) > + VPMIN %VMM(8), %VMM(7), %VMM(7) > > - VPTESTN %YMM7, %YMM7, %k1 > + VPTESTN %VMM(7), %VMM(7), %k1 > subq $(VEC_SIZE * -2), %rdi > - kortestd %k1, %k2 > + KORTEST %k1, %k2 > jz L(first_aligned_loop) > > - VPCMP $0, %YMM6, %YMMMATCH, %k3 > - VPTESTN %YMM8, %YMM8, %k1 > - ktestd %k1, %k1 > + VPCMPEQ %VMM(6), %VMATCH, %k3 > + VPTESTN %VMM(8), %VMM(8), %k1 > + > + /* If k1 is zero, then we found a CHAR match but no null-term. > + We can now safely throw out VEC1-4. */ > + KTEST %k1, %k1 > jz L(second_aligned_loop_prep) > > - kortestd %k2, %k3 > + KORTEST %k2, %k3 > jnz L(return_first_aligned_loop) > > + > .p2align 4,, 6 > L(first_vec_x1_or_x2_or_x3): > - VPCMP $0, %YMM4, %YMMMATCH, %k4 > - kmovd %k4, %eax > - testl %eax, %eax > + VPCMPEQ %VMM(4), %VMATCH, %k4 > + KMOV %k4, %VRAX > + bsr %VRAX, %VRAX > jz L(first_vec_x1_or_x2) > - bsrl %eax, %eax > leaq (VEC_SIZE * 3)(%r8, %rax, CHAR_SIZE), %rax > ret > > + > .p2align 4,, 8 > L(return_first_aligned_loop): > - VPTESTN %YMM5, %YMM5, %k0 > - kunpck %k0, %k1, %k0 > + VPTESTN %VMM(5), %VMM(5), %k0 > + > + /* Combined results from VEC5/6. */ > + kunpck_2x %k0, %k1, %k0 > kmov_2x %k0, %maskz_2x > > blsmsk %maskz_2x, %maskz_2x > - kunpck %k2, %k3, %k3 > + kunpck_2x %k2, %k3, %k3 > kmov_2x %k3, %maskm_2x > and %maskz_2x, %maskm_2x > jz L(first_vec_x1_or_x2_or_x3) > @@ -280,47 +290,62 @@ L(return_first_aligned_loop): > L(second_aligned_loop_prep): > L(second_aligned_loop_set_furthest_match): > movq %rdi, %rsi > - kunpck %k2, %k3, %k4 > - > + /* Ideally we would safe k2/k3 but `kmov/kunpck` take uops on > + port0 and have noticable overhead in the loop. */ > + VMOVA %VMM(5), %VMM(7) > + VMOVA %VMM(6), %VMM(8) > .p2align 4 > L(second_aligned_loop): > - VMOVU (VEC_SIZE * 4)(%rdi), %YMM1 > - VMOVU (VEC_SIZE * 5)(%rdi), %YMM2 > - > - VPCMP $0, %YMM1, %YMMMATCH, %k2 > - vpxord %YMM2, %YMMMATCH, %YMM3 > + VMOVU (VEC_SIZE * 4)(%rdi), %VMM(5) > + VMOVU (VEC_SIZE * 5)(%rdi), %VMM(6) > + VPCMPEQ %VMM(5), %VMATCH, %k2 > + vpxord %VMM(6), %VMATCH, %VMM(3) > > - VPMIN %YMM1, %YMM2, %YMM4 > - VPMIN %YMM3, %YMM4, %YMM3 > + VPMIN %VMM(5), %VMM(6), %VMM(4) > + VPMIN %VMM(3), %VMM(4), %VMM(3) > > - VPTESTN %YMM3, %YMM3, %k1 > + VPTESTN %VMM(3), %VMM(3), %k1 > subq $(VEC_SIZE * -2), %rdi > - kortestd %k1, %k2 > + KORTEST %k1, %k2 > jz L(second_aligned_loop) > - > - VPCMP $0, %YMM2, %YMMMATCH, %k3 > - VPTESTN %YMM4, %YMM4, %k1 > - ktestd %k1, %k1 > + VPCMPEQ %VMM(6), %VMATCH, %k3 > + VPTESTN %VMM(4), %VMM(4), %k1 > + KTEST %k1, %k1 > jz L(second_aligned_loop_set_furthest_match) > > - kortestd %k2, %k3 > - /* branch here because there is a significant advantage interms > - of output dependency chance in using edx. */ > + /* branch here because we know we have a match in VEC7/8 but > + might not in VEC5/6 so the latter is expected to be less > + likely. */ > + KORTEST %k2, %k3 > jnz L(return_new_match) > + > L(return_old_match): > - kmovq %k4, %rax > - bsrq %rax, %rax > - leaq (VEC_SIZE * 2)(%rsi, %rax, CHAR_SIZE), %rax > + VPCMPEQ %VMM(8), %VMATCH, %k0 > + KMOV %k0, %VRCX > + bsr %VRCX, %VRCX > + jnz L(return_old_match_ret) > + > + VPCMPEQ %VMM(7), %VMATCH, %k0 > + KMOV %k0, %VRCX > + bsr %VRCX, %VRCX > + subq $VEC_SIZE, %rsi > +L(return_old_match_ret): > + leaq (VEC_SIZE * 3)(%rsi, %rcx, CHAR_SIZE), %rax > ret > > + .p2align 4,, 10 > L(return_new_match): > - VPTESTN %YMM1, %YMM1, %k0 > - kunpck %k0, %k1, %k0 > + VPTESTN %VMM(5), %VMM(5), %k0 > + > + /* Combined results from VEC5/6. */ > + kunpck_2x %k0, %k1, %k0 > kmov_2x %k0, %maskz_2x > > blsmsk %maskz_2x, %maskz_2x > - kunpck %k2, %k3, %k3 > + kunpck_2x %k2, %k3, %k3 > kmov_2x %k3, %maskm_2x > + > + /* Match at end was out-of-bounds so use last known match. */ > and %maskz_2x, %maskm_2x > jz L(return_old_match) > > @@ -328,49 +353,53 @@ L(return_new_match): > leaq (VEC_SIZE * 2)(%rdi, %rax, CHAR_SIZE), %rax > ret > > + .p2align 4,, 4 > L(cross_page_boundary): > - /* eax contains all the page offset bits of src (rdi). `xor rdi, > - rax` sets pointer will all page offset bits cleared so > - offset of (PAGE_SIZE - VEC_SIZE) will get last aligned VEC > - before page cross (guranteed to be safe to read). Doing this > - as opposed to `movq %rdi, %rax; andq $-VEC_SIZE, %rax` saves > - a bit of code size. */ > xorq %rdi, %rax > - VMOVU (PAGE_SIZE - VEC_SIZE)(%rax), %YMM1 > - VPTESTN %YMM1, %YMM1, %k0 > - kmovd %k0, %ecx > + mov $-1, %VRDX > + VMOVU (PAGE_SIZE - VEC_SIZE)(%rax), %VMM(6) > + VPTESTN %VMM(6), %VMM(6), %k0 > + KMOV %k0, %VRSI > + > +# ifdef USE_AS_WCSRCHR > + movl %edi, %ecx > + and $(VEC_SIZE - 1), %ecx > + shrl $2, %ecx > +# endif > + shlx %VGPR(SHIFT_REG), %VRDX, %VRDX > > - /* Shift out zero CHAR matches that are before the begining of > - src (rdi). */ > # ifdef USE_AS_WCSRCHR > - movl %edi, %esi > - andl $(VEC_SIZE - 1), %esi > - shrl $2, %esi > + kmovb %edx, %k1 > +# else > + KMOV %VRDX, %k1 > # endif > - shrxl %SHIFT_REG, %ecx, %ecx > > - testl %ecx, %ecx > + /* Need to adjust result to VEC(1) so it can be re-used by > + L(return_vec_x0_test). The alternative is to collect VEC(1) > + will a page cross load which is far more expensive. */ > + VPCOMPRESS %VMM(6), %VMM(1){%k1}{z} > + > + /* We could technically just jmp back after the vpcompress but > + it doesn't save any 16-byte blocks. */ > + shrx %VGPR(SHIFT_REG), %VRSI, %VRSI > + test %VRSI, %VRSI > jz L(page_cross_continue) > > - /* Found zero CHAR so need to test for search CHAR. */ > - VPCMP $0, %YMMMATCH, %YMM1, %k1 > - kmovd %k1, %eax > - /* Shift out search CHAR matches that are before the begining of > - src (rdi). */ > - shrxl %SHIFT_REG, %eax, %eax > - > - /* Check if any search CHAR match in range. */ > - blsmskl %ecx, %ecx > - andl %ecx, %eax > - jz L(ret3) > - bsrl %eax, %eax > + /* Duplicate of return logic from ENTRY. Doesn't cause spill to > + next cache line so might as well copy it here. */ > + VPCMPEQ %VMATCH, %VMM(1), %k1 > + KMOV %k1, %VRAX > + blsmsk %VRSI, %VRSI > + and %VRSI, %VRAX > + jz L(ret_page_cross) > + bsr %VRAX, %VRAX > # ifdef USE_AS_WCSRCHR > leaq (%rdi, %rax, CHAR_SIZE), %rax > # else > addq %rdi, %rax > # endif > -L(ret3): > +L(ret_page_cross): > ret > - > + /* 1 byte till next cache line. */ > END(STRRCHR) > #endif > -- > 2.34.1 > Results For: strrchr align,freq ,len ,max_char ,pos ,seek ,__strrchr_evex ,__strrchr_evex_orig 0 ,1 ,1 ,127 ,0 ,0 ,3.544 ,3.517 ,1.007 0 ,1 ,1 ,127 ,0 ,23 ,3.516 ,3.443 ,1.021 0 ,1 ,10 ,127 ,9 ,0 ,3.696 ,3.703 ,0.998 0 ,1 ,10 ,127 ,9 ,23 ,3.686 ,3.694 ,0.998 0 ,1 ,1024 ,127 ,0 ,0 ,3.541 ,3.424 ,1.034 0 ,1 ,1024 ,127 ,0 ,23 ,33.578 ,34.335 ,0.978 0 ,1 ,1024 ,127 ,1024 ,0 ,32.236 ,33.703 ,0.956 0 ,1 ,1024 ,127 ,1024 ,23 ,32.255 ,33.207 ,0.971 0 ,1 ,1024 ,127 ,144 ,0 ,9.681 ,10.761 ,0.9 0 ,1 ,1024 ,127 ,144 ,23 ,32.131 ,33.112 ,0.97 0 ,1 ,1024 ,127 ,192 ,0 ,11.173 ,12.72 ,0.878 0 ,1 ,1024 ,127 ,192 ,23 ,32.363 ,33.122 ,0.977 0 ,1 ,1024 ,127 ,240 ,0 ,11.068 ,12.692 ,0.872 0 ,1 ,1024 ,127 ,240 ,23 ,33.127 ,34.004 ,0.974 0 ,1 ,1024 ,127 ,288 ,0 ,12.579 ,14.452 ,0.87 0 ,1 ,1024 ,127 ,288 ,23 ,32.186 ,33.59 ,0.958 0 ,1 ,1024 ,127 ,48 ,0 ,4.728 ,5.669 ,0.834 0 ,1 ,1024 ,127 ,48 ,23 ,33.103 ,35.064 ,0.944 0 ,1 ,1024 ,127 ,736 ,0 ,23.846 ,25.818 ,0.924 0 ,1 ,1024 ,127 ,736 ,23 ,32.278 ,34.687 ,0.931 0 ,1 ,1024 ,127 ,784 ,0 ,25.566 ,27.51 ,0.929 0 ,1 ,1024 ,127 ,784 ,23 ,34.801 ,35.27 ,0.987 0 ,1 ,1024 ,127 ,832 ,0 ,27.218 ,29.017 ,0.938 0 ,1 ,1024 ,127 ,832 ,23 ,35.255 ,36.369 ,0.969 0 ,1 ,1024 ,127 ,880 ,0 ,27.413 ,29.169 ,0.94 0 ,1 ,1024 ,127 ,880 ,23 ,35.739 ,38.252 ,0.934 0 ,1 ,1024 ,127 ,928 ,0 ,29.056 ,30.715 ,0.946 0 ,1 ,1024 ,127 ,928 ,23 ,34.646 ,36.301 ,0.954 0 ,1 ,1024 ,127 ,96 ,0 ,5.923 ,7.163 ,0.827 0 ,1 ,1024 ,127 ,96 ,23 ,31.587 ,33.085 ,0.955 0 ,1 ,1024 ,127 ,976 ,0 ,30.784 ,32.313 ,0.953 0 ,1 ,1024 ,127 ,976 ,23 ,35.76 ,36.116 ,0.99 0 ,1 ,1072 ,127 ,1024 ,0 ,32.421 ,33.863 ,0.957 0 ,1 ,1072 ,127 ,1024 ,23 ,35.049 ,37.781 ,0.928 0 ,1 ,11 ,127 ,10 ,0 ,3.7 ,3.705 ,0.999 0 ,1 ,11 ,127 ,10 ,23 ,3.697 ,3.699 ,0.999 0 ,1 ,112 ,127 ,144 ,0 ,5.914 ,7.112 ,0.832 0 ,1 ,112 ,127 ,144 ,23 ,6.616 ,8.659 ,0.764 0 ,1 ,112 ,127 ,16 ,0 ,3.565 ,3.576 ,0.997 