Luo, Yuanke via llvm-dev
2020-Aug-14 23:49 UTC
[llvm-dev] Intel AMX programming model discussion.
[Yuanke] AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. [Philip] This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? [Yuanke] In that case user need to configure the tile register by themselves. Spilling configure register is very expensive, because it clears all the tile data register to zero. In our proposal, compiler is responsible to deduce the shape for virtual of tile data register, allocate physical registers for them and then configure those physical register. We may build the dependency as you proposed and it can be used for machine IR check to ensure tile data register is configured before use. From: Philip Reames <listmail at philipreames.com> Sent: Saturday, August 15, 2020 1:17 AM To: Luo, Yuanke <yuanke.luo at intel.com>; llvm-dev at lists.llvm.org; florian_hahn at apple.com; Kaylor, Andrew <andrew.kaylor at intel.com>; Topper, Craig <craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com> Subject: Re: [llvm-dev] Intel AMX programming model discussion. On 8/14/20 6:27 AM, Luo, Yuanke via llvm-dev wrote: Hi, Intel Advanced Matrix Extensions (Intel AMX) is a new programming paradigm consisting of two components: a set of 2-dimensional registers (tiles) representing sub-arrays from a larger 2-dimensional memory image, and accelerators able to operate on tiles. Capability of Intel AMX implementation is enumerated by palettes. Two palettes are supported: palette 0 represents the initialized state and palette 1 consists of 8 tile registers of up to 1 KB size, which is controlled by a tile control register. The instruction manual is posted at https://software.intel.com/content/www/us/en/develop/download/intel-architecture-instruction-set-extensions-programming-reference.html. The AMX abi proposal is posted at https://groups.google.com/g/x86-64-abi/c/NRejFm7pwb4. This email is to discuss the programming model for AMX. Florian has introduced the matrix type and intrinsics in LLVM community. We'd like to adopt some ideas from it. Here is what we propose for the AMX programming model. 1. Data type. We'd like to have fixed vector type for AMX. Since the shape to AMX register can be configurable, the vector size is the maximum size of AMX register. That means the vector size is 1024 bytes. The C code may look like this. typedef int _tile_data __attribute__((__vector_size__(1024), __aligned__(64))); _tile_data tile; And the LLVM IR may look like this. @tile = dso_local local_unnamed_addr global <256 x i32> zeroinitializer, align 64 For llvm IR, it is nice to have a new type x86_amxtile that can be mapped to AMX registers. 2. AMX Intrinsics. The internal intrinsics are 1:1 mapped to AMX instructions. The parameter m, n, k identifies the shape of the tile. The shape can be variable, but it cannot exceed the size that AMX HW can support. Compiler can deduce shape of the tile from the AMX intrinsics. _tile_data _tile_loadd_internal(char m, short n, const void *base, int stride); _tile_data _tile_dpbssd_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); _tile_data _tile_dpbf16ps_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); void _tile_stored_internal(char m, short n, void *base, int stride, _tile_data tile); 3. User interfaces. The tile shape and tile data are combined into a struct in C language. The shape of the tile is only allowed to be initialized once. The user interface looks as this. 3 #define __DEFAULT_FN_AMX \ 4 __attribute__((__always_inline__, __nodebug__, __target__("amx-int8"))) 9 typedef struct __tile_str { 10 const char row; 11 const short col; 12 _tile_data tile; 13 }__tile; 14 15 __DEFAULT_FN_AMX 16 void __tile_loadd(__tile *dst, const void *base, long stride) { 17 dst->tile = _tile_loadd_internal(dst->row, dst->col, base, stride); 18 } 19 20 __DEFAULT_FN_AMX 21 void __tile_dpbsud(__tile *dst, __tile src1, __tile src2) { 22 dst->tile = _tile_dpbssd_internal(src1.row, src2.col, src1.col, dst->tile, src1.tile, src2.tile); 23 } 24 25 __DEFAULT_FN_AMX 26 void __tile_stored(void *base, long stride, __tile src) { 27 _tile_stored_internal(src.row, src.col, base, stride, src.tile); 28 } 4. Example code The example shows how to use the user interface in a function. 