This repository has been archived by the owner on Oct 12, 2022. It is now read-only.
-
-
Notifications
You must be signed in to change notification settings - Fork 426
/
math.d
166 lines (146 loc) · 4.65 KB
/
math.d
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
// Written in the D programming language.
/**
* Builtin mathematical intrinsics
*
* Source: $(DRUNTIMESRC core/_math.d)
* Macros:
* TABLE_SV = <table border="1" cellpadding="4" cellspacing="0">
* <caption>Special Values</caption>
* $0</table>
*
* NAN = $(RED NAN)
* SUP = <span style="vertical-align:super;font-size:smaller">$0</span>
* POWER = $1<sup>$2</sup>
* PLUSMN = ±
* INFIN = ∞
* PLUSMNINF = ±∞
* LT = <
* GT = >
*
* Copyright: Copyright Digital Mars 2000 - 2011.
* License: $(HTTP www.boost.org/LICENSE_1_0.txt, Boost License 1.0).
* Authors: $(HTTP digitalmars.com, Walter Bright),
* Don Clugston
*/
module core.math;
public:
@nogc:
/***********************************
* Returns cosine of x. x is in radians.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH cos(x)) $(TH invalid?))
* $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes) )
* $(TR $(TD $(PLUSMN)$(INFIN)) $(TD $(NAN)) $(TD yes) )
* )
* Bugs:
* Results are undefined if |x| >= $(POWER 2,64).
*/
real cos(real x) @safe pure nothrow; /* intrinsic */
/***********************************
* Returns sine of x. x is in radians.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH sin(x)) $(TH invalid?))
* $(TR $(TD $(NAN)) $(TD $(NAN)) $(TD yes))
* $(TR $(TD $(PLUSMN)0.0) $(TD $(PLUSMN)0.0) $(TD no))
* $(TR $(TD $(PLUSMNINF)) $(TD $(NAN)) $(TD yes))
* )
* Bugs:
* Results are undefined if |x| >= $(POWER 2,64).
*/
real sin(real x) @safe pure nothrow; /* intrinsic */
/*****************************************
* Returns x rounded to a long value using the current rounding mode.
* If the integer value of x is
* greater than long.max, the result is
* indeterminate.
*/
long rndtol(real x) @safe pure nothrow; /* intrinsic */
/*****************************************
* Returns x rounded to a long value using the FE_TONEAREST rounding mode.
* If the integer value of x is
* greater than long.max, the result is
* indeterminate.
*/
extern (C) real rndtonl(real x);
/***************************************
* Compute square root of x.
*
* $(TABLE_SV
* $(TR $(TH x) $(TH sqrt(x)) $(TH invalid?))
* $(TR $(TD -0.0) $(TD -0.0) $(TD no))
* $(TR $(TD $(LT)0.0) $(TD $(NAN)) $(TD yes))
* $(TR $(TD +$(INFIN)) $(TD +$(INFIN)) $(TD no))
* )
*/
@safe pure nothrow
{
float sqrt(float x); /* intrinsic */
double sqrt(double x); /* intrinsic */ /// ditto
real sqrt(real x); /* intrinsic */ /// ditto
}
/*******************************************
* Compute n * 2$(SUPERSCRIPT exp)
* References: frexp
*/
real ldexp(real n, int exp) @safe pure nothrow; /* intrinsic */
unittest {
static if (real.mant_dig == 113)
{
assert(ldexp(1, -16384) == 0x1p-16384L);
assert(ldexp(1, -16382) == 0x1p-16382L);
}
else static if (real.mant_dig == 106)
{
assert(ldexp(1, 1023) == 0x1p1023L);
assert(ldexp(1, -1022) == 0x1p-1022L);
assert(ldexp(1, -1021) == 0x1p-1021L);
}
else static if (real.mant_dig == 64)
{
assert(ldexp(1, -16384) == 0x1p-16384L);
assert(ldexp(1, -16382) == 0x1p-16382L);
}
else static if (real.mant_dig == 53)
{
assert(ldexp(1, 1023) == 0x1p1023L);
assert(ldexp(1, -1022) == 0x1p-1022L);
assert(ldexp(1, -1021) == 0x1p-1021L);
}
else
assert(false, "Only 128bit, 80bit and 64bit reals expected here");
}
/*******************************
* Returns |x|
*
* $(TABLE_SV
* $(TR $(TH x) $(TH fabs(x)))
* $(TR $(TD $(PLUSMN)0.0) $(TD +0.0) )
* $(TR $(TD $(PLUSMN)$(INFIN)) $(TD +$(INFIN)) )
* )
*/
real fabs(real x) @safe pure nothrow; /* intrinsic */
/**********************************
* Rounds x to the nearest integer value, using the current rounding
* mode.
* If the return value is not equal to x, the FE_INEXACT
* exception is raised.
* $(B nearbyint) performs
* the same operation, but does not set the FE_INEXACT exception.
*/
real rint(real x) @safe pure nothrow; /* intrinsic */
/***********************************
* Building block functions, they
* translate to a single x87 instruction.
*/
real yl2x(real x, real y) @safe pure nothrow; // y * log2(x)
real yl2xp1(real x, real y) @safe pure nothrow; // y * log2(x + 1)
unittest
{
version (INLINE_YL2X)
{
assert(yl2x(1024, 1) == 10);
assert(yl2xp1(1023, 1) == 10);
}
}