Soft Thresholding CUDA implementation - cuda

Question

I am wondering how should I implement a nice soft thresholding function kernel in CUDA?
The soft thresholding function is like following:
where lambda is the threshold, and x is the input vector or matrix. Suppose they are both real.
I prefer an existing code sample that runs reliably. I am reluctant to start from scratch. Anyone has done this before? Or knows where can I find a good sample code?

Answer 1

The two solutions proposed in the comments above, set up for an elementwise processing, are the following:
__global__ void myKernel1(float* __restrict__ x, float lambda, const int N)
{
int tid = threadIdx.x + blockIdx.x * blockDim.x;
if (tid < N) {
float xa = fabs(x[tid]);
x[tid] = (xa > lambda) ? x[tid] * ((xa - lambda) / xa) : 0;
}
}
and
__global__ void myKernel2(float* __restrict__ x, float lambda, const int N)
{
int tid = threadIdx.x + blockIdx.x * blockDim.x;
if (tid < N) {
float xa = fabs(x[tid]);
x[tid] = signbit(lambda-xa)*copysign(xa-lambda,x[tid]);
}
}
The disassembled codes for the two solutions are reported below. As noticed also by #njuffa, the second one seems to be in principle less burdened than the first one due to the lacking x/|x| division. However, as also noticed by #njuffa, this scenario will be likely memory bound rather than compute bound. However, perhaps this analysis gives indication that the second solution is preferrable when implemented as __device__ functions for non-elementwise computationS.
DISASSEMBLED CODE FOR THE FIRST SOLUTION
code for sm_21
Function : _Z9myKernel1Pffi
.headerflags #"EF_CUDA_SM20 EF_CUDA_PTX_SM(EF_CUDA_SM20)"
/*0000*/ MOV R1, c[0x1][0x100]; /* 0x2800440400005de4 */
/*0008*/ S2R R0, SR_CTAID.X; /* 0x2c00000094001c04 */
/*0010*/ S2R R3, SR_TID.X; /* 0x2c0000008400dc04 */
/*0018*/ IMAD R0, R0, c[0x0][0x8], R3; /* 0x2006400020001ca3 */
/*0020*/ ISETP.GE.AND P0, PT, R0, c[0x0][0x2c], PT; /* 0x1b0e4000b001dc23 */
/*0028*/ #P0 EXIT ; /* 0x80000000000001e7 */
/*0030*/ MOV32I R3, 0x4; /* 0x180000001000dde2 */
/*0038*/ SSY 0x90; /* 0x6000000140000007 */
/*0040*/ IMAD R16.CC, R0, R3, c[0x0][0x20]; /* 0x2007800080041ca3 */
/*0048*/ IMAD.HI.X R17, R0, R3, c[0x0][0x24]; /* 0x2086800090045ce3 */
/*0050*/ LD.E R2, [R16]; /* 0x8400000001009c85 */
/*0058*/ FSETP.GT.AND P0, PT, |R2|, c[0x0][0x28], PT; /* 0x220e4000a021dc80 */
/*0060*/ F2F.F32.F32 R5, |R2|; /* 0x1000000009215c44 */
/*0068*/ #P0 BRA 0x78; /* 0x40000000200001e7 */
/*0070*/ MOV.S R0, RZ; /* 0x28000000fc001df4 */
/*0078*/ FADD R4, |R2|, -c[0x0][0x28]; /* 0x50004000a0211d80 */
/*0080*/ JCAL 0x0; /* 0x1000000000010007 */
/*0088*/ FMUL.S R0, R2, R4; /* 0x5800000010201c10 */
/*0090*/ ST.E [R16], R0; /* 0x9400000001001c85 */
/*0098*/ EXIT ; /* 0x8000000000001de7 */
.................................
