598 lines
16 KiB
Forth
598 lines
16 KiB
Forth
# print out floats in decimal
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# https://research.swtch.com/ftoa
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#
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# Basic idea:
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# Ignoring sign, floating point numbers are represented as 1.mantissa * 2^exponent
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# Therefore, to print a float in decimal, we need to:
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# - compute its value without decimal point
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# - convert to an array of decimal digits
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# - print out the array while inserting the decimal point appropriately
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#
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# Basic complication: the computation generates numbers larger than an int can
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# hold. We need a way to represent big ints.
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#
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# Key insight: use a representation for big ints that's close to what we need
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# anyway, an array of decimal digits.
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#
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# Style note: we aren't creating a big int library here. The only operations
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# we need are halving and doubling. Following the link above, it seems more
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# comprehensible to keep these operations inlined so that we can track the
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# position of the decimal point with dispatch.
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#
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# This approach turns out to be fast enough for most purposes.
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# Optimizations, however, get wildly more complex.
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fn test-write-float-decimal-approximate-normal {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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# 0.5
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var half/xmm0: float <- rational 1, 2
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write-float-decimal-approximate s, half, 3
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check-stream-equal s, "0.5", "F - test-write-float-decimal-approximate-normal 0.5"
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# 0.25
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clear-stream s
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var quarter/xmm0: float <- rational 1, 4
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write-float-decimal-approximate s, quarter, 3
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check-stream-equal s, "0.25", "F - test-write-float-decimal-approximate-normal 0.25"
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# 0.75
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clear-stream s
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var three-quarters/xmm0: float <- rational 3, 4
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write-float-decimal-approximate s, three-quarters, 3
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check-stream-equal s, "0.75", "F - test-write-float-decimal-approximate-normal 0.75"
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# 0.125
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clear-stream s
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var eighth/xmm0: float <- rational 1, 8
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write-float-decimal-approximate s, eighth, 3
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check-stream-equal s, "0.125", "F - test-write-float-decimal-approximate-normal 0.125"
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# 0.0625; start using scientific notation
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clear-stream s
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var sixteenth/xmm0: float <- rational 1, 0x10
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write-float-decimal-approximate s, sixteenth, 3
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check-stream-equal s, "6.25e-2", "F - test-write-float-decimal-approximate-normal 0.0625"
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# sqrt(2); truncate floats with lots of digits after the decimal but not too many before
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clear-stream s
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var two-f/xmm0: float <- rational 2, 1
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var sqrt-2/xmm0: float <- square-root two-f
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write-float-decimal-approximate s, sqrt-2, 3
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check-stream-equal s, "1.414", "F - test-write-float-decimal-approximate-normal √2"
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}
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# print whole integers without decimals
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fn test-write-float-decimal-approximate-integer {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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# 1
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var one-f/xmm0: float <- rational 1, 1
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write-float-decimal-approximate s, one-f, 3
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check-stream-equal s, "1", "F - test-write-float-decimal-approximate-integer 1"
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# 2
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clear-stream s
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var two-f/xmm0: float <- rational 2, 1
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write-float-decimal-approximate s, two-f, 3
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check-stream-equal s, "2", "F - test-write-float-decimal-approximate-integer 2"
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# 10
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clear-stream s
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var ten-f/xmm0: float <- rational 0xa, 1
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write-float-decimal-approximate s, ten-f, 3
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check-stream-equal s, "10", "F - test-write-float-decimal-approximate-integer 10"
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# -10
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clear-stream s
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var minus-ten-f/xmm0: float <- rational -0xa, 1
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write-float-decimal-approximate s, minus-ten-f, 3
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check-stream-equal s, "-10", "F - test-write-float-decimal-approximate-integer -10"
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# 999
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clear-stream s
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var minus-ten-f/xmm0: float <- rational 0x3e7, 1
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write-float-decimal-approximate s, minus-ten-f, 3
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check-stream-equal s, "999", "F - test-write-float-decimal-approximate-integer 1000"
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# 1000 - start using scientific notation
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clear-stream s
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var minus-ten-f/xmm0: float <- rational 0x3e8, 1
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write-float-decimal-approximate s, minus-ten-f, 3
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check-stream-equal s, "1.00e3", "F - test-write-float-decimal-approximate-integer 1000"
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# 100,000
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clear-stream s
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var hundred-thousand/eax: int <- copy 0x186a0
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var hundred-thousand-f/xmm0: float <- convert hundred-thousand
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write-float-decimal-approximate s, hundred-thousand-f, 3
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check-stream-equal s, "1.00e5", "F - test-write-float-decimal-approximate-integer 100,000"
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}
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fn test-write-float-decimal-approximate-zero {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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var zero: float
