| /* Function powf vectorized with SSE4. |
| Copyright (C) 2014-2018 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #include <sysdep.h> |
| #include "svml_s_powf_data.h" |
| |
| .text |
| ENTRY (_ZGVbN4vv_powf_sse4) |
| /* |
| ALGORITHM DESCRIPTION: |
| |
| We are using the next identity: pow(x,y) = 2^(y * log2(x)). |
| |
| 1) log2(x) calculation |
| Here we use the following formula. |
| Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. |
| Let C ~= 1/ln(2), |
| Rcp1 ~= 1/X1, X2=Rcp1*X1, |
| Rcp2 ~= 1/X2, X3=Rcp2*X2, |
| Rcp3 ~= 1/X3, Rcp3C ~= C/X3. |
| Then |
| log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + |
| log2(X1*Rcp1*Rcp2*Rcp3C/C), |
| where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. |
| |
| The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), |
| Rcp3C, log2(C/Rcp3C) are taken from tables. |
| Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C |
| is exactly represented in target precision. |
| |
| log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = |
| = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = |
| = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = |
| = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., |
| where |
| cq=X1*Rcp1*Rcp2*Rcp3C-C, |
| a1=1/(C*ln(2))-1 is small, |
| a2=1/(2*C^2*ln2), |
| a3=1/(3*C^3*ln2), |
| ... |
| Log2 result is split by three parts: HH+HL+HLL |
| |
| 2) Calculation of y*log2(x) |
| Split y into YHi+YLo. |
| Get high PH and medium PL parts of y*log2|x|. |
| Get low PLL part of y*log2|x|. |
| Now we have PH+PL+PLL ~= y*log2|x|. |
| |
| 3) Calculation of 2^(y*log2(x)) |
| Let's represent PH+PL+PLL in the form N + j/2^expK + Z, |
| where expK=7 in this implementation, N and j are integers, |
| 0<=j<=2^expK-1, |Z|<2^(-expK-1). Hence |
| 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, |
| where 2^(j/2^expK) is stored in a table, and |
| 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. |
| We compute 2^(PH+PL+PLL) as follows: |
| Break PH into PHH + PHL, where PHH = N + j/2^expK. |
| Z = PHL + PL + PLL |
| Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 |
| Get 2^(j/2^expK) from table in the form THI+TLO. |
| Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). |
| Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: |
| ResHi := THI |
| ResLo := THI * Exp2Poly + TLO |
| Get exponent ERes of the result: |
| Res := ResHi + ResLo: |
| Result := ex(Res) + N. */ |
| |
| pushq %rbp |
| cfi_adjust_cfa_offset (8) |
| cfi_rel_offset (%rbp, 0) |
| movq %rsp, %rbp |
| cfi_def_cfa_register (%rbp) |
| andq $-64, %rsp |
| subq $256, %rsp |
| movaps %xmm0, %xmm3 |
| movhlps %xmm0, %xmm3 |
| movaps %xmm1, %xmm5 |
| movups %xmm8, 112(%rsp) |
| movaps %xmm5, %xmm2 |
| cvtps2pd %xmm3, %xmm8 |
| cvtps2pd %xmm5, %xmm7 |
| movups %xmm9, 96(%rsp) |
| movaps %xmm0, %xmm4 |
| cvtps2pd %xmm0, %xmm9 |
| movq __svml_spow_data@GOTPCREL(%rip), %rdx |
| movups %xmm10, 176(%rsp) |
| movups %xmm13, 48(%rsp) |
| movups _ExpMask(%rdx), %xmm6 |
| |
| /* preserve mantissa, set input exponent to 2^(-10) */ |
| movaps %xmm6, %xmm10 |
| andps %xmm8, %xmm6 |
| andps %xmm9, %xmm10 |
| |
| /* exponent bits selection */ |
