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1/*2 * Double-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#include "v_exp.h"13 14#if V_EXP_TABLE_BITS == 715/* maxerr: 1.88 +0.5 ulp16 rel error: 1.4337*2^-5317 abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */18#define C1 v_f64 (0x1.ffffffffffd43p-2)19#define C2 v_f64 (0x1.55555c75adbb2p-3)20#define C3 v_f64 (0x1.55555da646206p-5)21#define InvLn2 v_f64 (0x1.71547652b82fep7) /* N/ln2. */22#define Ln2hi v_f64 (0x1.62e42fefa39efp-8) /* ln2/N. */23#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-63)24#elif V_EXP_TABLE_BITS == 825/* maxerr: 0.54 +0.5 ulp26 rel error: 1.4318*2^-5827 abs error: 1.4299*2^-58 in [ -ln2/512, ln2/512 ]. */28#define C1 v_f64 (0x1.fffffffffffd4p-2)29#define C2 v_f64 (0x1.5555571d6b68cp-3)30#define C3 v_f64 (0x1.5555576a59599p-5)31#define InvLn2 v_f64 (0x1.71547652b82fep8)32#define Ln2hi v_f64 (0x1.62e42fefa39efp-9)33#define Ln2lo v_f64 (0x1.abc9e3b39803f3p-64)34#endif35 36#define N (1 << V_EXP_TABLE_BITS)37#define Tab __v_exp_data38#define IndexMask v_u64 (N - 1)39#define Shift v_f64 (0x1.8p+52)40#define Thres v_f64 (704.0)41 42VPCS_ATTR43static v_f64_t44specialcase (v_f64_t s, v_f64_t y, v_f64_t n)45{46 v_f64_t absn = v_abs_f64 (n);47 48 /* 2^(n/N) may overflow, break it up into s1*s2. */49 v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);50 v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);51 v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);52 v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));53 v_f64_t r1 = s1 * s1;54 v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;55 return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));56}57 58VPCS_ATTR59v_f64_t60V_NAME(exp) (v_f64_t x)61{62 v_f64_t n, r, r2, s, y, z;63 v_u64_t cmp, u, e, i;64 65 cmp = v_cond_u64 (v_abs_f64 (x) > Thres);66 67 /* n = round(x/(ln2/N)). */68 z = v_fma_f64 (x, InvLn2, Shift);69 u = v_as_u64_f64 (z);70 n = z - Shift;71 72 /* r = x - n*ln2/N. */73 r = x;74 r = v_fma_f64 (-Ln2hi, n, r);75 r = v_fma_f64 (-Ln2lo, n, r);76 77 e = u << (52 - V_EXP_TABLE_BITS);78 i = u & IndexMask;79 80 /* y = exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */81 r2 = r * r;82 y = v_fma_f64 (C2, r, C1);83 y = v_fma_f64 (C3, r2, y);84 y = v_fma_f64 (y, r2, r);85 86 /* s = 2^(n/N). */87 u = v_lookup_u64 (Tab, i);88 s = v_as_f64_u64 (u + e);89 90 if (unlikely (v_any_u64 (cmp)))91 return specialcase (s, y, n);92 return v_fma_f64 (y, s, s);93}94VPCS_ALIAS95#endif96