1 /*
2  * Single-precision scalar sinpi function.
3  *
4  * Copyright (c) 2023, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6  */
7 
8 #include "mathlib.h"
9 #include "math_config.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12 
13 /* Taylor series coefficents for sin(pi * x).  */
14 #define C0 0x1.921fb6p1f
15 #define C1 -0x1.4abbcep2f
16 #define C2 0x1.466bc6p1f
17 #define C3 -0x1.32d2ccp-1f
18 #define C4 0x1.50783p-4f
19 #define C5 -0x1.e30750p-8f
20 
21 #define Shift 0x1.0p+23f
22 
23 /* Approximation for scalar single-precision sinpi(x) - sinpif.
24    Maximum error: 2.48 ULP:
25    sinpif(0x1.d062b6p-2) got 0x1.fa8c06p-1
26 			want 0x1.fa8c02p-1.  */
27 float
28 sinpif (float x)
29 {
30   if (isinf (x))
31     return __math_invalidf (x);
32 
33   float r = asfloat (asuint (x) & ~0x80000000);
34   uint32_t sign = asuint (x) & 0x80000000;
35 
36   /* Edge cases for when sinpif should be exactly 0. (Integers)
37      0x1p23 is the limit for single precision to store any decimal places.  */
38   if (r >= 0x1p23f)
39     return 0;
40 
41   int32_t m = roundf (r);
42   if (m == r)
43     return 0;
44 
45   /* For very small inputs, squaring r causes underflow.
46      Values below this threshold can be approximated via sinpi(x) ~= pi*x.  */
47   if (r < 0x1p-31f)
48     return C0 * x;
49 
50   /* Any non-integer values >= 0x1p22f will be int + 0.5.
51      These values should return exactly 1 or -1.  */
52   if (r >= 0x1p22f)
53     {
54       uint32_t iy = ((m & 1) << 31) ^ asuint (-1.0f);
55       return asfloat (sign ^ iy);
56     }
57 
58   /* n = rint(|x|).  */
59   float n = r + Shift;
60   sign ^= (asuint (n) << 31);
61   n = n - Shift;
62 
63   /* r = |x| - n (range reduction into -1/2 .. 1/2).  */
64   r = r - n;
65 
66   /* y = sin(pi * r).  */
67   float r2 = r * r;
68   float y = fmaf (C5, r2, C4);
69   y = fmaf (y, r2, C3);
70   y = fmaf (y, r2, C2);
71   y = fmaf (y, r2, C1);
72   y = fmaf (y, r2, C0);
73 
74   /* Copy sign of x to sin(|x|).  */
75   return asfloat (asuint (y * r) ^ sign);
76 }
77 
78 PL_SIG (S, F, 1, sinpi, -0.9, 0.9)
79 PL_TEST_ULP (sinpif, 1.99)
80 PL_TEST_SYM_INTERVAL (sinpif, 0, 0x1p-31, 5000)
81 PL_TEST_SYM_INTERVAL (sinpif, 0x1p-31, 0.5, 10000)
82 PL_TEST_SYM_INTERVAL (sinpif, 0.5, 0x1p22f, 10000)
83 PL_TEST_SYM_INTERVAL (sinpif, 0x1p22f, inf, 10000)
84