51 void api(int cond, short row, short col) { 52 __tile a = {row, col}; 53 __tile b = {row, col}; 54 __tile c = {row, col}; 55 56 if(cond) { 57 __tile_loadd(&a, buf, STRIDE); 58 __tile_loadd(&b, buf, STRIDE); 59 __tile_loadd(&c, buf, STRIDE); 60 } else { 61 __tile_loadd(&a, buf2, STRIDE); 62 __tile_loadd(&b, buf2, STRIDE); 63 __tile_loadd(&c, buf2, STRIDE); 64 } 65 __tile_dpbsud(&c, a, b); 66 __tile_stored(buf, STRIDE, c); 67 } 5. LLVM IR The LLVM intrinsics IR take the row and column information as the input parameter, so that compiler can deduce the shape of tile data. The remaining parameters are what AMX instructions require. This is the LLVM IR corresponding to the example code. 12 define dso_local void @api(i32 %cond, i16 signext %row, i16 signext %col) local_unnamed_addr #2 { 13 entry: 14 %tobool = icmp eq i32 %cond, 0 15 %sext = shl i16 %col, 8 16 %conv.i31 = ashr exact i16 %sext, 8 17 br i1 %tobool, label %if.else, label %if.then 18 19 if.then: ; preds = %entry 20 %0 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 21 %1 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 22 %2 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 23 br label %if.end 24 25 if.else: ; preds = %entry 26 %3 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 27 %4 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 28 %5 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 29 br label %if.end 30 31 if.end: ; preds = %if.else, %if.then 32 %a.sroa.1186.0 = phi <256 x i32> [ %3, %if.else ], [ %0, %if.then ] 33 %b.sroa.1068.0 = phi <256 x i32> [ %4, %if.else ], [ %1, %if.then ] 34 %c.sroa.1149.0 = phi <256 x i32> [ %5, %if.else ], [ %2, %if.then ] 35 %6 = tail call <256 x i32> @llvm.x86.tdpbssd(i16 %row, i16 %conv.i31, i16 %conv.i31, <256 x i32> %c.sroa.1149.0, <256 x i32> %a.sroa.1186.0, <256 x i32> %b.sroa.1068.0) #3 36 tail call void @llvm.x86.tilestored64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32, <256 x i32> %6) #3 37 ret void 38 } 6. Shape propagation When in -O0 build, some general load/store for tile vector is generated by front-end. We need to root from AMX intrinsics to propagate the shape information to the virtual tile register. If the an AMX intrinsic use the result of load instruction, the shape is propagated to the load and the load is transformed to tile load intrinsic. If the store instruction uses any result of AMX intrinsic, the shape is propagated to store instruction and the store is transformed to tile store intrinsic 7. Machine IR Since the AMX intrinsics take the row and column as the input parameters, we can create a pseudo instruction corresponding to it. The AMX intrinsics are lowered to the pseudo AMX instruction which has extra row and column operands corresponding to AMX intrinsic. The real AMX instructions don't need the row and column operands. The row and column information should be configured by ldtilecfg before executing any AMX instruction. 8. Register allocation AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? 9. Use recommendation Due to the shape configure issue, we recommend user to define the tile shape at the entry of the function entry and inline function as much as possible. The AMX instructions focus on computation instead of storage, so global variable for tile data is not recommended. Thanks Yuanke _______________________________________________ LLVM Developers mailing list llvm-dev at lists.llvm.org<mailto:llvm-dev at lists.llvm.org> https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20200814/942ad926/attachment-0001.html>
Philip Reames via llvm-dev
2020-Aug-15 03:29 UTC
[llvm-dev] Intel AMX programming model discussion.
I find your answer unconvincing. I'm not going to debate it as I don't wish to take the time to build the appropriate context, but my initial response is skepticism. Philip On 8/14/20 4:49 PM, Luo, Yuanke wrote:> > [Yuanke] AMX register is special. It needs to be configured before use > and the config instruction is expensive. To avoid unnecessary tile > configure, we collect the tile shape information as much as possible > and combine them into one ldtilecfg instruction. The ldtilecfg > instruction should dominate any AMX instruction that access tile > register. On the other side, the ldtilecfg should post-dominated the > instruction that define the tile shape. For tile register spill, it > should avoid re-config due to the different tile shape, the spilled > register should be reloaded to the register that share the same tile > shape. Since tile register allocation is special and it may allocate > general virtual register to configure tile register, we can add a > sperate pass to do it before general register allocation pass. After > register allocation, the tile shape information is not needed anymore, > so we can transform the pseudo AMX instruction to real AMX instruction > by removing the row and column operands. > > [Philip] > > This seems complicated. > > Reading through the documentation, there appears to be a single global > tile config for all tile registers at any time. > > Why not simply model this tile config as a designated special register > and the tile instructions as having an implicit use of this register? > That would seem to ensure that the register allocator has all the > constraints needed. You'd need to teach it how to spill the special > registers with the appropriate instructions, but that seems a lot more > straight forward? > > [Yuanke] In that case user need to configure the tile register by > themselves. Spilling configure register is very expensive, because it > clears all the tile data register to zero. In our proposal, compiler > is responsible to deduce the shape for