Function : __cuda_sm20_div_rn_noftz_f32_slowpath
.headerflags #"EF_CUDA_SM20 EF_CUDA_PTX_SM(EF_CUDA_SM20)"
/*0000*/ SHL R0, R4, 0x1; /* 0x6000c00004401c03 */
/*0008*/ MOV32I R6, 0x1; /* 0x1800000004019de2 */
/*0010*/ SHL R3, R5, 0x1; /* 0x6000c0000450dc03 */
/*0018*/ IMAD.U32.U32.HI R0, R0, 0x100, -R6; /* 0x200cc00400001d43 */
/*0020*/ ISETP.GT.U32.AND P0, PT, R0, 0xfd, PT; /* 0x1a0ec003f401dc03 */
/*0028*/ IMAD.U32.U32.HI R3, R3, 0x100, -R6; /* 0x200cc0040030dd43 */
/*0030*/ ISETP.GT.U32.OR P0, PT, R3, 0xfd, P0; /* 0x1a20c003f431dc03 */
/*0038*/ #!P0 BRA 0x178; /* 0x40000004e00021e7 */
/*0040*/ FSETP.LE.AND P0, PT, |R4|, +INF , PT; /* 0x218edfe00041dc80 */
/*0048*/ #!P0 BRA 0x60; /* 0x40000000400021e7 */
/*0050*/ FSETP.LE.AND P0, PT, |R5|, +INF , PT; /* 0x218edfe00051dc80 */
/*0058*/ #P0 BRA 0x70; /* 0x40000000400001e7 */
/*0060*/ FADD R4, R4, R5; /* 0x5000000014411c00 */
/*0068*/ BRA 0x370; /* 0x4000000c00001de7 */
/*0070*/ SHL R7, R5, 0x1; /* 0x6000c0000451dc03 */
/*0078*/ SHL R6, R4, 0x1; /* 0x6000c00004419c03 */
/*0080*/ ISETP.EQ.U32.AND P2, PT, R7, RZ, PT; /* 0x190e0000fc75dc03 */
/*0088*/ ISETP.EQ.U32.AND P1, PT, R6, RZ, PT; /* 0x190e0000fc63dc03 */
/*0090*/ PSETP.AND.AND P0, PT, P1, P2, PT; /* 0x0c0e00000811dc04 */
/*0098*/ #P0 BRA 0xc0; /* 0x40000000800001e7 */
/*00a0*/ FSETP.EQ.AND P3, PT, |R4|, +INF , PT; /* 0x210edfe00047dc80 */
/*00a8*/ FSETP.EQ.AND P0, PT, |R5|, +INF , PT; /* 0x210edfe00051dc80 */
/*00b0*/ #!P3 BRA 0xd8; /* 0x4000000080002de7 */
/*00b8*/ #!P0 BRA 0xd8; /* 0x40000000600021e7 */
/*00c0*/ MOV32I R0, 0xffc00000; /* 0x1bff000000001de2 */
/*00c8*/ MUFU.RSQ R4, R0; /* 0xc800000014011c00 */
/*00d0*/ BRA 0x370; /* 0x4000000a60001de7 */
/*00d8*/ PSETP.OR.AND P0, PT, P0, P1, PT; /* 0x0c0e00004401dc04 */
/*00e0*/ #!P0 BRA 0x100; /* 0x40000000600021e7 */
/*00e8*/ LOP.XOR R0, R5, R4; /* 0x6800000010501c83 */
/*00f0*/ LOP32I.AND R4, R0, 0x80000000; /* 0x3a00000000011c02 */
/*00f8*/ BRA 0x370; /* 0x40000009c0001de7 */
/*0100*/ PSETP.OR.AND P0, PT, P3, P2, PT; /* 0x0c0e00004831dc04 */
/*0108*/ #!P0 BRA 0x130; /* 0x40000000800021e7 */
/*0110*/ LOP.XOR R0, R5, R4; /* 0x6800000010501c83 */
/*0118*/ LOP32I.AND R0, R0, 0x80000000; /* 0x3a00000000001c02 */
