/
arith-true.R
194 lines (156 loc) · 5.66 KB
/
arith-true.R
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
186
187
188
189
190
191
192
193
194
####=== Numerical / Arithmetic Tests
####--- ALL tests here should return TRUE !
###
### '##P': This lines give not 'T' but relevant ``Print output''
### --> d-p-q-r-tests.R for distribution things
.proctime00 <- proc.time()
opt.conformance <- 0
Meps <- .Machine $ double.eps
options(rErr.eps = 1e-30)
rErr <- function(approx, true, eps = .Options$rErr.eps)
{
if(is.null(eps)) { eps <- 1e-30; options(rErr.eps = eps) }
ifelse(Mod(true) >= eps,
1 - approx / true, # relative error
true - approx) # absolute error (e.g. when true=0)
}
abs(1- .Machine$double.xmin * 10^(-.Machine$double.min.exp*log10(2)))/Meps < 1e3
##P (1- .Machine$double.xmin * 10^(-.Machine$double.min.exp*log10(2)))/Meps
if(opt.conformance)#fails at least on SGI/IRIX 6.5
abs(1- .Machine$double.xmax * 10^(-.Machine$double.max.exp*log10(2)))/Meps < 1e3
## More IEEE Infinity/NaN checks
i1 <- pi / 0
i1 == (i2 <- 1:1 / 0:0)
is.infinite( i1) & is.infinite( i2) & i1 > 12 & i2 > 12
is.infinite(-i1) & is.infinite(-i2) & (-i1) < -12 & (-i2) < -12
is.nan(n1 <- 0 / 0)
is.nan( - n1)
i1 == i1 + i1
i1 == i1 * i1
is.nan(i1 - i1)
is.nan(i1 / i1)
1/0 == Inf & 0 ^ -1 == Inf
1/Inf == 0 & Inf ^ -1 == 0
!is.na(Inf) & !is.nan(Inf) & is.infinite(Inf) & !is.finite(Inf)
!is.na(-Inf)& !is.nan(-Inf)& is.infinite(-Inf)& !is.finite(-Inf)
is.na(NA) & !is.nan(NA) & !is.infinite(NA) & !is.finite(NA)
is.na(NaN) & is.nan(NaN) & !is.infinite(NaN) & !is.finite(NaN)
all(!is.nan(c(1,NA)))
all(c(F,T,F) == is.nan(c (1,NaN,NA)))
all(c(F,T,F) == is.nan(list(1,NaN,NA)))
## log() and "pow()" -- POSIX is not specific enough..
log(0) == -Inf
is.nan(log(-1))# TRUE and warning
rp <- c(1:2,Inf); rn <- rev(- rp)
r <- c(rn, 0, rp)
all(r^0 == 1)
all((rn ^ -3) == -((-rn) ^ -3))
#
all(c(1.1,2,Inf) ^ Inf == Inf)
all(c(1.1,2,Inf) ^ -Inf == 0)
.9 ^ Inf == 0
.9 ^ -Inf == Inf
## Wasn't ok in 0.64:
all(1^c(-Inf,Inf) == 1)
all(is.nan(rn ^ .5))# in some C's : (-Inf) ^ .5 gives Inf, instead of NaN
## Real Trig.:
cos(0) == 1
sin(3*pi/2) == cos(pi)
x <- rnorm(99)
all( sin(-x) == - sin(x))
all( cos(-x) == cos(x))
x <- 1:99/100
all(abs(1 - x / asin(sin(x))) <= 2*Meps)# "== 2*" for HP-UX
all(abs(1 - x / atan(tan(x))) < 2*Meps)
## Sun has asin(.) = acos(.) = 0 for these:
## is.nan(acos(1.1)) && is.nan(asin(-2)) [!]
## Complex Trig.:
abs(Im(cos(acos(1i))) - 1) < 2*Meps
abs(Im(sin(asin(1i))) - 1) < 2*Meps
##P (1 - Im(sin(asin(Ii))))/Meps
##P (1 - Im(cos(acos(Ii))))/Meps
abs(Im(asin(sin(1i))) - 1) < 2*Meps
cos(1i) == cos(-1i)# i.e. Im(acos(*)) gives + or - 1i:
abs(abs(Im(acos(cos(1i)))) - 1) < 4*Meps
.Random.seed <- c(0, 629, 6137, 22167) # want reproducible output
Isi <- Im(sin(asin(1i + rnorm(100))))
all(abs(Isi-1) < 100* Meps)
##P table(2*abs(Isi-1) / Meps)
Isi <- Im(cos(acos(1i + rnorm(100))))
all(abs(Isi-1) < 100* Meps)
##P table(2*abs(Isi-1) / Meps)
Isi <- Im(atan(tan(1i + rnorm(100)))) #-- tan(atan(..)) does NOT work (Math!)
all(abs(Isi-1) < 100* Meps)
##P table(2*abs(Isi-1) / Meps)
## polyroot():
all(abs(1 + polyroot(choose(8, 0:8))) < 1e-10)# maybe smaller..
