将两个数字x.xxxxxxe-x*10 ^ xx相乘无法正常工作

Question

我试图在我的代码中评估以下示例,但得到错误的答案:

julia> -1.259237254330301e-29*10^29 
-9.930838679817422e-11

答案显然是错误的,预计-1.259237254330301.我得到了正确的答案

julia> -1.259237254330301e-29*1e29
-1.2592372543303008

有谁知道原因？

Answer 1

尽管Floats有舍入错误,但错误结果的原因来自于在类型中使用带有溢出的整数算术:在64位OS 10 ^ 29上溢出(在JULIA中没有错误).

64-Bit OS: 10^18 =  = 1000000000000000000  (64-Bit Integers can hold up to ~ 9,22x10^18)

while: 10^19 turns to: -8446744073709551616 which is wrong, due to overflowing.

如果您选择保持该值的类型capabale结果是正确的:例如:

julia> -1.259237254330301e-29*Int128(10)^29
-1.2592372543303008

要么:

julia> -1.259237254330301e-29*big(10)^29
-1.259237254330300936796903330938514872571882315563023692882767533667837970629477