Re: [PATCH v2 2/7] x86: Improvement svml_s_atanhf8_core_avx2.S

[Noah Goldstein <goldstein.w.n@gmail.com>]

On Thu, Jun 9, 2022 at 9:01 AM H.J. Lu <hjl.tools@gmail.com> wrote:
>
> On Wed, Jun 8, 2022 at 5:05 PM Noah Goldstein <goldstein.w.n@gmail.com> wrote:
> >
> > Improvements are:
> >     1. Reduce code size (-60 bytes).
> >     2. Remove redundant move instructions.
> >     3. Slightly improve instruction selection/scheduling where
> >        possible.
> >     4. Prefer registers which get short instruction encoding.
> >     5. Shrink rodata usage (-32 bytes).
> >
> > The throughput improvement is not that significant (3-5%) as the
> > port 0 bottleneck is unavoidable.
> >
> >        Function, New Time, Old Time, New / Old
> > _ZGVdN8v_atanhf,    2.799,    2.923,     0.958
> > ---
> >  .../fpu/multiarch/svml_s_atanhf8_core_avx2.S  | 405 +++++++++---------
> >  1 file changed, 202 insertions(+), 203 deletions(-)
> >
> > diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
> > index c1ea1c3353..6113d366c2 100644
> > --- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
> > +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
> > @@ -30,305 +30,304 @@
> >   *
> >   */
> >
> > -/* Offsets for data table __svml_satanh_data_internal
> > - */
> > +/* Offsets for data table __svml_satanh_data_internal_avx512. Ordered
> > +   by use in the function. On cold-starts this might hhelp the
> > +   prefetcher. Possibly a better idea is to interleave start/end so
> > +   that the prefetcher is less likely to detect a stream and pull
> > +   irrelivant lines into cache.  */
> >  #define SgnMask                                0
> >  #define sOne                           32
> > -#define sPoly                          64
> > -#define iBrkValue                      320
> > -#define iOffExpoMask                   352
> > -#define sHalf                          384
> > -#define sSign                          416
> > -#define sTopMask12                     448
> > -#define TinyRange                      480
> > -#define sLn2                           512
> > +#define sTopMask12                     64
> > +#define TinyRange                      96
> > +#define iBrkValue                      128
> > +#define iOffExpoMask                   160
> > +#define sPoly                          192
> > +#define sLn2                           448
> > +#define sHalf                          480
> >
> >  #include <sysdep.h>
> > +#define ATANHF_DATA(x)                 ((x)+__svml_satanh_data_internal)
> >
> >         .section .text.avx2, "ax", @progbits
> >  ENTRY(_ZGVdN8v_atanhf_avx2)
> > -       pushq   %rbp
> > -       cfi_def_cfa_offset(16)
> > -       movq    %rsp, %rbp
> > -       cfi_def_cfa(6, 16)
> > -       cfi_offset(6, -16)
> > -       andq    $-32, %rsp
> > -       subq    $96, %rsp
> > -
> > +       /* Strip off the sign, so treat X as positive until right at the end */
> > +       vmovaps ATANHF_DATA(SgnMask)(%rip), %ymm2
> > +       vandps  %ymm2, %ymm0, %ymm3
> >         /* Load constants including One = 1 */
> > -       vmovups sOne+__svml_satanh_data_internal(%rip), %ymm5
> > -       vmovups sTopMask12+__svml_satanh_data_internal(%rip), %ymm13
> > -       vmovaps %ymm0, %ymm6
> > +       vmovups ATANHF_DATA(sOne)(%rip), %ymm5
> > +       vsubps  %ymm3, %ymm5, %ymm1
> > +       vmovups ATANHF_DATA(sTopMask12)(%rip), %ymm4
> >
> > -       /* Strip off the sign, so treat X as positive until right at the end */
> > -       vandps  SgnMask+__svml_satanh_data_internal(%rip), %ymm6, %ymm10
> > -       vsubps  %ymm10, %ymm5, %ymm1
> > +       vrcpps  %ymm1, %ymm7
> > +       vsubps  %ymm1, %ymm5, %ymm9
> > +       vandps  %ymm4, %ymm7, %ymm6
> > +       vsubps  %ymm3, %ymm9, %ymm7
> >
> > -       /*
> > -        * Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
> > -        * the upper part UHi being <= 12 bits long. Then we have
> > -        * atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
> > -        */
> > -       vaddps  %ymm10, %ymm10, %ymm14
> > +       /* No need to split sU when FMA is available */
> > +       vfnmadd213ps %ymm5, %ymm6, %ymm1
> > +       vmovaps %ymm0, %ymm8
> > +       vfmadd213ps %ymm0, %ymm0, %ymm0
> > +       vfnmadd231ps %ymm6, %ymm7, %ymm1
> >
> >         /*
> >          * Check whether |X| < 1, in which case we use the main function.
