x86-64: Add vector atanh/atanhf implementation to libmvec

Implement vectorized atanh/atanhf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector atanh/atanhf with regenerated ulps.

Reviewed-by: H.J. Lu <hjl.tools@gmail.com>

1 files changed, 361 insertions, 0 deletions

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
new file mode 100644
index 0000000000..77e46cb5b9
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanhf4_core_sse4.S
@@ -0,0 +1,361 @@
+/* Function atanhf vectorized with SSE4.
+   Copyright (C) 2021 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
+   https://www.gnu.org/licenses/.  */
+
+/*
+ * ALGORITHM DESCRIPTION:
+ *
+ *   Compute atanh(x) as 0.5 * log((1 + x)/(1 - x))
+ *
+ *   Special cases:
+ *
+ *   atanh(0)  = 0
+ *   atanh(+1) = +INF
+ *   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 <sysdep.h>
+
+        .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
+
+/*
+ * 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
+
+/*
+ * 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
+
+/*
+ * 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
+ */
+
+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
+ */
+
+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
+END(_ZGVbN4v_atanhf_sse4)
+
+        .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;
+#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