| psrlq $20, %xmm9 |
| orps _Two10(%rdx), %xmm6 |
| psrlq $20, %xmm8 |
| orps _Two10(%rdx), %xmm10 |
| |
| /* reciprocal approximation good to at least 11 bits */ |
| cvtpd2ps %xmm6, %xmm13 |
| cvtpd2ps %xmm10, %xmm1 |
| movlhps %xmm13, %xmm13 |
| movhlps %xmm5, %xmm2 |
| movlhps %xmm1, %xmm1 |
| movups %xmm12, 208(%rsp) |
| rcpps %xmm13, %xmm12 |
| movups %xmm11, 80(%rsp) |
| cvtps2pd %xmm2, %xmm11 |
| rcpps %xmm1, %xmm2 |
| movups %xmm14, 144(%rsp) |
| cvtps2pd %xmm12, %xmm14 |
| movups %xmm15, 160(%rsp) |
| cvtps2pd %xmm2, %xmm15 |
| shufps $221, %xmm8, %xmm9 |
| |
| /* round reciprocal to nearest integer, will have 1+9 mantissa bits */ |
| roundpd $0, %xmm14, %xmm14 |
| |
| /* biased exponent in DP format */ |
| pshufd $238, %xmm9, %xmm8 |
| roundpd $0, %xmm15, %xmm15 |
| cvtdq2pd %xmm8, %xmm1 |
| mulpd %xmm15, %xmm10 |
| mulpd %xmm14, %xmm6 |
| cvtdq2pd %xmm9, %xmm2 |
| subpd _One(%rdx), %xmm10 |
| subpd _One(%rdx), %xmm6 |
| |
| /* table lookup */ |
| movaps %xmm14, %xmm8 |
| movaps %xmm15, %xmm9 |
| psrlq $40, %xmm8 |
| psrlq $40, %xmm9 |
| movd %xmm8, %r8d |
| movd %xmm9, %eax |
| psubd _NMINNORM(%rdx), %xmm4 |
| movdqu _ABSMASK(%rdx), %xmm3 |
| pextrd $2, %xmm8, %r9d |
| pand %xmm5, %xmm3 |
| movups _Threshold(%rdx), %xmm8 |
| pextrd $2, %xmm9, %ecx |
| movaps %xmm8, %xmm9 |
| cmpltpd %xmm15, %xmm9 |
| cmpltpd %xmm14, %xmm8 |
| andps _Bias(%rdx), %xmm9 |
| movaps %xmm10, %xmm14 |
| andps _Bias(%rdx), %xmm8 |
| movaps %xmm6, %xmm15 |
| orps _Bias1(%rdx), %xmm9 |
| orps _Bias1(%rdx), %xmm8 |
| subpd %xmm9, %xmm2 |
| subpd %xmm8, %xmm1 |
| mulpd %xmm10, %xmm14 |
| mulpd %xmm6, %xmm15 |
| mulpd _L2(%rdx), %xmm2 |
| mulpd _L2(%rdx), %xmm1 |
| movups _poly_coeff_3(%rdx), %xmm9 |
| movaps %xmm9, %xmm8 |
| mulpd %xmm10, %xmm8 |
| mulpd %xmm6, %xmm9 |
| addpd _poly_coeff_4(%rdx), %xmm8 |
| addpd _poly_coeff_4(%rdx), %xmm9 |
| mulpd %xmm14, %xmm8 |
| mulpd %xmm15, %xmm9 |
| |
| /* reconstruction */ |
| addpd %xmm8, %xmm10 |
| addpd %xmm9, %xmm6 |
| movslq %eax, %rax |
| movslq %r8d, %r8 |
| movslq %ecx, %rcx |
| movslq %r9d, %r9 |
| movsd _Log2Rcp_lookup(%rdx,%rax), %xmm13 |
| movsd _Log2Rcp_lookup(%rdx,%r8), %xmm12 |
| movhpd _Log2Rcp_lookup(%rdx,%rcx), %xmm13 |
| movhpd _Log2Rcp_lookup(%rdx,%r9), %xmm12 |
| addpd %xmm10, %xmm13 |
| addpd %xmm6, %xmm12 |
| addpd %xmm13, %xmm2 |
| addpd %xmm12, %xmm1 |
| mulpd %xmm7, %xmm2 |
| mulpd %xmm11, %xmm1 |
| movups __dbInvLn2(%rdx), %xmm11 |
| movdqa %xmm4, %xmm12 |
| movaps %xmm11, %xmm10 |
| mulpd %xmm2, %xmm10 |
| mulpd %xmm1, %xmm11 |
| |
| /* to round down; if dR is an integer we will get R = 1, which is ok */ |
| movaps %xmm10, %xmm8 |
| movaps %xmm11, %xmm9 |
| subpd __dbHALF(%rdx), %xmm8 |
| subpd __dbHALF(%rdx), %xmm9 |
| addpd __dbShifter(%rdx), %xmm8 |
| addpd __dbShifter(%rdx), %xmm9 |
| movaps %xmm8, %xmm6 |
| movaps %xmm9, %xmm7 |
| subpd __dbShifter(%rdx), %xmm6 |
| subpd __dbShifter(%rdx), %xmm7 |
| |
| /* [0..1) */ |
| subpd %xmm6, %xmm10 |
| subpd %xmm7, %xmm11 |
| mulpd __dbC1(%rdx), %xmm10 |
| mulpd __dbC1(%rdx), %xmm11 |
| |
| /* hi bits */ |
| shufps $221, %xmm1, %xmm2 |
| movdqu _NMAXVAL(%rdx), %xmm1 |
| pcmpgtd %xmm1, %xmm12 |
| pcmpeqd %xmm1, %xmm4 |