> >          * Otherwise set the rangemask so that the callout will get used.
> >          * Note that this will also use the callout for NaNs since not(NaN < 1).
> >          */
> > -       vcmpnlt_uqps %ymm5, %ymm10, %ymm7
> > -       vsubps  %ymm1, %ymm5, %ymm9
> > -       vcmplt_oqps TinyRange+__svml_satanh_data_internal(%rip), %ymm10, %ymm4
> > -       vrcpps  %ymm1, %ymm11
> > -       vsubps  %ymm10, %ymm9, %ymm12
> > -       vandps  %ymm13, %ymm11, %ymm0
> > +       vcmpnlt_uqps %ymm5, %ymm3, %ymm14
> > +       vcmplt_oqps ATANHF_DATA(TinyRange)(%rip), %ymm3, %ymm15
> >
> > -       /* No need to split sU when FMA is available */
> > -       vfnmadd213ps %ymm5, %ymm0, %ymm1
> > -       vmovaps %ymm6, %ymm8
> > -       vfmadd213ps %ymm6, %ymm6, %ymm8
> > -       vfnmadd231ps %ymm0, %ymm12, %ymm1
> > +       /*
> > +        * Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
> > +        * the upper part UHi being <= 12 bits long. Then we have
> > +        * atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
> > +        */
> > +       vaddps  %ymm3, %ymm3, %ymm3
> >
> >         /*
> >          * Split V as well into upper 12 bits and lower part, so that we can get
> >          * a preliminary quotient estimate without rounding error.
> >          */
> > -       vandps  %ymm13, %ymm14, %ymm15
> > -       vmovmskps %ymm7, %edx
> > -       vsubps  %ymm15, %ymm14, %ymm7
> > +       vandps  %ymm4, %ymm3, %ymm4
> > +       vsubps  %ymm4, %ymm3, %ymm7
> >
> >         /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
> > -       vmulps  %ymm15, %ymm0, %ymm10
> > +       vmulps  %ymm4, %ymm6, %ymm4
> >
> >         /* Compute D = E + E^2 */
> >         vfmadd213ps %ymm1, %ymm1, %ymm1
> >
> > -       /* Record the sign for eventual reincorporation. */
> > -       vandps  sSign+__svml_satanh_data_internal(%rip), %ymm6, %ymm3
> > +       /* Record the sign for eventual reincorporation.  */
> > +       vandnps %ymm8, %ymm2, %ymm3
> >
> >         /* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
> > -       vorps   %ymm3, %ymm8, %ymm2
> > -       vmulps  %ymm7, %ymm0, %ymm8
> > +       vorps   %ymm3, %ymm0, %ymm13
> > +       vmulps  %ymm7, %ymm6, %ymm2
> >
> >         /*
> >          * Compute R * (VHi + VLo) * (1 + E + E^2)
> >          * = R *  (VHi + VLo) * (1 + D)
> >          * = QHi + (QHi * D + QLo + QLo * D)
> >          */
> > -       vmulps  %ymm1, %ymm10, %ymm9
> > -       vfmadd213ps %ymm8, %ymm8, %ymm1
> > -       vaddps  %ymm1, %ymm9, %ymm1
> >
> > -       /* reduction: compute r, n */
> > -       vmovups iBrkValue+__svml_satanh_data_internal(%rip), %ymm9
> > +       /*
> > +        * If less precision is acceptable the `vmulps %ymm1, %ymm4, %ymm9;
> > +        * vaddps %ymm1, %ymm9, %ymm1` can be replaced with
> > +        * `vfmadd231ps %ymm1, %ymm4, %ymm4`.
