xref: /freebsd/contrib/arm-optimized-routines/pl/math/v_log1p_2u5.c (revision 7ef62cebc2f965b0f640263e179276928885e33d)
1 /*
2  * Double-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 "estrin.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12 
13 #if V_SUPPORTED
14 
15 #define Ln2Hi v_f64 (0x1.62e42fefa3800p-1)
16 #define Ln2Lo v_f64 (0x1.ef35793c76730p-45)
17 #define HfRt2Top 0x3fe6a09e00000000 /* top32(asuint64(sqrt(2)/2)) << 32.  */
18 #define OneMHfRt2Top                                                           \
19   0x00095f6200000000 /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2)))      \
20 			<< 32.  */
21 #define OneTop12 0x3ff
22 #define BottomMask 0xffffffff
23 #define AbsMask 0x7fffffffffffffff
24 #define C(i) v_f64 (__log1p_data.coeffs[i])
25 
26 static inline v_f64_t
27 eval_poly (v_f64_t f)
28 {
29   v_f64_t f2 = f * f;
30   v_f64_t f4 = f2 * f2;
31   v_f64_t f8 = f4 * f4;
32   return ESTRIN_18 (f, f2, f4, f8, f8 * f8, C);
33 }
34 
35 VPCS_ATTR
36 NOINLINE static v_f64_t
37 specialcase (v_f64_t x, v_f64_t y, v_u64_t special)
38 {
39   return v_call_f64 (log1p, x, y, special);
40 }
41 
42 /* Vector log1p approximation using polynomial on reduced interval. Routine is a
43    modification of the algorithm used in scalar log1p, with no shortcut for k=0
44    and no narrowing for f and k. Maximum observed error is 2.46 ULP:
45     __v_log1p(0x1.654a1307242a4p+11) got 0x1.fd5565fb590f4p+2
46 				    want 0x1.fd5565fb590f6p+2 .  */
47 VPCS_ATTR v_f64_t V_NAME (log1p) (v_f64_t x)
48 {
49   v_u64_t ix = v_as_u64_f64 (x);
50   v_u64_t ia = ix & AbsMask;
51   v_u64_t special
52     = v_cond_u64 ((ia >= v_u64 (0x7ff0000000000000))
53 		  | (ix >= 0xbff0000000000000) | (ix == 0x8000000000000000));
54 
55 #if WANT_SIMD_EXCEPT
56   if (unlikely (v_any_u64 (special)))
57     x = v_sel_f64 (special, v_f64 (0), x);
58 #endif
59 
60   /* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f
61 			   is in [sqrt(2)/2, sqrt(2)]):
62      log1p(x) = k*log(2) + log1p(f).
63 
64      f may not be representable exactly, so we need a correction term:
65      let m = round(1 + x), c = (1 + x) - m.
66      c << m: at very small x, log1p(x) ~ x, hence:
67      log(1+x) - log(m) ~ c/m.
68 
69      We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m.  */
70 
71   /* Obtain correctly scaled k by manipulation in the exponent.
72      The scalar algorithm casts down to 32-bit at this point to calculate k and
73      u_red. We stay in double-width to obtain f and k, using the same constants
74      as the scalar algorithm but shifted left by 32.  */
75   v_f64_t m = x + 1;
76   v_u64_t mi = v_as_u64_f64 (m);
77   v_u64_t u = mi + OneMHfRt2Top;
78 
79   v_s64_t ki = v_as_s64_u64 (u >> 52) - OneTop12;
80   v_f64_t k = v_to_f64_s64 (ki);
81 
82   /* Reduce x to f in [sqrt(2)/2, sqrt(2)].  */
83   v_u64_t utop = (u & 0x000fffff00000000) + HfRt2Top;
84   v_u64_t u_red = utop | (mi & BottomMask);
85   v_f64_t f = v_as_f64_u64 (u_red) - 1;
86 
87   /* Correction term c/m.  */
88   v_f64_t cm = (x - (m - 1)) / m;
89 
90   /* Approximate log1p(x) on the reduced input using a polynomial. Because
91    log1p(0)=0 we choose an approximation of the form:
92       x + C0*x^2 + C1*x^3 + C2x^4 + ...
93    Hence approximation has the form f + f^2 * P(f)
94       where P(x) = C0 + C1*x + C2x^2 + ...
95    Assembling this all correctly is dealt with at the final step.  */
96   v_f64_t p = eval_poly (f);
97 
98   v_f64_t ylo = v_fma_f64 (k, Ln2Lo, cm);
99   v_f64_t yhi = v_fma_f64 (k, Ln2Hi, f);
100   v_f64_t y = v_fma_f64 (f * f, p, ylo + yhi);
101 
102   if (unlikely (v_any_u64 (special)))
103     return specialcase (v_as_f64_u64 (ix), y, special);
104 
105   return y;
106 }
107 VPCS_ALIAS
108 
109 PL_SIG (V, D, 1, log1p, -0.9, 10.0)
110 PL_TEST_ULP (V_NAME (log1p), 1.97)
111 PL_TEST_EXPECT_FENV (V_NAME (log1p), WANT_SIMD_EXCEPT)
112 PL_TEST_INTERVAL (V_NAME (log1p), -10.0, 10.0, 10000)
113 PL_TEST_INTERVAL (V_NAME (log1p), 0.0, 0x1p-23, 50000)
114 PL_TEST_INTERVAL (V_NAME (log1p), 0x1p-23, 0.001, 50000)
115 PL_TEST_INTERVAL (V_NAME (log1p), 0.001, 1.0, 50000)
116 PL_TEST_INTERVAL (V_NAME (log1p), 0.0, -0x1p-23, 50000)
117 PL_TEST_INTERVAL (V_NAME (log1p), -0x1p-23, -0.001, 50000)
118 PL_TEST_INTERVAL (V_NAME (log1p), -0.001, -1.0, 50000)
119 PL_TEST_INTERVAL (V_NAME (log1p), -1.0, inf, 5000)
120 #endif
121