virtual of tile data register, > allocate physical registers for them and then configure those physical > register. We may build the dependency as you proposed and it can be > used for machine IR check to ensure tile data register is configured > before use. > > *From:*Philip Reames <listmail at philipreames.com> > *Sent:* Saturday, August 15, 2020 1:17 AM > *To:* Luo, Yuanke <yuanke.luo at intel.com>; llvm-dev at lists.llvm.org; > florian_hahn at apple.com; Kaylor, Andrew <andrew.kaylor at intel.com>; > Topper, Craig <craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com> > *Subject:* Re: [llvm-dev] Intel AMX programming model discussion. > > On 8/14/20 6:27 AM, Luo, Yuanke via llvm-dev wrote: > > Hi, > > Intel Advanced Matrix Extensions (Intel AMX) is a new programming > paradigm consisting of two components: a set of 2-dimensional > registers (tiles) representing sub-arrays from a larger > 2-dimensional memory image, and accelerators able to operate on > tiles. Capability of Intel AMX implementation is enumerated by > palettes. Two palettes are supported: palette 0 represents the > initialized state and palette 1 consists of 8 tile registers of up > to 1 KB size, which is controlled by a tile control register. > > The instruction manual is posted at > https://software.intel.com/content/www/us/en/develop/download/intel-architecture-instruction-set-extensions-programming-reference.html. > > The AMX abi proposal is posted at > https://groups.google.com/g/x86-64-abi/c/NRejFm7pwb4 > <https://groups.google.com/g/x86-64-abi/c/NRejFm7pwb4>. > > This email is to discuss the programming model for AMX. > Florian has introduced the matrix type and intrinsics in LLVM > community. We’d like to adopt some ideas from it. > > Here is what we propose for the AMX programming model. > > 1. Data type. > > We’d like to have fixed vector type for AMX. Since the shape to > AMX register can be configurable, the vector size is the maximum > size of AMX register. That means the vector size is 1024 bytes. > > The C code may look like this. > > typedef int _tile_data __attribute__((__vector_size__(1024), > __aligned__(64))); > > _tile_data tile; > > And the LLVM IR may look like this. > > @tile = dso_local local_unnamed_addr global <256 x i32> > zeroinitializer, align 64 > > For llvm IR, it is nice to have a new type x86_amxtile that can be > mapped to AMX registers. > > 2.AMX Intrinsics. > > The internal intrinsics are 1:1 mapped to AMX instructions. The > parameter m, n, k identifies the shape of the tile. The shape can > be variable, but it cannot exceed the size that AMX HW can > support. Compiler can deduce shape of the tile from the AMX > intrinsics. > > _tile_data _tile_loadd_internal(char m, short n, const void *base, > int stride); > > _tile_data _tile_dpbssd_internal(char m, short n, short k, > _tile_data dst, _tile_data src1, _tile_data src2); > > _tile_data _tile_dpbf16ps_internal(char m, short n, short k, > _tile_data dst, _tile_data src1, _tile_data src2); > > void _tile_stored_internal(char m, short n, void *base, int > stride, _tile_data tile); > > 3.User interfaces. > > The tile shape and tile data are combined into a struct in C > language. The shape of the tile is only allowed to be initialized > once. The user interface looks as this. > > 3 #define __DEFAULT_FN_AMX \ > > 4 __attribute__((__always_inline__, __nodebug__, > __target__("amx-int8"))) > > 9 typedef struct __tile_str { > > 10 const char row; > > 11 const short col; > > 12 _tile_data tile; > > 13 }__tile; > > 14 > > 15 __DEFAULT_FN_AMX > > 16 void __tile_loadd(__tile *dst, const void *base, long stride) { > > 17 dst->tile = _tile_loadd_internal(dst->row, dst->col, base, > stride); > > 18 } > > 19 > > 20 __DEFAULT_FN_AMX > > 21 void __tile_dpbsud(__tile *dst, __tile src1, __tile src2) { > > 22 dst->tile = _tile_dpbssd_internal(src1.row, src2.col, > src1.col, dst->tile, src1.tile, src2.tile); > > 23 } > > 24 > > 25 __DEFAULT_FN_AMX > > 26 void __tile_stored(void *base, long stride, __tile src) { > > 27 _tile_stored_internal(src.row, src.col, base, stride, src.tile); > > 28 } > > 4.Example code > > The example shows how to use the user interface in a function. > > 51 void api(int cond, short row, short col) { > > 52 __tile a = {row, col}; > > 53 __tile b = {row, col}; > > 54 __tile c = {row, col}; > > 55 > > 56 if(cond) { > > 57 __tile_loadd(&a, buf, STRIDE); > > 58 __tile_loadd(&b, buf, STRIDE); > > 59 __tile_loadd(&c, buf, STRIDE); > > 60 } else { > > 61 __tile_loadd(&a, buf2, STRIDE); > > 62 __tile_loadd(&b, buf2, STRIDE); > > 63 __tile_loadd(&c, buf2, STRIDE); > > 64 } > > 65 __tile_dpbsud(&c, a, b); > > 66 __tile_stored(buf, STRIDE, c); > > 67 } > > 5.LLVM IR > > The LLVM intrinsics IR take the row and column information as the > input parameter, so that compiler can deduce the shape of tile > data. The remaining parameters are what AMX instructions require. > This is the LLVM IR corresponding to the example code. > > 12 define dso_local