> > +        */
> > +       vmulps  %ymm1, %ymm4, %ymm6
> > +       vfmadd213ps %ymm2, %ymm2, %ymm1
> > +       vaddps  %ymm1, %ymm6, %ymm1
> >
> >         /*
> >          * Now finally accumulate the high and low parts of the
> >          * argument to log1p, H + L, with a final compensated summation.
> >          */
> > -       vaddps  %ymm1, %ymm10, %ymm12
> > -       vsubps  %ymm12, %ymm10, %ymm11
> > +       vaddps  %ymm1, %ymm4, %ymm2
> > +
> > +       /* reduction: compute r, n */
> > +       vmovups ATANHF_DATA(iBrkValue)(%rip), %ymm9
> >
> >         /*
> >          * Now we feed into the log1p code, using H in place of _VARG1 and
> >          * later incorporating L into the reduced argument.
> >          * compute 1+x as high, low parts
> >          */
> > -       vmaxps  %ymm12, %ymm5, %ymm13
> > -       vminps  %ymm12, %ymm5, %ymm14
> > -       vaddps  %ymm11, %ymm1, %ymm0
> > -       vaddps  %ymm14, %ymm13, %ymm1
> > -       vpsubd  %ymm9, %ymm1, %ymm7
> > -       vsubps  %ymm1, %ymm13, %ymm15
> > -       vpsrad  $23, %ymm7, %ymm10
> > -       vpand   iOffExpoMask+__svml_satanh_data_internal(%rip), %ymm7, %ymm8
> > -       vaddps  %ymm15, %ymm14, %ymm13
> > -       vpslld  $23, %ymm10, %ymm11
> > -       vpaddd  %ymm9, %ymm8, %ymm15
> > -       vaddps  %ymm13, %ymm0, %ymm14
> > -       vcvtdq2ps %ymm10, %ymm0
> > -       vpsubd  %ymm11, %ymm5, %ymm12
> > +       vmaxps  %ymm2, %ymm5, %ymm0
> > +       vminps  %ymm2, %ymm5, %ymm6
> > +
> > +       /* This is needed for rounding (see `vaddps %ymm1, %ymm4, %ymm2`).  */
> > +       vsubps  %ymm2, %ymm4, %ymm2
> > +       vaddps  %ymm6, %ymm0, %ymm4
> > +       vpsubd  %ymm9, %ymm4, %ymm7
> > +       vsubps  %ymm4, %ymm0, %ymm4
> > +       vaddps  %ymm2, %ymm1, %ymm2
> > +       vmovaps ATANHF_DATA(iOffExpoMask)(%rip), %ymm1
> > +
> > +       vandps  %ymm1, %ymm7, %ymm0
> > +       vaddps  %ymm4, %ymm6, %ymm4
> > +       vandnps %ymm7, %ymm1, %ymm6
> > +       vmovups ATANHF_DATA(sPoly+0)(%rip), %ymm1
> > +       vpaddd  %ymm9, %ymm0, %ymm0
> > +       vaddps  %ymm4, %ymm2, %ymm4
> > +       vpsubd  %ymm6, %ymm5, %ymm6
> >
> >         /* polynomial evaluation */
> > -       vsubps  %ymm5, %ymm15, %ymm5
> > -       vmulps  %ymm14, %ymm12, %ymm1
> > -       vaddps  %ymm5, %ymm1, %ymm5
> > -       vmovups sPoly+224+__svml_satanh_data_internal(%rip), %ymm1
> > -       vfmadd213ps sPoly+192+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+160+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+128+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+96+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+64+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+32+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vfmadd213ps sPoly+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
> > -       vmulps  %ymm1, %ymm5, %ymm7
> > -       vfmadd213ps %ymm5, %ymm5, %ymm7
> > +       vsubps  %ymm5, %ymm0, %ymm2
> > +       vfmadd231ps %ymm4, %ymm6, %ymm2