/*0120*/ LOP32I.OR R4, R0, 0x7f800000; /* 0x39fe000000011c42 */
/*0128*/ BRA 0x370; /* 0x4000000900001de7 */
/*0130*/ ISETP.GE.AND P1, PT, R0, RZ, PT; /* 0x1b0e0000fc03dc23 */
/*0138*/ ISETP.GE.AND P0, PT, R3, RZ, PT; /* 0x1b0e0000fc31dc23 */
/*0140*/ #!P1 MOV32I R6, 0xffffffc0; /* 0x1bffffff0001a5e2 */
/*0148*/ #!P1 FFMA R4, R4, 1.84467440737095520000e+019, RZ; /* 0x307ed7e000412400 */
/*0150*/ #P1 MOV R6, RZ; /* 0x28000000fc0185e4 */
/*0158*/ #P0 BRA 0x180; /* 0x40000000800001e7 */
/*0160*/ FFMA R5, R5, 1.84467440737095520000e+019, RZ; /* 0x307ed7e000515c00 */
/*0168*/ IADD R6, R6, 0x40; /* 0x4800c00100619c03 */
/*0170*/ BRA 0x180; /* 0x4000000020001de7 */
/*0178*/ MOV R6, RZ; /* 0x28000000fc019de4 */
/*0180*/ IADD R7, R3, -0x7e; /* 0x4800fffe0831dc03 */
/*0188*/ MOV32I R9, 0x3f800000; /* 0x18fe000000025de2 */
/*0190*/ ISCADD R7, -R7, R5, 0x17; /* 0x410000001471dee3 */
/*0198*/ ISUB R3, R0, R3; /* 0x480000000c00dd03 */
/*01a0*/ MUFU.RCP R8, R7; /* 0xc800000010721c00 */
/*01a8*/ IADD R5, R0, -0x7e; /* 0x4800fffe08015c03 */
/*01b0*/ FFMA R9, -R7, R8, R9; /* 0x3012000020725e00 */
/*01b8*/ ISCADD R4, -R5, R4, 0x17; /* 0x4100000010511ee3 */
/*01c0*/ FFMA R5, R8, R9, R8; /* 0x3010000024815c00 */
/*01c8*/ FFMA R8, R4, R5, RZ; /* 0x307e000014421c00 */
/*01d0*/ FFMA R9, -R7, R8, R4; /* 0x3008000020725e00 */
/*01d8*/ FFMA R8, R9, R5, R8; /* 0x3010000014921c00 */
/*01e0*/ FFMA R7, -R7, R8, R4; /* 0x300800002071de00 */
/*01e8*/ FFMA R4, R7, R5, R8; /* 0x3010000014711c00 */
/*01f0*/ SHL R9, R4, 0x1; /* 0x6000c00004425c03 */
/*01f8*/ SHR.U32 R9, R9, 0x18; /* 0x5800c00060925c03 */
/*0200*/ IADD R0, R3, R9; /* 0x4800000024301c03 */
/*0208*/ IADD R6, R6, R0; /* 0x4800000000619c03 */
/*0210*/ IADD R0, R6, -0x1; /* 0x4800fffffc601c03 */
/*0218*/ ISETP.GT.U32.AND P0, PT, R0, 0xfd, PT; /* 0x1a0ec003f401dc03 */
/*0220*/ #P0 BRA 0x240; /* 0x40000000600001e7 */
/*0228*/ ISUB R0, R6, R9; /* 0x4800000024601d03 */
/*0230*/ ISCADD R4, R0, R4, 0x17; /* 0x4000000010011ee3 */
/*0238*/ BRA 0x370; /* 0x40000004c0001de7 */
/*0240*/ ISETP.LE.AND P0, PT, R6, 0xfe, PT; /* 0x198ec003f861dc23 */
/*0248*/ #P0 BRA 0x268; /* 0x40000000600001e7 */
