diff options
Diffstat (limited to 'pl/math/v_expf.c')
-rw-r--r-- | pl/math/v_expf.c | 83 |
1 files changed, 83 insertions, 0 deletions
diff --git a/pl/math/v_expf.c b/pl/math/v_expf.c new file mode 100644 index 0000000..a422e69 --- /dev/null +++ b/pl/math/v_expf.c @@ -0,0 +1,83 @@ +/* + * Single-precision vector e^x function. + * + * Copyright (c) 2019-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "mathlib.h" +#if V_SUPPORTED + +static const float Poly[] = { + /* maxerr: 1.45358 +0.5 ulp. */ + 0x1.0e4020p-7f, + 0x1.573e2ep-5f, + 0x1.555e66p-3f, + 0x1.fffdb6p-2f, + 0x1.ffffecp-1f, +}; +#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, v_u32_t cmp1, v_f32_t scale) +{ + /* 2^n may overflow, break it up into s1*s2. */ + v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000); + 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 cmp2 = v_cond_u32 (absn > v_f32 (192.0f)); + v_u32_t r2 = v_as_u32_f32 (s1 * s1); + v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1); + /* Similar to r1 but avoids double rounding in the subnormal range. */ + v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale)); + return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0)); +} + +VPCS_ATTR +v_f32_t +V_NAME(expf) (v_f32_t x) +{ + v_f32_t n, r, r2, scale, p, q, poly, absn, z; + v_u32_t cmp, e; + + /* exp(x) = 2^n (1 + poly(r)), with 1 + 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)); + r2 = r * r; + p = v_fma_f32 (C0, r, C1); + q = v_fma_f32 (C2, r, C3); + q = v_fma_f32 (p, r2, q); + p = C4 * r; + poly = v_fma_f32 (q, r2, p); + if (unlikely (v_any_u32 (cmp))) + return specialcase (poly, n, e, absn, cmp, scale); + return v_fma_f32 (poly, scale, scale); +} +VPCS_ALIAS +#endif |