> > +       vfmadd213ps ATANHF_DATA(sPoly+32)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+64)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+96)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+128)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+160)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+192)(%rip), %ymm2, %ymm1
> > +       vfmadd213ps ATANHF_DATA(sPoly+224)(%rip), %ymm2, %ymm1
> > +
> > +       vmulps  %ymm1, %ymm2, %ymm1
> > +       vfmadd213ps %ymm2, %ymm2, %ymm1
> >
> >         /* final reconstruction */
> > -       vfmadd132ps sLn2+__svml_satanh_data_internal(%rip), %ymm7, %ymm0
> > +       vpsrad  $23, %ymm7, %ymm6
> > +       vcvtdq2ps %ymm6, %ymm2
> > +       vfmadd132ps ATANHF_DATA(sLn2)(%rip), %ymm1, %ymm2
> >
> >         /* Finally, halve the result and reincorporate the sign */
> > -       vxorps  sHalf+__svml_satanh_data_internal(%rip), %ymm3, %ymm3
> > -       vmulps  %ymm0, %ymm3, %ymm0
> > -       vblendvps %ymm4, %ymm2, %ymm0, %ymm0
> > +       vxorps  ATANHF_DATA(sHalf)(%rip), %ymm3, %ymm3
> > +       vmulps  %ymm2, %ymm3, %ymm2
> > +       vmovmskps %ymm14, %edx
> >         testl   %edx, %edx
> >
> > +       vblendvps %ymm15, %ymm13, %ymm2, %ymm0
> >         /* Go to special inputs processing branch */
> >         jne     L(SPECIAL_VALUES_BRANCH)
> > -       # LOE rbx r12 r13 r14 r15 edx ymm0 ymm6
> > -
> > -       /* Restore registers
> > -        * and exit the function
> > -        */
> > -
> > -L(EXIT):
> > -       movq    %rbp, %rsp
> > -       popq    %rbp
> > -       cfi_def_cfa(7, 8)
> > -       cfi_restore(6)
> > +       # LOE rbx rdx r12 r13 r14 r15 ymm0
> > +       /* No registers to restore on fast path.  */
> >         ret
> > -       cfi_def_cfa(6, 16)
> > -       cfi_offset(6, -16)
> >
> > -       /* Branch to process
> > -        * special inputs
> > -        */
> >
> > +       /* Cold case. edx has 1s where there was a special value that
> > +          needs to be handled by a atanhf call. Optimize for code size
> > +          moreso than speed here. */
> >  L(SPECIAL_VALUES_BRANCH):
> > -       vmovups %ymm6, 32(%rsp)
> > -       vmovups %ymm0, 64(%rsp)
> > -       # LOE rbx r12 r13 r14 r15 edx ymm0
> > -
> > -       xorl    %eax, %eax
> > -       # LOE rbx r12 r13 r14 r15 eax edx
> > -
> > -       vzeroupper
> > -       movq    %r12, 16(%rsp)
> > -       /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
> > -       movl    %eax, %r12d
> > -       movq    %r13, 8(%rsp)
> > -       /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
> > -       movl    %edx, %r13d
> > -       movq    %r14, (%rsp)
> > -       /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
> > -       # LOE rbx r15 r12d r13d
> > -
> > -       /* Range mask
> > -        * bits check
> > +       # LOE rbx rdx r12 r13 r14 r15 ymm0 ymm8
> > +    /* Use r13 to save/restore the stack. This allows us to use rbp as
> > +       callee save register saving code size. */
> > +       pushq   %r13
> > +       cfi_adjust_cfa_offset(8)
> > +       cfi_offset(r13, -16)
> > +       /* Need to callee save registers to preserve state across tanhf calls.