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write-float-decimal-approximate s, zero, 3
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check-stream-equal s, "0", "F - test-write-float-decimal-approximate-zero"
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}
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fn test-write-float-decimal-approximate-negative-zero {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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var n: int
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copy-to n, 0x80000000
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var negative-zero/xmm0: float <- reinterpret n
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write-float-decimal-approximate s, negative-zero, 3
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check-stream-equal s, "-0", "F - test-write-float-decimal-approximate-negative-zero"
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}
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fn test-write-float-decimal-approximate-infinity {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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var n: int
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# 0|11111111|00000000000000000000000
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# 0111|1111|1000|0000|0000|0000|0000|0000
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copy-to n, 0x7f800000
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var infinity/xmm0: float <- reinterpret n
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write-float-decimal-approximate s, infinity, 3
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check-stream-equal s, "Inf", "F - test-write-float-decimal-approximate-infinity"
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}
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fn test-write-float-decimal-approximate-negative-infinity {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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var n: int
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copy-to n, 0xff800000
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var negative-infinity/xmm0: float <- reinterpret n
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write-float-decimal-approximate s, negative-infinity, 3
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check-stream-equal s, "-Inf", "F - test-write-float-decimal-approximate-negative-infinity"
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}
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fn test-write-float-decimal-approximate-not-a-number {
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var s-storage: (stream byte 0x10)
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var s/ecx: (addr stream byte) <- address s-storage
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var n: int
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copy-to n, 0xffffffff # exponent must be all 1's, and mantissa must be non-zero
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var nan/xmm0: float <- reinterpret n
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write-float-decimal-approximate s, nan, 3
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check-stream-equal s, "NaN", "F - test-write-float-decimal-approximate-not-a-number"
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}
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fn render-float-decimal screen: (addr screen), in: float, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
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var s-storage: (stream byte 0x10)
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var s/esi: (addr stream byte) <- address s-storage
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write-float-decimal-approximate s, in, precision
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var width/eax: int <- copy 0
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var height/ecx: int <- copy 0
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width, height <- screen-size screen
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var result/eax: int <- draw-stream-rightward screen, s, x, width, y, color, background-color
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return result
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}
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# 'precision' controls the maximum width past which we resort to scientific notation
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fn write-float-decimal-approximate out: (addr stream byte), in: float, precision: int {
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# - special names
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var bits/eax: int <- reinterpret in
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compare bits, 0
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{
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break-if-!=
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write out, "0"
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return
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}
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compare bits, 0x80000000
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{
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break-if-!=
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write out, "-0"
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return
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}
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compare bits, 0x7f800000
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{
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break-if-!=
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write out, "Inf"
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return
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}
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compare bits, 0xff800000
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{
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break-if-!=
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write out, "-Inf"
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return
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}
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var exponent/ecx: int <- copy bits
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exponent <- shift-right 0x17 # 23 bits of mantissa
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exponent <- and 0xff
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exponent <- subtract 0x7f
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compare exponent, 0x80
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{
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break-if-!=
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write out, "NaN"
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return
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}
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# - regular numbers
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var sign/edx: int <- copy bits
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sign <- shift-right 0x1f
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{
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compare sign, 1
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break-if-!=
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append-byte out, 0x2d/minus
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}
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# v = 1.mantissa (in base 2) << 0x17
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var v/ebx: int <- copy bits
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v <- and 0x7fffff
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v <- or 0x00800000 # insert implicit 1
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# e = exponent - 0x17
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var e/ecx: int <- copy exponent
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e <- subtract 0x17 # move decimal place from before mantissa to after
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# initialize buffer with decimal representation of v
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# unlike https://research.swtch.com/ftoa, no ascii here
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var buf-storage: (array byte 0x7f)
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var buf/edi: (addr array byte) <- address buf-storage
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var n/eax: int <- decimal-digits v, buf
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# I suspect we can do without reversing, but we'll follow https://research.swtch.com/ftoa
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# closely for now.
