diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/expm1f_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/expm1f_advsimd.c | 62 |
1 files changed, 12 insertions, 50 deletions
diff --git a/sysdeps/aarch64/fpu/expm1f_advsimd.c b/sysdeps/aarch64/fpu/expm1f_advsimd.c index a0616ec754..8303ca296e 100644 --- a/sysdeps/aarch64/fpu/expm1f_advsimd.c +++ b/sysdeps/aarch64/fpu/expm1f_advsimd.c @@ -18,27 +18,18 @@ <https://www.gnu.org/licenses/>. */ #include "v_math.h" -#include "poly_advsimd_f32.h" +#include "v_expm1f_inline.h" static const struct data { - float32x4_t poly[5]; - float invln2_and_ln2[4]; - float32x4_t shift; - int32x4_t exponent_bias; + struct v_expm1f_data d; #if WANT_SIMD_EXCEPT uint32x4_t thresh; #else float32x4_t oflow_bound; #endif } data = { - /* Generated using fpminimax with degree=5 in [-log(2)/2, log(2)/2]. */ - .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), - V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, - /* Stores constants: invln2, ln2_hi, ln2_lo, 0. */ - .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, - .shift = V4 (0x1.8p23f), - .exponent_bias = V4 (0x3f800000), + .d = V_EXPM1F_DATA, #if !WANT_SIMD_EXCEPT /* Value above which expm1f(x) should overflow. Absolute value of the underflow bound is greater than this, so it catches both cases - there is @@ -55,67 +46,38 @@ static const struct data #define TinyBound v_u32 (0x34000000 << 1) static float32x4_t VPCS_ATTR NOINLINE -special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +special_case (float32x4_t x, uint32x4_t special, const struct data *d) { - return v_call_f32 (expm1f, x, y, special); + return v_call_f32 ( + expm1f, x, expm1f_inline (v_zerofy_f32 (x, special), &d->d), special); } /* Single-precision vector exp(x) - 1 function. - The maximum error is 1.51 ULP: - _ZGVnN4v_expm1f (0x1.8baa96p-2) got 0x1.e2fb9p-2 - want 0x1.e2fb94p-2. */ + The maximum error is 1.62 ULP: + _ZGVnN4v_expm1f(0x1.85f83p-2) got 0x1.da9f4p-2 + want 0x1.da9f44p-2. */ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (expm1) (float32x4_t x) { const struct data *d = ptr_barrier (&data); - uint32x4_t ix = vreinterpretq_u32_f32 (x); #if WANT_SIMD_EXCEPT + uint32x4_t ix = vreinterpretq_u32_f32 (x); /* If fp exceptions are to be triggered correctly, fall back to scalar for |x| < 2^-23, |x| > oflow_bound, Inf & NaN. Add ix to itself for shift-left by 1, and compare with thresh which was left-shifted offline - this is effectively an absolute compare. */ uint32x4_t special = vcgeq_u32 (vsubq_u32 (vaddq_u32 (ix, ix), TinyBound), d->thresh); - if (__glibc_unlikely (v_any_u32 (special))) - x = v_zerofy_f32 (x, special); #else /* Handles very large values (+ve and -ve), +/-NaN, +/-Inf. */ uint32x4_t special = vcagtq_f32 (x, d->oflow_bound); #endif - /* Reduce argument to smaller range: - Let i = round(x / ln2) - and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. - exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 - where 2^i is exact because i is an integer. */ - float32x4_t invln2_and_ln2 = vld1q_f32 (d->invln2_and_ln2); - float32x4_t j - = vsubq_f32 (vfmaq_laneq_f32 (d->shift, x, invln2_and_ln2, 0), d->shift); - int32x4_t i = vcvtq_s32_f32 (j); - float32x4_t f = vfmsq_laneq_f32 (x, j, invln2_and_ln2, 1); - f = vfmsq_laneq_f32 (f, j, invln2_and_ln2, 2); - - /* Approximate expm1(f) using polynomial. - Taylor expansion for expm1(x) has the form: - x + ax^2 + bx^3 + cx^4 .... - So we calculate the polynomial P(f) = a + bf + cf^2 + ... - and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ - float32x4_t p = v_horner_4_f32 (f, d->poly); - p = vfmaq_f32 (f, vmulq_f32 (f, f), p); - - /* Assemble the result. - expm1(x) ~= 2^i * (p + 1) - 1 - Let t = 2^i. */ - int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias); - float32x4_t t = vreinterpretq_f32_s32 (u); - if (__glibc_unlikely (v_any_u32 (special))) - return special_case (vreinterpretq_f32_u32 (ix), - vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t), - special); + return special_case (x, special, d); /* expm1(x) ~= p * t + (t - 1). */ - return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t); + return expm1f_inline (x, &d->d); } libmvec_hidden_def (V_NAME_F1 (expm1)) HALF_WIDTH_ALIAS_F1 (expm1) |