> >          */
> > +       pushq   %rbx
> > +       cfi_adjust_cfa_offset(8)
> > +       cfi_offset(rbx, -24)
> > +       pushq   %rbp
> > +       cfi_adjust_cfa_offset(8)
> > +       cfi_offset(rbp, -32)
> > +       movq    %rsp, %r13
> > +       cfi_def_cfa_register(r13)
> >
> > -L(RANGEMASK_CHECK):
> > -       btl     %r12d, %r13d
> > +       /* Align stack and make room for 2x ymm vectors.  */
> > +       andq    $-32, %rsp
> > +       addq    $-64, %rsp
> >
> > -       /* Call scalar math function */
> > -       jc      L(SCALAR_MATH_CALL)
> > -       # LOE rbx r15 r12d r13d
> > +       /* Save all already computed inputs.  */
> > +       vmovups %ymm0, (%rsp)
> > +       /* Save origional input (ymm8 unchanged up to this point).  */
> > +       vmovups %ymm8, 32(%rsp)
> >
> > -       /* Special inputs
> > -        * processing loop
> > -        */
> > +       vzeroupper
> >
> > +       /* edx has 1s where there was a special value that needs to be handled
> > +          by a atanhf call.  */
> > +       movl    %edx, %ebx
> >  L(SPECIAL_VALUES_LOOP):
> > -       incl    %r12d
> > -       cmpl    $8, %r12d
> > -
> > -       /* Check bits in range mask */
> > -       jl      L(RANGEMASK_CHECK)
> > -       # LOE rbx r15 r12d r13d
> > -
> > -       movq    16(%rsp), %r12
> > -       cfi_restore(12)
> > -       movq    8(%rsp), %r13
> > -       cfi_restore(13)
> > -       movq    (%rsp), %r14
> > -       cfi_restore(14)
> > -       vmovups 64(%rsp), %ymm0
> > -
> > -       /* Go to exit */
> > -       jmp     L(EXIT)
> > -       /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
> > -       /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
> > -       /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
> > -       .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
> > -       # LOE rbx r12 r13 r14 r15 ymm0
> > -
> > -       /* Scalar math fucntion call
> > -        * to process special input
> > -        */
> > -
> > -L(SCALAR_MATH_CALL):
> > -       movl    %r12d, %r14d
> > -       movss   32(%rsp, %r14, 4), %xmm0
> > +       # LOE rbx rbp r12 r13 r14 r15
> > +       /* use rbp as index for special value that is saved across calls to
> > +          atanhf. We technically don't need a callee save register here as offset
> > +          to rsp is always [0, 28] so we can restore rsp by realigning to 64.
> > +          Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
> > +          in the loop. Realigning also costs more code size.  */
> > +       xorl    %ebp, %ebp
> > +       tzcntl  %ebx, %ebp
> > +
> > +       /* Scalar math fucntion call to process special input.  */
> > +       movss   32(%rsp, %rbp, 4), %xmm0
> >         call    atanhf@PLT
> > -       # LOE rbx r14 r15 r12d r13d xmm0
> >
> > -       movss   %xmm0, 64(%rsp, %r14, 4)
> > +       /* No good way to avoid the store-forwarding fault this will cause on
> > +          return. `lfence` avoids the SF fault but at greater cost as it
> > +          serialized stack/callee save restoration.  */
> > +       movss   %xmm0, (%rsp, %rbp, 4)
> > +
> > +       blsrl   %ebx, %ebx
> > +       jnz     L(SPECIAL_VALUES_LOOP)
> > +       # LOE r12 r13 r14 r15
> > +
> >
> > -       /* Process special inputs in loop */
> > -       jmp     L(SPECIAL_VALUES_LOOP)
> > -       # LOE rbx r15 r12d r13d
> > +       /* All results have been written to 32(%rsp).  */
>                                                                 Why 32
> here?  Did you mean 32 bytes at %rsp?


Correct. Fixed in V2.
