[PATCH v4 2/7] x86: Improve svml_s_atanhf8_core_avx2.S
H.J. Lu
hjl.tools@gmail.com
Thu Jun 9 19:34:34 GMT 2022
On Thu, Jun 9, 2022 at 11:16 AM 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..43eb423831 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
> + more so 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 original 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 (%rsp). */
> + 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
>
LGTM.
Thanks.
--
H.J.
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