我正在努力弄清楚如何最好地为科学和/或数学函数编写单元测试。我搜索了GNU C库的源代码，用于sin()和cos()函数的单元测试，并且遇到了atest-sincos.c源文件，如下所示。 （可以找到here）
有人可以引导我浏览此文件并提供一个粗略的想法这里正在测试的内容吗？我看到看起来非常像用于数值求解微分方程的Runge-Kutta算法，也可能与列表值进行比较，但我不太确定。这里的任何指导都是非常受欢迎的。
/* Copyright (C) 1997-2016 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Geoffrey Keating <Geoff.Keating@anu.edu.au>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <stdio.h>
#include <math.h>
#include <gmp.h>
#include <string.h>
#include <limits.h>
#include <assert.h>
#define PRINT_ERRORS 0
#define N 0
#define N2 20
#define FRAC (32 * 4)
#define mpbpl (CHAR_BIT * sizeof (mp_limb_t))
#define SZ (FRAC / mpbpl + 1)
typedef mp_limb_t mp1[SZ], mp2[SZ * 2];
/* These strings have exactly 100 hex digits in them. */
static const char sin1[101] =
"d76aa47848677020c6e9e909c50f3c3289e511132f518b4def"
"b6ca5fd6c649bdfb0bd9ff1edcd4577655b5826a3d3b50c264";
static const char cos1[101] =
"8a51407da8345c91c2466d976871bd29a2373a894f96c3b7f2"
"300240b760e6fa96a94430a52d0e9e43f3450e3b8ff99bc934";
static const char hexdig[] = "0123456789abcdef";
static void
print_mpn_hex (const mp_limb_t *x, unsigned size)
{
char value[size + 1];
unsigned i;
const unsigned final = (size * 4 > SZ * mpbpl) ? SZ * mpbpl / 4 : size;
memset (value, '0', size);
for (i = 0; i < final ; i++)
value[size-1-i] = hexdig[x[i * 4 / mpbpl] >> (i * 4) % mpbpl & 0xf];
value[size] = '\0';
fputs (value, stdout);
}
static void
sincosx_mpn (mp1 si, mp1 co, mp1 xx, mp1 ix)
{
int i;
mp2 s[4], c[4];
mp1 tmp, x;
if (ix == NULL)
{
memset (si, 0, sizeof (mp1));
memset (co, 0, sizeof (mp1));
co[SZ-1] = 1;
memcpy (x, xx, sizeof (mp1));
}
else
mpn_sub_n (x, xx, ix, SZ);
for (i = 0; i < 1 << N; i++)
{
#define add_shift_mulh(d,x,s1,s2,sh,n) \
do { \
if (s2 != NULL) { \
if (sh > 0) { \
assert (sh < mpbpl); \
mpn_lshift (tmp, s1, SZ, sh); \
if (n) \
mpn_sub_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \
else \
mpn_add_n (tmp,tmp,s2+FRAC/mpbpl,SZ); \
} else { \
if (n) \
mpn_sub_n (tmp,s1,s2+FRAC/mpbpl,SZ); \
else \
mpn_add_n (tmp,s1,s2+FRAC/mpbpl,SZ); \
} \
mpn_mul_n(d,tmp,x,SZ); \
} else \
mpn_mul_n(d,s1,x,SZ); \
assert(N+sh < mpbpl); \
if (N+sh > 0) mpn_rshift(d,d,2*SZ,N+sh); \
} while(0)
#define summ(d,ss,s,n) \
do { \
mpn_add_n(tmp,s[1]+FRAC/mpbpl,s[2]+FRAC/mpbpl,SZ); \
mpn_lshift(tmp,tmp,SZ,1); \
mpn_add_n(tmp,tmp,s[0]+FRAC/mpbpl,SZ); \
mpn_add_n(tmp,tmp,s[3]+FRAC/mpbpl,SZ); \
mpn_divmod_1(tmp,tmp,SZ,6); \
