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https://github.com/freebsd/freebsd-src
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072a4ba82a
Sponsored by: Arm Ltd
76 lines
1.9 KiB
C
76 lines
1.9 KiB
C
/*
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* Double-precision vector e^(x+tail) function.
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*
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* Copyright (c) 2019-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "v_math.h"
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#include "math_config.h"
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#if V_SUPPORTED
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#include "v_exp_tail.h"
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#define C1 v_f64 (C1_scal)
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#define C2 v_f64 (C2_scal)
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#define C3 v_f64 (C3_scal)
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#define InvLn2 v_f64 (InvLn2_scal)
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#define Ln2hi v_f64 (Ln2hi_scal)
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#define Ln2lo v_f64 (Ln2lo_scal)
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#define IndexMask v_u64 (IndexMask_scal)
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#define Shift v_f64 (Shift_scal)
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#define Thres v_f64 (Thres_scal)
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VPCS_ATTR
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static v_f64_t
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specialcase (v_f64_t s, v_f64_t y, v_f64_t n)
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{
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v_f64_t absn = v_abs_f64 (n);
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/* 2^(n/N) may overflow, break it up into s1*s2. */
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v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);
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v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);
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v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);
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v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));
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v_f64_t r1 = s1 * s1;
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v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;
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return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));
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}
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VPCS_ATTR
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v_f64_t V_NAME (exp_tail) (v_f64_t x, v_f64_t xtail)
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{
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v_f64_t n, r, s, y, z;
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v_u64_t cmp, u, e, i;
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cmp = v_cond_u64 (v_abs_f64 (x) > Thres);
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/* n = round(x/(ln2/N)). */
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z = v_fma_f64 (x, InvLn2, Shift);
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u = v_as_u64_f64 (z);
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n = z - Shift;
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/* r = x - n*ln2/N. */
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r = x;
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r = v_fma_f64 (-Ln2hi, n, r);
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r = v_fma_f64 (-Ln2lo, n, r);
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e = u << (52 - V_EXP_TAIL_TABLE_BITS);
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i = u & IndexMask;
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/* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
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y = v_fma_f64 (C3, r, C2);
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y = v_fma_f64 (y, r, C1);
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y = v_fma_f64 (y, r, v_f64 (1.0));
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y = v_fma_f64 (y, r, xtail);
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/* s = 2^(n/N). */
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u = v_lookup_u64 (Tab, i);
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s = v_as_f64_u64 (u + e);
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if (unlikely (v_any_u64 (cmp)))
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return specialcase (s, y, n);
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return v_fma_f64 (y, s, s);
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}
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#endif
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