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Diffstat (limited to 'math/aarch64/advsimd/expf.c')
-rw-r--r-- | math/aarch64/advsimd/expf.c | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/math/aarch64/advsimd/expf.c b/math/aarch64/advsimd/expf.c new file mode 100644 index 000000000000..e5b1f020d1a0 --- /dev/null +++ b/math/aarch64/advsimd/expf.c @@ -0,0 +1,130 @@ +/* + * Single-precision vector e^x function. + * + * Copyright (c) 2019-2024, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ +#include "v_math.h" +#include "test_defs.h" +#include "test_sig.h" + +static const struct data +{ + float32x4_t c1, c3, c4, inv_ln2; + float ln2_hi, ln2_lo, c0, c2; + uint32x4_t exponent_bias, special_offset, special_bias; +#if !WANT_SIMD_EXCEPT + float32x4_t special_bound, scale_thresh; +#endif +} data = { + /* maxerr: 1.45358 +0.5 ulp. */ + .c0 = 0x1.0e4020p-7f, + .c1 = V4 (0x1.573e2ep-5f), + .c2 = 0x1.555e66p-3f, + .c3 = V4 (0x1.fffdb6p-2f), + .c4 = V4 (0x1.ffffecp-1f), + .inv_ln2 = V4 (0x1.715476p+0f), + .ln2_hi = 0x1.62e4p-1f, + .ln2_lo = 0x1.7f7d1cp-20f, + .exponent_bias = V4 (0x3f800000), + .special_offset = V4 (0x82000000), + .special_bias = V4 (0x7f000000), +#if !WANT_SIMD_EXCEPT + .special_bound = V4 (126.0f), + .scale_thresh = V4 (192.0f), +#endif +}; + +#define C(i) d->poly[i] + +#if WANT_SIMD_EXCEPT + +# define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */ +# define BigBound v_u32 (0x42800000) /* asuint (0x1p6). */ +# define SpecialBound v_u32 (0x22800000) /* BigBound - TinyBound. */ + +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp) +{ + /* If fenv exceptions are to be triggered correctly, fall back to the scalar + routine to special lanes. */ + return v_call_f32 (expf, x, y, cmp); +} + +#else + +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1, + float32x4_t scale, const struct data *d) +{ + /* 2^n may overflow, break it up into s1*s2. */ + uint32x4_t b = vandq_u32 (vclezq_f32 (n), d->special_offset); + float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, d->special_bias)); + float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b)); + uint32x4_t cmp2 = vcagtq_f32 (n, d->scale_thresh); + float32x4_t r2 = vmulq_f32 (s1, s1); + // (s2 + p*s2)*s1 = s2(p+1)s1 + float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1); + /* Similar to r1 but avoids double rounding in the subnormal range. */ + float32x4_t r0 = vfmaq_f32 (scale, poly, scale); + float32x4_t r = vbslq_f32 (cmp1, r1, r0); + return vbslq_f32 (cmp2, r2, r); +} + +#endif + +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (exp) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + float32x4_t ln2_c02 = vld1q_f32 (&d->ln2_hi); + +#if WANT_SIMD_EXCEPT + /* asuint(x) - TinyBound >= BigBound - TinyBound. */ + uint32x4_t cmp = vcgeq_u32 ( + vsubq_u32 (vandq_u32 (vreinterpretq_u32_f32 (x), v_u32 (0x7fffffff)), + TinyBound), + SpecialBound); + float32x4_t xm = x; + /* If any lanes are special, mask them with 1 and retain a copy of x to allow + special case handler to fix special lanes later. This is only necessary if + fenv exceptions are to be triggered correctly. */ + if (unlikely (v_any_u32 (cmp))) + x = vbslq_f32 (cmp, v_f32 (1), x); +#endif + + /* 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]. */ + float32x4_t n = vrndaq_f32 (vmulq_f32 (x, d->inv_ln2)); + float32x4_t r = vfmsq_laneq_f32 (x, n, ln2_c02, 0); + r = vfmsq_laneq_f32 (r, n, ln2_c02, 1); + uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtq_s32_f32 (n)), 23); + float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, d->exponent_bias)); + +#if !WANT_SIMD_EXCEPT + uint32x4_t cmp = vcagtq_f32 (n, d->special_bound); +#endif + + float32x4_t r2 = vmulq_f32 (r, r); + float32x4_t p = vfmaq_laneq_f32 (d->c1, r, ln2_c02, 2); + float32x4_t q = vfmaq_laneq_f32 (d->c3, r, ln2_c02, 3); + q = vfmaq_f32 (q, p, r2); + p = vmulq_f32 (d->c4, r); + float32x4_t poly = vfmaq_f32 (p, q, r2); + + if (unlikely (v_any_u32 (cmp))) +#if WANT_SIMD_EXCEPT + return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp); +#else + return special_case (poly, n, e, cmp, scale, d); +#endif + + return vfmaq_f32 (scale, poly, scale); +} + +HALF_WIDTH_ALIAS_F1 (exp) + +TEST_SIG (V, F, 1, exp, -9.9, 9.9) +TEST_ULP (V_NAME_F1 (exp), 1.49) +TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (exp), WANT_SIMD_EXCEPT) +TEST_INTERVAL (V_NAME_F1 (exp), 0, 0xffff0000, 10000) +TEST_SYM_INTERVAL (V_NAME_F1 (exp), 0x1p-14, 0x1p8, 500000) |