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
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
This file describe the framework for testing MPC functions.
===========================================================
Functionality
-------------
The test suite usually perform 3 kinds of tests for a given function:
1. it verifies that the result returned by the function matches with
precomputed data written in a '.dat' file,
2. it checks that the function computes coherent results in low and high
precision,
3. optionally, it performs additional checks specific to the function under
test.
The test suite provides support for the first two items. This ensures that all
function tests using the framework execute a set of verifications in a
systematic way.
How to add a test for a new function?
-------------------------------------
1. The test framework does support only functions with exactly one output
parameter. An ad hoc solution must be used for functions with other
prototypes. For an adaptation to a function with two output parameters, see
tsin_cos.c file.
If you want to use the system checking against data sets or the random tests,
you will need to describe the function prototype in a file (procedure detailed
in 2.) and to define several macros (detailed in 3.). Then, you can call the
data_check_template() function for checking against a data set (see 4.) or the
tgeneric_template() function for random values (see 5.).
In both cases, the 'mpc-test.h' header file must be included.
2. First write a description of the function interface describing, in this
order, the name of the function, the return value, the set of input
parameters, and the set of output parameters.
For instance, the description file of the mpc_add function (excerpt of
add.dsc) is displayed below:
# Description file of the function
NAME:
mpc_add
RETURN:
mpc_inex
OUTPUT:
mpc_ptr
INPUT:
mpc_srcptr
mpc_srcptr
mpc_rnd_t
The integer value returned by MPC functions is usually the inexact flag. In
that case, the return value type must be denoted as 'mpc_inex'. Other types
are generally the C type that appears in the function prototype.
The easiest way is to adapt a description file of a function with the same
prototype.
3. Second, define at least the MPC_FUNCTION_CALL macro.
Because the framework is common to all MPC function (or so), the
data_check_template() and the tgeneric_template() functions are written in a
generic manner. Both function are defined in its own file that the user must
include. They call the function under test through several macros
defined by the user before the inclusion of the corresponding file.
The definition of each macro specifies the name of the function under test and
the parameters in use along with their type.
Four macros can be of interest:
In all cases, the macro MPC_FUNCTION_CALL must
MPC_FUNCTION_CALL: mandatory, it describes a simple call to the function,
MPC_FUNCTION_CALL_SYMMETRIC: optional, it describes a function call with a
switch of two parameters, it is useful for automatically checking the
consistency of symmetric functions, i. e. f(a,b) == f(b,a),
MPC_FUNCTION_CALL_REUSE_OP1
MPC_FUNCTION_CALL_REUSE_OP2
MPC_FUNCTION_CALL_REUSE_OP3
the last three macros can be used to check that the result is not affected by
the reuse of an input variable as output parameter
Here is how these macros are defined for the mpc_add function:
#define MPC_FUNCTION_CALL \
P[0].mpc_inex = mpc_add (P[1].mpc, P[2].mpc, P[3].mpc, P[4].mpc_rnd)
#define MPC_FUNCTION_CALL_SYMMETRIC \
P[0].mpc_inex = mpc_add (P[1].mpc, P[3].mpc, P[2].mpc, P[4].mpc_rnd)
#define MPC_FUNCTION_CALL_REUSE_OP1 \
P[0].mpc_inex = mpc_add (P[1].mpc, P[1].mpc, P[3].mpc, P[4].mpc_rnd)
#define MPC_FUNCTION_CALL_REUSE_OP2 \
P[0].mpc_inex = mpc_add (P[1].mpc, P[2].mpc, P[1].mpc, P[4].mpc_rnd)
4. For precomputed values.
The test framework can check the result of the function on given parameters
against a reference value written in a file.
The file "data_check.tpl" must be included after the definition of
MPC_FUNCTION_CALL macros and the data_check_template() function can be used in
the code.
The first parameter of data_check_template() is the name of the description
file of the function and the second is the name of the data file.
As an example, here is the function call for testing mpc_add():
data_check_template ("add.dsc", "add.dat");
The data file contains a sequence of input and output values in the order
given by the function prototype. So, output values are usually first, as it is
the case for most MPC functions.
Here is an excerpt of 'add.dat' (the data set for mpc_add()):
# special values (following ISO C99 standard)
0 0 53 -inf 53 -inf 53 -inf 53 -inf 53 -inf 53 -inf N Z
# pure real argument
+ 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-105 53 -0 N N
The ternary value associated with an mpfr_t result is described as:
"?" it should not be checked
"+" if the computed result is greater than the exact mathematical result
"0" if the computed result is exactly the mathematical result
"-" if the computed result is less than the exact mathematical result
The mpc_inex value is a pair of ternary values.
The values for mpfr_t and mpc_t parameters come along with their
precision. Use prefixes "0b" for values in base two, "0x" for values in base
sixteen, no prefix for value in base ten. In all bases, "nan" is NaN, "inf"
is infinity; the sign of infinity and zero is checked if it is specified in
the data file, otherwise it is ignored.
The MPFR rounding mode is denoted by
"N" for rounding to nearest
"Z" for rounding towards zero
"U" for rounding towards plus infinity
"D" for rounding towards minus infinity
The MPC rounding mode is a pair of MPFR rounding mode.
Thus, the following line from 'add.dat'
0 0 53 -inf 53 -inf 53 -inf 53 -inf 53 -inf 53 -inf N Z
indicates that
(-inf +i * -inf) + (-inf +i * -inf)
should be exactly
-inf +i * -inf
in 53-bit precision with rounding to nearest for the real part
and rounding toward minus infinity for the imaginary part.
The line
+ 0 53 0x10000000000001p-52 53 -0 53 +1 53 -0 53 0x10000000000001p-105 53 -0 N N
indicates that
(+1 +i * -0) + (0x10000000000001p-105 +i * -0)
is
0x10000000000001p-52 +i * -0
in 53-bit precision when rounding both part to nearest, the real part is
actually an overestimation of the exact result (ternary value: +), while the
imaginary part is exact.
5. Test with random values
The framework also provides generic tests with random values.
The file "tgeneric.tpl" must be included after the definition of
MPC_FUNCTION_CALL macros and the tgeneric_template() function can be used in
the code.
The first parameter of tgeneric_template() is the description file of the
function under test. The second and third parameter are the minimum and
maximum precision for input and output parameters. The fourth is the iteration
step in the precision range. The last parameter is the maximum
exponent. Usually, the range of random parameter has to be restricted for a
reasonable testing time.
As an example, here is the function call for testing mpc_add():
tgeneric_template ("add.dsc", 2, 1024, 7, 128);
|
