diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/v_log1pf_inline.h')
| -rw-r--r-- | sysdeps/aarch64/fpu/v_log1pf_inline.h | 71 |
1 files changed, 49 insertions, 22 deletions
diff --git a/sysdeps/aarch64/fpu/v_log1pf_inline.h b/sysdeps/aarch64/fpu/v_log1pf_inline.h index 643a6cdcfc..73e45a942e 100644 --- a/sysdeps/aarch64/fpu/v_log1pf_inline.h +++ b/sysdeps/aarch64/fpu/v_log1pf_inline.h @@ -25,54 +25,81 @@ struct v_log1pf_data { - float32x4_t poly[8], ln2; uint32x4_t four; int32x4_t three_quarters; + float c0, c3, c5, c7; + float32x4_t c4, c6, c1, c2, ln2; }; /* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients (1, -0.5) are not stored as they can be generated more efficiently. */ #define V_LOG1PF_CONSTANTS_TABLE \ { \ - .poly \ - = { V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f), \ - V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f), \ - V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) }, \ - .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \ - .three_quarters = V4 (0x3f400000) \ + .c0 = 0x1.5555aap-2f, .c1 = V4 (-0x1.000038p-2f), \ + .c2 = V4 (0x1.99675cp-3f), .c3 = -0x1.54ef78p-3f, \ + .c4 = V4 (0x1.28a1f4p-3f), .c5 = -0x1.0da91p-3f, \ + .c6 = V4 (0x1.abcb6p-4f), .c7 = -0x1.6f0d5ep-5f, \ + .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \ + .three_quarters = V4 (0x3f400000) \ } static inline float32x4_t -eval_poly (float32x4_t m, const float32x4_t *c) +eval_poly (float32x4_t m, const struct v_log1pf_data *d) { - /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner (main routine - uses split Estrin, but this way reduces register pressure in the calling - routine). */ - float32x4_t q = vfmaq_f32 (v_f32 (-0.5), m, c[0]); + /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */ + float32x4_t c0357 = vld1q_f32 (&d->c0); + float32x4_t q = vfmaq_laneq_f32 (v_f32 (-0.5), m, c0357, 0); float32x4_t m2 = vmulq_f32 (m, m); - q = vfmaq_f32 (m, m2, q); - float32x4_t p = v_pw_horner_6_f32 (m, m2, c + 1); + float32x4_t p67 = vfmaq_laneq_f32 (d->c6, m, c0357, 3); + float32x4_t p45 = vfmaq_laneq_f32 (d->c4, m, c0357, 2); + float32x4_t p23 = vfmaq_laneq_f32 (d->c2, m, c0357, 1); + float32x4_t p = vfmaq_f32 (p45, m2, p67); + p = vfmaq_f32 (p23, m2, p); + p = vfmaq_f32 (d->c1, m, p); p = vmulq_f32 (m2, p); - return vfmaq_f32 (q, m2, p); + p = vfmaq_f32 (m, m2, p); + return vfmaq_f32 (p, m2, q); } static inline float32x4_t -log1pf_inline (float32x4_t x, const struct v_log1pf_data d) +log1pf_inline (float32x4_t x, const struct v_log1pf_data *d) { - /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no - special-case handling. See that file for details of the algorithm. */ + /* Helper for calculating log(x + 1). */ + + /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m + is in [-0.25, 0.5]): + log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). + + We approximate log1p(m) with a polynomial, then scale by + k*log(2). Instead of doing this directly, we use an intermediate + scale factor s = 4*k*log(2) to ensure the scale is representable + as a normalised fp32 number. */ float32x4_t m = vaddq_f32 (x, v_f32 (1.0f)); + + /* Choose k to scale x to the range [-1/4, 1/2]. */ int32x4_t k - = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d.three_quarters), + = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters), v_s32 (0xff800000)); uint32x4_t ku = vreinterpretq_u32_s32 (k); - float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d.four, ku)); + + /* Scale up to ensure that the scale factor is representable as normalised + fp32 number, and scale m down accordingly. */ + float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku)); + + /* Scale x by exponent manipulation. */ float32x4_t m_scale = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku)); m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s)); - float32x4_t p = eval_poly (m_scale, d.poly); + + /* Evaluate polynomial on the reduced interval. */ + float32x4_t p = eval_poly (m_scale, d); + + /* The scale factor to be applied back at the end - by multiplying float(k) + by 2^-23 we get the unbiased exponent of k. */ float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f)); - return vfmaq_f32 (p, scale_back, d.ln2); + + /* Apply the scaling back. */ + return vfmaq_f32 (p, scale_back, d->ln2); } #endif |