## gamma():
abs(gamma(1/2)^2 - pi) < 4* Meps
r <- rlnorm(5000)
all(abs(rErr(gamma(r+1), r*gamma(r))) < 500 * Meps)
n <- 10; all( gamma(1:n) == cumprod(c(1,1:(n-1))))
n <- 20; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 100*Meps)
n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps)
n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps)
all(is.nan(gamma(0:-4))) # + warn.
## fft():
ok <- TRUE
##test EXTENSIVELY: for(N in 1:100) {
cat(".")
for(n in c(1:30, 1000:1050)) {
x <- rnorm(n)
er <- Mod(rErr(fft(fft(x), inverse = TRUE)/n, x*(1+0i)))
n.ok <- all(er < 1e-8) & quantile(er, 0.95, names=FALSE) < 10000*Meps
if(!n.ok) cat("\nn=",n,": quantile(rErr, c(.95,1)) =",
formatC(quantile(er, prob= c(.95,1))),"\n")
ok <- ok & n.ok
}
cat("\n")
##test EXTENSIVELY: }
ok
## var():
for(n in 2:10)
print(all.equal(n*(n-1)*var(diag(n)),
matrix(c(rep(c(n-1,rep(-1,n)),n-1), n-1), nr=n, nc=n),
tol = 20*Meps))# use tol=0 to see rel.error
## pmin() & pmax() -- "attributes" !
v1 <- c(a=2)
m1 <- cbind( 2:4,3)
m2 <- cbind(a=2:4,2)
all( pmax(v1, 1:3) == pmax(1:3, v1) & pmax(1:3, v1) == c(2,2,3))
all( pmin(v1, 1:3) == pmin(1:3, v1) & pmin(1:3, v1) == c(1,2,2))
oo <- options(warn = -1)# These four lines each would give 3-4 warnings :
all( pmax(m1, 1:7) == pmax(1:7, m1) & pmax(1:7, m1) == c(2:4,4:7))
all( pmin(m1, 1:7) == pmin(1:7, m1) & pmin(1:7, m1) == c(1:3,3,3,3,2))
all( pmax(m2, 1:7) == pmax(1:7, m2) & pmax(1:7, m2) == pmax(1:7, m1))
all( pmin(m2, 1:7) == pmin(1:7, m2) & pmin(1:7, m2) == c(1:3,2,2,2,2))
options(oo)
## pretty()
stopifnot(pretty(1:15) == seq(0,16, by=2),
pretty(1:15, h=2) == seq(0,15, by=5),
pretty(1) == 0:1,
pretty(pi) == c(2,4),
pretty(pi, n=6) == 2:4,
pretty(pi, n=10) == 2:5,
pretty(pi, shr=.1)== c(3, 3.5))
## gave infinite loop [R 0.64; Solaris], seealso PR#390 :
all(pretty((1-1e-5)*c(1,1+3*Meps), 7) == seq(0,1,len=3))
n <- 1000
x12 <- matrix(NA, 2,n); x12[,1] <- c(2.8,3) # Bug PR#673
for(j in 1:2) x12[j, -1] <- round(rnorm(n-1), dig = rpois(n-1, lam=3.5) - 2)
for(i in 1:n) {
lp <- length(p <- pretty(x <- sort(x12[,i])))
stopifnot(p[1] <= x[1] & x[2] <= p[lp],
all(x==0) || all.equal(p, rev(-pretty(-x)), tol = 10*Meps))
}
## PR#741:
pi != (pi0 <- pi + 2*.Machine$double.eps)
is.na(match(c(1,pi,pi0), pi)[3])
## PR#749:
all(is.na(c(NA && TRUE, TRUE && NA, NA && NA,
NA || FALSE,FALSE || NA, NA || NA)))
all((c(NA || TRUE, TRUE || NA,
!c(NA && FALSE,FALSE && NA))))
is.na(mean(c(1,NA,NA)[-1], trim = .1, na.rm = TRUE))
## Last Line:
cat('Time elapsed: ', proc.time() - .proctime00,'\n')