Rmpfr可以做到使用mpfr_set_str字符串转换...
val <- mpfr("1e309")
## 1 'mpfr' number of precision 17 bits
## [1] 9.999997e308
# set a precision (assume base 10)...
est_prec <- function(e) floor(e/log10(2)) + 1
val <- mpfr("1e309", est_prec(309))
## 1 'mpfr' number of precision 1027 bits
## [1]1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
.mpfr2bigz(val)
## Big Integer ('bigz') :
## [1] 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
# extract exponent from a scientific notation string
get_exp <- function(sci) as.numeric(gsub("^.*e",'', sci))
# Put it together
sci2bigz <- function(str) {
.mpfr2bigz(mpfr(str, est_prec(get_exp(str))))
}
val <- sci2bigz(paste0(format(Const("pi", 1027)), "e309"))
identical(val, .mpfr2bigz(Const("pi",1027)*mpfr(10,1027)^309))
## [1] TRUE
## Big Integer ('bigz') :
## [1] 3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587004
至于为什么上存储的数大于.Machine$double.xmax
,上浮点编码在IEEE规范的文档时,R常见问题和维基百科进入所有的行话,但我发现它有助于只定义条款(使用?'.Machine'
)...
double.xmax
(最大标准化浮点数)=
(1 - double.neg.eps) * double.base^double.max.exp
其中
double.neg.eps
(一个小的正浮点数x使得1 - X = 1)!= double.base^double.neg.ulp.digits
其中
double.neg.ulp.digits
=最大负整数,使得1 - double.base^i != 1
和
double.max.exp
= double.base溢出的最小正功率和
double.base
(浮点数表示的基数)= 2(二进制数)。
考虑有限浮点数可以与另一个区别开来吗?在IEEE规范告诉我们,对于一个binary64数11位都将用于指数,所以我们的2^(11-1)-1=1023
最大的指数,但我们希望的是溢出最大指数所以double.max.exp
是1024
# Maximum number of representations
# double.base^double.max.exp
base <- mpfr(2, 2048)
max.exp <- mpfr(1024, 2048)
# This is where the big part of the 1.79... comes from
base^max.exp
## 1 'mpfr' number of precision 2048 bits
## [1] 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216
# Smallest definitive unit.
# Find the largest negative integer...
neg.ulp.digits <- -64; while((1 - 2^neg.ulp.digits) == 1)
neg.ulp.digits <<- neg.ulp.digits + 1
neg.ulp.digits
## [1] -53
# It makes a real small number...
neg.eps <- base^neg.ulp.digits
neg.eps
## 1 'mpfr' number of precision 2048 bits
## [1] 1.11022302462515654042363166809082031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-16
# Largest difinitive floating point number less than 1
# times the number of representations
xmax <- (1-neg.eps) * base^max.exp
xmax
## 1 'mpfr' number of precision 2048 bits
## [1] 179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
identical(asNumeric(xmax), .Machine$double.xmax)
## [1] TRUE
您可能会发现阅读有用的文档,特别是'?as.bigz'的Note部分。 – joran 2013-02-11 18:22:43
谢谢乔兰。我错过了最后一行。令人烦恼的是,我现在不能使用科学记数法! – 2013-02-11 18:42:31
是的,但你可以做'as.bigz(10)^ 309'。事实上,你可以这样做:''%e%'< - function(x,y)as.bigz(x)* 10^as.bigz(y); 1%e%309' – 2013-02-11 19:18:15