if (n) \
mpn_sub_n (d,ss,tmp,SZ); \
else \
mpn_add_n (d,ss,tmp,SZ); \
} while (0)
add_shift_mulh (s[0], x, co, NULL, 0, 0); /* s0 = h * c; */
add_shift_mulh (c[0], x, si, NULL, 0, 0); /* c0 = h * s; */
add_shift_mulh (s[1], x, co, c[0], 1, 1); /* s1 = h * (c - c0/2); */
add_shift_mulh (c[1], x, si, s[0], 1, 0); /* c1 = h * (s + s0/2); */
add_shift_mulh (s[2], x, co, c[1], 1, 1); /* s2 = h * (c - c1/2); */
add_shift_mulh (c[2], x, si, s[1], 1, 0); /* c2 = h * (s + s1/2); */
add_shift_mulh (s[3], x, co, c[2], 0, 1); /* s3 = h * (c - c2); */
add_shift_mulh (c[3], x, si, s[2], 0, 0); /* c3 = h * (s + s2); */
summ (si, si, s, 0); /* s = s + (s0+2*s1+2*s2+s3)/6; */
summ (co, co, c, 1); /* c = c - (c0+2*c1+2*c2+c3)/6; */
}
#undef add_shift_mulh
#undef summ
}
static int
mpn_bitsize (const mp_limb_t *SRC_PTR, mp_size_t SIZE)
{
int i, j;
for (i = SIZE - 1; i > 0; i--)
if (SRC_PTR[i] != 0)
break;
for (j = mpbpl - 1; j >= 0; j--)
if ((SRC_PTR[i] & (mp_limb_t)1 << j) != 0)
break;
return i * mpbpl + j;
}
static int
do_test (void)
{
mp1 si, co, x, ox, xt, s2, c2, s3, c3;
int i;
int sin_errors = 0, cos_errors = 0;
int sin_failures = 0, cos_failures = 0;
mp1 sin_maxerror, cos_maxerror;
int sin_maxerror_s = 0, cos_maxerror_s = 0;
const double sf = pow (2, mpbpl);
/* assert(mpbpl == mp_bits_per_limb); */
assert(FRAC / mpbpl * mpbpl == FRAC);
memset (sin_maxerror, 0, sizeof (mp1));
memset (cos_maxerror, 0, sizeof (mp1));
memset (xt, 0, sizeof (mp1));
xt[(FRAC - N2) / mpbpl] = (mp_limb_t)1 << (FRAC - N2) % mpbpl;
for (i = 0; i < 1 << N2; i++)
{
int s2s, s3s, c2s, c3s, j;
double ds2,dc2;
mpn_mul_1 (x, xt, SZ, i);
sincosx_mpn (si, co, x, i == 0 ? NULL : ox);
memcpy (ox, x, sizeof (mp1));
ds2 = sin (i / (double) (1 << N2));
dc2 = cos (i / (double) (1 << N2));
for (j = SZ-1; j >= 0; j--)
{
s2[j] = (mp_limb_t) ds2;
ds2 = (ds2 - s2[j]) * sf;
c2[j] = (mp_limb_t) dc2;
dc2 = (dc2 - c2[j]) * sf;
}
if (mpn_cmp (si, s2, SZ) >= 0)
mpn_sub_n (s3, si, s2, SZ);
else
mpn_sub_n (s3, s2, si, SZ);
if (mpn_cmp (co, c2, SZ) >= 0)
mpn_sub_n (c3, co, c2, SZ);
else
mpn_sub_n (c3, c2, co, SZ);
s2s = mpn_bitsize (s2, SZ);
s3s = mpn_bitsize (s3, SZ);
c2s = mpn_bitsize (c2, SZ);
c3s = mpn_bitsize (c3, SZ);
if ((s3s >= 0 && s2s - s3s < 54)
|| (c3s >= 0 && c2s - c3s < 54)
|| 0)
{
#if PRINT_ERRORS
printf ("%06x ", i * (0x100000 / (1 << N2)));
print_mpn_hex(si, (FRAC / 4) + 1);
putchar (' ');
