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逆向辛克莱 1974 年计算器神技：只用 HP-35 一半的 ROM
Reversing Sinclair's amazing 1974 calculator hack - half the ROM of the HP-35
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这篇文章深入逆向分析了 1974 年 Sinclair Scientific 计算器：它只用 HP-35 一半容量的 ROM 就实现了科学计算功能，作者通过仿真还原了其精妙的算法技巧。文中还介绍了这款首款单芯片科学计算器的兴衰，以及 Sinclair 为省成本采取的种种极端手段（如把 π 和 e 常数印在机壳上）。
为什么经久不衰：它展示了在极端硬件限制下用软件巧思替代硬件资源的经典案例，这种'少即是多'的工程智慧至今仍有启发意义。
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ROM 空间不足，Sinclair 干脆把常数印在机壳上
科学计算器通常内置 e 和 π 等常数，但 ROM 里没有空间存放它们。Sinclair Scientific 用了一个绝妙的解决方案：把常数印在计算器外壳上。
sirsar查看英文原文
This is great. Scientific calculators usually provide constants such as e and π but there was no space in the ROM for these constants. The Sinclair Scientific used the brilliant solution of printing the constants on the calculator's case
便宜归便宜，精度和速度太差，实际只是玩具
虽然巧妙又便宜，但这台机器速度慢、精度低，实际不可用。它号称'三位精度'，其实只在某些情况下达到。聪明的学生很快就能发现它根本算不了的问题。总之它是个玩具，真要用于学业还得花钱买 HP-35 或后来的 TI SR-5x。
znmeb查看英文原文
While clever and inexpensive, the low speed and low accuracy of this device made it unusable. It was billed as "3-figure accuracy", but in fact it only got that on some cases. A bright undergrad or grad student could quickly uncover useful problems that it flat out couldn't solve. In short, it was a toy. Anyone basing one's academic grade on this thing was a fool. You really did have to spend the money for an HP-35, or the later Texas Instruments SR-5x calculators that were less expensive.
Sinclair 工程哲学：抠到极限、勉强能用，但便宜得惊人
这太 Sinclair 了。勉强够用到能用的程度（'最好也就三位小数精度'、'算 sin 1 要 7.5 秒'、π 和 e 印在外壳上而不是塞进 ROM），但确实有用，而且便宜得离谱。Sinclair 的产品里，工程师抠每一分钱的手法近乎滑稽：ZX81 的视频电路滥用 Z80 的 DRAM 刷新机制，机械上只用两颗螺丝固定 PCB。我对他们的巧思赞叹不已，也同样被它气得够呛。
anyfoo查看英文原文
That is so classic Sinclair. Barely working enough to be useful ("three decimal places of accuracy at best", "sin 1 takes about 7.5 seconds", and constants like pi and e are written on the case instead of fitting in ROM), but useful nonetheless, and dirt cheap. Sinclair products were almost comical in how ingeniously their engineers shaved off any pennies they could. In the ZX81, the video circuit is a bizarre and extremely interesting contraption that abuses the Z80's DRAM refresh circuitry, and on the mechanical side only two screws hold down the PCB to the case, despite there being many more intended screw holes in both PCB and case (someone must have figured out that hey, it still holds in place with two). I have marveled a lot at what the engineers came up with, and cursed at it just as much. For the ZX81's ingenious video circuit and sleek case, you get a device with chips that get dangerously (literally painfully) hot, and most CPU time used for drawing the screen--without the ability to set individual pixels in any way. The keyboard "cable" plugged into the PCB is just an extension of the paper-like foil that makes up the terrible, terrible keyboard, and that can easily self-destruct when disassembling your ZX81: The foil does not like any amount of bending, including the bending when you fold the case open. I could go on an on about how clever Sinclair's engineering was to barely stay past the line of what makes a working product so brilliantly.
Sinclair 的天才在于把技术平民化，哪怕因此淘汰自己
这既是 Clive Sinclair 的天才也是他的诅咒：他搅动市场、完全不顾后果，实际上是在和自己竞争，然后转向别的领域。我一直认为这是最好的发明家——不挤奶，而是把一个领域民主化到自己都被淘汰的程度。想象一下，如果他没有证明 20 美元以下的计算器和 100 美元以下的电脑是可能的，今天的世界可能会很不一样。
jacquesm查看英文原文
I love these articles. At the end there is this bit: "The Sinclair Scientific came out in 1974 and was the first single-chip scientific calculator (if you ignore the display driver chips). It was stylishly compact, just 3/4 inch thick. It originally sold for the price of $119.95 or £49.95 and by the end of the year was available as a kit for the amazingly low price of £9.95. Unfortunately, as calculator prices collapsed, so did Sinclair Radionics' profits, and the company was broken up in 1979 after heavy losses." In a nutshell that is both the genius and the curse of Clive Sinclair, he moved markets with complete disregard for the consequences effectively out-competing himself and the would move on to some other field. I always thought that was the best kind of inventor, the one that doesn't care about milking the cows they field, but that democratizes a field to the point that they themselves become obsolete. Imagine if he had not shown that you can have < $20 calculators or < $100 computers, that would have had major impact on so many people, their careers and the solutions they built that the world would probably look different today. More Sir Clive, less Zuckerberg and the like.
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