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1/*2 * Single-precision vector e^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: 0.36565 +0.5 ulp. */15 0x1.6a6000p-10f,16 0x1.12718ep-7f,17 0x1.555af0p-5f,18 0x1.555430p-3f,19 0x1.fffff4p-2f,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#define InvLn2 v_f32 (0x1.715476p+0f)29#define Ln2hi v_f32 (0x1.62e4p-1f)30#define Ln2lo v_f32 (0x1.7f7d1cp-20f)31 32VPCS_ATTR33static v_f32_t34specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)35{36 /* 2^n may overflow, break it up into s1*s2. */37 v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);38 v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);39 v_f32_t s2 = v_as_f32_u32 (e - b);40 v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));41 v_f32_t r1 = s1 * s1;42 v_f32_t r0 = poly * s1 * s2;43 return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));44}45 46VPCS_ATTR47v_f32_t48V_NAME(expf_1u) (v_f32_t x)49{50 v_f32_t n, r, scale, poly, absn, z;51 v_u32_t cmp, e;52 53 /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]54 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */55#if 156 z = v_fma_f32 (x, InvLn2, Shift);57 n = z - Shift;58 r = v_fma_f32 (n, -Ln2hi, x);59 r = v_fma_f32 (n, -Ln2lo, r);60 e = v_as_u32_f32 (z) << 23;61#else62 z = x * InvLn2;63 n = v_round_f32 (z);64 r = v_fma_f32 (n, -Ln2hi, x);65 r = v_fma_f32 (n, -Ln2lo, r);66 e = v_as_u32_s32 (v_round_s32 (z)) << 23;67#endif68 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));69 absn = v_abs_f32 (n);70 cmp = v_cond_u32 (absn > v_f32 (126.0f));71 poly = v_fma_f32 (C0, r, C1);72 poly = v_fma_f32 (poly, r, C2);73 poly = v_fma_f32 (poly, r, C3);74 poly = v_fma_f32 (poly, r, C4);75 poly = v_fma_f32 (poly, r, v_f32 (1.0f));76 poly = v_fma_f32 (poly, r, v_f32 (1.0f));77 if (unlikely (v_any_u32 (cmp)))78 return specialcase (poly, n, e, absn);79 return scale * poly;80}81#endif82