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76 lines
1.9 KiB
76 lines
1.9 KiB
/*
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* Single-precision vector 2^x function.
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*
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* Copyright (c) 2019, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include "mathlib.h"
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#include "v_math.h"
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#if V_SUPPORTED
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static const float Poly[] = {
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/* maxerr: 0.878 ulp. */
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0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f
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};
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#define C0 v_f32 (Poly[0])
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#define C1 v_f32 (Poly[1])
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#define C2 v_f32 (Poly[2])
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#define C3 v_f32 (Poly[3])
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#define C4 v_f32 (Poly[4])
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#define C5 v_f32 (Poly[5])
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#define Shift v_f32 (0x1.8p23f)
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#define InvLn2 v_f32 (0x1.715476p+0f)
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#define Ln2hi v_f32 (0x1.62e4p-1f)
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#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
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VPCS_ATTR
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static v_f32_t
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specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
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{
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/* 2^n may overflow, break it up into s1*s2. */
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v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
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v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
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v_f32_t s2 = v_as_f32_u32 (e - b);
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v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));
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v_f32_t r1 = s1 * s1;
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v_f32_t r0 = poly * s1 * s2;
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return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
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}
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VPCS_ATTR
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v_f32_t
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V_NAME(exp2f_1u) (v_f32_t x)
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{
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v_f32_t n, r, scale, poly, absn;
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v_u32_t cmp, e;
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/* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
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x = n + r, with r in [-1/2, 1/2]. */
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#if 0
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v_f32_t z;
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z = x + Shift;
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n = z - Shift;
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r = x - n;
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e = v_as_u32_f32 (z) << 23;
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#else
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n = v_round_f32 (x);
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r = x - n;
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e = v_as_u32_s32 (v_round_s32 (x)) << 23;
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#endif
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scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
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absn = v_abs_f32 (n);
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cmp = v_cond_u32 (absn > v_f32 (126.0f));
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poly = v_fma_f32 (C0, r, C1);
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poly = v_fma_f32 (poly, r, C2);
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poly = v_fma_f32 (poly, r, C3);
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poly = v_fma_f32 (poly, r, C4);
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poly = v_fma_f32 (poly, r, C5);
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poly = v_fma_f32 (poly, r, v_f32 (1.0f));
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if (unlikely (v_any_u32 (cmp)))
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return specialcase (poly, n, e, absn);
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return scale * poly;
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}
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#endif
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