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x86: Improve svml_s_atanhf8_core_avx2.S

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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
This commit is contained in:
Noah Goldstein 2022-06-09 11:16:35 -07:00
parent 73bae395cf
commit 65897e9916
1 changed files with 205 additions and 206 deletions
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411
sysdeps/x86_64/fpu/multiarch/svml_s_atanhf8_core_avx2.S
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@ -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 SgnMask 0
#define sOne 32 #define sOne 32
#define sPoly 64 #define sTopMask12 64
#define iBrkValue 320 #define TinyRange 96
#define iOffExpoMask 352 #define iBrkValue 128
#define sHalf 384 #define iOffExpoMask 160
#define sSign 416 #define sPoly 192
#define sTopMask12 448 #define sLn2 448
#define TinyRange 480 #define sHalf 480
#define sLn2 512
#include <sysdep.h> #include <sysdep.h>
#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
.section .text.avx2, "ax", @progbits .section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_atanhf_avx2) 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
/* Load constants including One = 1 */
vmovups sOne+__svml_satanh_data_internal(%rip), %ymm5
vmovups sTopMask12+__svml_satanh_data_internal(%rip), %ymm13
vmovaps %ymm0, %ymm6
/* Strip off the sign, so treat X as positive until right at the end */ /* Strip off the sign, so treat X as positive until right at the end */
vandps SgnMask+__svml_satanh_data_internal(%rip), %ymm6, %ymm10 vmovaps ATANHF_DATA(SgnMask)(%rip), %ymm2
vsubps %ymm10, %ymm5, %ymm1 vandps %ymm2, %ymm0, %ymm3
/* Load constants including One = 1 */
vmovups ATANHF_DATA(sOne)(%rip), %ymm5
vsubps %ymm3, %ymm5, %ymm1
vmovups ATANHF_DATA(sTopMask12)(%rip), %ymm4
/* vrcpps %ymm1, %ymm7
* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces, vsubps %ymm1, %ymm5, %ymm9
* the upper part UHi being <= 12 bits long. Then we have vandps %ymm4, %ymm7, %ymm6
* atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)). vsubps %ymm3, %ymm9, %ymm7
*/
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. * Check whether |X| < 1, in which case we use the main function.
* Otherwise set the rangemask so that the callout will get used. * 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). * Note that this will also use the callout for NaNs since not(NaN < 1).
*/ */
vcmpnlt_uqps %ymm5, %ymm10, %ymm7 vcmpnlt_uqps %ymm5, %ymm3, %ymm14
vsubps %ymm1, %ymm5, %ymm9 vcmplt_oqps ATANHF_DATA(TinyRange)(%rip), %ymm3, %ymm15
vcmplt_oqps TinyRange+__svml_satanh_data_internal(%rip), %ymm10, %ymm4
vrcpps %ymm1, %ymm11
vsubps %ymm10, %ymm9, %ymm12
vandps %ymm13, %ymm11, %ymm0
/* No need to split sU when FMA is available */ /*
vfnmadd213ps %ymm5, %ymm0, %ymm1 * Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
vmovaps %ymm6, %ymm8 * the upper part UHi being <= 12 bits long. Then we have
vfmadd213ps %ymm6, %ymm6, %ymm8 * atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
vfnmadd231ps %ymm0, %ymm12, %ymm1 */
vaddps %ymm3, %ymm3, %ymm3
/* /*
* Split V as well into upper 12 bits and lower part, so that we can get * Split V as well into upper 12 bits and lower part, so that we can get
* a preliminary quotient estimate without rounding error. * a preliminary quotient estimate without rounding error.
