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1/*2 * Single-precision vector 2^x function.3 *4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.5 * See https://llvm.org/LICENSE.txt for license information.6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception7 */8 9#include "mathlib.h"10#include "v_math.h"11#if V_SUPPORTED12 13static const float Poly[] = {14 /* maxerr: 0.878 ulp. */15 0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f16};17#define C0 v_f32 (Poly[0])18#define C1 v_f32 (Poly[1])19#define C2 v_f32 (Poly[2])20#define C3 v_f32 (Poly[3])21#define C4 v_f32 (Poly[4])22#define C5 v_f32 (Poly[5])23 24#define Shift v_f32 (0x1.8p23f)25#define InvLn2 v_f32 (0x1.715476p+0f)26#define Ln2hi v_f32 (0x1.62e4p-1f)27#define Ln2lo v_f32 (0x1.7f7d1cp-20f)28 29VPCS_ATTR30static v_f32_t31specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)32{33 /* 2^n may overflow, break it up into s1*s2. */34 v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);35 v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);36 v_f32_t s2 = v_as_f32_u32 (e - b);37 v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));38 v_f32_t r1 = s1 * s1;39 v_f32_t r0 = poly * s1 * s2;40 return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));41}42 43VPCS_ATTR44v_f32_t45V_NAME(exp2f_1u) (v_f32_t x)46{47 v_f32_t n, r, scale, poly, absn;48 v_u32_t cmp, e;49 50 /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]51 x = n + r, with r in [-1/2, 1/2]. */52#if 053 v_f32_t z;54 z = x + Shift;55 n = z - Shift;56 r = x - n;57 e = v_as_u32_f32 (z) << 23;58#else59 n = v_round_f32 (x);60 r = x - n;61 e = v_as_u32_s32 (v_round_s32 (x)) << 23;62#endif63 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));64 absn = v_abs_f32 (n);65 cmp = v_cond_u32 (absn > v_f32 (126.0f));66 poly = v_fma_f32 (C0, r, C1);67 poly = v_fma_f32 (poly, r, C2);68 poly = v_fma_f32 (poly, r, C3);69 poly = v_fma_f32 (poly, r, C4);70 poly = v_fma_f32 (poly, r, C5);71 poly = v_fma_f32 (poly, r, v_f32 (1.0f));72 if (unlikely (v_any_u32 (cmp)))73 return specialcase (poly, n, e, absn);74 return scale * poly;75}76#endif77