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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: 1.45358 +0.5 ulp. */15 0x1.0e4020p-7f,16 0x1.573e2ep-5f,17 0x1.555e66p-3f,18 0x1.fffdb6p-2f,19 0x1.ffffecp-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#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, v_u32_t cmp1, v_f32_t scale)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 (0x82000000);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 cmp2 = v_cond_u32 (absn > v_f32 (192.0f));41 v_u32_t r2 = v_as_u32_f32 (s1 * s1);42 v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);43 /* Similar to r1 but avoids double rounding in the subnormal range. */44 v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));45 return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));46}47 48VPCS_ATTR49v_f32_t50V_NAME(expf) (v_f32_t x)51{52 v_f32_t n, r, r2, scale, p, q, poly, absn, z;53 v_u32_t cmp, e;54 55 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]56 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */57#if 158 z = v_fma_f32 (x, InvLn2, Shift);59 n = z - Shift;60 r = v_fma_f32 (n, -Ln2hi, x);61 r = v_fma_f32 (n, -Ln2lo, r);62 e = v_as_u32_f32 (z) << 23;63#else64 z = x * InvLn2;65 n = v_round_f32 (z);66 r = v_fma_f32 (n, -Ln2hi, x);67 r = v_fma_f32 (n, -Ln2lo, r);68 e = v_as_u32_s32 (v_round_s32 (z)) << 23;69#endif70 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));71 absn = v_abs_f32 (n);72 cmp = v_cond_u32 (absn > v_f32 (126.0f));73 r2 = r * r;74 p = v_fma_f32 (C0, r, C1);75 q = v_fma_f32 (C2, r, C3);76 q = v_fma_f32 (p, r2, q);77 p = C4 * r;78 poly = v_fma_f32 (q, r2, p);79 if (unlikely (v_any_u32 (cmp)))80 return specialcase (poly, n, e, absn, cmp, scale);81 return v_fma_f32 (poly, scale, scale);82}83VPCS_ALIAS84#endif85