1 /* 2 * Single-precision vector e^x function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 11 static const float Poly[] = { 12 /* maxerr: 0.36565 +0.5 ulp. */ 13 0x1.6a6000p-10f, 14 0x1.12718ep-7f, 15 0x1.555af0p-5f, 16 0x1.555430p-3f, 17 0x1.fffff4p-2f, 18 }; 19 #define C0 v_f32 (Poly[0]) 20 #define C1 v_f32 (Poly[1]) 21 #define C2 v_f32 (Poly[2]) 22 #define C3 v_f32 (Poly[3]) 23 #define C4 v_f32 (Poly[4]) 24 25 #define Shift v_f32 (0x1.8p23f) 26 #define InvLn2 v_f32 (0x1.715476p+0f) 27 #define Ln2hi v_f32 (0x1.62e4p-1f) 28 #define Ln2lo v_f32 (0x1.7f7d1cp-20f) 29 30 static float32x4_t VPCS_ATTR NOINLINE 31 specialcase (float32x4_t poly, float32x4_t n, uint32x4_t e, float32x4_t absn) 32 { 33 /* 2^n may overflow, break it up into s1*s2. */ 34 uint32x4_t b = (n <= v_f32 (0.0f)) & v_u32 (0x83000000); 35 float32x4_t s1 = vreinterpretq_f32_u32 (v_u32 (0x7f000000) + b); 36 float32x4_t s2 = vreinterpretq_f32_u32 (e - b); 37 uint32x4_t cmp = absn > v_f32 (192.0f); 38 float32x4_t r1 = s1 * s1; 39 float32x4_t r0 = poly * s1 * s2; 40 return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1)) 41 | (~cmp & vreinterpretq_u32_f32 (r0))); 42 } 43 44 float32x4_t VPCS_ATTR 45 _ZGVnN4v_expf_1u (float32x4_t x) 46 { 47 float32x4_t n, r, scale, poly, absn, z; 48 uint32x4_t cmp, e; 49 50 /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] 51 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 52 #if 1 53 z = vfmaq_f32 (Shift, x, InvLn2); 54 n = z - Shift; 55 r = vfmaq_f32 (x, n, -Ln2hi); 56 r = vfmaq_f32 (r, n, -Ln2lo); 57 e = vreinterpretq_u32_f32 (z) << 23; 58 #else 59 z = x * InvLn2; 60 n = vrndaq_f32 (z); 61 r = vfmaq_f32 (x, n, -Ln2hi); 62 r = vfmaq_f32 (r, n, -Ln2lo); 63 e = vreinterpretq_u32_s32 (vcvtaq_s32_f32 (z)) << 23; 64 #endif 65 scale = vreinterpretq_f32_u32 (e + v_u32 (0x3f800000)); 66 absn = vabsq_f32 (n); 67 cmp = absn > v_f32 (126.0f); 68 poly = vfmaq_f32 (C1, C0, r); 69 poly = vfmaq_f32 (C2, poly, r); 70 poly = vfmaq_f32 (C3, poly, r); 71 poly = vfmaq_f32 (C4, poly, r); 72 poly = vfmaq_f32 (v_f32 (1.0f), poly, r); 73 poly = vfmaq_f32 (v_f32 (1.0f), poly, r); 74 if (unlikely (v_any_u32 (cmp))) 75 return specialcase (poly, n, e, absn); 76 return scale * poly; 77 } 78