0 ,1 ,112 ,127 ,16 ,23 ,7.888 ,8.337 ,0.946 0 ,1 ,112 ,127 ,256 ,0 ,5.916 ,6.985 ,0.847 0 ,1 ,112 ,127 ,256 ,23 ,6.581 ,8.642 ,0.762 0 ,1 ,112 ,127 ,64 ,0 ,5.352 ,6.955 ,0.77 0 ,1 ,112 ,127 ,64 ,23 ,7.401 ,8.403 ,0.881 0 ,1 ,112 ,127 ,96 ,0 ,7.084 ,7.239 ,0.979 0 ,1 ,112 ,127 ,96 ,23 ,6.146 ,7.451 ,0.825 0 ,1 ,1120 ,127 ,1024 ,0 ,32.469 ,34.045 ,0.954 0 ,1 ,1120 ,127 ,1024 ,23 ,37.041 ,37.475 ,0.988 0 ,1 ,1168 ,127 ,1024 ,0 ,32.342 ,34.027 ,0.95 0 ,1 ,1168 ,127 ,1024 ,23 ,41.858 ,42.644 ,0.982 0 ,1 ,12 ,127 ,11 ,0 ,3.723 ,3.729 ,0.998 0 ,1 ,12 ,127 ,11 ,23 ,3.729 ,3.714 ,1.004 0 ,1 ,1216 ,127 ,1024 ,0 ,32.631 ,34.11 ,0.957 0 ,1 ,1216 ,127 ,1024 ,23 ,39.96 ,40.846 ,0.978 0 ,1 ,1264 ,127 ,1024 ,0 ,32.411 ,33.803 ,0.959 0 ,1 ,1264 ,127 ,1024 ,23 ,40.231 ,41.592 ,0.967 0 ,1 ,128 ,127 ,0 ,0 ,3.492 ,3.474 ,1.005 0 ,1 ,128 ,127 ,0 ,23 ,9.893 ,11.676 ,0.847 0 ,1 ,128 ,127 ,112 ,0 ,5.956 ,6.956 ,0.856 0 ,1 ,128 ,127 ,112 ,23 ,10.68 ,12.006 ,0.89 0 ,1 ,128 ,127 ,128 ,0 ,9.81 ,10.775 ,0.91 0 ,1 ,128 ,127 ,128 ,23 ,8.669 ,9.809 ,0.884 0 ,1 ,128 ,127 ,144 ,0 ,10.021 ,10.81 ,0.927 0 ,1 ,128 ,127 ,144 ,23 ,9.02 ,10.357 ,0.871 0 ,1 ,128 ,127 ,192 ,0 ,9.76 ,10.873 ,0.898 0 ,1 ,128 ,127 ,192 ,23 ,8.848 ,10.049 ,0.88 0 ,1 ,128 ,127 ,240 ,0 ,9.979 ,10.941 ,0.912 0 ,1 ,128 ,127 ,240 ,23 ,8.658 ,10.027 ,0.863 0 ,1 ,128 ,127 ,288 ,0 ,10.064 ,11.29 ,0.891 0 ,1 ,128 ,127 ,288 ,23 ,8.632 ,9.855 ,0.876 0 ,1 ,128 ,127 ,32 ,0 ,4.695 ,5.663 ,0.829 0 ,1 ,128 ,127 ,32 ,23 ,9.803 ,11.638 ,0.842 0 ,1 ,128 ,127 ,48 ,0 ,4.642 ,5.951 ,0.78 0 ,1 ,128 ,127 ,48 ,23 ,9.872 ,11.125 ,0.887 0 ,1 ,128 ,127 ,80 ,0 ,5.074 ,6.474 ,0.784 0 ,1 ,128 ,127 ,80 ,23 ,9.745 ,11.426 ,0.853 0 ,1 ,128 ,127 ,96 ,0 ,6.501 ,7.481 ,0.869 0 ,1 ,128 ,127 ,96 ,23 ,8.717 ,10.366 ,0.841 0 ,1 ,13 ,127 ,12 ,0 ,3.737 ,3.739 ,1.0 0 ,1 ,13 ,127 ,12 ,23 ,3.715 ,3.723 ,0.998 0 ,1 ,1312 ,127 ,1024 ,0 ,32.427 ,34.083 ,0.951 0 ,1 ,1312 ,127 ,1024 ,23 ,43.614 ,44.317 ,0.984 0 ,1 ,14 ,127 ,13 ,0 ,3.739 ,3.748 ,0.997 0 ,1 ,14 ,127 ,13 ,23 ,3.721 ,3.723 ,0.999 0 ,1 ,144 ,127 ,128 ,0 ,10.539 ,10.65 ,0.99 0 ,1 ,144 ,127 ,128 ,23 ,9.751 ,11.0 ,0.886 0 ,1 ,15 ,127 ,14 ,0 ,3.727 ,3.723 ,1.001 0 ,1 ,15 ,127 ,14 ,23 ,3.746 ,3.761 ,0.996 0 ,1 ,16 ,127 ,0 ,0 ,3.416 ,3.418 ,0.999 0 ,1 ,16 ,127 ,0 ,23 ,3.436 ,3.446 ,0.997 0 ,1 ,16 ,127 ,144 ,0 ,3.619 ,3.628 ,0.997 0 ,1 ,16 ,127 ,144 ,23 ,4.019 ,4.016 ,1.001 0 ,1 ,16 ,127 ,15 ,0 ,3.727 ,3.728 ,1.0 0 ,1 ,16 ,127 ,15 ,23 ,3.733 ,3.737 ,0.999 0 ,1 ,16 ,127 ,16 ,0 ,3.42 ,3.416 ,1.001 0 ,1 ,16 ,127 ,16 ,23 ,3.974 ,3.956 ,1.005 0 ,1 ,16 ,127 ,192 ,0 ,3.592 ,3.595 ,0.999 0 ,1 ,16 ,127 ,192 ,23 ,3.981 ,3.992 ,0.997 0 ,1 ,16 ,127 ,240 ,0 ,3.562 ,3.58 ,0.995 0 ,1 ,16 ,127 ,240 ,23 ,3.973 ,3.91 ,1.016 0 ,1 ,16 ,127 ,256 ,0 ,3.529 ,3.523 ,1.002 0 ,1 ,16 ,127 ,256 ,23 ,4.114 ,4.057 ,1.014 0 ,1 ,16 ,127 ,288 ,0 ,3.634 ,3.672 ,0.99 0 ,1 ,16 ,127 ,288 ,23 ,4.061 ,4.511 ,0.9 0 ,1 ,16 ,127 ,48 ,0 ,3.539 ,3.546 ,0.998 0 ,1 ,16 ,127 ,48 ,23 ,4.021 ,4.002 ,1.005 0 ,1 ,16 ,127 ,64 ,0 ,3.514 ,3.512 ,1.001 0 ,1 ,16 ,127 ,64 ,23 ,3.973 ,3.968 ,1.001 0 ,1 ,16 ,127 ,96 ,0 ,3.523 ,3.528 ,0.998 0 ,1 ,16 ,127 ,96 ,23 ,4.019 ,4.016 ,1.001 0 ,1 ,160 ,127 ,144 ,0 ,9.98 ,10.889 ,0.917 0 ,1 ,160 ,127 ,144 ,23 ,9.568 ,11.164 ,0.857 0 ,1 ,160 ,127 ,16 ,0 ,3.6 ,3.606 ,0.998 0 ,1 ,160 ,127 ,16 ,23 ,12.466 ,13.468 ,0.926 0 ,1 ,160 ,127 ,256 ,0 ,9.782 ,10.864 ,0.9 0 ,1 ,160 ,127 ,256 ,23 ,8.74 ,10.167 ,0.86 0 ,1 ,160 ,127 ,64 ,0 ,5.308 ,6.514 ,0.815 0 ,1 ,160 ,127 ,64 ,23 ,10.168 ,11.726 ,0.867 0 ,1 ,160 ,127 ,96 ,0 ,6.254 ,7.071 ,0.885 0 ,1 ,160 ,127 ,96 ,23 ,8.791 ,10.18 ,0.864 0 ,1 ,17 ,127 ,16 ,0 ,3.755 ,3.747 ,1.002 0 ,1 ,17 ,127 ,16 ,23 ,3.749 ,3.742 ,1.002 0 ,1 ,176 ,127 ,128 ,0 ,10.071 ,10.816 ,0.931 0 ,1 ,176 ,127 ,128 ,23 ,9.842 ,10.987 ,0.896 0 ,1 ,176 ,127 ,160 ,0 ,9.943 ,10.917 ,0.911 0 ,1 ,176 ,127 ,160 ,23 ,9.401 ,10.855 ,0.866 0 ,1 ,176 ,127 ,32 ,0 ,4.799 ,5.122 ,0.937 0 ,1 ,176 ,127 ,32 ,23 ,9.912 ,11.536 ,0.859 0 ,1 ,1760 ,127 ,2048 ,0 ,72.585 ,67.02 ,1.083 0 ,1 ,1760 ,127 ,2048 ,23 ,72.354 ,70.53 ,1.026 0 ,1 ,1760 ,127 ,288 ,0 ,13.012 ,14.359 ,0.906 0 ,1 ,1760 ,127 ,288 ,23 ,53.579 ,75.066 ,0.714 0 ,1 ,18 ,127 ,17 ,0 ,3.723 ,3.734 ,0.997 0 ,1 ,18 ,127 ,17 ,23 ,3.719 ,3.723 ,0.999 0 ,1 ,1808 ,127 ,2048 ,0 ,74.738 ,72.933 ,1.025 0 ,1 ,1808 ,127 ,2048 ,23 ,73.708 ,69.817 ,1.056 0 ,1 ,1808 ,127 ,240 ,0 ,11.466 ,12.936 ,0.886 0 ,1 ,1808 ,127 ,240 ,23 ,52.31 ,74.244 ,0.705 0 ,1 ,1856 ,127 ,192 ,0 ,11.493 ,12.777 ,0.9 0 ,1 ,1856 ,127 ,192 ,23 ,56.637 ,75.554 ,0.75 0 ,1 ,1856 ,127 ,2048 ,0 ,76.752 ,75.005 ,1.023 0 ,1 ,1856 ,127 ,2048 ,23 ,75.763 ,75.647 ,1.002 0 ,1 ,19 ,127 ,18 ,0 ,3.733 ,3.737 ,0.999 0 ,1 ,19 ,127 ,18 ,23 ,3.709 ,3.721 ,0.997 0 ,1 ,1904 ,127 ,144 ,0 ,9.908 ,10.968 ,0.903 0 ,1 ,1904 ,127 ,144 ,23 ,54.074 ,73.718 ,0.734 0 ,1 ,1904 ,127 ,2048 ,0 ,76.284 ,74.221 ,1.028 0 ,1 ,1904 ,127 ,2048 ,23 ,76.677 ,75.992 ,1.009 0 ,1 ,192 ,127 ,176 ,0 ,9.472 ,10.994 ,0.862 0 ,1 ,192 ,127 ,176 ,23 ,11.123 ,12.382 ,0.898 0 ,1 ,1952 ,127 ,2048 ,0 ,78.545 ,76.143 ,1.032 0 ,1 ,1952 ,127 ,2048 ,23 ,77.067 ,79.001 ,0.976 0 ,1 ,1952 ,127 ,96 ,0 ,5.921 ,7.117 ,0.832 0 ,1 ,1952 ,127 ,96 ,23 ,78.832 ,77.729 ,1.014 0 ,1 ,2 ,127 ,1 ,0 ,3.567 ,3.564 ,1.001 0 ,1 ,2 ,127 ,1 ,23 ,3.474 ,3.479 ,0.999 0 ,1 ,20 ,127 ,19 ,0 ,3.735 ,3.735 ,1.0 0 ,1 ,20 ,127 ,19 ,23 ,3.724 ,3.732 ,0.998 0 ,1 ,2000 ,127 ,2048 ,0 ,79.702 ,75.814 ,1.051 0 ,1 ,2000 ,127 ,2048 ,23 ,82.662 ,80.546 ,1.026 0 ,1 ,2000 ,127 ,48 ,0 ,4.641 ,5.922 ,0.784 0 ,1 ,2000 ,127 ,48 ,23 ,78.879 ,80.783 ,0.976 0 ,1 ,2048 ,127 ,0 ,0 ,3.782 ,3.626 ,1.043 0 ,1 ,2048 ,127 ,0 ,23 ,88.244 ,81.961 ,1.077 0 ,1 ,2048 ,127 ,1024 ,0 ,32.647 ,34.351 ,0.95 0 ,1 ,2048 ,127 ,1024 ,23 ,63.059 ,63.135 ,0.999 0 ,1 ,2048 ,127 ,128 ,0 ,10.048 ,10.918 ,0.92 0 ,1 ,2048 ,127 ,128 ,23 ,59.186 ,76.42 ,0.774 0 ,1 ,2048 ,127 ,144 ,0 ,9.887 ,10.926 ,0.905 0 ,1 ,2048 ,127 ,144 ,23 ,58.821 ,78.417 ,0.75 0 ,1 ,2048 ,127 ,1760 ,0 ,72.29 ,65.89 ,1.097 0 ,1 ,2048 ,127 ,1760 ,23 ,67.317 ,70.046 ,0.961 0 ,1 ,2048 ,127 ,1808 ,0 ,74.84 ,72.362 ,1.034 0 ,1 ,2048 ,127 ,1808 ,23 ,66.716 ,67.123 ,0.994 0 ,1 ,2048 ,127 ,1856 ,0 ,76.885 ,73.468 ,1.047 0 ,1 ,2048 ,127 ,1856 ,23 ,65.625 ,65.874 ,0.996 0 ,1 ,2048 ,127 ,1904 ,0 ,76.289 ,73.484 ,1.038 0 ,1 ,2048 ,127 ,1904 ,23 ,68.284 ,72.223 ,0.945 0 ,1 ,2048 ,127 ,192 ,0 ,11.595 ,12.834 ,0.903 0 ,1 ,2048 ,127 ,192 ,23 ,83.689 ,78.987 ,1.06 0 ,1 ,2048 ,127 ,1952 ,0 ,77.785 ,75.969 ,1.024 0 ,1 ,2048 ,127 ,1952 ,23 ,66.755 ,70.554 ,0.946 0 ,1 ,2048 ,127 ,2000 ,0 ,78.418 ,75.695 ,1.036 0 ,1 ,2048 ,127 ,2000 ,23 ,71.465 ,70.069 ,1.02 0 ,1 ,2048 ,127 ,2048 ,0 ,77.747 ,79.151 ,0.982 0 ,1 ,2048 ,127 ,2048 ,23 ,79.178 ,75.595 ,1.047 0 ,1 ,2048 ,127 ,240 ,0 ,11.527 ,12.989 ,0.887 0 ,1 ,2048 ,127 ,240 ,23 ,69.117 ,80.272 ,0.861 0 ,1 ,2048 ,127 ,256 ,0 ,13.007 ,14.606 ,0.891 0 ,1 ,2048 ,127 ,256 ,23 ,83.298 ,73.27 ,1.137 0 ,1 ,2048 ,127 ,288 ,0 ,12.933 ,14.597 ,0.886 0 ,1 ,2048 ,127 ,288 ,23 ,82.111 ,83.34 ,0.985 0 ,1 ,2048 ,127 ,32 ,0 ,4.737 ,4.775 ,0.992 0 ,1 ,2048 ,127 ,32 ,23 ,78.505 ,82.154 ,0.956 0 ,1 ,2048 ,127 ,4096 ,0 ,81.364 ,81.725 ,0.996 0 ,1 ,2048 ,127 ,4096 ,23 ,80.334 ,74.208 ,1.083 0 ,1 ,2048 ,127 ,48 ,0 ,4.651 ,5.776 ,0.805 0 ,1 ,2048 ,127 ,48 ,23 ,85.128 ,83.639 ,1.018 0 ,1 ,2048 ,127 ,512 ,0 ,19.777 ,20.435 ,0.968 0 ,1 ,2048 ,127 ,512 ,23 ,72.706 ,76.171 ,0.955 0 ,1 ,2048 ,127 ,64 ,0 ,7.221 ,8.125 ,0.889 0 ,1 ,2048 ,127 ,64 ,23 ,78.534 ,81.715 ,0.961 0 ,1 ,2048 ,127 ,96 ,0 ,6.214 ,7.207 ,0.862 0 ,1 ,2048 ,127 ,96 ,23 ,82.681 ,82.298 ,1.005 0 ,1 ,208 ,127 ,16 ,0 ,3.591 ,3.628 ,0.99 0 ,1 ,208 ,127 ,16 ,23 ,11.938 ,13.415 ,0.89 0 ,1 ,208 ,127 ,192 ,0 ,11.149 ,12.75 ,0.874 0 ,1 ,208 ,127 ,192 ,23 ,11.712 ,13.415 ,0.873 0 ,1 ,208 ,127 ,256 ,0 ,11.173 ,12.8 ,0.873 0 ,1 ,208 ,127 ,256 ,23 ,10.529 ,12.765 ,0.825 0 ,1 ,208 ,127 ,48 ,0 ,4.648 ,5.711 ,0.814 0 ,1 ,208 ,127 ,48 ,23 ,11.612 ,13.052 ,0.89 0 ,1 ,208 ,127 ,64 ,0 ,5.235 ,6.257 ,0.837 0 ,1 ,208 ,127 ,64 ,23 ,11.809 ,13.386 ,0.882 0 ,1 ,2096 ,127 ,2048 ,0 ,80.173 ,79.245 ,1.012 0 ,1 ,2096 ,127 ,2048 ,23 ,71.71 ,74.296 ,0.965 0 ,1 ,21 ,127 ,20 ,0 ,3.705 ,3.715 ,0.997 0 ,1 ,21 ,127 ,20 ,23 ,3.699 ,3.703 ,0.999 0 ,1 ,2144 ,127 ,2048 ,0 ,81.623 ,79.436 ,1.028 0 ,1 ,2144 ,127 ,2048 ,23 ,69.342 ,69.534 ,0.997 0 ,1 ,2192 ,127 ,2048 ,0 ,79.678 ,81.904 ,0.973 0 ,1 ,2192 ,127 ,2048 ,23 ,70.794 ,72.831 ,0.972 0 ,1 ,22 ,127 ,21 ,0 ,3.69 ,3.695 ,0.999 0 ,1 ,22 ,127 ,21 ,23 ,3.691 ,3.7 ,0.997 0 ,1 ,224 ,127 ,128 ,0 ,10.675 ,10.772 ,0.991 0 ,1 ,224 ,127 ,128 ,23 ,12.065 ,12.436 ,0.97 0 ,1 ,224 ,127 ,208 ,0 ,11.13 ,12.897 ,0.863 0 ,1 ,224 ,127 ,208 ,23 ,11.075 ,12.8 ,0.865 0 ,1 ,224 ,127 ,288 ,0 ,11.031 ,12.636 ,0.873 0 ,1 ,224 ,127 ,288 ,23 ,10.654 ,12.748 ,0.836 0 ,1 ,224 ,127 ,32 ,0 ,4.819 ,4.812 ,1.001 0 ,1 ,224 ,127 ,32 ,23 ,11.908 ,13.53 ,0.88 0 ,1 ,224 ,127 ,512 ,0 ,11.124 ,12.704 ,0.876 0 ,1 ,224 ,127 ,512 ,23 ,10.477 ,12.634 ,0.829 0 ,1 ,2240 ,127 ,2048 ,0 ,80.648 ,76.87 ,1.049 0 ,1 ,2240 ,127 ,2048 ,23 ,71.957 ,72.525 ,0.992 0 ,1 ,2288 ,127 ,2048 ,0 ,80.434 ,76.598 ,1.05 0 ,1 ,2288 ,127 ,2048 ,23 ,72.331 ,73.156 ,0.989 0 ,1 ,23 ,127 ,22 ,0 ,3.704 ,3.709 ,0.999 0 ,1 ,23 ,127 ,22 ,23 ,3.733 ,3.727 ,1.002 0 ,1 ,2336 ,127 ,2048 ,0 ,79.963 ,74.387 ,1.075 0 ,1 ,2336 ,127 ,2048 ,23 ,72.296 ,72.702 ,0.994 0 ,1 ,24 ,127 ,23 ,0 ,3.71 ,3.719 ,0.998 0 ,1 ,24 ,127 ,23 ,23 ,3.704 ,3.759 ,0.985 0 ,1 ,240 ,127 ,224 ,0 ,11.049 ,12.695 ,0.87 0 ,1 ,240 ,127 ,224 ,23 ,11.624 ,13.28 ,0.875 0 ,1 ,25 ,127 ,24 ,0 ,3.733 ,3.749 ,0.996 0 ,1 ,25 ,127 ,24 ,23 ,3.698 ,3.695 ,1.001 0 ,1 ,256 ,127 ,0 ,0 ,3.37 ,3.366 ,1.001 0 ,1 ,256 ,127 ,0 ,23 ,13.22 ,14.761 ,0.896 0 ,1 ,256 ,127 ,112 ,0 ,6.14 ,7.417 ,0.828 0 ,1 ,256 ,127 ,112 ,23 ,11.638 ,13.641 ,0.853 0 ,1 ,256 ,127 ,144 ,0 ,9.767 ,10.759 ,0.908 0 ,1 ,256 ,127 ,144 ,23 ,13.663 ,14.306 ,0.955 0 ,1 ,256 ,127 ,16 ,0 ,3.506 ,3.647 ,0.961 0 ,1 ,256 ,127 ,16 ,23 ,14.096 ,16.019 ,0.88 0 ,1 ,256 ,127 ,160 ,0 ,9.716 ,10.87 ,0.894 0 ,1 ,256 ,127 ,160 ,23 ,12.678 ,14.429 ,0.879 0 ,1 ,256 ,127 ,192 ,0 ,11.156 ,12.571 ,0.887 0 ,1 ,256 ,127 ,192 ,23 ,13.887 ,14.705 ,0.944 0 ,1 ,256 ,127 ,208 ,0 ,11.074 ,12.458 ,0.889 0 ,1 ,256 ,127 ,208 ,23 ,13.711 ,14.331 ,0.957 0 ,1 ,256 ,127 ,240 ,0 ,11.224 ,12.857 ,0.873 0 ,1 ,256 ,127 ,240 ,23 ,13.125 ,14.22 ,0.923 0 ,1 ,256 ,127 ,256 ,0 ,12.597 ,14.283 ,0.882 0 ,1 ,256 ,127 ,256 ,23 ,12.154 ,14.09 ,0.863 0 ,1 ,256 ,127 ,288 ,0 ,12.885 ,14.712 ,0.876 0 ,1 ,256 ,127 ,288 ,23 ,12.466 ,14.646 ,0.851 0 ,1 ,256 ,127 ,48 ,0 ,4.674 ,5.7 ,0.82 0 ,1 ,256 ,127 ,48 ,23 ,13.01 ,14.715 ,0.884 0 ,1 ,256 ,127 ,64 ,0 ,5.267 ,6.387 ,0.825 0 ,1 ,256 ,127 ,64 ,23 ,13.105 ,15.062 ,0.87 0 ,1 ,256 ,127 ,96 ,0 ,6.543 ,6.909 ,0.947 0 ,1 ,256 ,127 ,96 ,23 ,11.623 ,13.606 ,0.854 0 ,1 ,26 ,127 ,25 ,0 ,3.7 ,3.709 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diff --git a/sysdeps/x86_64/multiarch/strrchr-evex.S b/sysdeps/x86_64/multiarch/strrchr-evex.S index 992b45fb47..45487dc87a 100644 --- a/sysdeps/x86_64/multiarch/strrchr-evex.S +++ b/sysdeps/x86_64/multiarch/strrchr-evex.S @@ -26,25 +26,30 @@ # define STRRCHR __strrchr_evex # endif -# define VMOVU vmovdqu64 -# define VMOVA vmovdqa64 +# include "x86-evex256-vecs.h" # ifdef USE_AS_WCSRCHR -# define SHIFT_REG esi - -# define kunpck kunpckbw +# define RCX_M cl +# define SHIFT_REG rcx +# define VPCOMPRESS vpcompressd +# define kunpck_2x kunpckbw # define kmov_2x kmovd # define maskz_2x ecx # define maskm_2x eax # define CHAR_SIZE 4 # define VPMIN vpminud # define VPTESTN vptestnmd +# define VPTEST vptestmd # define VPBROADCAST vpbroadcastd +# define VPCMPEQ vpcmpeqd # define VPCMP vpcmpd -# else -# define SHIFT_REG edi -# define kunpck kunpckdq +# define USE_WIDE_CHAR +# else +# define RCX_M ecx +# define SHIFT_REG rdi +# define VPCOMPRESS vpcompressb +# define kunpck_2x kunpckdq # define kmov_2x kmovq # define maskz_2x rcx # define maskm_2x rax @@ -52,58 +57,48 @@ # define CHAR_SIZE 1 # define VPMIN vpminub # define VPTESTN vptestnmb +# define VPTEST vptestmb # define VPBROADCAST vpbroadcastb +# define VPCMPEQ vpcmpeqb # define VPCMP vpcmpb # endif -# define XMMZERO xmm16 -# define YMMZERO ymm16 -# define YMMMATCH ymm17 -# define YMMSAVE ymm18 +# include "reg-macros.h" -# define YMM1 ymm19 -# define YMM2 ymm20 -# define