| por %xmm4, %xmm12 |
| movdqa %xmm3, %xmm1 |
| movdqu _INF(%rdx), %xmm4 |
| pcmpgtd %xmm4, %xmm1 |
| pcmpeqd %xmm4, %xmm3 |
| |
| /* iAbsX = iAbsX&iAbsMask */ |
| pand __iAbsMask(%rdx), %xmm2 |
| por %xmm3, %xmm1 |
| |
| /* iRangeMask = (iAbsX>iDomainRange) */ |
| pcmpgtd __iDomainRange(%rdx), %xmm2 |
| por %xmm1, %xmm12 |
| movups __lbLOWKBITS(%rdx), %xmm3 |
| por %xmm2, %xmm12 |
| |
| /* low K bits */ |
| movaps %xmm3, %xmm2 |
| andps %xmm9, %xmm3 |
| andps %xmm8, %xmm2 |
| psrlq $11, %xmm8 |
| |
| /* dpP= _dbT+lJ*T_ITEM_GRAN */ |
| movd %xmm2, %r10d |
| psrlq $11, %xmm9 |
| movd %xmm3, %ecx |
| |
| /* NB : including +/- sign for the exponent!! */ |
| psllq $52, %xmm8 |
| psllq $52, %xmm9 |
| pextrw $4, %xmm2, %r11d |
| pextrw $4, %xmm3, %r8d |
| movmskps %xmm12, %eax |
| shll $3, %r10d |
| shll $3, %ecx |
| shll $3, %r11d |
| shll $3, %r8d |
| movq 13952(%rdx,%r10), %xmm6 |
| movq 13952(%rdx,%rcx), %xmm7 |
| movhpd 13952(%rdx,%r11), %xmm6 |
| movhpd 13952(%rdx,%r8), %xmm7 |
| mulpd %xmm6, %xmm10 |
| mulpd %xmm7, %xmm11 |
| addpd %xmm10, %xmm6 |
| addpd %xmm11, %xmm7 |
| paddq %xmm8, %xmm6 |
| paddq %xmm9, %xmm7 |
| cvtpd2ps %xmm6, %xmm1 |
| cvtpd2ps %xmm7, %xmm4 |
| movlhps %xmm4, %xmm1 |
| testl %eax, %eax |
| jne .LBL_1_3 |
| |
| .LBL_1_2: |
| cfi_remember_state |
| movups 112(%rsp), %xmm8 |
| movaps %xmm1, %xmm0 |
| movups 96(%rsp), %xmm9 |
| movups 176(%rsp), %xmm10 |
| movups 80(%rsp), %xmm11 |
| movups 208(%rsp), %xmm12 |
| movups 48(%rsp), %xmm13 |
| movups 144(%rsp), %xmm14 |
| movups 160(%rsp), %xmm15 |
| movq %rbp, %rsp |
| cfi_def_cfa_register (%rsp) |
| popq %rbp |
| cfi_adjust_cfa_offset (-8) |
| cfi_restore (%rbp) |
| ret |
| |
| .LBL_1_3: |
| cfi_restore_state |
| movups %xmm0, 64(%rsp) |
| movups %xmm5, 128(%rsp) |
| movups %xmm1, 192(%rsp) |
| je .LBL_1_2 |
| |
| xorb %cl, %cl |
| xorl %edx, %edx |
| movq %rsi, 8(%rsp) |
| movq %rdi, (%rsp) |
| movq %r12, 40(%rsp) |
| cfi_offset_rel_rsp (12, 40) |
| movb %cl, %r12b |
| movq %r13, 32(%rsp) |
| cfi_offset_rel_rsp (13, 32) |
| movl %eax, %r13d |
| movq %r14, 24(%rsp) |
| cfi_offset_rel_rsp (14, 24) |
| movl %edx, %r14d |
| movq %r15, 16(%rsp) |
| cfi_offset_rel_rsp (15, 16) |
| cfi_remember_state |
| |
| .LBL_1_6: |
| btl %r14d, %r13d |
| jc .LBL_1_12 |
| |
| .LBL_1_7: |
| lea 1(%r14), %esi |
| btl %esi, %r13d |
| jc .LBL_1_10 |
| |
| .LBL_1_8: |
| incb %r12b |
| addl $2, %r14d |
| cmpb $16, %r12b |
| jb .LBL_1_6 |
| |
| movq 8(%rsp), %rsi |
| movq (%rsp), %rdi |
| movq 40(%rsp), %r12 |
| cfi_restore (%r12) |
| movq 32(%rsp), %r13 |
| cfi_restore (%r13) |
| movq 24(%rsp), %r14 |
| cfi_restore (%r14) |
| movq 16(%rsp), %r15 |
| cfi_restore (%r15) |
| movups 192(%rsp), %xmm1 |
| jmp .LBL_1_2 |
| |
| .LBL_1_10: |
| cfi_restore_state |
| movzbl %r12b, %r15d |
| movss 68(%rsp,%r15,8), %xmm0 |
| movss 132(%rsp,%r15,8), %xmm1 |
| |
| call JUMPTARGET(__powf_finite) |
| |
| movss %xmm0, 196(%rsp,%r15,8) |
| jmp .LBL_1_8 |
| |
| .LBL_1_12: |
| movzbl %r12b, %r15d |
| movss 64(%rsp,%r15,8), %xmm0 |
| movss 128(%rsp,%r15,8), %xmm1 |
| |
| call JUMPTARGET(__powf_finite) |
| |
| movss %xmm0, 192(%rsp,%r15,8) |
| jmp .LBL_1_7 |
| |
| END (_ZGVbN4vv_powf_sse4) |