*/ */
vandps %ymm13, %ymm14, %ymm15 vandps %ymm4, %ymm3, %ymm4
vmovmskps %ymm7, %edx vsubps %ymm4, %ymm3, %ymm7
vsubps %ymm15, %ymm14, %ymm7
/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */ /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
vmulps %ymm15, %ymm0, %ymm10 vmulps %ymm4, %ymm6, %ymm4
/* Compute D = E + E^2 */ /* Compute D = E + E^2 */
vfmadd213ps %ymm1, %ymm1, %ymm1 vfmadd213ps %ymm1, %ymm1, %ymm1
/* Record the sign for eventual reincorporation. */ /* Record the sign for eventual reincorporation. */
vandps sSign+__svml_satanh_data_internal(%rip), %ymm6, %ymm3 vandnps %ymm8, %ymm2, %ymm3
/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */ /* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
vorps %ymm3, %ymm8, %ymm2 vorps %ymm3, %ymm0, %ymm13
vmulps %ymm7, %ymm0, %ymm8 vmulps %ymm7, %ymm6, %ymm2
/* /*
* Compute R * (VHi + VLo) * (1 + E + E^2) * Compute R * (VHi + VLo) * (1 + E + E^2)
* = R * (VHi + VLo) * (1 + D) * = R * (VHi + VLo) * (1 + D)
* = QHi + (QHi * D + QLo + QLo * 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 * Now finally accumulate the high and low parts of the
* argument to log1p, H + L, with a final compensated summation. * argument to log1p, H + L, with a final compensated summation.
*/ */
vaddps %ymm1, %ymm10, %ymm12 vaddps %ymm1, %ymm4, %ymm2
vsubps %ymm12, %ymm10, %ymm11
/* reduction: compute r, n */
vmovups ATANHF_DATA(iBrkValue)(%rip), %ymm9
/* /*
* Now we feed into the log1p code, using H in place of _VARG1 and * Now we feed into the log1p code, using H in place of _VARG1 and
* later incorporating L into the reduced argument. * later incorporating L into the reduced argument.
* compute 1+x as high, low parts * compute 1+x as high, low parts
*/ */
vmaxps %ymm12, %ymm5, %ymm13 vmaxps %ymm2, %ymm5, %ymm0
vminps %ymm12, %ymm5, %ymm14 vminps %ymm2, %ymm5, %ymm6
vaddps %ymm11, %ymm1, %ymm0
vaddps %ymm14, %ymm13, %ymm1 /* This is needed for rounding (see `vaddps %ymm1, %ymm4, %ymm2`). */
vpsubd %ymm9, %ymm1, %ymm7 vsubps %ymm2, %ymm4, %ymm2
vsubps %ymm1, %ymm13, %ymm15 vaddps %ymm6, %ymm0, %ymm4
vpsrad $23, %ymm7, %ymm10 vpsubd %ymm9, %ymm4, %ymm7
vpand iOffExpoMask+__svml_satanh_data_internal(%rip), %ymm7, %ymm8 vsubps %ymm4, %ymm0, %ymm4
vaddps %ymm15, %ymm14, %ymm13 vaddps %ymm2, %ymm1, %ymm2
vpslld $23, %ymm10, %ymm11 vmovaps ATANHF_DATA(iOffExpoMask)(%rip), %ymm1
vpaddd %ymm9, %ymm8, %ymm15
vaddps %ymm13, %ymm0, %ymm14 vandps %ymm1, %ymm7, %ymm0
vcvtdq2ps %ymm10, %ymm0 vaddps %ymm4, %ymm6, %ymm4
vpsubd %ymm11, %ymm5, %ymm12 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 */ /* polynomial evaluation */
vsubps %ymm5, %ymm15, %ymm5 vsubps %ymm5, %ymm0, %ymm2
vmulps %ymm14, %ymm12, %ymm1 vfmadd231ps %ymm4, %ymm6, %ymm2
vaddps %ymm5, %ymm1, %ymm5 vfmadd213ps ATANHF_DATA(sPoly+32)(%rip), %ymm2, %ymm1
vmovups sPoly+224+__svml_satanh_data_internal(%rip), %ymm1 vfmadd213ps ATANHF_DATA(sPoly+64)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+192+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vfmadd213ps ATANHF_DATA(sPoly+96)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+160+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vfmadd213ps ATANHF_DATA(sPoly+128)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+128+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vfmadd213ps ATANHF_DATA(sPoly+160)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+96+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vfmadd213ps ATANHF_DATA(sPoly+192)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+64+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vfmadd213ps ATANHF_DATA(sPoly+224)(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+32+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+__svml_satanh_data_internal(%rip), %ymm5, %ymm1 vmulps %ymm1, %ymm2, %ymm1
vmulps %ymm1, %ymm5, %ymm7 vfmadd213ps %ymm2, %ymm2, %ymm1
vfmadd213ps %ymm5, %ymm5, %ymm7
/* final reconstruction */ /* 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 */ /* Finally, halve the result and reincorporate the sign */
vxorps sHalf+__svml_satanh_data_internal(%rip), %ymm3, %ymm3 vxorps ATANHF_DATA(sHalf)(%rip), %ymm3, %ymm3