> > +       vmovups (%rsp), %ymm0
> > +       /* Restore rsp.  */
> > +       movq    %r13, %rsp
> > +       cfi_def_cfa_register(rsp)
> > +       /* Restore callee save registers.  */
> > +       popq    %rbp
> > +       cfi_adjust_cfa_offset(-8)
> > +       cfi_restore(rbp)
> > +       popq    %rbx
> > +       cfi_adjust_cfa_offset(-8)
> > +       cfi_restore(rbp)
> > +       popq    %r13
> > +       cfi_adjust_cfa_offset(-8)
> > +       cfi_restore(r13)
> > +       ret
> >  END(_ZGVdN8v_atanhf_avx2)
> >
> >         .section .rodata, "a"
> >         .align  32
> > -
> >  #ifdef __svml_satanh_data_internal_typedef
> >  typedef unsigned int VUINT32;
> > -typedef struct {
> > +typedef struct{
> >         __declspec(align(32)) VUINT32 SgnMask[8][1];
> >         __declspec(align(32)) VUINT32 sOne[8][1];
> > -       __declspec(align(32)) VUINT32 sPoly[8][8][1];
> > -       __declspec(align(32)) VUINT32 iBrkValue[8][1];
> > -       __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
> > -       __declspec(align(32)) VUINT32 sHalf[8][1];
> > -       __declspec(align(32)) VUINT32 sSign[8][1];
> >         __declspec(align(32)) VUINT32 sTopMask12[8][1];
> >         __declspec(align(32)) VUINT32 TinyRange[8][1];
> > +       __declspec(align(32)) VUINT32 iBrkValue[8][1];
> > +       __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
> > +       __declspec(align(32)) VUINT32 sPoly[8][8][1];
> >         __declspec(align(32)) VUINT32 sLn2[8][1];
> > +       __declspec(align(32)) VUINT32 sHalf[8][1];
> >  } __svml_satanh_data_internal;
> >  #endif
> >  __svml_satanh_data_internal:
> >         /* SgnMask */
> > -       .long   0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
> > +       .long   0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
> > +       .long   0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
> >         /* sOne = SP 1.0 */
> >         .align  32
> > -       .long   0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
> > -       /* sPoly[] = SP polynomial */
> > +       .long   0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
> > +       .long   0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
> > +       /* sTopMask12 */
> > +       .align  32
> > +       .long   0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
> > +       .long   0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
> > +       /* TinyRange */
> >         .align  32
> > -       .long   0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
> > -       .long   0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
> > -       .long   0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
> > -       .long   0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
> > -       .long   0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
> > -       .long   0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
> > -       .long   0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
> > -       .long   0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
> > +       .long   0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
> > +       .long   0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
> >         /* iBrkValue = SP 2/3 */
> >         .align  32
> > -       .long   0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
> > +       .long   0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
> > +       .long   0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
> >         /* iOffExpoMask = SP significand mask */
> >         .align  32
> > -       .long   0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
> > -       /* sHalf */
> > -       .align  32
> > -       .long   0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
> > -       /* sSign */
> > -       .align  32
> > -       .long   0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
> > -       /* sTopMask12 */
> > -       .align  32
> > -       .long   0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
> > -       /* TinyRange */
> > +       .long   0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
> > +       .long   0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
> > +       /* sPoly[] = SP polynomial */
> >         .align  32
> > -       .long   0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
> > +       .long   0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed
> > +       .long   0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
> > +       .long   0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3
> > +       .long   0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
> > +       .long   0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12
> > +       .long   0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
> > +       .long   0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37
> > +       .long   0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
> > +       .long   0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190
> > +       .long   0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
> > +       .long   0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e
> > +       .long   0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
> > +       .long   0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94
> > +       .long   0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
> > +       .long   0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
> > +       .long   0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
> >         /* sLn2 = SP ln(2) */
> >         .align  32
> > -       .long   0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
> > +       .long   0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
> > +       .long   0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
> > +       /* sHalf */
> > +       .align  32
> > +       .long   0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
> > +       .long   0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
> >         .align  32
> >         .type   __svml_satanh_data_internal, @object
> >         .size   __svml_satanh_data_internal, .-__svml_satanh_data_internal
> > --
> > 2.34.1
> >
>
>
> --
> H.J.