1 /*
2 * Single-precision vector log(1+x) function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "v_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #if V_SUPPORTED
13
14 #define AbsMask 0x7fffffff
15 #define TinyBound 0x340 /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */
16 #define MinusOne 0xbf800000
17 #define Ln2 (0x1.62e43p-1f)
18 #define Four 0x40800000
19 #define ThreeQuarters v_u32 (0x3f400000)
20
21 #define C(i) v_f32 (__log1pf_data.coeffs[i])
22
23 static inline v_f32_t
eval_poly(v_f32_t m)24 eval_poly (v_f32_t m)
25 {
26 #ifdef V_LOG1PF_1U3
27
28 /* Approximate log(1+m) on [-0.25, 0.5] using Horner scheme. */
29 v_f32_t p = v_fma_f32 (C (8), m, C (7));
30 p = v_fma_f32 (p, m, C (6));
31 p = v_fma_f32 (p, m, C (5));
32 p = v_fma_f32 (p, m, C (4));
33 p = v_fma_f32 (p, m, C (3));
34 p = v_fma_f32 (p, m, C (2));
35 p = v_fma_f32 (p, m, C (1));
36 p = v_fma_f32 (p, m, C (0));
37 return v_fma_f32 (m, m * p, m);
38
39 #elif defined(V_LOG1PF_2U5)
40
41 /* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */
42 v_f32_t p_12 = v_fma_f32 (m, C (1), C (0));
43 v_f32_t p_34 = v_fma_f32 (m, C (3), C (2));
44 v_f32_t p_56 = v_fma_f32 (m, C (5), C (4));
45 v_f32_t p_78 = v_fma_f32 (m, C (7), C (6));
46
47 v_f32_t m2 = m * m;
48 v_f32_t p_02 = v_fma_f32 (m2, p_12, m);
49 v_f32_t p_36 = v_fma_f32 (m2, p_56, p_34);
50 v_f32_t p_79 = v_fma_f32 (m2, C (8), p_78);
51
52 v_f32_t m4 = m2 * m2;
53 v_f32_t p_06 = v_fma_f32 (m4, p_36, p_02);
54
55 return v_fma_f32 (m4, m4 * p_79, p_06);
56
57 #else
58 #error No precision specified for v_log1pf
59 #endif
60 }
61
62 static inline float
handle_special(float x)63 handle_special (float x)
64 {
65 uint32_t ix = asuint (x);
66 uint32_t ia = ix & AbsMask;
67 if (ix == 0xff800000 || ia > 0x7f800000 || ix > 0xbf800000)
68 {
69 /* x == -Inf => log1pf(x) = NaN.
70 x < -1.0 => log1pf(x) = NaN.
71 x == +/-NaN => log1pf(x) = NaN. */
72 #if WANT_SIMD_EXCEPT
73 return __math_invalidf (asfloat (ia));
74 #else
75 return NAN;
76 #endif
77 }
78 if (ix == 0xbf800000)
79 {
80 /* x == -1.0 => log1pf(x) = -Inf. */
81 #if WANT_SIMD_EXCEPT
82 return __math_divzerof (ix);
83 #else
84 return -INFINITY;
85 #endif
86 }
87 /* |x| < TinyBound => log1p(x) = x. */
88 return x;
89 }
90
91 /* Vector log1pf approximation using polynomial on reduced interval. Accuracy is
92 the same as for the scalar algorithm, i.e. worst-case error when using Estrin
93 is roughly 2.02 ULP:
94 log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */
V_NAME(log1pf)95 VPCS_ATTR v_f32_t V_NAME (log1pf) (v_f32_t x)
96 {
97 v_u32_t ix = v_as_u32_f32 (x);
98 v_u32_t ia12 = (ix >> 20) & v_u32 (0x7f8);
99 v_u32_t special_cases
100 = v_cond_u32 (ia12 - v_u32 (TinyBound) >= (0x7f8 - TinyBound))
101 | v_cond_u32 (ix >= MinusOne);
102 v_f32_t special_arg = x;
103
104 #if WANT_SIMD_EXCEPT
105 if (unlikely (v_any_u32 (special_cases)))
106 /* Side-step special lanes so fenv exceptions are not triggered
107 inadvertently. */
108 x = v_sel_f32 (special_cases, v_f32 (1), x);
109 #endif
110
111 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
112 is in [-0.25, 0.5]):
113 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
114
115 We approximate log1p(m) with a polynomial, then scale by
116 k*log(2). Instead of doing this directly, we use an intermediate
117 scale factor s = 4*k*log(2) to ensure the scale is representable
118 as a normalised fp32 number. */
119
120 v_f32_t m = x + v_f32 (1.0f);
121
122 /* Choose k to scale x to the range [-1/4, 1/2]. */
123 v_s32_t k = (v_as_s32_f32 (m) - ThreeQuarters) & v_u32 (0xff800000);
124
125 /* Scale x by exponent manipulation. */
126 v_f32_t m_scale = v_as_f32_u32 (v_as_u32_f32 (x) - v_as_u32_s32 (k));
127
128 /* Scale up to ensure that the scale factor is representable as normalised
129 fp32 number, and scale m down accordingly. */
130 v_f32_t s = v_as_f32_u32 (v_u32 (Four) - k);
131 m_scale = m_scale + v_fma_f32 (v_f32 (0.25f), s, v_f32 (-1.0f));
132
133 /* Evaluate polynomial on the reduced interval. */
134 v_f32_t p = eval_poly (m_scale);
135
136 /* The scale factor to be applied back at the end - by multiplying float(k)
137 by 2^-23 we get the unbiased exponent of k. */
138 v_f32_t scale_back = v_to_f32_s32 (k) * v_f32 (0x1p-23f);
139
140 /* Apply the scaling back. */
141 v_f32_t y = v_fma_f32 (scale_back, v_f32 (Ln2), p);
142
143 if (unlikely (v_any_u32 (special_cases)))
144 return v_call_f32 (handle_special, special_arg, y, special_cases);
145 return y;
146 }
147 VPCS_ALIAS
148
149 PL_SIG (V, F, 1, log1p, -0.9, 10.0)
150 PL_TEST_ULP (V_NAME (log1pf), 1.53)
151 PL_TEST_EXPECT_FENV (V_NAME (log1pf), WANT_SIMD_EXCEPT)
152 PL_TEST_INTERVAL (V_NAME (log1pf), -10.0, 10.0, 10000)
153 PL_TEST_INTERVAL (V_NAME (log1pf), 0.0, 0x1p-23, 30000)
154 PL_TEST_INTERVAL (V_NAME (log1pf), 0x1p-23, 0.001, 50000)
155 PL_TEST_INTERVAL (V_NAME (log1pf), 0.001, 1.0, 50000)
156 PL_TEST_INTERVAL (V_NAME (log1pf), 0.0, -0x1p-23, 30000)
157 PL_TEST_INTERVAL (V_NAME (log1pf), -0x1p-23, -0.001, 30000)
158 PL_TEST_INTERVAL (V_NAME (log1pf), -0.001, -1.0, 50000)
159 PL_TEST_INTERVAL (V_NAME (log1pf), -1.0, inf, 1000)
160 #endif
161