/*0250*/ LOP32I.AND R0, R4, 0x80000000; /* 0x3a00000000401c02 */
/*0258*/ LOP32I.OR R4, R0, 0x7f800000; /* 0x39fe000000011c42 */
/*0260*/ BRA 0x370; /* 0x4000000420001de7 */
/*0268*/ ISETP.GT.AND P0, PT, R6, RZ, PT; /* 0x1a0e0000fc61dc23 */
/*0270*/ #P0 BRA 0x370; /* 0x40000003e00001e7 */
/*0278*/ ISETP.GE.AND P0, PT, R6, -0x18, PT; /* 0x1b0effffa061dc23 */
/*0280*/ #P0 BRA 0x298; /* 0x40000000400001e7 */
/*0288*/ LOP32I.AND R4, R4, 0x80000000; /* 0x3a00000000411c02 */
/*0290*/ BRA 0x370; /* 0x4000000360001de7 */
/*0298*/ FFMA.RP R3, R7, R5, R8; /* 0x311000001470dc00 */
/*02a0*/ FFMA.RM R0, R7, R5, R8; /* 0x3090000014701c00 */
/*02a8*/ FFMA.RZ R5, R7, R5, R8; /* 0x3190000014715c00 */
/*02b0*/ FSET.NEU.AND R3, R0, R3, PT; /* 0x168e00000c00dc00 */
/*02b8*/ I2I.S32.S32 R7, -R6; /* 0x1c0000001921df84 */
/*02c0*/ LOP32I.AND R5, R5, 0x7fffff; /* 0x3801fffffc515c02 */
/*02c8*/ ISETP.EQ.AND P0, PT, R7, RZ, PT; /* 0x190e0000fc71dc23 */
/*02d0*/ LOP32I.AND R0, R4, 0x80000000; /* 0x3a00000000401c02 */
/*02d8*/ I2I.S32.S32 R3, -R3; /* 0x1c0000000d20df84 */
/*02e0*/ I2I.S32.S32 R4, -R6; /* 0x1c00000019211f84 */
/*02e8*/ LOP32I.OR R7, R5, 0x800000; /* 0x380200000051dc42 */
/*02f0*/ #P0 BRA.U 0x328; /* 0x40000000c00081e7 */
/*02f8*/ #!P0 IADD R5, R6, 0x20; /* 0x4800c00080616003 */
/*0300*/ #!P0 SHL R5, R7, R5; /* 0x6000000014716003 */
/*0308*/ #!P0 ICMP.EQ.U32 R5, RZ, 0x1, R5; /* 0x310ac00007f16003 */
/*0310*/ #!P0 SHR.U32 R7, R7, R4; /* 0x580000001071e003 */
/*0318*/ #!P0 LOP.OR R3, R3, R5; /* 0x680000001430e043 */
/*0320*/ NOP; /* 0x4000000000001de4 */
/*0328*/ SHL R4, R7, 0x1e; /* 0x6000c00078711c03 */
/*0330*/ SHR.U32 R5, R4, 0x1f; /* 0x5800c0007c415c03 */
/*0338*/ LOP.AND R4, R7, 0x1; /* 0x6800c00004711c03 */
/*0340*/ LOP.OR R3, R3, R5; /* 0x680000001430dc43 */
/*0348*/ LOP.AND R3, R4, R3; /* 0x680000000c40dc03 */
/*0350*/ SHR.U32 R4, R7, 0x1; /* 0x5800c00004711c03 */
/*0358*/ ISETP.NE.U32.AND P0, PT, R3, RZ, PT; /* 0x1a8e0000fc31dc03 */
/*0360*/ #P0 IADD R4, R4, 0x1; /* 0x4800c00004410003 */
/*0368*/ LOP.OR R4, R0, R4; /* 0x6800000010011c43 */
/*0370*/ RET ; /* 0x9000000000001de7 */
......................................................