void @api(i32 %cond, i16 signext %row, i16 > signext %col) local_unnamed_addr #2 { > > 13 entry: > > 14 %tobool = icmp eq i32 %cond, 0 > > 15 %sext = shl i16 %col, 8 > > 16 %conv.i31 = ashr exact i16 %sext, 8 > > 17 br i1 %tobool, label %if.else, label %if.then > > 18 > > 19 if.then: ; preds = %entry > > 20 %0 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf, i64 0, i64 0), i64 32) #3 > > 21 %1 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf, i64 0, i64 0), i64 32) #3 > > 22 %2 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf, i64 0, i64 0), i64 32) #3 > > 23 br label %if.end > > 24 > > 25 if.else: ; preds = %entry > > 26 %3 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf2, i64 0, i64 0), i64 32) #3 > > 27 %4 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf2, i64 0, i64 0), i64 32) #3 > > 28 %5 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, > i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x > i8]* @buf2, i64 0, i64 0), i64 32) #3 > > 29 br label %if.end > > 30 > > 31 if.end: ; preds > %if.else, %if.then > > 32 %a.sroa.1186.0 = phi <256 x i32> [ %3, %if.else ], [ %0, > %if.then ] > > 33 %b.sroa.1068.0 = phi <256 x i32> [ %4, %if.else ], [ %1, > %if.then ] > > 34 %c.sroa.1149.0 = phi <256 x i32> [ %5, %if.else ], [ %2, > %if.then ] > > 35 %6 = tail call <256 x i32> @llvm.x86.tdpbssd(i16 %row, i16 > %conv.i31, i16 %conv.i31, <256 x i32> %c.sroa.1149.0, <256 x i32> > %a.sroa.1186.0, <256 x i32> %b.sroa.1068.0) #3 > > 36 tail call void @llvm.x86.tilestored64(i16 %row, i16 > %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* > @buf, i64 0, i64 0), i64 32, <256 x i32> %6) #3 > > 37 ret void > > 38 } > > 6.Shape propagation > > When in -O0 build, some general load/store for tile vector is > generated by front-end. We need to root from AMX intrinsics to > propagate the shape information to the virtual tile register. If > the an AMX intrinsic use the result of load instruction, the shape > is propagated to the load and the load is transformed to tile load > intrinsic. If the store instruction uses any result of AMX > intrinsic, the shape is propagated to store instruction and the > store is transformed to tile store intrinsic > > 7.Machine IR > > Since the AMX intrinsics take the row and column as the input > parameters, we can create a pseudo instruction corresponding to > it. The AMX intrinsics are lowered to the pseudo AMX instruction > which has extra row and column operands corresponding to AMX > intrinsic. The real AMX instructions don’t need the row and column > operands. The row and column information should be configured by > ldtilecfg before executing any AMX instruction. > > 8.Register allocation > > AMX register is special. It needs to be configured before use and > the config instruction is expensive. To avoid unnecessary tile > configure, we collect the tile shape information as much as > possible and combine them into one ldtilecfg instruction. The > ldtilecfg instruction should dominate any AMX instruction that > access tile register. On the other side, the ldtilecfg should > post-dominated the instruction that define the tile shape. For > tile register spill, it should avoid re-config due to the > different tile shape, the spilled register should be reloaded to > the register that share the same tile shape. Since tile register > allocation is special and it may allocate general virtual register > to configure tile register, we can add a sperate pass to do it > before general register allocation pass. After register > allocation, the tile shape information is not needed anymore, so > we can transform the pseudo AMX instruction to real AMX > instruction by removing the row and column operands. > > This seems complicated. > > Reading through the documentation, there appears to be a single global > tile config for all tile registers at any time. > > Why not simply model this tile config as a designated special register > and the tile instructions as having an implicit use of this register? > That would seem to ensure that the register allocator has all the > constraints needed. You'd need to teach it how to spill the special > registers with the appropriate instructions, but that seems a lot more > straight forward? > > 9.Use recommendation > > Due to the shape configure issue, we recommend user to define the > tile shape at the entry of the function entry and inline function > as much as possible. The AMX instructions focus on computation > instead of storage, so global variable for tile data is not > recommended. > > Thanks > > Yuanke > > > > _______________________________________________ > > LLVM Developers mailing list > > llvm-dev at lists.llvm.org <mailto:llvm-dev at lists.llvm.org> > > https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev >-------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20200814/8a4244f0/attachment.html>
Luo, Yuanke via llvm-dev
2020-Aug-15 06:06 UTC
[llvm-dev] Intel AMX programming model discussion.
