From patchwork Tue Feb 1 19:10:50 2022 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Noah Goldstein X-Patchwork-Id: 50642 Return-Path: X-Original-To: patchwork@sourceware.org Delivered-To: patchwork@sourceware.org Received: from server2.sourceware.org (localhost [IPv6:::1]) by sourceware.org (Postfix) with ESMTP id B65273857818 for ; Tue, 1 Feb 2022 19:11:24 +0000 (GMT) DKIM-Filter: OpenDKIM Filter v2.11.0 sourceware.org B65273857818 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=sourceware.org; s=default; t=1643742684; bh=dpQRvfUJZS/R4V5JqccjHIPzKGCFXWbrKWYCU79fkFs=; h=To:Subject:Date:List-Id:List-Unsubscribe:List-Archive:List-Post: List-Help:List-Subscribe:From:Reply-To:From; b=mrDbdkX5QjOHU80Jpt7n1kse7S2eD342ik8icJRDfikR8lN9MKlx/+mbFKb/oCEWn VzqC4a7j2UcBu5A0bDs14NPTo5jFMW6Ppve7HNaJZRouKBVBQh0YnqTqOc/BsLRw/8 050WGyVt+AWZGDOvTco+DTwrACgASxwMemOPkG9A= X-Original-To: libc-alpha@sourceware.org Delivered-To: libc-alpha@sourceware.org Received: from mail-qk1-x735.google.com (mail-qk1-x735.google.com [IPv6:2607:f8b0:4864:20::735]) by sourceware.org (Postfix) with ESMTPS id BC09A3858D35 for ; Tue, 1 Feb 2022 19:10:59 +0000 (GMT) DMARC-Filter: OpenDMARC Filter v1.4.1 sourceware.org BC09A3858D35 Received: by mail-qk1-x735.google.com with SMTP id w8so16031551qkw.8 for ; Tue, 01 Feb 2022 11:10:59 -0800 (PST) X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20210112; h=x-gm-message-state:from:to:cc:subject:date:message-id:mime-version :content-transfer-encoding; bh=dpQRvfUJZS/R4V5JqccjHIPzKGCFXWbrKWYCU79fkFs=; b=GmrxA7AQU/gtz+mm7to6hfkO+tt/VT261HVkrQUUFq43oAMbOyT21ijZ8djt3q8kn6 g9lPPz7Q90WzDUKcmUPVflOyDFLv3o3QkU9d3F7hPX6yoobLrA4CEXQ63XDpdyDJB4WT mNcB0BH+sxyLNP+wC5/DSKOhCT5jd0aAb0KlxGc6C2jGNDLp6pEmdsABq2h27NbYIwxQ 6+ipkZgCcZ/LDvxJrnKE89Fwxvx5ZHvt07yhEVB+hinCnVYvCtBfoYC1VXAOzmAqz16K ZqwEZds5rf3IxE7WVFoPP7oG2DHUgV6Uxg5vASBPM1+cL/QNyUuxnql6x9+QRAiSIZCP 1F+g== X-Gm-Message-State: AOAM533rjvHr1GpLfrvNauzijjq+Bemno9aaTWAV3ONBEEthakk1JrEc dS8tIAMxvhO0fiCrHfarORr/WuHxC10= X-Google-Smtp-Source: ABdhPJwdlad6DK6ElxRpOLRyLg7dThbtrsDjEx8xp18qnFFK+52E2XbTeOsv2DHEfnqnFdMP0ZWcUw== X-Received: by 2002:a37:84f:: with SMTP id 76mr17452343qki.591.1643742657699; Tue, 01 Feb 2022 11:10:57 -0800 (PST) Received: from localhost.localdomain (mobile-130-126-255-38.near.illinois.edu. [130.126.255.38]) by smtp.googlemail.com with ESMTPSA id s34sm10749484qtc.88.2022.02.01.11.10.56 (version=TLS1_3 cipher=TLS_AES_256_GCM_SHA384 bits=256/256); Tue, 01 Feb 2022 11:10:57 -0800 (PST) To: libc-alpha@sourceware.org Subject: [PATCH v1] x86: Optimize svml_s_atanhf_core_{ss4|avx2|avx512}.S Date: Tue, 1 Feb 2022 13:10:50 -0600 Message-Id: <20220201191050.169899-1-goldstein.w.n@gmail.com> X-Mailer: git-send-email 2.25.1 MIME-Version: 1.0 X-Spam-Status: No, score=-11.8 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, DKIM_VALID_EF, FREEMAIL_FROM, GIT_PATCH_0, KAM_LOTSOFHASH, RCVD_IN_DNSWL_NONE, SPF_HELO_NONE, SPF_PASS, TXREP, T_SCC_BODY_TEXT_LINE autolearn=ham autolearn_force=no version=3.4.4 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-Patchwork-Original-From: Noah Goldstein via Libc-alpha From: Noah Goldstein Reply-To: Noah Goldstein Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org Sender: "Libc-alpha" No bug. Optimizations are: 1. Reduce code size avx512: -58 bytes avx2: -53 bytes sse4: -54 bytes 2. Reduce rodata size avx512: -128 bytes avx2: -32 bytes sse4: -16 bytes 3. Remove register save/restores and stack adjustement from the fast path. 4. Slightly improve instruction selection/scheduling where possible. 5. Slightly improve register choices to remove redundant moves and/or use register that get smaller instruction encoding (avx2/sse4 only). The result is ~7% speedup for avx2/sse4 and ~17% speedup for avx512. Results from geomean of 40 benchtest runs: Function, New Time, Old Time, New / Old _ZGVbN4v_atanhf, 22.492, 24.143, 0.932 _ZGVcN8v_atanhf, 23.606, 25.231, 0.936 _ZGVdN8v_atanhf, 15.768, 16.841, 0.936 _ZGVeN16v_atanhf, 11.434, 13.816, 0.828 All math and mathvec tests are passing. --- .../multiarch/svml_s_atanhf16_core_avx512.S | 662 +++++++++--------- .../fpu/multiarch/svml_s_atanhf4_core_sse4.S | 576 +++++++-------- .../fpu/multiarch/svml_s_atanhf8_core_avx2.S | 545 +++++++------- 3 files changed, 834 insertions(+), 949 deletions(-) diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S index f863f4f959..fbd84b2c8e 100644 --- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf16_core_avx512.S @@ -31,363 +31,343 @@ * */ -/* Offsets for data table __svml_satanh_data_internal_avx512 - */ -#define Log_tbl_H 0 -#define Log_tbl_L 128 -#define One 256 -#define AbsMask 320 -#define AddB5 384 -#define RcpBitMask 448 -#define poly_coeff3 512 -#define poly_coeff2 576 -#define poly_coeff1 640 -#define poly_coeff0 704 -#define Half 768 -#define L2H 832 -#define L2L 896 + + /* Offsets for data table __svml_satanh_data_internal_avx512. */ +#define AbsMask 0 +#define One 64 +#define AddB5 128 +#define RcpBitMask 192 +#define Log_tbl_L_lo 256 +#define Log_tbl_L_hi 320 +#define Log_tbl_H_lo 384 +#define Log_tbl_H_hi 448 +#define L2H 512 +#define L2L 576 +#define poly_coeff3 640 +#define poly_coeff2 704 +#define poly_coeff1 768 #include +#define TANHF_DATA(x) (x) + __svml_satanh_data_internal_avx512 - .text - .section .text.exex512,"ax",@progbits + .text + .section .text.exex512, "ax", @progbits ENTRY(_ZGVeN16v_atanhf_skx) - pushq %rbp - cfi_def_cfa_offset(16) - movq %rsp, %rbp - cfi_def_cfa(6, 16) - cfi_offset(6, -16) - andq $-64, %rsp - subq $192, %rsp - vmovups One+__svml_satanh_data_internal_avx512(%rip), %zmm4 - -/* round reciprocals to 1+5b mantissas */ - vmovups AddB5+__svml_satanh_data_internal_avx512(%rip), %zmm14 - vmovups