vmulps %ymm0, %ymm3, %ymm0 vmulps %ymm2, %ymm3, %ymm2
vblendvps %ymm4, %ymm2, %ymm0, %ymm0 vmovmskps %ymm14, %edx
testl %edx, %edx testl %edx, %edx
vblendvps %ymm15, %ymm13, %ymm2, %ymm0
/* Go to special inputs processing branch */ /* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH) jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm6 # LOE rbx rdx r12 r13 r14 r15 ymm0
/* No registers to restore on fast path. */
/* Restore registers
* and exit the function
*/
L(EXIT):
movq %rbp, %rsp
popq %rbp
cfi_def_cfa(7, 8)
cfi_restore(6)
ret 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): L(SPECIAL_VALUES_BRANCH):
vmovups %ymm6, 32(%rsp) # LOE rbx rdx r12 r13 r14 r15 ymm0 ymm8
vmovups %ymm0, 64(%rsp) /* Use r13 to save/restore the stack. This allows us to use rbp as
# LOE rbx r12 r13 r14 r15 edx ymm0 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)
xorl %eax, %eax /* Align stack and make room for 2x ymm vectors. */
# LOE rbx r12 r13 r14 r15 eax edx andq $-32, %rsp
addq $-64, %rsp
/* Save all already computed inputs. */
vmovups %ymm0, (%rsp)
/* Save original input (ymm8 unchanged up to this point). */
vmovups %ymm8, 32(%rsp)
vzeroupper 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
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx r15 r12d r13d
/* Special inputs
* processing loop
*/
/* 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): L(SPECIAL_VALUES_LOOP):
incl %r12d # LOE rbx rbp r12 r13 r14 r15
cmpl $8, %r12d /* 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
/* Check bits in range mask */ /* Scalar math fucntion call to process special input. */
jl L(RANGEMASK_CHECK) movss 32(%rsp, %rbp, 4), %xmm0
# 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
call atanhf@PLT 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)
/* Process special inputs in loop */ blsrl %ebx, %ebx
jmp L(SPECIAL_VALUES_LOOP) jnz L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d # LOE r12 r13 r14 r15
/* 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) END(_ZGVdN8v_atanhf_avx2)
.section .rodata, "a" .section .rodata, "a"
.align 32 .align 32
#ifdef __svml_satanh_data_internal_typedef #ifdef __svml_satanh_data_internal_typedef
typedef unsigned int VUINT32; typedef unsigned int VUINT32;
typedef struct { typedef struct{
__declspec(align(32)) VUINT32 SgnMask[8][1]; __declspec(align(32)) VUINT32 SgnMask[8][1];
__declspec(align(32)) VUINT32 sOne[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 sTopMask12[8][1];
__declspec(align(32)) VUINT32 TinyRange[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 sLn2[8][1];
__declspec(align(32)) VUINT32 sHalf[8][1];
} __svml_satanh_data_internal; } __svml_satanh_data_internal;
#endif #endif
__svml_satanh_data_internal: __svml_satanh_data_internal:
/* SgnMask */ /* SgnMask */
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/* sOne = SP 1.0 */ /* sOne = SP 1.0 */
.align 32 .align 32
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* sPoly[] = SP polynomial */ .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.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 */
/* iBrkValue = SP 2/3 */
.align 32
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 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 */ /* sTopMask12 */
.align 32 .align 32
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000 .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
/* TinyRange */ /* TinyRange */
.align 32 .align 32
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000 .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
/* iBrkValue = SP 2/3 */
.align 32
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
/* iOffExpoMask = SP significand mask */
.align 32
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
/* sPoly[] = SP polynomial */
.align 32
.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) */ /* sLn2 = SP ln(2) */
.align 32 .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 .align 32
.type __svml_satanh_data_internal, @object .type __svml_satanh_data_internal, @object
.size __svml_satanh_data_internal, .-__svml_satanh_data_internal .size __svml_satanh_data_internal, .-__svml_satanh_data_internal