print_mpn_hex (co, (FRAC / 4) + 1);
putchar ('\n');
fputs (" ", stdout);
print_mpn_hex (s2, (FRAC / 4) + 1);
putchar (' ');
print_mpn_hex (c2, (FRAC / 4) + 1);
putchar ('\n');
printf (" %c%c ",
s3s >= 0 && s2s-s3s < 54 ? s2s - s3s == 53 ? 'e' : 'F' : 'P',
c3s >= 0 && c2s-c3s < 54 ? c2s - c3s == 53 ? 'e' : 'F' : 'P');
print_mpn_hex (s3, (FRAC / 4) + 1);
putchar (' ');
print_mpn_hex (c3, (FRAC / 4) + 1);
putchar ('\n');
#endif
sin_errors += s2s - s3s == 53;
cos_errors += c2s - c3s == 53;
sin_failures += s2s - s3s < 53;
cos_failures += c2s - c3s < 53;
}
if (s3s >= sin_maxerror_s
&& mpn_cmp (s3, sin_maxerror, SZ) > 0)
{
memcpy (sin_maxerror, s3, sizeof (mp1));
sin_maxerror_s = s3s;
}
if (c3s >= cos_maxerror_s
&& mpn_cmp (c3, cos_maxerror, SZ) > 0)
{
memcpy (cos_maxerror, c3, sizeof (mp1));
cos_maxerror_s = c3s;
}
}
/* Check Range-Kutta against precomputed values of sin(1) and cos(1). */
memset (x, 0, sizeof (mp1));
x[FRAC / mpbpl] = (mp_limb_t)1 << FRAC % mpbpl;
sincosx_mpn (si, co, x, ox);
memset (s2, 0, sizeof (mp1));
memset (c2, 0, sizeof (mp1));
for (i = 0; i < 100 && i < FRAC / 4; i++)
{
s2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, sin1[i])
- hexdig)
<< (FRAC - i * 4 - 4) % mpbpl);
c2[(FRAC - i * 4 - 4) / mpbpl] |= ((mp_limb_t) (strchr (hexdig, cos1[i])
- hexdig)
<< (FRAC - i * 4 - 4) % mpbpl);
}
if (mpn_cmp (si, s2, SZ) >= 0)
mpn_sub_n (s3, si, s2, SZ);
else
mpn_sub_n (s3, s2, si, SZ);
if (mpn_cmp (co, c2, SZ) >= 0)
mpn_sub_n (c3, co, c2, SZ);
else
mpn_sub_n (c3, c2, co, SZ);
printf ("sin:\n");
printf ("%d failures; %d errors; error rate %0.2f%%\n",
sin_failures, sin_errors, sin_errors * 100.0 / (double) (1 << N2));
fputs ("maximum error: ", stdout);
print_mpn_hex (sin_maxerror, (FRAC / 4) + 1);
fputs ("\nerror in sin(1): ", stdout);
print_mpn_hex (s3, (FRAC / 4) + 1);
fputs ("\n\ncos:\n", stdout);
printf ("%d failures; %d errors; error rate %0.2f%%\n",
cos_failures, cos_errors, cos_errors * 100.0 / (double) (1 << N2));
fputs ("maximum error: ", stdout);
print_mpn_hex (cos_maxerror, (FRAC / 4) + 1);
fputs ("\nerror in cos(1): ", stdout);
print_mpn_hex (c3, (FRAC / 4) + 1);
putchar ('\n');
return (sin_failures == 0 && cos_failures == 0) ? 0 : 1;
}
#define TIMEOUT 600
#define TEST_FUNCTION do_test ()
#include "../test-skeleton.c"
答案 0 :(得分：0)
是的，处理器分别是。将glibc计算的sin和cos值与在sin'=cos, cos'=-sin大整数上建模的多精度定点浮点数中计算的mpn的Runge-Kutta解进行比较。
如果我读得正确，步数可能对于4阶RK4来说是过度杀伤，但比抱歉更安全。