RcpBitMask+__svml_satanh_data_internal_avx512(%rip), %zmm1 - vmovaps %zmm0, %zmm11 - vandps AbsMask+__svml_satanh_data_internal_avx512(%rip), %zmm11, %zmm6 - -/* 1+y */ - vaddps {rn-sae}, %zmm4, %zmm6, %zmm9 - -/* 1-y */ - vsubps {rn-sae}, %zmm6, %zmm4, %zmm8 - vxorps %zmm6, %zmm11, %zmm10 - -/* Yp_high */ - vsubps {rn-sae}, %zmm4, %zmm9, %zmm2 - -/* -Ym_high */ - vsubps {rn-sae}, %zmm4, %zmm8, %zmm5 - -/* RcpP ~ 1/Yp */ - vrcp14ps %zmm9, %zmm12 - -/* RcpM ~ 1/Ym */ - vrcp14ps %zmm8, %zmm13 - -/* input outside (-1, 1) ? */ - vcmpps $21, {sae}, %zmm4, %zmm6, %k0 - vpaddd %zmm14, %zmm12, %zmm15 - vpaddd %zmm14, %zmm13, %zmm0 - -/* Yp_low */ - vsubps {rn-sae}, %zmm2, %zmm6, %zmm3 - vandps %zmm1, %zmm15, %zmm7 - vandps %zmm1, %zmm0, %zmm12 - -/* Ym_low */ - vaddps {rn-sae}, %zmm5, %zmm6, %zmm5 - -/* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low */ - vfmsub213ps {rn-sae}, %zmm4, %zmm7, %zmm9 - -/* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low */ - vfmsub231ps {rn-sae}, %zmm12, %zmm8, %zmm4 - vmovups Log_tbl_L+__svml_satanh_data_internal_avx512(%rip), %zmm8 - vmovups Log_tbl_L+64+__svml_satanh_data_internal_avx512(%rip), %zmm13 - -/* exponents */ - vgetexpps {sae}, %zmm7, %zmm15 - vfmadd231ps {rn-sae}, %zmm7, %zmm3, %zmm9 - -/* Table lookups */ - vmovups __svml_satanh_data_internal_avx512(%rip), %zmm6 - vgetexpps {sae}, %zmm12, %zmm14 - vfnmadd231ps {rn-sae}, %zmm12, %zmm5, %zmm4 - -/* Prepare table index */ - vpsrld $18, %zmm7, %zmm3 - vpsrld $18, %zmm12, %zmm2 - vmovups Log_tbl_H+64+__svml_satanh_data_internal_avx512(%rip), %zmm7 - vmovups poly_coeff1+__svml_satanh_data_internal_avx512(%rip), %zmm12 - -/* Km-Kp */ - vsubps {rn-sae}, %zmm15, %zmm14, %zmm1 - kmovw %k0, %edx - vmovaps %zmm3, %zmm0 - vpermi2ps %zmm13, %zmm8, %zmm3 - vpermt2ps %zmm13, %zmm2, %zmm8 - vpermi2ps %zmm7, %zmm6, %zmm0 - vpermt2ps %zmm7, %zmm2, %zmm6 - vsubps {rn-sae}, %zmm3, %zmm8, %zmm5 - -/* K*L2H + Th */ - vmovups L2H+__svml_satanh_data_internal_avx512(%rip), %zmm2 - -/* K*L2L + Tl */ - vmovups L2L+__svml_satanh_data_internal_avx512(%rip), %zmm3 - -/* polynomials */ - vmovups poly_coeff3+__svml_satanh_data_internal_avx512(%rip), %zmm7 - vmovups poly_coeff0+__svml_satanh_data_internal_avx512(%rip), %zmm13 - -/* table values */ - vsubps {rn-sae}, %zmm0, %zmm6, %zmm0 - vfmadd231ps {rn-sae}, %zmm1, %zmm2, %zmm0 - vfmadd213ps {rn-sae}, %zmm5, %zmm3, %zmm1 - vmovups poly_coeff2+__svml_satanh_data_internal_avx512(%rip), %zmm3 - vmovaps %zmm3, %zmm2 - vfmadd231ps {rn-sae}, %zmm9, %zmm7, %zmm2 - vfmadd231ps {rn-sae}, %zmm4, %zmm7, %zmm3 - vfmadd213ps {rn-sae}, %zmm12, %zmm9, %zmm2 - vfmadd213ps {rn-sae}, %zmm12, %zmm4, %zmm3 - vfmadd213ps {rn-sae}, %zmm13, %zmm9, %zmm2 - vfmadd213ps {rn-sae}, %zmm13, %zmm4, %zmm3 - -/* (K*L2L + Tl) + Rp*PolyP */ - vfmadd213ps {rn-sae}, %zmm1, %zmm9, %zmm2 - vorps Half+__svml_satanh_data_internal_avx512(%rip), %zmm10, %zmm9 - -/* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM */ - vfnmadd213ps {rn-sae}, %zmm2, %zmm4, %zmm3 - vaddps {rn-sae}, %zmm3, %zmm0, %zmm4 - vmulps {rn-sae}, %zmm9, %zmm4, %zmm0 - testl %edx, %edx - -/* Go to special inputs processing branch */ - jne L(SPECIAL_VALUES_BRANCH) - # LOE rbx r12 r13 r14 r15 edx zmm0 zmm11 - -/* Restore registers - * and exit the function - */ + vandps TANHF_DATA(AbsMask)(%rip), %zmm0, %zmm6 + vmovups TANHF_DATA(One)(%rip), %zmm4 -L(EXIT): - movq %rbp, %rsp - popq %rbp - cfi_def_cfa(7, 8) - cfi_restore(6) - ret - cfi_def_cfa(6, 16) - cfi_offset(6, -16) - -/* Branch to process - * special inputs - */ + /* 1+y. */ + vaddps {rn-sae}, %zmm4, %zmm6, %zmm9 -L(SPECIAL_VALUES_BRANCH): - vmovups %zmm11, 64(%rsp) - vmovups %zmm0, 128(%rsp) - # LOE rbx r12 r13 r14 r15 edx zmm0 - - 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: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ - .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 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: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ - .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 - movl %edx, %r13d - movq %r14, (%rsp) - /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ - .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 - # LOE rbx r15 r12d r13d - -/* Range mask - * bits check - */ + /* 1-y. */ + vsubps {rn-sae}, %zmm6, %zmm4, %zmm8 -L(RANGEMASK_CHECK): - btl %r12d, %r13d + /* round reciprocals to 1+5b mantissas. */ + vmovups TANHF_DATA(AddB5)(%rip), %zmm14 + vmovups TANHF_DATA(RcpBitMask)(%rip), %zmm1 -/* Call scalar math function */ - jc L(SCALAR_MATH_CALL) - # LOE rbx r15 r12d r13d + /* RcpP ~ 1/Yp. */ + vrcp14ps %zmm9, %zmm12 -/* Special inputs - * processing loop - */ + /* RcpM ~ 1/Ym. */ + vrcp14ps %zmm8, %zmm13 -L(SPECIAL_VALUES_LOOP): - incl %r12d - cmpl $16, %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 128(%rsp), %zmm0 - -/* Go to exit */ - jmp L(EXIT) - /* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */ - .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22 - /* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */ - .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22 - /* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */ - .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22 - # LOE rbx r12 r13 r14 r15 zmm0 - -/* Scalar math fucntion call - * to process special input - */ + /* Yp_high. */ + vsubps {rn-sae}, %zmm4, %zmm9, %zmm2 + + /* -Ym_high. */ + vsubps {rn-sae}, %zmm4, %zmm8, %zmm5 + + + /* input outside (-1, 1) ?. */ + vpaddd %zmm14, %zmm12, %zmm15 + vpaddd %zmm14, %zmm13, %zmm12 + + /* Yp_low. */ + vsubps {rn-sae}, %zmm2, %zmm6, %zmm3 + vandps %zmm1, %zmm15, %zmm7 + vandps %zmm1, %zmm12, %zmm12 + + /* Ym_low. */ + vaddps {rn-sae}, %zmm5, %zmm6, %zmm5 + + /* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low. */ + vfmsub213ps {rn-sae}, %zmm4, %zmm7, %zmm9 + + /* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low. */ + vfmsub213ps {rn-sae}, %zmm4, %zmm12, %zmm8 -L(SCALAR_MATH_CALL): - movl %r12d, %r14d - movss 64(%rsp,%r14,4), %xmm0 - call atanhf@PLT - # LOE rbx r14 r15 r12d r13d xmm0 + vmovups TANHF_DATA(Log_tbl_L_lo)(%rip), %zmm10 + vmovups TANHF_DATA(Log_tbl_L_hi)(%rip), %zmm13 - movss %xmm0, 128(%rsp,%r14,4) + /* exponents. */ + vfmadd231ps {rn-sae}, %zmm7, %zmm3, %zmm9 + vgetexpps {sae}, %zmm7, %zmm15 -/* Process special inputs in loop */ - jmp L(SPECIAL_VALUES_LOOP) - # LOE rbx r15 r12d r13d + + /* Table lookups. */ + vfnmadd231ps {rn-sae}, %zmm12, %zmm5, %zmm8 + vgetexpps {sae}, %zmm12, %zmm14 + + + /* Prepare table index. */ + vpsrld $18, %zmm7, %zmm3 + vpsrld $18, %zmm12, %zmm2 + vmovups TANHF_DATA(Log_tbl_H_lo)(%rip), %zmm11 + vmovups TANHF_DATA(Log_tbl_H_hi)(%rip), %zmm7 + /* Km-Kp. */ + + vmovaps %zmm3, %zmm5 + vpermi2ps %zmm13, %zmm10, %zmm3 + vpermt2ps %zmm13, %zmm2, %zmm10 + vpermi2ps %zmm7, %zmm11, %zmm5 + vpermt2ps %zmm7, %zmm2, %zmm11 + vsubps {rn-sae}, %zmm15, %zmm14, %zmm1 + vsubps {rn-sae}, %zmm3, %zmm10, %zmm7 + + /* K*L2H + Th. */ + vmovups TANHF_DATA(L2H)(%rip), %zmm2 + + /* K*L2L + Tl. */ + vmovups TANHF_DATA(L2L)(%rip), %zmm3 + + /* table values. */ + vsubps {rn-sae}, %zmm5, %zmm11, %zmm5 + vfmadd231ps {rn-sae}, %zmm1, %zmm2, %zmm5 + vfmadd213ps {rn-sae}, %zmm7, %zmm3, %zmm1 + /* polynomials. */ + vmovups TANHF_DATA(poly_coeff3)(%rip), %zmm7 + vmovups TANHF_DATA(poly_coeff2)(%rip), %zmm10 + vmovaps %zmm10, %zmm14 + // vfmadd231ps {rn-sae}, %zmm9, %zmm7, %zmm10 + vfmadd231ps {rn-sae}, %zmm8, %zmm7, %zmm14 + vmovups TANHF_DATA(poly_coeff1)(%rip), %zmm12 + vfmadd213ps {rn-sae}, %zmm12, %zmm9, %zmm10 + vfmadd213ps {rn-sae}, %zmm12, %zmm8, %zmm14 + vfmadd213ps {rn-sae}, %zmm4, %zmm9, %zmm10 + vfmadd213ps {rn-sae}, %zmm4, %zmm8, %zmm14 + + /* (K*L2L + Tl) + Rp*PolyP. */ + vfmadd213ps {rn-sae}, %zmm1, %zmm9, %zmm10 + + vandps %zmm12, %zmm4, %zmm12 + vpternlogq $246, %zmm0, %zmm6, %zmm12 + + /* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM. */ + vfnmadd213ps {rn-sae}, %zmm10, %zmm8, %zmm14 + vaddps {rn-sae}, %zmm14, %zmm5, %zmm8 + + vcmpps $21, {sae}, %zmm4, %zmm6, %k0 + kmovw %k0, %edx + testl %edx, %edx + + /* Go to special inputs processing branch. */ + jne L(SPECIAL_VALUES_BRANCH) + vmulps {rn-sae}, %zmm12, %zmm8, %zmm0 + + ret + + /* Branch to process special inputs. */ +L(SPECIAL_VALUES_BRANCH): + pushq %rbp + /* Need to callee save registers to preserve state across tanhf calls. + */ + pushq %r13 + pushq %r12 + movq %rsp, %rbp + + /* Align stack and make room for 2x zmm vectors. */ + andq $-64, %rsp + addq $-128, %rsp + vmulps {rn-sae}, %zmm12, %zmm8, %zmm1 + vmovaps %zmm1, (%rsp) + vmovaps %zmm0, 64(%rsp) + + vzeroupper + + /* edx has 1s where there was a special value that needs to be handled + by a tanhf call. */ + movl %edx, %r13d +L(SPECIAL_VALUES_LOOP): + /* use r12 as index for special value that is saved across calls to + tanhf. We technically don't need a callee save register here as offset + to rsp is always [0, 56] so we can restore rsp by realigning to 64. + Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions + in the loop. */ + xorl %r12d, %r12d + tzcntl %r13d, %r12d + + /* Scalar math fucntion call to process special input. */ + movss 64(%rsp, %r12, 4), %xmm0 + call atanhf@PLT + + /* 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, %r12, 4) + + blsr %r13d, %r13d + jnz L(SPECIAL_VALUES_LOOP) + + /* All results have been written to 64(%rsp). */ + vmovaps (%rsp), %zmm0 + /* Restore rsp. */ + movq %rbp, %rsp + /* Restore callee save registers. */ + popq %r12 + popq %r13 + popq %rbp + ret END(_ZGVeN16v_atanhf_skx) - .section .rodata, "a" - .align 64 + .section .rodata, "a" + .align 64 #ifdef __svml_satanh_data_internal_avx512_typedef -typedef unsigned int VUINT32; -typedef struct { - __declspec(align(64)) VUINT32 Log_tbl_H[32][1]; - __declspec(align(64)) VUINT32 Log_tbl_L[32][1]; - __declspec(align(64)) VUINT32 One[16][1]; - __declspec(align(64)) VUINT32 AbsMask[16][1]; - __declspec(align(64)) VUINT32 AddB5[16][1]; - __declspec(align(64)) VUINT32 RcpBitMask[16][1]; - __declspec(align(64)) VUINT32 poly_coeff3[16][1]; - __declspec(align(64)) VUINT32 poly_coeff2[16][1]; - __declspec(align(64)) VUINT32 poly_coeff1[16][1]; - __declspec(align(64)) VUINT32 poly_coeff0[16][1]; - __declspec(align(64)) VUINT32 Half[16][1]; - __declspec(align(64)) VUINT32 L2H[16][1]; - __declspec(align(64)) VUINT32 L2L[16][1]; - } __svml_satanh_data_internal_avx512; + typedef unsigned int VUINT32; + typedef struct{ + __declspec (align(64))VUINT32 AbsMask[16][1]; + __declspec (align(64))VUINT32 One[16][1]; + __declspec (align(64))VUINT32 AddB5[16][1]; + __declspec (align(64))VUINT32 RcpBitMask[16][1]; + __declspec (align(64))VUINT32 Log_tbl_L_lo[16][1]; + __declspec (align(64))VUINT32 Log_tbl_L_hi[16][1]; + __declspec (align(64))VUINT32 Log_tbl_H_lo[16][1]; + __declspec (align(64))VUINT32 Log_tbl_H_hi[16][1]; + __declspec (align(64))VUINT32 L2H[16][1]; + __declspec (align(64))VUINT32 L2L[16][1]; + __declspec (align(64))VUINT32 poly_coeff3[16][1]; + __declspec (align(64))VUINT32 poly_coeff2[16][1]; + __declspec (align(64))VUINT32 poly_coeff1[16][1]; + }__svml_satanh_data_internal_avx512; #endif __svml_satanh_data_internal_avx512: - /*== Log_tbl_H ==*/ - .long 0x00000000 - .long 0x3cfc0000 - .long 0x3d780000 - .long 0x3db78000 - .long 0x3df10000 - .long 0x3e14c000 - .long 0x3e300000 - .long 0x3e4a8000 - .long 0x3e648000 - .long 0x3e7dc000 - .long 0x3e8b4000 - .long 0x3e974000 - .long 0x3ea30000 - .long 0x3eae8000 - .long 0x3eb9c000 - .long 0x3ec4e000 - .long 0x3ecfa000 - .long 0x3eda2000 - .long 0x3ee48000 - .long 0x3eeea000 - .long 0x3ef8a000 - .long 0x3f013000 - .long 0x3f05f000 - .long 0x3f0aa000 - .long 0x3f0f4000 - .long 0x3f13d000 - .long 0x3f184000 - .long 0x3f1ca000 - .long 0x3f20f000 - .long 0x3f252000 - .long 0x3f295000 - .long 0x3f2d7000 - /*== Log_tbl_L ==*/ - .align 64 - .long 0x00000000 - .long 0x3726c39e - .long 0x38a30c01 - .long 0x37528ae5 - .long 0x38e0edc5 - .long 0xb8ab41f8 - .long 0xb7cf8f58 - .long 0x3896a73d - .long 0xb5838656 - .long 0x380c36af - .long 0xb8235454 - .long 0x3862bae1 - .long 0x38c5e10e - .long 0x38dedfac - .long 0x38ebfb5e - .long 0xb8e63c9f - .long 0xb85c1340 - .long 0x38777bcd - .long 0xb6038656 - .long 0x37d40984 - .long 0xb8b85028 - .long 0xb8ad5a5a - .long 0x3865c84a - .long 0x38c3d2f5 - .long 0x383ebce1 - .long 0xb8a1ed76 - .long 0xb7a332c4 - .long 0xb779654f - .long 0xb8602f73 - .long 0x38f85db0 - .long 0x37b4996f - .long 0xb8bfb3ca - /*== One ==*/ - .align 64 - .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 - /*== AbsMask ==*/ - .align 64 - .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff - /*== AddB5 ==*/ - .align 64 - .long 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000 - /*== RcpBitMask ==*/ - .align 64 - .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000 - /*== poly_coeff3 ==*/ - .align 64 - .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810 - /*== poly_coeff2 ==*/ - .align 64 - .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e - /*== poly_coeff1 ==*/ - .align 64 - .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 - /*== poly_coeff0 ==*/ - .align 64 - .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 - /*== Half ==*/ - .align 64 - .long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000 - /*== L2H = log(2)_high ==*/ - .align 64 - .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000 - /*== L2L = log(2)_low ==*/ - .align 64 - .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 - .align 64 - .type __svml_satanh_data_internal_avx512,@object - .size __svml_satanh_data_internal_avx512,.-__svml_satanh_data_internal_avx512 + /* AbsMask. */ + .align 64 + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + /* One. */ + .align 64 + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + /* AddB5. */ + .align 64 + .long 0x00020000, 0x00020000, 0x00020000, 0x00020000 + .long 0x00020000, 0x00020000, 0x00020000, 0x00020000 + .long 0x00020000, 0x00020000, 0x00020000, 0x00020000 + .long 0x00020000, 0x00020000, 0x00020000, 0x00020000 + /* RcpBitMask. */ + .align 64 + .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000 + .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000 + .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000 + .long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000 + /* Log_tbl_L_lo. */ + .align 64 + .long 0x00000000 + .long 0x3726c39e + .long 0x38a30c01 + .long 0x37528ae5 + .long 0x38e0edc5 + .long 0xb8ab41f8 + .long 0xb7cf8f58 + .long 0x3896a73d + .long 0xb5838656 + .long 0x380c36af + .long 0xb8235454 + .long 0x3862bae1 + .long 0x38c5e10e + .long 0x38dedfac + .long 0x38ebfb5e + .long 0xb8e63c9f + /* Log_tbl_L_hi. */ + .align 64 + .long 0xb85c1340 + .long 0x38777bcd + .long 0xb6038656 + .long 0x37d40984 + .long 0xb8b85028 + .long 0xb8ad5a5a + .long 0x3865c84a + .long 0x38c3d2f5 + .long 0x383ebce1 + .long 0xb8a1ed76 + .long 0xb7a332c4 + .long 0xb779654f + .long 0xb8602f73 + .long 0x38f85db0 + .long 0x37b4996f + .long 0xb8bfb3ca + /* Log_tbl_H_lo. */ + .align 64 + .long 0x00000000 + .long 0x3cfc0000 + .long 0x3d780000 + .long 0x3db78000 + .long 0x3df10000 + .long 0x3e14c000 + .long 0x3e300000 + .long 0x3e4a8000 + .long 0x3e648000 + .long 0x3e7dc000 + .long 0x3e8b4000 + .long 0x3e974000 + .long 0x3ea30000 + .long 0x3eae8000 + .long 0x3eb9c000 + .long 0x3ec4e000 + /* Log_tbl_H_hi. */ + .align 64 + .long 0x3ecfa000 + .long 0x3eda2000 + .long 0x3ee48000 + .long 0x3eeea000 + .long 0x3ef8a000 + .long 0x3f013000 + .long 0x3f05f000 + .long 0x3f0aa000 + .long 0x3f0f4000 + .long 0x3f13d000 + .long 0x3f184000 + .long 0x3f1ca000 + .long 0x3f20f000 + .long 0x3f252000 + .long 0x3f295000 + .long 0x3f2d7000 + /* L2H = log(2)_high. */ + .align 64 + .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000 + .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000 + .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000 + .long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000 + /* L2L = log(2)_low. */ + .align 64 + .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 + .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 + .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 + .long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4 + /* poly_coeff3. */ + .align 64 + .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810 + .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810 + .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810 + .long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810 + /* poly_coeff2. */ + .align 64 + .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e + .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e + .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e + .long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e + /* poly_coeff1. */ + .align 64 + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 + .align 64 + .type __svml_satanh_data_internal_avx512, @object + .size __svml_satanh_data_internal_avx512, .