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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: 1.962 ulp. */15 0x1.59977ap-10f,16 0x1.3ce9e4p-7f,17 0x1.c6bd32p-5f,18 0x1.ebf9bcp-3f,19 0x1.62e422p-1f,20};21#define C0 v_f32 (Poly[0])22#define C1 v_f32 (Poly[1])23#define C2 v_f32 (Poly[2])24#define C3 v_f32 (Poly[3])25#define C4 v_f32 (Poly[4])26 27#define Shift v_f32 (0x1.8p23f)28 29VPCS_ATTR30static v_f32_t31specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)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 (0x82000000);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 cmp2 = v_cond_u32 (absn > v_f32 (192.0f));38 v_u32_t r2 = v_as_u32_f32 (s1 * s1);39 v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);40 /* Similar to r1 but avoids double rounding in the subnormal range. */41 v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));42 return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));43}44 45VPCS_ATTR46v_f32_t47V_NAME(exp2f) (v_f32_t x)48{49 v_f32_t n, r, r2, scale, p, q, poly, absn;50 v_u32_t cmp, e;51 52 /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]53 x = n + r, with r in [-1/2, 1/2]. */54#if 055 v_f32_t z;56 z = x + Shift;57 n = z - Shift;58 r = x - n;59 e = v_as_u32_f32 (z) << 23;60#else61 n = v_round_f32 (x);62 r = x - n;63 e = v_as_u32_s32 (v_round_s32 (x)) << 23;64#endif65 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));66 absn = v_abs_f32 (n);67 cmp = v_cond_u32 (absn > v_f32 (126.0f));68 r2 = r * r;69 p = v_fma_f32 (C0, r, C1);70 q = v_fma_f32 (C2, r, C3);71 q = v_fma_f32 (p, r2, q);72 p = C4 * r;73 poly = v_fma_f32 (q, r2, p);74 if (unlikely (v_any_u32 (cmp)))75 return specialcase (poly, n, e, absn, cmp, scale);76 return v_fma_f32 (poly, scale, scale);77}78VPCS_ALIAS79#endif80