llvm-project
84 строки · 2.3 Кб
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-exception
7*/
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. */150x1.0e4020p-7f,160x1.573e2ep-5f,170x1.555e66p-3f,180x1.fffdb6p-2f,190x1.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_ATTR
33static 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. */37v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);38v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);39v_f32_t s2 = v_as_f32_u32 (e - b);40v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));41v_u32_t r2 = v_as_u32_f32 (s1 * s1);42v_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. */44v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));45return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));46}
47
48VPCS_ATTR
49v_f32_t
50V_NAME(expf) (v_f32_t x)51{
52v_f32_t n, r, r2, scale, p, q, poly, absn, z;53v_u32_t cmp, e;54
55/* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]56x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
57#if 158z = v_fma_f32 (x, InvLn2, Shift);59n = z - Shift;60r = v_fma_f32 (n, -Ln2hi, x);61r = v_fma_f32 (n, -Ln2lo, r);62e = v_as_u32_f32 (z) << 23;63#else64z = x * InvLn2;65n = v_round_f32 (z);66r = v_fma_f32 (n, -Ln2hi, x);67r = v_fma_f32 (n, -Ln2lo, r);68e = v_as_u32_s32 (v_round_s32 (z)) << 23;69#endif70scale = v_as_f32_u32 (e + v_u32 (0x3f800000));71absn = v_abs_f32 (n);72cmp = v_cond_u32 (absn > v_f32 (126.0f));73r2 = r * r;74p = v_fma_f32 (C0, r, C1);75q = v_fma_f32 (C2, r, C3);76q = v_fma_f32 (p, r2, q);77p = C4 * r;78poly = v_fma_f32 (q, r2, p);79if (unlikely (v_any_u32 (cmp)))80return specialcase (poly, n, e, absn, cmp, scale);81return v_fma_f32 (poly, scale, scale);82}
83VPCS_ALIAS
84#endif85