| /* |
| * Single-precision vector e^x function. |
| * |
| * Copyright (c) 2019, Arm Limited. |
| * SPDX-License-Identifier: MIT |
| */ |
| |
| #include "mathlib.h" |
| #include "v_math.h" |
| #if V_SUPPORTED |
| |
| static const float Poly[] = { |
| /* maxerr: 0.36565 +0.5 ulp. */ |
| 0x1.6a6000p-10f, |
| 0x1.12718ep-7f, |
| 0x1.555af0p-5f, |
| 0x1.555430p-3f, |
| 0x1.fffff4p-2f, |
| }; |
| #define C0 v_f32 (Poly[0]) |
| #define C1 v_f32 (Poly[1]) |
| #define C2 v_f32 (Poly[2]) |
| #define C3 v_f32 (Poly[3]) |
| #define C4 v_f32 (Poly[4]) |
| |
| #define Shift v_f32 (0x1.8p23f) |
| #define InvLn2 v_f32 (0x1.715476p+0f) |
| #define Ln2hi v_f32 (0x1.62e4p-1f) |
| #define Ln2lo v_f32 (0x1.7f7d1cp-20f) |
| |
| VPCS_ATTR |
| static v_f32_t |
| specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn) |
| { |
| /* 2^n may overflow, break it up into s1*s2. */ |
| v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000); |
| v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b); |
| v_f32_t s2 = v_as_f32_u32 (e - b); |
| v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f)); |
| v_f32_t r1 = s1 * s1; |
| v_f32_t r0 = poly * s1 * s2; |
| return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0))); |
| } |
| |
| VPCS_ATTR |
| v_f32_t |
| V_NAME(expf_1u) (v_f32_t x) |
| { |
| v_f32_t n, r, scale, poly, absn, z; |
| v_u32_t cmp, e; |
| |
| /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] |
| x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ |
| #if 1 |
| z = v_fma_f32 (x, InvLn2, Shift); |
| n = z - Shift; |
| r = v_fma_f32 (n, -Ln2hi, x); |
| r = v_fma_f32 (n, -Ln2lo, r); |
| e = v_as_u32_f32 (z) << 23; |
| #else |
| z = x * InvLn2; |
| n = v_round_f32 (z); |
| r = v_fma_f32 (n, -Ln2hi, x); |
| r = v_fma_f32 (n, -Ln2lo, r); |
| e = v_as_u32_s32 (v_round_s32 (z)) << 23; |
| #endif |
| scale = v_as_f32_u32 (e + v_u32 (0x3f800000)); |
| absn = v_abs_f32 (n); |
| cmp = v_cond_u32 (absn > v_f32 (126.0f)); |
| poly = v_fma_f32 (C0, r, C1); |
| poly = v_fma_f32 (poly, r, C2); |
| poly = v_fma_f32 (poly, r, C3); |
| poly = v_fma_f32 (poly, r, C4); |
| poly = v_fma_f32 (poly, r, v_f32 (1.0f)); |
| poly = v_fma_f32 (poly, r, v_f32 (1.0f)); |
| if (unlikely (v_any_u32 (cmp))) |
| return specialcase (poly, n, e, absn); |
| return scale * poly; |
| } |
| #endif |