Hi Philip, Your idea make sense to me in my first thought. Thank you for the idea. I will take more time to think it over to see it can help to reduce the complexity of tile register allocation. Yuanke From: Philip Reames <listmail at philipreames.com> Sent: Saturday, August 15, 2020 11:29 AM To: Luo, Yuanke <yuanke.luo at intel.com>; llvm-dev at lists.llvm.org; florian_hahn at apple.com; Kaylor, Andrew <andrew.kaylor at intel.com>; Topper, Craig <craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com> Subject: Re: [llvm-dev] Intel AMX programming model discussion. I find your answer unconvincing. I'm not going to debate it as I don't wish to take the time to build the appropriate context, but my initial response is skepticism. Philip On 8/14/20 4:49 PM, Luo, Yuanke wrote: [Yuanke] AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. [Philip] This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? [Yuanke] In that case user need to configure the tile register by themselves. Spilling configure register is very expensive, because it clears all the tile data register to zero. In our proposal, compiler is responsible to deduce the shape for virtual of tile data register, allocate physical registers for them and then configure those physical register. We may build the dependency as you proposed and it can be used for machine IR check to ensure tile data register is configured before use. From: Philip Reames <listmail at philipreames.com><mailto:listmail at philipreames.com> Sent: Saturday, August 15, 2020 1:17 AM To: Luo, Yuanke <yuanke.luo at intel.com><mailto:yuanke.luo at intel.com>; llvm-dev at lists.llvm.org<mailto:llvm-dev at lists.llvm.org>; florian_hahn at apple.com<mailto:florian_hahn at apple.com>; Kaylor, Andrew <andrew.kaylor at intel.com><mailto:andrew.kaylor at intel.com>; Topper, Craig <craig.topper at intel.com><mailto:craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com><mailto:hongjiu.lu at intel.com> Subject: Re: [llvm-dev] Intel AMX programming model discussion. On 8/14/20 6:27 AM, Luo, Yuanke via llvm-dev wrote: Hi, Intel Advanced Matrix Extensions (Intel AMX) is a new programming paradigm consisting of two components: a set of 2-dimensional registers (tiles) representing sub-arrays from a larger 2-dimensional memory image, and accelerators able to operate on tiles. Capability of Intel AMX implementation is enumerated by palettes. Two palettes are supported: palette 0 represents the initialized state and palette 1 consists of 8 tile registers of up to 1 KB size, which is controlled by a tile control register. The instruction manual is posted at https://software.intel.com/content/www/us/en/develop/download/intel-architecture-instruction-set-extensions-programming-reference.html. The AMX abi proposal is posted at https://groups.google.com/g/x86-64-abi/c/NRejFm7pwb4. This email is to discuss the programming model for AMX. Florian has introduced the matrix type and intrinsics in LLVM community. We'd like to adopt some ideas from it. Here is what we propose for the AMX programming model. 1. Data type. We'd like to have fixed vector type for AMX. Since the shape to AMX register can be configurable, the vector size is the maximum size of AMX register. That means the vector size is 1024 bytes. The C code may look like this. typedef int _tile_data __attribute__((__vector_size__(1024), __aligned__(64))); _tile_data tile; And the LLVM IR may look like this. @tile = dso_local local_unnamed_addr global <256 x i32> zeroinitializer, align 64 For llvm IR, it is nice to have a new type x86_amxtile that can be mapped to AMX registers. 2. AMX Intrinsics. The internal intrinsics are 1:1 mapped to AMX instructions. The parameter m, n, k identifies the shape of the tile. The shape can be variable, but it cannot exceed the size that AMX HW can support. Compiler can deduce shape of the tile from the AMX intrinsics. _tile_data _tile_loadd_internal(char m, short n, const void *base, int stride); _tile_data _tile_dpbssd_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); _tile_data _tile_dpbf16ps_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); void _tile_stored_internal(char m, short n, void *base, int stride, _tile_data tile); 3. User interfaces. The tile shape and tile data are combined into a struct in C language. The shape of the tile is only allowed to be initialized once. The user interface looks as this. 3 #define __DEFAULT_FN_AMX \ 4 __attribute__((__always_inline__, __nodebug__, __target__("amx-int8"))) 9 typedef struct __tile_str { 10 const char row; 11 const short col; 12 _tile_data tile; 13 }__tile; 14 15 __DEFAULT_FN_AMX 16 void __tile_loadd(__tile *dst, const void *base, long stride) { 17 dst->tile = _tile_loadd_internal(dst->row, dst->col, base, stride); 18 } 19 20 __DEFAULT_FN_AMX 21 void __tile_dpbsud(__tile *dst, __tile src1, __tile src2) { 22 dst->tile = _tile_dpbssd_internal(src1.row, src2.col, src1.col, dst->tile, src1.tile, src2.tile); 23 } 24 25 __DEFAULT_FN_AMX 26 void __tile_stored(void *base, long stride, __tile src) { 27 _tile_stored_internal(src.row, src.col, base, stride, src.tile); 28 } 4. Example code The example shows how to use the user interface in a function. 51 void api(int cond, short row, short col) { 52 __tile a = {row, col}; 53 __tile b = {row, col}; 54 __tile c = {row, col}; 55 56 if(cond) { 57 __tile_loadd(&a, buf, STRIDE); 58 __tile_loadd(&b, buf, STRIDE); 59 __tile_loadd(&c, buf, STRIDE); 60 } else { 61 __tile_loadd(&a, buf2, STRIDE); 62 __tile_loadd(&b, buf2, STRIDE); 63 __tile_loadd(&c, buf2, STRIDE); 64 } 65 __tile_dpbsud(&c, a, b); 66 __tile_stored(buf, STRIDE, c); 67 } 5. LLVM IR The LLVM intrinsics IR take the row and column information as the input parameter, so that compiler can deduce the shape of tile data. The remaining parameters are what AMX instructions require. This is the LLVM IR corresponding to the example code. 12 define dso_local void @api(i32 %cond, i16 signext %row, i16 signext %col) local_unnamed_addr #2 { 13 entry: 14 %tobool = icmp eq i32 %cond, 0 15 %sext = shl i16 %col, 8 16 %conv.i31 = ashr exact i16 %sext, 8 17 br i1 %tobool, label %if.else, label %if.then 18 19 if.then: ; preds = %entry 20 %0 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 21 %1 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 22 %2 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 23 br label %if.end 24 25 if.else: ; preds = %entry 26 %3 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 27 %4 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 28 %5 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 29 br label %if.end 30 31 if.end: ; preds = %if.else, %if.then 32 %a.sroa.1186.0 = phi <256 x i32> [ %3, %if.else ], [ %0, %if.then ] 33 %b.sroa.1068.0 = phi <256 x i32> [ %4, %if.else ], [ %1, %if.then ] 34 %c.sroa.1149.0 = phi <256 x i32> [ %5, %if.else ], [ %2, %if.then ] 35 %6 = tail call <256 x i32> @llvm.x86.tdpbssd(i16 %row, i16 %conv.i31, i16 %conv.i31, <256 x i32> %c.sroa.1149.0, <256 x i32> %a.sroa.1186.0, <256 x i32> %b.sroa.1068.0) #3 36 tail call void @llvm.x86.tilestored64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32, <256 x i32> %6) #3 37 ret void 38 } 6. Shape propagation When in -O0 build, some general load/store for tile vector is generated by front-end. We need to root from AMX intrinsics to propagate the shape information to the virtual tile register. If the an AMX intrinsic use the result of load instruction, the shape is propagated to the load and the load is transformed to tile load intrinsic. If the store instruction uses any result of AMX intrinsic, the shape is propagated to store instruction and the store is transformed to tile store intrinsic 7. Machine IR Since the AMX intrinsics take the row and column as the input parameters, we can create a pseudo instruction corresponding to it. The AMX intrinsics are lowered to the pseudo AMX instruction which has extra row and column operands corresponding to AMX intrinsic. The real AMX instructions don't need the row and column operands. The row and column information should be configured by ldtilecfg before executing any AMX instruction. 8. Register allocation AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? 9. Use recommendation Due to the shape configure issue, we recommend user to define the tile shape at the entry of the function entry and inline function as much as possible. The AMX instructions focus on computation instead of storage, so global variable for tile data is not recommended. Thanks Yuanke _______________________________________________ LLVM Developers mailing list llvm-dev at lists.llvm.org<mailto:llvm-dev at lists.llvm.org> https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20200815/12bb4e37/attachment.html>
Kaylor, Andrew via llvm-dev
2020-Aug-18 23:58 UTC
[llvm-dev] Intel AMX programming model discussion.
