OpenCores
URL https://opencores.org/ocsvn/forwardcom/forwardcom/trunk

Subversion Repositories forwardcom

[/] [forwardcom/] [libraries/] [sincosf.as] - Blame information for rev 151

Go to most recent revision | Details | Compare with Previous | View Log

Line No. Rev Author Line
1 111 Agner
/*********************************  sincosf.as  *******************************
2
* Author:        Agner Fog
3
* date created:  2020-04-29
4
* Last modified: 2021-04-25
5
* Version:       1.11
6
* Project:       ForwardCom library math.li
7
* Description:   sin, cos, and tan functions. Calculate in radians, single precision
8
*                The argument x can be a scalar or a vector
9
*                The return value will be a vector with the same length
10
* C declaration: float sin(float x);
11
* C declaration: float cos(float x);
12
* C declaration: float tan(float x);
13
* C declaration: struct {float s; float c;} sincos(float x);
14
*
15
* This code is adapted from C++ vector class library www.github.com/vectorclass
16
* Copyright 2020-2021 GNU General Public License http://www.gnu.org/licenses
17
*****************************************************************************/
18
 
19
 
20
// define constants
21
% M_2_PI = 0.636619772367581343076       // 2./pi
22
 
23
% P0sinf = -1.6666654611E-1
24
% P1sinf = 8.3321608736E-3
25
% P2sinf = -1.9515295891E-4
26
% P0cosf = 4.166664568298827E-2
27
% P1cosf = -1.388731625493765E-3
28
% P2cosf = 2.443315711809948E-5
29
 
30
% DP1F = 0.78515625 * 2.
31
% DP2F = 2.4187564849853515625E-4 * 2.
32
% DP3F = 3.77489497744594108E-8 * 2.
33
 
34
 
35
code section execute align = 4
36
 
37
public _sinf:    function, reguse = 0, 0x1BF
38
public _cosf:    function, reguse = 0, 0x1BF
39
public _sincosf: function, reguse = 0, 0x1BF
40
public _tanf:    function, reguse = 0, 0x1BF
41
 
42
// common entry for sin and sincos functions
43
_sinf function
44
_sincosf:
45
 
46
/* registers:
47
  v0 = x
48
  v1 = abs(x)
49
  v1 = quadrant
50
  v2 = x^2
51
  v3 = x^3
52
  v4 = x^4
53
  v5 = temp
54
  v5 = sin
55
  v6 = unused (vacant flag for calling function)
56
  v7 = cos
57
  v8 = abs(x) reduced modulo pi/2
58
*/
59
 
60
// Find quadrant:
61
//      0 -   pi/4 => 0
62
//   pi/4 - 3*pi/4 => 1
63
// 3*pi/4 - 5*pi/4 => 2
64
// 5*pi/4 - 7*pi/4 => 3
65
// 7*pi/4 - 8*pi/4 => 4
66
 
67
// reduce modulo pi/2, with extended precision
68
//nop
69
float v1 = clear_bit(v0, 31)                    // abs(x)
70
float v5 = v1 * M_2_PI
71
float v5 = round(v5, 0)   // round to integer
72
 
73
// x = ((xa - y * DP1) - y * DP2) - y * DP3;
74
float v8 = v5 * (-DP1F) + v1
75
float v8 = v5 * (-DP2F) + v8
76
float v8 = v5 * (-DP3F) + v8
77
 
78
float v3 = !(v5 > ((1 << 22) + 0.0))            // check for loss of precision and overflow, but not NAN
79
float v1 = v5 + ((1 << 23) + 0.0)               // add magic number 2^23 to get integer into lowest bit
80
float v8 = v3 ? v8 : 0                          // zero if out of range. result will be -1, 0, or 1
81
 
82
// Taylor expansion of sin and cos, valid for -pi/4 <= x <= pi/4
83
// s = polynomial_2(x^2, P0sinf, P1sinf, P2sinf) * (x*x^2) + x;
84
 
85
float v2 = v8 * v8        // x^2
86
float v3 = v8 * v2        // x^3
87
float v4 = v2 * v2        // x^4
88
float v5 = replace(v8, P0sinf)                   // broadcast to same length as x
89
float v5 = v2 * P1sinf + v5
90
float v5 = v4 * P2sinf + v5
91
float v5 = v5 * v3 + v8                          // sin
92
 
93
// c = polynomial_2(x2, P0cosf, P1cosf, P2cosf) * (x2*x2) + nmul_add(0.5f, x2, 1.0f);
94
float v7 = replace(v8, P0cosf)                   // broadcast to same length as x
95
float v7 = v2 * P1cosf + v7
96
float v7 = v4 * P2cosf + v7
97
float v3 = replace(v8, 1.0)
98
float v3 = v2 * (-0.5) + v3                       // 1 - 0.5*x^2
99
float v7 = v7 * v4 + v3                           // cos
100
 
101
// swap sin and cos if odd quadrant
102
float v3 = v1 ? v7 : v5        // sin
103
float v4 = v1 ? v5 : v7        // cos
104
 
105
// get sign of sin
106
int32  v5 = v1 << 30            // get bit 1 into sign bit, x modulo pi/2 = 2 or 3
107
int32  v5 ^= v0                 // toggle with sign of original x
108
int32  v5 = and(v5, 1 << 31)    // isolate sign bit
109
float  v0 = v3 ^ v5             // apply sign bit to sin
110
 
111
// get sign of cos
112
int32  v1 = v1 + 1              // change sign when x modulo pi/2 = 1 or 2
113
int32  v1 = v1 << 30            // get bit 1 into sign bit
114
int32  v1 = and(v1, 1 << 31)    // isolate sign bit
115
float  v1 = v4 ^ v1             // apply sign bit to cos
116
 
117
// return sin in v0, cos in v1
118
return
119
_sinf end
120
 
121
// cosine function
122
_cosf function
123
call _sincosf
124
float v0 = v1                                   // cos is in v1
125
return
126
_cosf end
127
 
128
// tangent function
129
_tanf function
130
call _sincosf
131
float v0 = v0 / v1                              // tan(x) = sin(x)/cos(x)
132
return
133
_tanf end
134
 
135
code end

powered by: WebSVN 2.1.0

© copyright 1999-2024 OpenCores.org, equivalent to Oliscience, all rights reserved. OpenCores®, registered trademark.