1 /* 2 * Single-precision vector 2^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: 0.878 ulp. */ 13 0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f 14 }; 15 #define C0 v_f32 (Poly[0]) 16 #define C1 v_f32 (Poly[1]) 17 #define C2 v_f32 (Poly[2]) 18 #define C3 v_f32 (Poly[3]) 19 #define C4 v_f32 (Poly[4]) 20 #define C5 v_f32 (Poly[5]) 21 22 #define Shift v_f32 (0x1.8p23f) 23 #define InvLn2 v_f32 (0x1.715476p+0f) 24 #define Ln2hi v_f32 (0x1.62e4p-1f) 25 #define Ln2lo v_f32 (0x1.7f7d1cp-20f) 26 27 static float32x4_t VPCS_ATTR NOINLINE 28 specialcase (float32x4_t poly, float32x4_t n, uint32x4_t e, float32x4_t absn) 29 { 30 /* 2^n may overflow, break it up into s1*s2. */ 31 uint32x4_t b = (n <= v_f32 (0.0f)) & v_u32 (0x83000000); 32 float32x4_t s1 = vreinterpretq_f32_u32 (v_u32 (0x7f000000) + b); 33 float32x4_t s2 = vreinterpretq_f32_u32 (e - b); 34 uint32x4_t cmp = absn > v_f32 (192.0f); 35 float32x4_t r1 = s1 * s1; 36 float32x4_t r0 = poly * s1 * s2; 37 return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1)) 38 | (~cmp & vreinterpretq_u32_f32 (r0))); 39 } 40 41 float32x4_t VPCS_ATTR 42 _ZGVnN4v_exp2f_1u (float32x4_t x) 43 { 44 float32x4_t n, r, scale, poly, absn; 45 uint32x4_t cmp, e; 46 47 /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] 48 x = n + r, with r in [-1/2, 1/2]. */ 49 #if 0 50 float32x4_t z; 51 z = x + Shift; 52 n = z - Shift; 53 r = x - n; 54 e = vreinterpretq_u32_f32 (z) << 23; 55 #else 56 n = vrndaq_f32 (x); 57 r = x - n; 58 e = vreinterpretq_u32_s32 (vcvtaq_s32_f32 (x)) << 23; 59 #endif 60 scale = vreinterpretq_f32_u32 (e + v_u32 (0x3f800000)); 61 absn = vabsq_f32 (n); 62 cmp = absn > v_f32 (126.0f); 63 poly = vfmaq_f32 (C1, C0, r); 64 poly = vfmaq_f32 (C2, poly, r); 65 poly = vfmaq_f32 (C3, poly, r); 66 poly = vfmaq_f32 (C4, poly, r); 67 poly = vfmaq_f32 (C5, poly, r); 68 poly = vfmaq_f32 (v_f32 (1.0f), poly, r); 69 if (unlikely (v_any_u32 (cmp))) 70 return specialcase (poly, n, e, absn); 71 return scale * poly; 72 } 73