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浮点标准 IEEE754 精要
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=== 精度限制 === '''Precision limitations on decimal values in [0, 1]:''' * Decimals between 2^−24 (minimum positive subnormal) and 2^−14 (maximum subnormal): fixed interval 2^−24 * Decimals between 2^−14 (minimum positive normal) and 2^−13: fixed interval 2^−24 * Decimals between 2^−13 and 2^−12: fixed interval 2^−23 * Decimals between 2^−12 and 2^−11: fixed interval 2^−22 * Decimals between 2^−11 and 2^−10: fixed interval 2^−21 * Decimals between 2^−10 and 2^−9: fixed interval 2^−20 * Decimals between 2^−9 and 2^−8: fixed interval 2^−19 * Decimals between 2^−8 and 2^−7: fixed interval 2^−18 * Decimals between 2^−7 and 2^−6: fixed interval 2^−17 * Decimals between 2^−6 and 2^−5: fixed interval 2^−16 * Decimals between 2^−5 and 2^−4: fixed interval 2^−15 * Decimals between 2^−4 and 2^−3: fixed interval 2^−14 * Decimals between 2^−3 and 2^−2: fixed interval 2^−13 * Decimals between 2^−2 and 2^−1: fixed interval 2^−12 * Decimals between 2^−1 and 2^−0: fixed interval 2^−11 '''Precision limitations on decimal values in [1, 2048]:''' * Decimals between 1 and 2: fixed interval 2^−10 (1+2^−10 is the next largest float after 1) ≈ 0.001 * Decimals between 2 and 4: fixed interval 2^−9 ≈ 0.002 * Decimals between 4 and 8: fixed interval 2^−8 ≈ 0.004 * Decimals between 8 and 16: fixed interval 2^−7 ≈ 0.008 * Decimals between 16 and 32: fixed interval 2^−6 ≈ 0.016 * Decimals between 32 and 64: fixed interval 2^−5 ≈ 0.031 * Decimals between 64 and 128: fixed interval 2^−4 = 0.0625 * Decimals between 128 and 256: fixed interval 2^−3 = 0.125 * Decimals between 256 and 512: fixed interval 2^−2 = 0.25 * Decimals between 512 and 1024: fixed interval 2^−1 = 0.5 * Decimals between 1024 and 2048: fixed interval 2^0 = 1 '''Precision limitations on integer values''' * Integers between 0 and 2048 can be exactly represented (and also between −2048 and 0) * Integers between 2048 and 4096 round to a multiple of 2 (even number) * Integers between 4096 and 8192 round to a multiple of 4 * Integers between 8192 and 16384 round to a multiple of 8 * Integers between 16384 and 32768 round to a multiple of 16 * Integers between 32768 and 65519 round to a multiple of 32 * Integers above 65519 are rounded to "infinity" if using round-to-even, or above 65535 if using round-to-zero, or above 65504 if using round-to-infinity. <br>
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