Function : __cuda_sm20_div_rn_f32
.headerflags #"EF_CUDA_SM20 EF_CUDA_PTX_SM(EF_CUDA_SM20)"
/*0000*/ MUFU.RCP R3, R5; /* 0xc80000001050dc00 */
/*0008*/ MOV32I R6, 0x3f800000; /* 0x18fe000000019de2 */
/*0010*/ LOP32I.AND R0, R4, 0x7fffff; /* 0x3801fffffc401c02 */
/*0018*/ FFMA.FTZ R6, -R5, R3, R6; /* 0x300c00000c519e40 */
/*0020*/ LOP32I.OR R0, R0, 0x3f800000; /* 0x38fe000000001c42 */
/*0028*/ FFMA.FTZ R3, R3, R6, R3; /* 0x300600001830dc40 */
/*0030*/ FFMA.FTZ R6, R0, R3, RZ; /* 0x307e00000c019c40 */
/*0038*/ FFMA.FTZ R7, -R5, R6, R0; /* 0x300000001851de40 */
/*0040*/ FFMA.FTZ R6, R7, R3, R6; /* 0x300c00000c719c40 */
/*0048*/ FFMA.FTZ R0, -R5, R6, R0; /* 0x3000000018501e40 */
/*0050*/ LOP32I.AND R7, R4, 0xff800000; /* 0x3bfe00000041dc02 */
/*0058*/ FFMA.FTZ R6, R0, R3, R6; /* 0x300c00000c019c40 */
/*0060*/ FFMA.FTZ R0, R6, R7, RZ; /* 0x307e00001c601c40 */
/*0068*/ LOP32I.AND R3, R0, 0x7fffffff; /* 0x39fffffffc00dc02 */
/*0070*/ MOV32I R6, 0x7effffef; /* 0x19fbffffbc019de2 */
/*0078*/ IADD32I R3, R3, -0x800010; /* 0x0bfdffffc030dc02 */
/*0080*/ ISETP.GT.U32.AND P0, PT, R3, R6, PT; /* 0x1a0e00001831dc03 */
/*0088*/ #!P0 BRA 0xa8; /* 0x40000000600021e7 */
/*0090*/ JCAL 0x0; /* 0x1000000000010007 */
/*0098*/ MOV R0, R4; /* 0x2800000010001de4 */
/*00a0*/ NOP; /* 0x4000000000001de4 */
/*00a8*/ MOV R4, R0; /* 0x2800000000011de4 */
/*00b0*/ RET ; /* 0x9000000000001de7 */
.......................................
DISASSEMBLED CODE FOR THE SECOND SOLUTION
code for sm_21
Function : _Z9myKernel2Pffi
.headerflags #"EF_CUDA_SM20 EF_CUDA_PTX_SM(EF_CUDA_SM20)"
/*0000*/ MOV R1, c[0x1][0x100]; /* 0x2800440400005de4 */
/*0008*/ S2R R0, SR_CTAID.X; /* 0x2c00000094001c04 */
/*0010*/ S2R R2, SR_TID.X; /* 0x2c00000084009c04 */
/*0018*/ IMAD R0, R0, c[0x0][0x8], R2; /* 0x2004400020001ca3 */
/*0020*/ ISETP.GE.AND P0, PT, R0, c[0x0][0x2c], PT; /* 0x1b0e4000b001dc23 */
/*0028*/ #P0 BRA.U 0x98; /* 0x40000001a00081e7 */
/*0030*/ #!P0 MOV32I R3, 0x4; /* 0x180000001000e1e2 */
/*0038*/ #!P0 IMAD R2.CC, R0, R3, c[0x0][0x20]; /* 0x200780008000a0a3 */
/*0040*/ #!P0 IMAD.HI.X R3, R0, R3, c[0x0][0x24]; /* 0x208680009000e0e3 */
/*0048*/ #!P0 LD.E R0, [R2]; /* 0x8400000000202085 */
/*0050*/ #!P0 FADD R5, |R0|, -c[0x0][0x28]; /* 0x50004000a0016180 */
/*0058*/ #!P0 FADD R4, -|R0|, c[0x0][0x28]; /* 0x50004000a0012280 */
/*0060*/ #!P0 LOP32I.AND R0, R0, 0x80000000; /* 0x3a00000000002002 */
/*0068*/ #!P0 LOP32I.AND R5, R5, 0x7fffffff; /* 0x39fffffffc516002 */
/*0070*/ #!P0 SHR.U32 R4, R4, 0x1f; /* 0x5800c0007c412003 */
/*0078*/ #!P0 LOP.OR R5, R0, R5; /* 0x6800000014016043 */
/*0080*/ #!P0 I2F.F32.S32 R0, R4; /* 0x1800000011202204 */
/*0088*/ #!P0 FMUL R0, R0, R5; /* 0x5800000014002000 */
/*0090*/ #!P0 ST.E [R2], R0; /* 0x9400000000202085 */
/*0098*/ EXIT ; /* 0x8000000000001de7 */
.................................
EDIT
A follow-up of this post has appeared in Soft thresholding in CUDA.