-__svml_satanh_data_internal_avx512 diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S index 7927e01f0c..e1a8a28a3d 100644 --- a/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S @@ -28,334 +28,278 @@ * atanh(-1) = -INF * atanh(x) = NaN if |x| > 1, or if x is a NaN or INF * - */ - -/* Offsets for data table __svml_satanh_data_internal - */ -#define SgnMask 0 -#define sOne 16 -#define sPoly 32 -#define iBrkValue 160 -#define iOffExpoMask 176 -#define sHalf 192 -#define sSign 208 -#define sTopMask12 224 -#define TinyRange 240 -#define sLn2 256 +*/ -#include - .text - .section .text.sse4,"ax",@progbits -ENTRY(_ZGVbN4v_atanhf_sse4) - subq $72, %rsp - cfi_def_cfa_offset(80) - movaps %xmm0, %xmm5 - -/* Load constants including One = 1 */ - movups sOne+__svml_satanh_data_internal(%rip), %xmm4 - movaps %xmm5, %xmm3 - -/* Strip off the sign, so treat X as positive until right at the end */ - movups SgnMask+__svml_satanh_data_internal(%rip), %xmm7 - movaps %xmm4, %xmm8 - andps %xmm5, %xmm7 - movaps %xmm4, %xmm10 - movups sTopMask12+__svml_satanh_data_internal(%rip), %xmm11 - movaps %xmm4, %xmm14 - movaps %xmm11, %xmm9 + /* Offsets for data table __svml_satanh_data_internal. */ +#define sOne 0 +#define SgnMask 16 +#define sTopMask12 32 +#define iBrkValue 48 +#define iOffExpoMask 64 +#define sPoly 80 +#define sLn2 208 +#define TinyRange 224 -/* - * 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)). - */ - movaps %xmm7, %xmm12 - -/* - * 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). - */ - movaps %xmm7, %xmm6 - movaps %xmm7, %xmm2 - cmpnltps %xmm4, %xmm6 - cmpltps TinyRange+__svml_satanh_data_internal(%rip), %xmm2 - mulps %xmm5, %xmm3 - subps %xmm7, %xmm8 - addps %xmm7, %xmm12 - movmskps %xmm6, %edx - subps %xmm8, %xmm10 - addps %xmm5, %xmm3 - subps %xmm7, %xmm10 - andps %xmm8, %xmm9 - -/* - * 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 - */ - movaps %xmm4, %xmm7 - -/* - * Now compute R = 1/(UHi+ULo) * (1 - E) and the error term E - * The first FMR is exact (we force R to 12 bits just in case it - * isn't already, to make absolutely sure), and since E is ~ 2^-12, - * the rounding error in the other one is acceptable. - */ - rcpps %xmm9, %xmm15 - subps %xmm9, %xmm8 - andps %xmm11, %xmm15 -/* - * Split V as well into upper 12 bits and lower part, so that we can get - * a preliminary quotient estimate without rounding error. - */ - andps %xmm12, %xmm11 - mulps %xmm15, %xmm9 - addps %xmm8, %xmm10 - subps %xmm11, %xmm12 - -/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */ - mulps %xmm15, %xmm11 - mulps %xmm15, %xmm10 - subps %xmm9, %xmm14 - mulps %xmm12, %xmm15 - subps %xmm10, %xmm14 - -/* Compute D = E + E^2 */ - movaps %xmm14, %xmm13 - movaps %xmm4, %xmm8 - mulps %xmm14, %xmm13 - -/* reduction: compute r,n */ - movdqu iBrkValue+__svml_satanh_data_internal(%rip), %xmm9 - addps %xmm13, %xmm14 +#include +#define TANHF_DATA(x) (x) + __svml_satanh_data_internal -/* - * Compute R * (VHi + VLo) * (1 + E + E^2) - * = R * (VHi + VLo) * (1 + D) - * = QHi + (QHi * D + QLo + QLo * D) - */ - movaps %xmm14, %xmm0 - mulps %xmm15, %xmm14 - mulps %xmm11, %xmm0 - addps %xmm14, %xmm15 - movdqu iOffExpoMask+__svml_satanh_data_internal(%rip), %xmm12 - movaps %xmm4, %xmm14 - -/* Record the sign for eventual reincorporation. */ - movups sSign+__svml_satanh_data_internal(%rip), %xmm1 - addps %xmm15, %xmm0 + .text + .section .text.sse4, "ax", @progbits +ENTRY(_ZGVbN4v_atanhf_sse4) + movaps %xmm0, %xmm5 + + /* Load constants including One = 1. */ + movups TANHF_DATA(sOne)(%rip), %xmm4 + movaps %xmm5, %xmm3 + + /* Strip off the sign, so treat X as positive until right at the end. + */ + movups TANHF_DATA(SgnMask)(%rip), %xmm1 + movaps %xmm4, %xmm2 + andps %xmm1, %xmm0 + movaps %xmm4, %xmm10 + movups TANHF_DATA(sTopMask12)(%rip), %xmm11 + movaps %xmm4, %xmm14 + movaps %xmm11, %xmm9 + + + /* 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)). */ + movaps %xmm0, %xmm6 + mulps %xmm5, %xmm3 + subps %xmm0, %xmm2 + addps %xmm0, %xmm6 + subps %xmm2, %xmm10 + addps %xmm5, %xmm3 + subps %xmm0, %xmm10 + andps %xmm2, %xmm9 + + + /* Now compute R = 1/(UHi+ULo) * (1 - E) and the error term E The first + FMR is exact (we force R to 12 bits just in case it isn't already, to + make absolutely sure), and since E is ~ 2^-12, the rounding error in the + other one is acceptable. */ + rcpps %xmm9, %xmm7 + subps %xmm9, %xmm2 + andps %xmm11, %xmm7 + + + /* Split V as well into upper 12 bits and lower part, so that we can get + a preliminary quotient estimate without rounding error. */ + + andps %xmm6, %xmm11 + mulps %xmm7, %xmm9 + addps %xmm2, %xmm10 + subps %xmm11, %xmm6 + + /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo. + */ + mulps %xmm7, %xmm11 + mulps %xmm7, %xmm10 + subps %xmm9, %xmm14 + mulps %xmm6, %xmm7 + subps %xmm10, %xmm14 + + /* Compute D = E + E^2. */ + movaps %xmm14, %xmm13 + movaps %xmm4, %xmm8 + mulps %xmm14, %xmm13 + + /* reduction: compute r,n. */ + movdqu TANHF_DATA(iBrkValue)(%rip), %xmm9 + addps %xmm13, %xmm14 + + /* + * Compute R * (VHi + VLo) * (1 + E + E^2) + * = R * (VHi + VLo) * (1 + D) + * = QHi + (QHi * D + QLo + QLo * D) + */ + movaps %xmm14, %xmm2 + mulps %xmm7, %xmm14 + mulps %xmm11, %xmm2 + addps %xmm14, %xmm7 + movdqu TANHF_DATA(iOffExpoMask)(%rip), %xmm12 + movaps %xmm4, %xmm14 + + /* Record the sign for eventual reincorporation. */ + addps %xmm7, %xmm2 + + + /* Now finally accumulate the high and low parts of the argument to + log1p, H + L, with a final compensated summation. */ + movaps %xmm2, %xmm6 + andnps %xmm5, %xmm1 + movaps %xmm4, %xmm7 + /* Or the sign bit in with the tiny result to handle atanh(-0) + correctly. */ + addps %xmm11, %xmm6 + maxps %xmm6, %xmm7 + minps %xmm6, %xmm8 + subps %xmm6, %xmm11 + movaps %xmm7, %xmm10 + addps %xmm8, %xmm10 + addps %xmm11, %xmm2 + subps %xmm10, %xmm7 + psubd %xmm9, %xmm10 + addps %xmm8, %xmm7 + pand %xmm10, %xmm12 + psrad $23, %xmm10 + cvtdq2ps %xmm10, %xmm13 + addps %xmm7, %xmm2 + + /* final reconstruction. */ + pslld $23, %xmm10 + paddd %xmm9, %xmm12 + psubd %xmm10, %xmm14 + + /* polynomial evaluation. */ + subps %xmm4, %xmm12 + mulps %xmm14, %xmm2 + movups TANHF_DATA(sPoly)(%rip), %xmm7 + addps %xmm12, %xmm2 + mulps %xmm2, %xmm7 + + + /* Finally, halve the result and reincorporate the sign. */ + addps TANHF_DATA(sPoly + 16)(%rip), %xmm7 + mulps %xmm2, %xmm7 + addps TANHF_DATA(sPoly + 32)(%rip), %xmm7 + mulps %xmm2, %xmm7 + addps TANHF_DATA(sPoly + 48)(%rip), %xmm7 + mulps %xmm2, %xmm7 + addps TANHF_DATA(sPoly + 64)(%rip), %xmm7 + mulps %xmm2, %xmm7 + addps TANHF_DATA(sPoly + 80)(%rip), %xmm7 + mulps %xmm2, %xmm7 + addps TANHF_DATA(sPoly + 96)(%rip), %xmm7 + mulps %xmm2, %xmm7 + movaps TANHF_DATA(sPoly + 112)(%rip), %xmm6 + addps %xmm6, %xmm7 + mulps %xmm2, %xmm7 + mulps %xmm2, %xmm7 + mulps TANHF_DATA(sLn2)(%rip), %xmm13 + /* We can build `sHalf` with `sPoly & sOne`. */ + andps %xmm4, %xmm6 + orps %xmm1, %xmm3 + xorps %xmm6, %xmm1 + + addps %xmm2, %xmm7 + addps %xmm13, %xmm7 + mulps %xmm7, %xmm1 + + /* 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). */ + cmpleps %xmm0, %xmm4 + movmskps %xmm4, %edx + cmpltps TANHF_DATA(TinyRange)(%rip), %xmm0 + + andps %xmm0, %xmm3 + andnps %xmm1, %xmm0 + orps %xmm3, %xmm0 + + testl %edx, %edx + /* Go to special inputs processing branch. */ + jne L(SPECIAL_VALUES_BRANCH) + + /* No registers to restore on fast path. */ + ret + + /* Branch to process special inputs. */ +L(SPECIAL_VALUES_BRANCH): + subq $56, %rsp -/* - * Now finally accumulate the high and low parts of the - * argument to log1p, H + L, with a final compensated summation. - */ - movaps %xmm0, %xmm6 - andps %xmm5, %xmm1 - -/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */ - orps %xmm1, %xmm3 - addps %xmm11, %xmm6 - maxps %xmm6, %xmm7 - minps %xmm6, %xmm8 - subps %xmm6, %xmm11 - movaps %xmm7, %xmm10 - andps %xmm2, %xmm3 - addps %xmm8, %xmm10 - addps %xmm11, %xmm0 - subps %xmm10, %xmm7 - psubd %xmm9, %xmm10 - addps %xmm7, %xmm8 - pand %xmm10, %xmm12 - psrad $23, %xmm10 - cvtdq2ps %xmm10, %xmm13 - addps %xmm8, %xmm0 - -/* final reconstruction */ - mulps sLn2+__svml_satanh_data_internal(%rip), %xmm13 - pslld $23, %xmm10 - paddd %xmm9, %xmm12 - psubd %xmm10, %xmm14 - -/* polynomial evaluation */ - subps %xmm4, %xmm12 - mulps %xmm0, %xmm14 - movups sPoly+112+__svml_satanh_data_internal(%rip), %xmm0 - addps %xmm12, %xmm14 - mulps %xmm14, %xmm0 - -/* Finally, halve the result and reincorporate the sign */ - movups sHalf+__svml_satanh_data_internal(%rip), %xmm4 - pxor %xmm1, %xmm4 - addps sPoly+96+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+80+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+64+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+48+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+32+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+16+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - addps sPoly+__svml_satanh_data_internal(%rip), %xmm0 - mulps %xmm14, %xmm0 - mulps %xmm14, %xmm0 - addps %xmm0, %xmm14 - movaps %xmm2, %xmm0 - addps %xmm13, %xmm14 - mulps %xmm14, %xmm4 - andnps %xmm4, %xmm0 - orps %xmm3, %xmm0 - testl %edx, %edx - -/* Go to special inputs processing branch */ - jne L(SPECIAL_VALUES_BRANCH) - # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5 - -/* Restore registers - * and exit the function - */ - -L(EXIT): - addq $72, %rsp - cfi_def_cfa_offset(8) - ret - cfi_def_cfa_offset(80) - -/* Branch to process - * special inputs - */ + movups %xmm5, (%rsp) + movups %xmm0, 16(%rsp) -L(SPECIAL_VALUES_BRANCH): - movups %xmm5, 32(%rsp) - movups %xmm0, 48(%rsp) - # LOE rbx rbp r12 r13 r14 r15 edx - - xorl %eax, %eax - movq %r12, 16(%rsp) - cfi_offset(12, -64) - movl %eax, %r12d - movq %r13, 8(%rsp) - cfi_offset(13, -72) - movl %edx, %r13d - movq %r14, (%rsp) - cfi_offset(14, -80) - # LOE rbx rbp r15 r12d r13d - -/* Range mask - * bits check - */ - -L(RANGEMASK_CHECK): - btl %r12d, %r13d - -/* Call scalar math function */ - jc L(SCALAR_MATH_CALL) - # LOE rbx rbp r15 r12d r13d - -/* Special inputs - * processing loop - */ + movq %r12, 32(%rsp) + movq %r13, 40(%rsp) + /* edx has 1s where there was a special value that needs to be handled + by a tanhf call. */ + movl %edx, %r13d L(SPECIAL_VALUES_LOOP): - incl %r12d - cmpl $4, %r12d - -/* Check bits in range mask */ - jl L(RANGEMASK_CHECK) - # LOE rbx rbp r15 r12d r13d - - movq 16(%rsp), %r12 - cfi_restore(12) - movq 8(%rsp), %r13 - cfi_restore(13) - movq (%rsp), %r14 - cfi_restore(14) - movups 48(%rsp), %xmm0 - -/* Go to exit */ - jmp L(EXIT) - cfi_offset(12, -64) - cfi_offset(13, -72) - cfi_offset(14, -80) - # LOE rbx rbp r12 r13 r14 r15 xmm0 - -/* Scalar math fucntion call - * to process special input - */ - -L(SCALAR_MATH_CALL): - movl %r12d, %r14d - movss 32(%rsp,%r14,4), %xmm0 - call atanhf@PLT - # LOE rbx rbp r14 r15 r12d r13d xmm0 - - movss %xmm0, 48(%rsp,%r14,4) - -/* Process special inputs in loop */ - jmp L(SPECIAL_VALUES_LOOP) - # LOE rbx rbp r15 r12d r13d + /* use r12 as index for special value that is saved across calls to + tanhf. We technically don't need a callee save register here as offset + to rsp is always [0, 12] so we can restore rsp by realigning to 64. + Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions + in the loop. */ + xorl %r12d, %r12d + bsfl %r13d, %r12d + + /* Scalar math fucntion call to process special input. */ + movss (%rsp, %r12, 4), %xmm0 + call atanhf@PLT + /* 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, 16(%rsp, %r12, 4) + + leal -1(%r13), %eax + andl %eax, %r13d + jnz L(SPECIAL_VALUES_LOOP) + + /* All results have been written to 16(%rsp). */ + vmovups 16(%rsp), %xmm0 + movq 32(%rsp), %r12 + movq 40(%rsp), %r13 + addq $56, %rsp + ret END(_ZGVbN4v_atanhf_sse4) - .section .rodata, "a" - .align 16 + .section .rodata, "a" + .align 16 #ifdef __svml_satanh_data_internal_typedef -typedef unsigned int VUINT32; -typedef struct { - __declspec(align(16)) VUINT32 SgnMask[4][1]; - __declspec(align(16)) VUINT32 sOne[4][1]; - __declspec(align(16)) VUINT32 sPoly[8][4][1]; - __declspec(align(16)) VUINT32 iBrkValue[4][1]; - __declspec(align(16)) VUINT32 iOffExpoMask[4][1]; - __declspec(align(16)) VUINT32 sHalf[4][1]; - __declspec(align(16)) VUINT32 sSign[4][1]; - __declspec(align(16)) VUINT32 sTopMask12[4][1]; - __declspec(align(16)) VUINT32 TinyRange[4][1]; - __declspec(align(16)) VUINT32 sLn2[4][1]; -} __svml_satanh_data_internal; + typedef unsigned int VUINT32; + typedef struct{ + __declspec (align(16))VUINT32 sOne[4][1]; + __declspec (align(16))VUINT32 SgnMask[4][1]; + __declspec (align(16))VUINT32 sTopMask12[4][1]; + __declspec (align(16))VUINT32 iBrkValue[4][1]; + __declspec (align(16))VUINT32 iOffExpoMask[4][1]; + __declspec (align(16))VUINT32 sPoly[8][4][1]; + __declspec (align(16))VUINT32 sLn2[4][1]; + __declspec (align(16))VUINT32 TinyRange[4][1]; + }__svml_satanh_data_internal; #endif + __svml_satanh_data_internal: - /*== SgnMask ==*/ - .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff - /*== sOne = SP 1.0 ==*/ - .align 16 - .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 - /*== sPoly[] = SP polynomial ==*/ - .align 16 - .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */ - .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */ - .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */ - .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */ - .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */ - .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */ - .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */ - .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */ - /*== iBrkValue = SP 2/3 ==*/ - .align 16 - .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab - /*== iOffExpoMask = SP significand mask ==*/ - .align 16 - .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff - /*== sHalf ==*/ - .align 16 - .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000 - /*== sSign ==*/ - .align 16 - .long 0x80000000, 0x80000000, 0x80000000, 0x80000000 - /*== sTopMask12 ==*/ - .align 16 - .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000 - /*== TinyRange ==*/ - .align 16 - .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000 - /*== sLn2 = SP ln(2) ==*/ - .align 16 - .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 - .align 16 - .type __svml_satanh_data_internal,@object - .size __svml_satanh_data_internal,.-__svml_satanh_data_internal + /* sOne = SP 1.0. */ + .align 16 + .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 + /* SgnMask. */ + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + /* sTopMask12. */ + .align 16 + .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000 + /* iBrkValue = SP 2/3. */ + .align 16 + .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab + /* iOffExpoMask = SP significand mask. */ + .align 16 + .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff + + /* sPoly[] = SP polynomial. */ + .align 16 + .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7. */ + .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6. */ + .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5. */ + .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4. */ + .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3. */ + .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2. */ + .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1. */ + .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0. */ + + /* sLn2 = SP ln(2). */ + .align 16 + .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 + /* TinyRange. */ + .align 16 + .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000 + .align 16 + .type __svml_satanh_data_internal, @object + .size __svml_satanh_data_internal, .-__svml_satanh_data_internal 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 e67fb5dc92..982029e648 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 @@ -30,306 +30,267 @@ * */ -/* Offsets for data table __svml_satanh_data_internal - */ -#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 + + /* Offsets for data table __svml_satanh_data_internal. */ +#define SgnMask 0 +#define sOne 32 +#define sTopMask12 64 +#define TinyRange 96 +#define iBrkValue 128 +#define iOffExpoMask 160 +#define sPoly 192 +#define sLn2 448 +#define sHalf 480 #include +#define TANHF_DATA(x) (x) + __svml_satanh_data_internal - .text - .section .text.avx2,"ax",@progbits + .text + .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 - -/* 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 */ - vandps SgnMask+__svml_satanh_data_internal(%rip), %ymm6, %ymm10 - vsubps %ymm10, %ymm5, %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 %ymm10, %ymm10, %ymm14 - -/* - * 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 - -/* No need to split sU when FMA is available */ - vfnmadd213ps %ymm5, %ymm0, %ymm1 - vmovaps %ymm6, %ymm8 - vfmadd213ps %ymm6, %ymm6, %ymm8 - vfnmadd231ps %ymm0, %ymm12, %ymm1 - -/* - * 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 - -/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */ - vmulps %ymm15, %ymm0, %ymm10 - -/* Compute D = E + E^2 */ - vfmadd213ps %ymm1, %ymm1, %ymm1 - -/* Record the sign for eventual reincorporation. */ - vandps sSign+__svml_satanh_data_internal(%rip), %ymm6, %ymm3 - -/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */ - vorps %ymm3, %ymm8, %ymm2 - vmulps %ymm7, %ymm0, %ymm8 - -/* - * 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 - -/* - * 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 - -/* - * 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 - -/* 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 - -/* final reconstruction */ - vfmadd132ps sLn2+__svml_satanh_data_internal(%rip), %ymm7, %ymm0 - -/* 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 - testl %edx, %edx - -/* 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) - ret - cfi_def_cfa(6, 16) - cfi_offset(6, -16) - -/* Branch to process - * special inputs - */ - + /* Strip off the sign, so treat X as positive until right at the end. + */ + vmovaps TANHF_DATA(SgnMask)(%rip), %ymm2 + vandps %ymm2, %ymm0, %ymm3 + /* Load constants including One = 1. */ + vmovups TANHF_DATA(sOne)(%rip), %ymm5 + vsubps %ymm3, %ymm5, %ymm1 + vmovups TANHF_DATA(sTopMask12)(%rip), %ymm4 + + vrcpps %ymm1, %ymm7 + vsubps %ymm1, %ymm5, %ymm9 + vandps %ymm4, %ymm7, %ymm6 + vsubps %ymm3, %ymm9, %ymm7 + + /* 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, %ymm3, %ymm14 + vcmplt_oqps TANHF_DATA(TinyRange)(%rip), %ymm3, %ymm15 + + /* 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 %ymm4, %ymm3, %ymm4 + vsubps %ymm4, %ymm3, %ymm7 + + /* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo. + */ + vmulps %ymm4, %ymm6, %ymm4 + + /* Compute D = E + E^2. */ + vfmadd213ps %ymm1, %ymm1, %ymm1 + + /* 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, %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) + */ + /* 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, %ymm4, %ymm2 + + /* reduction: compute r,n. */ + vmovups TANHF_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 %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 TANHF_DATA(iOffExpoMask)(%rip), %ymm1 + + vandps %ymm1, %ymm7, %ymm0 + vaddps %ymm4, %ymm6, %ymm4 + vandnps %ymm7, %ymm1, %ymm6 + vmovups TANHF_DATA(sPoly)(%rip), %ymm1 + vpaddd %ymm9, %ymm0, %ymm0 + vaddps %ymm4, %ymm2, %ymm4 + vpsubd %ymm6, %ymm5, %ymm6 + + /* polynomial evaluation. */ + vsubps %ymm5, %ymm0, %ymm2 + vfmadd231ps %ymm4, %ymm6, %ymm2 + vfmadd213ps TANHF_DATA(sPoly + 32)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 64)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 96)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 128)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 160)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 192)(%rip), %ymm2, %ymm1 + vfmadd213ps TANHF_DATA(sPoly + 224)(%rip), %ymm2, %ymm1 + + vmulps %ymm1, %ymm2, %ymm1 + vfmadd213ps %ymm2, %ymm2, %ymm1 + + /* final reconstruction. */ + vpsrad $23, %ymm7, %ymm6 + vcvtdq2ps %ymm6, %ymm2 + vfmadd132ps TANHF_DATA(sLn2)(%rip), %ymm1, %ymm2 + + /* Finally, halve the result and reincorporate the sign. */ + vxorps TANHF_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) + + /* No registers to restore on fast path. */ + ret + + + /* Branch to process special inputs. */ 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 - */ - -L(RANGEMASK_CHECK): - btl %r12d, %r13d - -/* Call scalar math function */ - jc L(SCALAR_MATH_CALL) - # LOE rbx r15 r12d r13d - -/* Special inputs - * processing loop - */ - + pushq %rbp + /* Need to callee save registers to preserve state across tanhf calls. + */ + pushq %r12 + pushq %r13 + movq %rsp, %rbp + + /* Align stack and make room for 2x ymm vectors. */ + andq $-32, %rsp + addq $-64, %rsp + + /* Save origional input (ymm0 unchanged up to this point). */ + vmovups %ymm0, (%rsp) + /* Save all already computed inputs. */ + vmovups %ymm8, 32(%rsp) + + vzeroupper + + /* edx has 1s where there was a special value that needs to be handled + by a tanhf call. */ + movl %edx, %r13d 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 - call atanhf@PLT - # LOE rbx r14 r15 r12d r13d xmm0 - - movss %xmm0, 64(%rsp,%r14,4) - -/* Process special inputs in loop */ - jmp L(SPECIAL_VALUES_LOOP) - # LOE rbx r15 r12d r13d + /* use r12 as index for special value that is saved across calls to + tanhf. 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. */ + xorl %r12d, %r12d + tzcntl %r13d, %r12d + + /* Scalar math fucntion call to process special input. */ + movss 32(%rsp, %r12, 4), %xmm0 + call atanhf@PLT + /* 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, %r12, 4) + + blsr %r13d, %r13d + jnz L(SPECIAL_VALUES_LOOP) + + /* All results have been written to 32(%rsp). */ + vmovups (%rsp), %ymm0 + movq %rbp, %rsp + popq %r13 + popq %r12 + popq %rbp + ret END(_ZGVdN8v_atanhf_avx2) - .section .rodata, "a" - .align 32 - + .section .rodata, "a" + .align 32 #ifdef __svml_satanh_data_internal_typedef -typedef unsigned int VUINT32; -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 sLn2[8][1]; -} __svml_satanh_data_internal; + typedef unsigned int VUINT32; + typedef struct{ + __declspec (align(32))VUINT32 SgnMask[8][1]; + __declspec (align(32))VUINT32 sOne[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 - /*== sOne = SP 1.0 ==*/ - .align 32 - .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 - /*== sPoly[] = SP polynomial ==*/ - .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 ==*/ - .align 32 - .long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000 - /*== TinyRange ==*/ - .align 32 - .long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000 - /*== sLn2 = SP ln(2) ==*/ - .align 32 - .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218 - .align 32 - .type __svml_satanh_data_internal,@object - .size __svml_satanh_data_internal,.-__svml_satanh_data_internal + /* SgnMask. */ + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff + /* sOne = SP 1.0. */ + .align 32 + .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 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). */ + .align 32 + .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