Download PDF by Underwood Dudley: Mathematical cranks

By Underwood Dudley

ISBN-10: 0883855070

ISBN-13: 9780883855072

A pleasant selection of articles approximately those that declare they've got completed the mathematically most unlikely (squaring the circle, duplicating the cube); those who imagine they've got performed whatever they've got now not (proving Fermat's final Theorem); those who pray in matrices; those that locate the yankee Revolution governed by way of the quantity fifty seven; those who have in universal eccentric mathematical perspectives, a few light (thinking we must always count number through 12s rather than 10s), a few strange (thinking that second-order differential equations will resolve all difficulties of economics, politics and philosophy). it is a actually particular ebook. it truly is written with wit and elegance and is part of people arithmetic.

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If not, return to step 2. 4. Write the product registers to product and go home. cmul: Listing ; ****** ; classic multiply cmul proc uses bx cx dx si di, multiplicand:dword, multiplier:dword, product:word local numbits:byte, mltpcnd:qword pushf cld sub ax, ax lea s1, word ptr multiplicand lea di, word ptr mltpcnd mov cx, 2 movsw rep stosw ;clear upper words stosw mov bx, ax ;clear register to be used to form product cx, ax mov dx, ax byte ptr numbits, 32 49 NUMERICAL METHODS test-multiplier: shr rcr jnc add adc adc adc decrement_counter: shl rcl rcl rcl dec jnz exit: mov mov mov mov mov popf ret cmul endp word ptr multiplier[2], 1 word ptr multiplier, 1 decrement -counter ax, word ptr mltpcnd bx, word ptr mltpcnd[2] cx, word ptr mltpcnd[4] dx, word ptr mltpcnd[6] word ptr mltpcnd, 1 word ptr mltpcnd[2], 1 word ptr mltpcnd[4], 1 word ptr mltpcnd[6], 1 byte ptr numbits test-multiplier di, word word ptr word ptr word ptr word ptr ptr product [di], ax [di] [2], bx [di][4], cx [di][6], dx One possible variation of this example is to employ the “early-out” method.

They added some speed to the floating-point routines and decreased code size. Until a few years ago, the kind of progress usually seen in these machines was an increase in the size of the data types available and the addition of hardware arithmetic. The 386 and 486 can do some 64-bit arithmetic and have nice shift instructions, SHLD and SHRD, that will happily shift the bits of the second operand into the first and put the number of bits shifted in a third operand. This is done in a single stroke, with the bits of one operand shifted directly into the other, easing normalization of long integers and making for fast binary multiplies and divides.

Using this method, 4 is still 0100, but -4 becomes 1100. Recall that one’s complement is a bit-by-bit complement, so that all ones become zeros and all zeros become ones. The two’s complement is obtained by adding a one to the one’s complement. This method eliminates the dual representation of zero-zero is only 0000 (represented as a three-bit signed binary number)-but one quirk is that the range of values that can be represented is slightly more negative than positive (see the chart below). That is not the case with the other two methods described.

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Mathematical cranks by Underwood Dudley


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