1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision scalar cospi function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "mathlib.h"
9*f3087befSAndrew Turner #include "math_config.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner #include "poly_scalar_f64.h"
13*f3087befSAndrew Turner
14*f3087befSAndrew Turner /* Taylor series coefficents for sin(pi * x).
15*f3087befSAndrew Turner C2 coefficient (orginally ~=5.16771278) has been split into two parts:
16*f3087befSAndrew Turner C2_hi = 4, C2_lo = C2 - C2_hi (~=1.16771278)
17*f3087befSAndrew Turner This change in magnitude reduces floating point rounding errors.
18*f3087befSAndrew Turner C2_hi is then reintroduced after the polynomial approxmation. */
19*f3087befSAndrew Turner static const double poly[]
20*f3087befSAndrew Turner = { 0x1.921fb54442d184p1, -0x1.2aef39896f94bp0, 0x1.466bc6775ab16p1,
21*f3087befSAndrew Turner -0x1.32d2cce62dc33p-1, 0x1.507834891188ep-4, -0x1.e30750a28c88ep-8,
22*f3087befSAndrew Turner 0x1.e8f48308acda4p-12, -0x1.6fc0032b3c29fp-16, 0x1.af86ae521260bp-21,
23*f3087befSAndrew Turner -0x1.012a9870eeb7dp-25 };
24*f3087befSAndrew Turner
25*f3087befSAndrew Turner #define Shift 0x1.8p+52
26*f3087befSAndrew Turner
27*f3087befSAndrew Turner /* Approximation for scalar double-precision cospi(x).
28*f3087befSAndrew Turner Maximum error: 3.13 ULP:
29*f3087befSAndrew Turner cospi(0x1.160b129300112p-21) got 0x1.fffffffffd16bp-1
30*f3087befSAndrew Turner want 0x1.fffffffffd16ep-1. */
31*f3087befSAndrew Turner double
arm_math_cospi(double x)32*f3087befSAndrew Turner arm_math_cospi (double x)
33*f3087befSAndrew Turner {
34*f3087befSAndrew Turner if (isinf (x) || isnan (x))
35*f3087befSAndrew Turner return __math_invalid (x);
36*f3087befSAndrew Turner
37*f3087befSAndrew Turner double ax = asdouble (asuint64 (x) & ~0x8000000000000000);
38*f3087befSAndrew Turner
39*f3087befSAndrew Turner /* Edge cases for when cospif should be exactly 1. (Integers)
40*f3087befSAndrew Turner 0x1p53 is the limit for single precision to store any decimal places. */
41*f3087befSAndrew Turner if (ax >= 0x1p53)
42*f3087befSAndrew Turner return 1;
43*f3087befSAndrew Turner
44*f3087befSAndrew Turner /* If x is an integer, return +- 1, based upon if x is odd. */
45*f3087befSAndrew Turner uint64_t m = (uint64_t) ax;
46*f3087befSAndrew Turner if (m == ax)
47*f3087befSAndrew Turner return (m & 1) ? -1 : 1;
48*f3087befSAndrew Turner
49*f3087befSAndrew Turner /* For very small inputs, squaring r causes underflow.
50*f3087befSAndrew Turner Values below this threshold can be approximated via
51*f3087befSAndrew Turner cospi(x) ~= 1. */
52*f3087befSAndrew Turner if (ax < 0x1p-63)
53*f3087befSAndrew Turner return 1;
54*f3087befSAndrew Turner
55*f3087befSAndrew Turner /* Any non-integer values >= 0x1x51 will be int +0.5.
56*f3087befSAndrew Turner These values should return exactly 0. */
57*f3087befSAndrew Turner if (ax >= 0x1p51)
58*f3087befSAndrew Turner return 0;
59*f3087befSAndrew Turner
60*f3087befSAndrew Turner /* n = rint(|x|). */
61*f3087befSAndrew Turner double n = ax + Shift;
62*f3087befSAndrew Turner uint64_t sign = asuint64 (n) << 63;
63*f3087befSAndrew Turner n = n - Shift;
64*f3087befSAndrew Turner
65*f3087befSAndrew Turner /* We know that cospi(x) = sinpi(0.5 - x)
66*f3087befSAndrew Turner range reduction and offset into sinpi range -1/2 .. 1/2
67*f3087befSAndrew Turner r = 0.5 - |x - rint(x)|. */
68*f3087befSAndrew Turner double r = 0.5 - fabs (ax - n);
69*f3087befSAndrew Turner
70*f3087befSAndrew Turner /* y = sin(r). */
71*f3087befSAndrew Turner double r2 = r * r;
72*f3087befSAndrew Turner double y = horner_9_f64 (r2, poly);
73*f3087befSAndrew Turner y = y * r;
74*f3087befSAndrew Turner
75*f3087befSAndrew Turner /* Reintroduce C2_hi. */
76*f3087befSAndrew Turner y = fma (-4 * r2, r, y);
77*f3087befSAndrew Turner
78*f3087befSAndrew Turner /* As all values are reduced to -1/2 .. 1/2, the result of cos(x) always be
79*f3087befSAndrew Turner positive, therefore, the sign must be introduced based upon if x rounds to
80*f3087befSAndrew Turner odd or even. */
81*f3087befSAndrew Turner return asdouble (asuint64 (y) ^ sign);
82*f3087befSAndrew Turner }
83*f3087befSAndrew Turner
84*f3087befSAndrew Turner #if WANT_EXPERIMENTAL_MATH
85*f3087befSAndrew Turner double
cospi(double x)86*f3087befSAndrew Turner cospi (double x)
87*f3087befSAndrew Turner {
88*f3087befSAndrew Turner return arm_math_cospi (x);
89*f3087befSAndrew Turner }
90*f3087befSAndrew Turner #endif
91*f3087befSAndrew Turner
92*f3087befSAndrew Turner #if WANT_TRIGPI_TESTS
93*f3087befSAndrew Turner TEST_ULP (arm_math_cospi, 2.63)
94*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_cospi, 0, 0x1p-63, 5000)
95*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_cospi, 0x1p-63, 0.5, 10000)
96*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_cospi, 0.5, 0x1p51f, 10000)
97*f3087befSAndrew Turner TEST_SYM_INTERVAL (arm_math_cospi, 0x1p51f, inf, 10000)
98*f3087befSAndrew Turner #endif
99