1 /* 2 * Helper for single-precision routines which calculate log(1 + x) and do not 3 * need special-case handling 4 * 5 * Copyright (c) 2022-2024, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 9 #ifndef MATH_V_LOG1PF_INLINE_H 10 #define MATH_V_LOG1PF_INLINE_H 11 12 #include "v_math.h" 13 #include "v_poly_f32.h" 14 15 struct v_log1pf_data 16 { 17 uint32x4_t four; 18 int32x4_t three_quarters; 19 float c0, c3, c5, c7; 20 float32x4_t c4, c6, c1, c2, ln2; 21 }; 22 23 /* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients 24 (1, -0.5) are not stored as they can be generated more efficiently. */ 25 #define V_LOG1PF_CONSTANTS_TABLE \ 26 { \ 27 .c0 = 0x1.5555aap-2f, .c1 = V4 (-0x1.000038p-2f), \ 28 .c2 = V4 (0x1.99675cp-3f), .c3 = -0x1.54ef78p-3f, \ 29 .c4 = V4 (0x1.28a1f4p-3f), .c5 = -0x1.0da91p-3f, \ 30 .c6 = V4 (0x1.abcb6p-4f), .c7 = -0x1.6f0d5ep-5f, \ 31 .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \ 32 .three_quarters = V4 (0x3f400000) \ 33 } 34 35 static inline float32x4_t 36 eval_poly (float32x4_t m, const struct v_log1pf_data *d) 37 { 38 /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner. */ 39 float32x4_t c0357 = vld1q_f32 (&d->c0); 40 float32x4_t q = vfmaq_laneq_f32 (v_f32 (-0.5), m, c0357, 0); 41 float32x4_t m2 = vmulq_f32 (m, m); 42 float32x4_t p67 = vfmaq_laneq_f32 (d->c6, m, c0357, 3); 43 float32x4_t p45 = vfmaq_laneq_f32 (d->c4, m, c0357, 2); 44 float32x4_t p23 = vfmaq_laneq_f32 (d->c2, m, c0357, 1); 45 float32x4_t p = vfmaq_f32 (p45, m2, p67); 46 p = vfmaq_f32 (p23, m2, p); 47 p = vfmaq_f32 (d->c1, m, p); 48 p = vmulq_f32 (m2, p); 49 p = vfmaq_f32 (m, m2, p); 50 return vfmaq_f32 (p, m2, q); 51 } 52 53 static inline float32x4_t 54 log1pf_inline (float32x4_t x, const struct v_log1pf_data *d) 55 { 56 /* Helper for calculating log(x + 1). */ 57 58 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m 59 is in [-0.25, 0.5]): 60 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). 61 62 We approximate log1p(m) with a polynomial, then scale by 63 k*log(2). Instead of doing this directly, we use an intermediate 64 scale factor s = 4*k*log(2) to ensure the scale is representable 65 as a normalised fp32 number. */ 66 float32x4_t m = vaddq_f32 (x, v_f32 (1.0f)); 67 68 /* Choose k to scale x to the range [-1/4, 1/2]. */ 69 int32x4_t k 70 = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters), 71 v_s32 (0xff800000)); 72 uint32x4_t ku = vreinterpretq_u32_s32 (k); 73 74 /* Scale up to ensure that the scale factor is representable as normalised 75 fp32 number, and scale m down accordingly. */ 76 float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku)); 77 78 /* Scale x by exponent manipulation. */ 79 float32x4_t m_scale 80 = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku)); 81 m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s)); 82 83 /* Evaluate polynomial on the reduced interval. */ 84 float32x4_t p = eval_poly (m_scale, d); 85 86 /* The scale factor to be applied back at the end - by multiplying float(k) 87 by 2^-23 we get the unbiased exponent of k. */ 88 float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f)); 89 90 /* Apply the scaling back. */ 91 return vfmaq_f32 (p, scale_back, d->ln2); 92 } 93 94 #endif // MATH_V_LOG1PF_INLINE_H 95