-
Notifications
You must be signed in to change notification settings - Fork 204
/
Copy patharith-true.R
220 lines (183 loc) · 7.19 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
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
####=== Numerical / Arithmetic Tests
####--- ALL tests here should return TRUE !
###
### '##P': These lines don't give TRUE but relevant ``Print output''
### --> d-p-q-r-tests.R for distribution things
.proctime00 <- proc.time()
opt.conformance <- 0
Meps <- .Machine $ double.eps
## this uses random inputs, so set the seed
set.seed(1)
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
iNA <- as.integer(NA)
!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)
is.na(iNA) & !is.nan(iNA) & !is.infinite(iNA) & !is.finite(iNA)
## These are "double"s:
all(!is.nan(c(1.,NA)))
all(c(FALSE,TRUE,FALSE) == is.nan(c (1.,NaN,NA)))
## lists are no longer allowed
## all(c(FALSE,TRUE,FALSE) == 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, NA, NaN)
all(r^0 == 1)
ir <- suppressWarnings(as.integer(r))
all(ir^0 == 1)
all(ir^0L == 1)# not in R <= 2.15.0
all( 1^r == 1)# not in R 0.64
all(1L^r == 1)
all(1L^ir == 1)# not in R <= 2.15.0
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(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)) [!]
## gamma()
abs(gamma(1/2)^2 - pi) < 4* Meps
r <- rlnorm(5000) # NB random, and next has failed for some seed
all(abs(rErr(gamma(r+1), r*gamma(r))) < 500 * Meps)
## more accurate for integers n <= 50 since R 1.8.0 Sol8: perfect
n <- 20; all( gamma(1:n) == cumprod(c(1,1:(n-1))))# Lnx: up too n=28
n <- 50; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 20*Meps)#Lnx: f=2
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)
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:-47))) # + warn.
## choose() {and lchoose}:
n51 <- c(196793068630200, 229591913401900, 247959266474052)
abs(c(n51, rev(n51))- choose(51, 23:28)) <= 2
all(choose(0:4,2) == c(0,0,1,3,6))
## 3 to 8 units off and two NaN's in 1.8.1
## psi[gamma](x) and derivatives:
## psi == digamma:
gEuler <- 0.577215664901532860606512# = Euler's gamma
abs(digamma(1) + gEuler) < 32*Meps # i386 Lx: = 2.5*Meps
all.equal(digamma(1) - digamma(1/2), log(4), tolerance = 32*Meps)# Linux: < 1*Meps!
n <- 1:12
all.equal(digamma(n),
- gEuler + c(0, cumsum(1/n)[-length(n)]),tolerance = 32*Meps)#i386 Lx: 1.3 Meps
all.equal(digamma(n + 1/2),
- gEuler - log(4) + 2*cumsum(1/(2*n-1)),tolerance = 32*Meps)#i386 Lx: 1.8 Meps
## higher psigamma:
all.equal(psigamma(1, deriv=c(1,3,5)),
pi^(2*(1:3)) * c(1/6, 1/15, 8/63), tolerance = 32*Meps)
x <- c(-100,-3:2, -99.9, -7.7, seq(-3,3, length=61), 5.1, 77)
## Intel icc showed a < 1ulp difference in the second.
stopifnot(all.equal( digamma(x), psigamma(x,0), tolerance = 2*Meps),
all.equal(trigamma(x), psigamma(x,1), tolerance = 2*Meps))# TRUE (+ NaN warnings)
## very large x:
x <- 1e30 ^ (1:10)
a.relE <- function(appr, true) abs(1 - appr/true)
stopifnot(a.relE(digamma(x), log(x)) < 1e-13,
a.relE(trigamma(x), 1/x) < 1e-13)
x <- sqrt(x[2:6]); stopifnot(a.relE(psigamma(x,2), - 1/x^2) < 1e-13)
x <- 10^(10*(2:6));stopifnot(a.relE(psigamma(x,5), +24/x^5) < 1e-13)
## 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),
tolerance = 20*Meps)) # use tolerance = 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)), tolerance = 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))))
## not sure what the point of this is: it gives mean(numeric(0)), that is NaN
(z <- mean(rep(NA_real_, 2), trim = .1, na.rm = TRUE))
is.na(z)
## Last Line:
cat('Time elapsed: ', proc.time() - .proctime00,'\n')