YMM3 ymm21 -# define YMM4 ymm22 -# define YMM5 ymm23 -# define YMM6 ymm24 -# define YMM7 ymm25 -# define YMM8 ymm26 - - -# define VEC_SIZE 32 +# define VMATCH VMM(0) +# define CHAR_PER_VEC (VEC_SIZE / CHAR_SIZE) # define PAGE_SIZE 4096 - .section .text.evex, "ax", @progbits -ENTRY(STRRCHR) + + .section SECTION(.text), "ax", @progbits +ENTRY_P2ALIGN(STRRCHR, 6) movl %edi, %eax - /* Broadcast CHAR to YMMMATCH. */ - VPBROADCAST %esi, %YMMMATCH + /* Broadcast CHAR to VMATCH. */ + VPBROADCAST %esi, %VMATCH andl $(PAGE_SIZE - 1), %eax cmpl $(PAGE_SIZE - VEC_SIZE), %eax jg L(cross_page_boundary) -L(page_cross_continue): - VMOVU (%rdi), %YMM1 - /* k0 has a 1 for each zero CHAR in YMM1. */ - VPTESTN %YMM1, %YMM1, %k0 - kmovd %k0, %ecx - testl %ecx, %ecx + VMOVU (%rdi), %VMM(1) + /* k0 has a 1 for each zero CHAR in VEC(1). */ + VPTESTN %VMM(1), %VMM(1), %k0 + KMOV %k0, %VRSI + test %VRSI, %VRSI jz L(aligned_more) /* fallthrough: zero CHAR in first VEC. */ - - /* K1 has a 1 for each search CHAR match in YMM1. */ - VPCMP $0, %YMMMATCH, %YMM1, %k1 - kmovd %k1, %eax +L(page_cross_return): + /* K1 has a 1 for each search CHAR match in VEC(1). */ + VPCMPEQ %VMATCH, %VMM(1), %k1 + KMOV %k1, %VRAX /* Build mask up until first zero CHAR (used to mask of potential search CHAR matches past the end of the string). */ - blsmskl %ecx, %ecx - andl %ecx, %eax + blsmsk %VRSI, %VRSI + and %VRSI, %VRAX jz L(ret0) - /* Get last match (the `andl` removed any out of bounds - matches). */ - bsrl %eax, %eax + /* Get last match (the `and` removed any out of bounds matches). + */ + bsr %VRAX, %VRAX # ifdef USE_AS_WCSRCHR leaq (%rdi, %rax, CHAR_SIZE), %rax # else @@ -116,22 +111,22 @@ L(ret0): search path for earlier matches. */ .p2align 4,, 6 L(first_vec_x1): - VPCMP $0, %YMMMATCH, %YMM2, %k1 - kmovd %k1, %eax - blsmskl %ecx, %ecx + VPCMPEQ %VMATCH, %VMM(2), %k1 + KMOV %k1, %VRAX + blsmsk %VRCX, %VRCX /* eax non-zero if search CHAR in range. */ - andl %ecx, %eax + and %VRCX, %VRAX jnz L(first_vec_x1_return) - /* fallthrough: no match in YMM2 then need to check for earlier - matches (in YMM1). */ + /* fallthrough: no match in VEC(2) then need to check for + earlier matches (in VEC(1)). */ .p2align 4,, 4 L(first_vec_x0_test): - VPCMP $0, %YMMMATCH, %YMM1, %k1 - kmovd %k1, %eax - testl %eax, %eax + VPCMPEQ %VMATCH, %VMM(1), %k1 + KMOV %k1, %VRAX + test %VRAX, %VRAX jz L(ret1) - bsrl %eax, %eax + bsr %VRAX, %VRAX # ifdef USE_AS_WCSRCHR leaq (%rsi, %rax, CHAR_SIZE), %rax # else @@ -142,129 +137,144 @@ L(ret1): .p2align 4,, 10 L(first_vec_x1_or_x2): - VPCMP $0, %YMM3, %YMMMATCH, %k3 - VPCMP $0, %YMM2, %YMMMATCH, %k2 + VPCMPEQ %VMM(3), %VMATCH, %k3 + VPCMPEQ %VMM(2), %VMATCH, %k2 /* K2 and K3 have 1 for any search CHAR match. Test if any - matches between either of them. Otherwise check YMM1. */ - kortestd %k2, %k3 + matches between either of them. Otherwise check VEC(1). */ + KORTEST %k2, %k3 jz L(first_vec_x0_test) - /* Guranteed that YMM2 and YMM3 are within range so merge the - two bitmasks then get last result. */ - kunpck %k2, %k3, %k3 - kmovq %k3, %rax - bsrq %rax, %rax - leaq (VEC_SIZE)(%r8, %rax, CHAR_SIZE), %rax + /* Guranteed that VEC(2) and VEC(3) are within range so merge + the two bitmasks then get last result. */ + kunpck_2x %k2, %k3, %k3 + kmov_2x %k3, %maskm_2x + bsr %maskm_2x, %maskm_2x + leaq (VEC_SIZE * 1)(%r8, %rax, CHAR_SIZE), %rax ret - .p2align 4,, 6 + .p2align 4,, 7 L(first_vec_x3): - VPCMP $0, %YMMMATCH, %YMM4, %k1 - kmovd %k1, %eax - blsmskl %ecx, %ecx - /* If no search CHAR match in range check YMM1/YMM2/YMM3. */ - andl %ecx, %eax + VPCMPEQ %VMATCH, %VMM(4), %k1 + KMOV %k1, %VRAX + blsmsk %VRCX, %VRCX + /* If no search CHAR match in range check VEC(1)/VEC(2)/VEC(3). + */ + and %VRCX, %VRAX jz L(first_vec_x1_or_x2) - bsrl %eax, %eax + bsr %VRAX, %VRAX leaq (VEC_SIZE * 3)(%rdi, %rax, CHAR_SIZE), %rax ret + .p2align 4,, 6 L(first_vec_x0_x1_test): - VPCMP $0, %YMMMATCH, %YMM2, %k1 - kmovd %k1, %eax - /* Check YMM2 for last match first. If no match try YMM1. */ - testl %eax, %eax + VPCMPEQ %VMATCH, %VMM(2), %k1 + KMOV %k1, %VRAX + /* Check VEC(2) for last match first. If no match try VEC(1). + */ + test %VRAX, %VRAX jz L(first_vec_x0_test) .p2align 4,, 4 L(first_vec_x1_return): - bsrl %eax, %eax + bsr %VRAX, %VRAX leaq (VEC_SIZE)(%rdi, %rax, CHAR_SIZE), %rax ret + .p2align 4,, 10 L(first_vec_x2): - VPCMP $0, %YMMMATCH, %YMM3, %k1 - kmovd %k1, %eax - blsmskl %ecx, %ecx - /* Check YMM3 for last match first. If no match try YMM2/YMM1. - */ - andl %ecx, %eax + VPCMPEQ %VMATCH, %VMM(3), %k1 + KMOV %k1, %VRAX + blsmsk %VRCX, %VRCX + /* Check VEC(3) for last match first. If no match try + VEC(2)/VEC(1). */ + and %VRCX, %VRAX jz L(first_vec_x0_x1_test) - bsrl %eax, %eax + bsr %VRAX, %VRAX leaq (VEC_SIZE * 2)(%rdi, %rax, CHAR_SIZE), %rax ret - .p2align 4 + .p2align 4,, 12 L(aligned_more): - /* Need to keep original pointer incase YMM1 has last match. */ +L(page_cross_continue): + /* Need to keep original pointer incase VEC(1) has last match. + */ movq %rdi, %rsi andq $-VEC_SIZE, %rdi - VMOVU VEC_SIZE(%rdi), %YMM2 - VPTESTN %YMM2, %YMM2, %k0 - kmovd %k0, %ecx - testl %ecx, %ecx + + VMOVU VEC_SIZE(%rdi), %VMM(2) + VPTESTN %VMM(2), %VMM(2), %k0 + KMOV %k0, %VRCX + + test %VRCX, %VRCX jnz L(first_vec_x1) - VMOVU (VEC_SIZE * 2)(%rdi), %YMM3 - VPTESTN %YMM3, %YMM3, %k0 - kmovd %k0, %ecx - testl %ecx, %ecx + VMOVU (VEC_SIZE * 2)(%rdi), %VMM(3) + VPTESTN %VMM(3), %VMM(3), %k0 + KMOV %k0, %VRCX + + test %VRCX, %VRCX jnz L(first_vec_x2) - VMOVU (VEC_SIZE * 3)(%rdi), %YMM4 - VPTESTN %YMM4, %YMM4, %k0 - kmovd %k0, %ecx + VMOVU (VEC_SIZE * 3)(%rdi), %VMM(4) + VPTESTN %VMM(4), %VMM(4), %k0 + KMOV %k0, %VRCX movq %rdi, %r8 - testl %ecx, %ecx + test %VRCX, %VRCX jnz L(first_vec_x3) andq $-(VEC_SIZE * 2), %rdi - .p2align 4 + .p2align 4,, 10 L(first_aligned_loop): - /* Preserve YMM1, YMM2, YMM3, and YMM4 until we can gurantee - they don't store a match. */ - VMOVA (VEC_SIZE * 4)(%rdi), %YMM5 - VMOVA (VEC_SIZE * 5)(%rdi), %YMM6 + /* Preserve VEC(1), VEC(2), VEC(3), and VEC(4) until we can + gurantee they don't store a match. */ + VMOVA (VEC_SIZE * 4)(%rdi), %VMM(5) + VMOVA (VEC_SIZE * 5)(%rdi), %VMM(6) - VPCMP $0, %YMM5, %YMMMATCH, %k2 - vpxord %YMM6, %YMMMATCH, %YMM7 + VPCMPEQ %VMM(5), %VMATCH, %k2 + vpxord %VMM(6), %VMATCH, %VMM(7) - VPMIN %YMM5, %YMM6, %YMM8 - VPMIN %YMM8, %YMM7, %YMM7 + VPMIN %VMM(5), %VMM(6), %VMM(8) + VPMIN %VMM(8), %VMM(7), %VMM(7) - VPTESTN %YMM7, %YMM7, %k1 + VPTESTN %VMM(7), %VMM(7), %k1 subq $(VEC_SIZE * -2), %rdi - kortestd %k1, %k2 + KORTEST %k1, %k2 jz L(first_aligned_loop) - VPCMP $0, %YMM6, %YMMMATCH, %k3 - VPTESTN %YMM8, %YMM8, %k1 - ktestd %k1, %k1 + VPCMPEQ %VMM(6), %VMATCH, %k3 + VPTESTN %VMM(8), %VMM(8), %k1 + + /* If k1 is zero, then we found a CHAR match but no null-term. + We can now safely throw out VEC1-4. */ + KTEST %k1, %k1 jz L(second_aligned_loop_prep) - kortestd %k2, %k3 + KORTEST %k2, %k3 jnz L(return_first_aligned_loop) + .p2align 4,, 6 L(first_vec_x1_or_x2_or_x3): - VPCMP $0, %YMM4, %YMMMATCH, %k4 - kmovd %k4, %eax - testl %eax, %eax + VPCMPEQ %VMM(4), %VMATCH, %k4 + KMOV %k4, %VRAX + bsr %VRAX, %VRAX jz L(first_vec_x1_or_x2) - bsrl %eax, %eax leaq (VEC_SIZE * 3)(%r8, %rax, CHAR_SIZE), %rax ret + .p2align 4,, 8 L(return_first_aligned_loop): - VPTESTN %YMM5, %YMM5, %k0 - kunpck %k0, %k1, %k0 + VPTESTN %VMM(5), %VMM(5), %k0 + + /* Combined results from VEC5/6. */ + kunpck_2x %k0, %k1, %k0 kmov_2x %k0, %maskz_2x blsmsk %maskz_2x, %maskz_2x - kunpck %k2, %k3, %k3 + kunpck_2x %k2, %k3, %k3 kmov_2x %k3, %maskm_2x and %maskz_2x, %maskm_2x jz L(first_vec_x1_or_x2_or_x3) @@ -280,47 +290,62 @@ L(return_first_aligned_loop): L(second_aligned_loop_prep): L(second_aligned_loop_set_furthest_match): movq %rdi, %rsi - kunpck %k2, %k3, %k4 - + /* Ideally we would safe k2/k3 but `kmov/kunpck` take uops on + port0 and have noticable overhead in the loop. */ + VMOVA %VMM(5), %VMM(7) + VMOVA %VMM(6), %VMM(8) .p2align 4 L(second_aligned_loop): - VMOVU (VEC_SIZE * 4)(%rdi), %YMM1 - VMOVU (VEC_SIZE * 5)(%rdi), %YMM2 - - VPCMP $0, %YMM1, %YMMMATCH, %k2 - vpxord %YMM2, %YMMMATCH, %YMM3 + VMOVU (VEC_SIZE * 4)(%rdi), %VMM(5) + VMOVU (VEC_SIZE * 5)(%rdi), %VMM(6) + VPCMPEQ %VMM(5), %VMATCH, %k2 + vpxord %VMM(6), %VMATCH, %VMM(3) - VPMIN %YMM1, %YMM2, %YMM4 - VPMIN %YMM3, %YMM4, %YMM3 + VPMIN %VMM(5), %VMM(6), %VMM(4) + VPMIN %VMM(3), %VMM(4), %VMM(3) - VPTESTN %YMM3, %YMM3, %k1 + VPTESTN %VMM(3), %VMM(3), %k1 subq $(VEC_SIZE * -2), %rdi - kortestd %k1, %k2 + KORTEST %k1, %k2 jz L(second_aligned_loop) - - VPCMP $0, %YMM2, %YMMMATCH, %k3 - VPTESTN %YMM4, %YMM4, %k1 - ktestd %k1, %k1 + VPCMPEQ %VMM(6), %VMATCH, %k3 + VPTESTN %VMM(4), %VMM(4), %k1 + KTEST %k1, %k1 jz L(second_aligned_loop_set_furthest_match) - kortestd %k2, %k3 - /* branch here because there is a significant advantage interms - of output dependency chance in using edx. */ + /* branch here because we know we have a match in VEC7/8 but + might not in VEC5/6 so the latter is expected to be less + likely. */ + KORTEST %k2, %k3 jnz L(return_new_match) + L(return_old_match): - kmovq %k4, %rax - bsrq %rax, %rax - leaq (VEC_SIZE * 2)(%rsi, %rax, CHAR_SIZE), %rax + VPCMPEQ %VMM(8), %VMATCH, %k0 + KMOV %k0, %VRCX + bsr %VRCX, %VRCX + jnz L(return_old_match_ret) + + VPCMPEQ %VMM(7), %VMATCH, %k0 + KMOV %k0, %VRCX + bsr %VRCX, %VRCX + subq $VEC_SIZE, %rsi +L(return_old_match_ret): + leaq (VEC_SIZE * 3)(%rsi, %rcx, CHAR_SIZE), %rax ret + .p2align 4,, 10 L(return_new_match): - VPTESTN %YMM1, %YMM1, %k0 - kunpck %k0, %k1, %k0 + VPTESTN %VMM(5), %VMM(5), %k0 + + /* Combined results from VEC5/6. */ + kunpck_2x %k0, %k1, %k0 kmov_2x %k0, %maskz_2x blsmsk %maskz_2x, %maskz_2x - kunpck %k2, %k3, %k3 + kunpck_2x %k2, %k3, %k3 kmov_2x %k3, %maskm_2x + + /* Match at end was out-of-bounds so use last known match. */ and %maskz_2x, %maskm_2x jz L(return_old_match) @@ -328,49 +353,53 @@ L(return_new_match): leaq (VEC_SIZE * 2)(%rdi, %rax, CHAR_SIZE), %rax ret + .p2align 4,, 4 L(cross_page_boundary): - /* eax contains all the page offset bits of src (rdi). `xor rdi, - rax` sets pointer will all page offset bits cleared so - offset of (PAGE_SIZE - VEC_SIZE) will get last aligned VEC - before page cross (guranteed to be safe to read). Doing this - as opposed to `movq %rdi, %rax; andq $-VEC_SIZE, %rax` saves - a bit of code size. */ xorq %rdi, %rax - VMOVU (PAGE_SIZE - VEC_SIZE)(%rax), %YMM1 - VPTESTN %YMM1, %YMM1, %k0 - kmovd %k0, %ecx + mov $-1, %VRDX + VMOVU (PAGE_SIZE - VEC_SIZE)(%rax), %VMM(6) + VPTESTN %VMM(6), %VMM(6), %k0 + KMOV %k0, %VRSI + +# ifdef USE_AS_WCSRCHR + movl %edi, %ecx + and $(VEC_SIZE - 1), %ecx + shrl $2, %ecx +# endif + shlx %VGPR(SHIFT_REG), %VRDX, %VRDX - /* Shift out zero CHAR matches that are before the begining of - src (rdi). */ # ifdef USE_AS_WCSRCHR - movl %edi, %esi - andl $(VEC_SIZE - 1), %esi - shrl $2, %esi + kmovb %edx, %k1 +# else + KMOV %VRDX, %k1 # endif - shrxl %SHIFT_REG, %ecx, %ecx - testl %ecx, %ecx + /* Need to adjust result to VEC(1) so it can be re-used by + L(return_vec_x0_test). The alternative is to collect VEC(1) + will a page cross load which is far more expensive. */ + VPCOMPRESS %VMM(6), %VMM(1){%k1}{z} + + /* We could technically just jmp back after the vpcompress but + it doesn't save any 16-byte blocks. */ + shrx %VGPR(SHIFT_REG), %VRSI, %VRSI + test %VRSI, %VRSI jz L(page_cross_continue) - /* Found zero CHAR so need to test for search CHAR. */ - VPCMP $0, %YMMMATCH, %YMM1, %k1 - kmovd %k1, %eax - /* Shift out search CHAR matches that are before the begining of - src (rdi). */ - shrxl %SHIFT_REG, %eax, %eax - - /* Check if any search CHAR match in range. */ - blsmskl %ecx, %ecx - andl %ecx, %eax - jz L(ret3) - bsrl %eax, %eax + /* Duplicate of return logic from ENTRY. Doesn't cause spill to + next cache line so might as well copy it here. */ + VPCMPEQ %VMATCH, %VMM(1), %k1 + KMOV %k1, %VRAX + blsmsk %VRSI, %VRSI + and %VRSI, %VRAX + jz L(ret_page_cross) + bsr %VRAX, %VRAX # ifdef USE_AS_WCSRCHR leaq (%rdi, %rax, CHAR_SIZE), %rax # else addq %rdi, %rax # endif -L(ret3): +L(ret_page_cross): ret - + /* 1 byte till next cache line. */ END(STRRCHR) #endif