Babbage difference and Quake's Fast Inverse Square Root

Understanding Quake’s Fast Inverse Square Root – BetterExplained

在某个帖子里我放过厥词"Quake判断某个整数是不是平方数"。说错了。判断是不是平方数步长为2n+1一点都不高档；输入为32位时，16步可以判断出。

该文说到:  Floating-point numbers are stored by computers in mantissa-exponent form.

mantissa是啥？网上说: When a regular number is written in scientific notation, it is written with two significant components: the mantissa and the exponent. 即 52976 = 5.2976E4, 5.2976 is the mantissa.

另一种我认为准确的说法: 52796 = 10 ** 4.722601020190381, the mantissa is 0.722601020190381，即the fractional part of a common logarithm representing the digits of the associated number but not its magnitude，词源: Latin: 'sth added', of Etruscan origin. 伊特鲁里亚文明是伊特鲁里亚地区(今意大利半岛及科西嘉岛)于公元前12世纪至前1世纪所发展出来的文明。该文明的全盛时期为前6世纪。

IEEE Standard for Binary Floating-Point Arithmetic (754-1985): Numbers in the single and double formats are composed of the following three fields:
1) 1-bit sign s
2) Biased exponent e
3) Fraction f = b₁b₂...b_p-1

The common logarithm is the logarithm with base 10.  The natural logarithm of a number is its logarithm to the base of the mathematical constant e. Log base 2, also known as binary logarithm, is the inverse function of the power of two functions.

IEEE-754 Floating Point Converter (h-schmidt.net)

上面：1. The mantissa (also known as significand or fraction); 2. 可以在位和数之间相互转换。

x86下*((int*)&f1) = 0x5f3759df; printf("%g\n", f1)证实了endian-neutral. This C code has been reported to be endian-neutral (supposedly tested it on a Macintosh). 也许可以说，Intel和IEEE都是I字辈的，所以Intel的浮点数遵循IEEE，是big endian的。果子哥则被发词典链接，which解释English里mandatory是啥意思：

有人有当爸爸瘾啊，拍个广告也要找“小头爸爸和大头儿子"。XX哥赖好降了一辈。

f'(y) = -2y^-3，还是个偏导数哩？