The AMX registers are complicated. The single configuration register (which is mostly used implicitly, similar to MXCSR for floating point) controls the shape of all the tile registers, and if you change the tile configuration every single tile register is cleared. In practice, if we have to change the the configuration while any of the tile registers are live, performance is going to be terrible. We need to handle this case for correctness, but users of this programming interface will need to have enough awareness of the performance issues and the hardware details to prevent this. We'll also want a diagnostic that lets the user know when this has happened. When the tile configuration is set, the shape of each tile is locked in, so the individual tile registers aren't interchangeable at that point. If a function needs 2x4 tiles, 4x2 tiles, and 4x4 tiles, the configuration needs to be set with this in mind. The shape isn't explicit in every instruction and intrinsic. It must be deduced. And again, we'll need a way to tell the user when efficient allocation can't be done. In practice, I don't expect any function to be using more than three tile shapes. The implication of all this is that I don't think the greedy register allocator is well suited to figure all of this out. We need a special pass to pre-allocate these registers. If the function is written in a way that makes good performance possible, it should be a relatively simple task to allocate everything with minimal spilling. If it isn't possible to get good performance, we don't need to do anything especially clever. We can just do something straightforward that is correct and let the user know that they aren't going to be happy with the results. -Andy From: Philip Reames <listmail at philipreames.com> Sent: Friday, August 14, 2020 8:29 PM To: Luo, Yuanke <yuanke.luo at intel.com>; llvm-dev at lists.llvm.org; florian_hahn at apple.com; Kaylor, Andrew <andrew.kaylor at intel.com>; Topper, Craig <craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com> Subject: Re: [llvm-dev] Intel AMX programming model discussion. I find your answer unconvincing. I'm not going to debate it as I don't wish to take the time to build the appropriate context, but my initial response is skepticism. Philip On 8/14/20 4:49 PM, Luo, Yuanke wrote: [Yuanke] AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. [Philip] This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? [Yuanke] In that case user need to configure the tile register by themselves. Spilling configure register is very expensive, because it clears all the tile data register to zero. In our proposal, compiler is responsible to deduce the shape for virtual of tile data register, allocate physical registers for them and then configure those physical register. We may build the dependency as you proposed and it can be used for machine IR check to ensure tile data register is configured before use. From: Philip Reames <listmail at philipreames.com><mailto:listmail at philipreames.com> Sent: Saturday, August 15, 2020 1:17 AM To: Luo, Yuanke <yuanke.luo at intel.com><mailto:yuanke.luo at intel.com>; llvm-dev at lists.llvm.org<mailto:llvm-dev at lists.llvm.org>; florian_hahn at apple.com<mailto:florian_hahn at apple.com>; Kaylor, Andrew <andrew.kaylor at intel.com><mailto:andrew.kaylor at intel.com>; Topper, Craig <craig.topper at intel.com><mailto:craig.topper at intel.com>; Lu, Hongjiu <hongjiu.lu at intel.com><mailto:hongjiu.lu at intel.com> Subject: Re: [llvm-dev] Intel AMX programming model discussion. On 8/14/20 6:27 AM, Luo, Yuanke via llvm-dev wrote: Hi, Intel Advanced Matrix Extensions (Intel AMX) is a new programming paradigm consisting of two components: a set of 2-dimensional registers (tiles) representing sub-arrays from a larger 2-dimensional memory image, and accelerators able to operate on tiles. Capability of Intel AMX implementation is enumerated by palettes. Two palettes are supported: palette 0 represents the initialized state and palette 1 consists of 8 tile registers of up to 1 KB size, which is controlled by a tile control register. The instruction manual is posted at https://software.intel.com/content/www/us/en/develop/download/intel-architecture-instruction-set-extensions-programming-reference.html. The AMX abi proposal is posted at https://groups.google.com/g/x86-64-abi/c/NRejFm7pwb4. This email is to discuss the programming model for AMX. Florian has introduced the matrix type and intrinsics in LLVM community. We'd like to adopt some ideas from it. Here is what we propose for the AMX programming model. 1. Data type. We'd like to have fixed vector type for AMX. Since the shape to AMX register can be configurable, the vector size is the maximum size of AMX register. That means the vector size is 1024 bytes. The C code may look like this. typedef int _tile_data __attribute__((__vector_size__(1024), __aligned__(64))); _tile_data tile; And the LLVM IR may look like this. @tile = dso_local local_unnamed_addr global <256 x i32> zeroinitializer, align 64 For llvm IR, it is nice to have a new type x86_amxtile that can be mapped to AMX registers. 2. AMX Intrinsics. The internal intrinsics are 1:1 mapped to AMX instructions. The parameter m, n, k identifies the shape of the tile. The shape can be variable, but it cannot exceed the size that AMX HW can support. Compiler can deduce shape of the tile from the AMX intrinsics. _tile_data _tile_loadd_internal(char m, short n, const void *base, int stride); _tile_data _tile_dpbssd_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); _tile_data _tile_dpbf16ps_internal(char m, short n, short k, _tile_data dst, _tile_data src1, _tile_data src2); void _tile_stored_internal(char m, short n, void *base, int stride, _tile_data tile); 3. User interfaces. The tile shape and tile data are combined into a struct in C language. The shape of the tile is only allowed to be initialized once. The user interface looks as this. 3 #define __DEFAULT_FN_AMX \ 4 __attribute__((__always_inline__, __nodebug__, __target__("amx-int8"))) 9 typedef struct __tile_str { 10 const char row; 11 const short col; 12 _tile_data tile; 13 }__tile; 14 15 __DEFAULT_FN_AMX 16 void __tile_loadd(__tile *dst, const void *base, long stride) { 17 dst->tile = _tile_loadd_internal(dst->row, dst->col, base, stride); 18 } 19 20 __DEFAULT_FN_AMX 21 void __tile_dpbsud(__tile *dst, __tile src1, __tile src2) { 22 dst->tile = _tile_dpbssd_internal(src1.row, src2.col, src1.col, dst->tile, src1.tile, src2.tile); 23 } 24 25 __DEFAULT_FN_AMX 26 void __tile_stored(void *base, long stride, __tile src) { 27 _tile_stored_internal(src.row, src.col, base, stride, src.tile); 28 } 4. Example code The example shows how to use the user interface in a function. 51 void api(int cond, short row, short col) { 52 __tile a = {row, col}; 53 __tile b = {row, col}; 54 __tile c = {row, col}; 55 56 if(cond) { 57 __tile_loadd(&a, buf, STRIDE); 58 __tile_loadd(&b, buf, STRIDE); 59 __tile_loadd(&c, buf, STRIDE); 60 } else { 61 __tile_loadd(&a, buf2, STRIDE); 62 __tile_loadd(&b, buf2, STRIDE); 63 __tile_loadd(&c, buf2, STRIDE); 64 } 65 __tile_dpbsud(&c, a, b); 66 __tile_stored(buf, STRIDE, c); 67 } 5. LLVM IR The LLVM intrinsics IR take the row and column information as the input parameter, so that compiler can deduce the shape of tile data. The remaining parameters are what AMX instructions require. This is the LLVM IR corresponding to the example code. 12 define dso_local void @api(i32 %cond, i16 signext %row, i16 signext %col) local_unnamed_addr #2 { 13 entry: 14 %tobool = icmp eq i32 %cond, 0 15 %sext = shl i16 %col, 8 16 %conv.i31 = ashr exact i16 %sext, 8 17 br i1 %tobool, label %if.else, label %if.then 18 19 if.then: ; preds = %entry 20 %0 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 21 %1 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 22 %2 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32) #3 23 br label %if.end 24 25 if.else: ; preds = %entry 26 %3 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 27 %4 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 28 %5 = tail call <256 x i32> @llvm.x86.tileloadd64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf2, i64 0, i64 0), i64 32) #3 29 br label %if.end 30 31 if.end: ; preds = %if.else, %if.then 32 %a.sroa.1186.0 = phi <256 x i32> [ %3, %if.else ], [ %0, %if.then ] 33 %b.sroa.1068.0 = phi <256 x i32> [ %4, %if.else ], [ %1, %if.then ] 34 %c.sroa.1149.0 = phi <256 x i32> [ %5, %if.else ], [ %2, %if.then ] 35 %6 = tail call <256 x i32> @llvm.x86.tdpbssd(i16 %row, i16 %conv.i31, i16 %conv.i31, <256 x i32> %c.sroa.1149.0, <256 x i32> %a.sroa.1186.0, <256 x i32> %b.sroa.1068.0) #3 36 tail call void @llvm.x86.tilestored64(i16 %row, i16 %conv.i31, i8* getelementptr inbounds ([1024 x i8], [1024 x i8]* @buf, i64 0, i64 0), i64 32, <256 x i32> %6) #3 37 ret void 38 } 6. Shape propagation When in -O0 build, some general load/store for tile vector is generated by front-end. We need to root from AMX intrinsics to propagate the shape information to the virtual tile register. If the an AMX intrinsic use the result of load instruction, the shape is propagated to the load and the load is transformed to tile load intrinsic. If the store instruction uses any result of AMX intrinsic, the shape is propagated to store instruction and the store is transformed to tile store intrinsic 7. Machine IR Since the AMX intrinsics take the row and column as the input parameters, we can create a pseudo instruction corresponding to it. The AMX intrinsics are lowered to the pseudo AMX instruction which has extra row and column operands corresponding to AMX intrinsic. The real AMX instructions don't need the row and column operands. The row and column information should be configured by ldtilecfg before executing any AMX instruction. 8. Register allocation AMX register is special. It needs to be configured before use and the config instruction is expensive. To avoid unnecessary tile configure, we collect the tile shape information as much as possible and combine them into one ldtilecfg instruction. The ldtilecfg instruction should dominate any AMX instruction that access tile register. On the other side, the ldtilecfg should post-dominated the instruction that define the tile shape. For tile register spill, it should avoid re-config due to the different tile shape, the spilled register should be reloaded to the register that share the same tile shape. Since tile register allocation is special and it may allocate general virtual register to configure tile register, we can add a sperate pass to do it before general register allocation pass. After register allocation, the tile shape information is not needed anymore, so we can transform the pseudo AMX instruction to real AMX instruction by removing the row and column operands. This seems complicated. Reading through the documentation, there appears to be a single global tile config for all tile registers at any time. Why not simply model this tile config as a designated special register and the tile instructions as having an implicit use of this register? That would seem to ensure that the register allocator has all the constraints needed. You'd need to teach it how to spill the special registers with the appropriate instructions, but that seems a lot more straight forward? 9. Use recommendation Due to the shape configure issue, we recommend user to define the tile shape at the entry of the function entry and inline function as much as possible. The AMX instructions focus on computation instead of storage, so global variable for tile data is not recommended. Thanks Yuanke _______________________________________________ LLVM Developers mailing list llvm-dev at lists.llvm.org<mailto:llvm-dev at lists.llvm.org> https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.llvm.org/pipermail/llvm-dev/attachments/20200818/b47ff3c2/attachment.html>