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reverse-digits buf, n
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# loop if e > 0
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{
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compare e, 0
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break-if-<=
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n <- double-array-of-decimal-digits buf, n
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e <- decrement
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loop
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}
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var dp/edx: int <- copy n
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# loop if e < 0
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{
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compare e, 0
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break-if->=
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n, dp <- halve-array-of-decimal-digits buf, n, dp
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e <- increment
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loop
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}
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_write-float-array-of-decimal-digits out, buf, n, dp, precision
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}
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# store the decimal digits of 'n' into 'buf', units first
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# n must be positive
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fn decimal-digits n: int, _buf: (addr array byte) -> _/eax: int {
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var buf/edi: (addr array byte) <- copy _buf
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var i/ecx: int <- copy 0
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var curr/eax: int <- copy n
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var curr-byte/edx: int <- copy 0
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{
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compare curr, 0
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break-if-=
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curr, curr-byte <- integer-divide curr, 0xa
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var dest/ebx: (addr byte) <- index buf, i
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copy-byte-to *dest, curr-byte
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i <- increment
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loop
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}
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return i
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}
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fn reverse-digits _buf: (addr array byte), n: int {
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var buf/esi: (addr array byte) <- copy _buf
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var left/ecx: int <- copy 0
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var right/edx: int <- copy n
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right <- decrement
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{
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compare left, right
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break-if->=
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{
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var l-a/ecx: (addr byte) <- index buf, left
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var r-a/edx: (addr byte) <- index buf, right
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var l/ebx: byte <- copy-byte *l-a
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var r/eax: byte <- copy-byte *r-a
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copy-byte-to *l-a, r
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copy-byte-to *r-a, l
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}
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left <- increment
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right <- decrement
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loop
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}
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}
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fn double-array-of-decimal-digits _buf: (addr array byte), _n: int -> _/eax: int {
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var buf/edi: (addr array byte) <- copy _buf
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# initialize delta
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var delta/edx: int <- copy 0
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{
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var curr/ebx: (addr byte) <- index buf, 0
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var tmp/eax: byte <- copy-byte *curr
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compare tmp, 5
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break-if-<
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delta <- copy 1
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}
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# loop
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var x/eax: int <- copy 0
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var i/ecx: int <- copy _n
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i <- decrement
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{
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compare i, 0
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break-if-<=
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# x += 2*buf[i]
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{
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var tmp/ecx: (addr byte) <- index buf, i
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var tmp2/ecx: byte <- copy-byte *tmp
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x <- add tmp2
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x <- add tmp2
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}
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# x, buf[i+delta] = x/10, x%10
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{
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var dest-index/ecx: int <- copy i
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dest-index <- add delta
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var dest/edi: (addr byte) <- index buf, dest-index
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var next-digit/edx: int <- copy 0
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x, next-digit <- integer-divide x, 0xa
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copy-byte-to *dest, next-digit
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}
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#
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i <- decrement
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loop
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}
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# final patch-up
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var n/eax: int <- copy _n
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compare delta, 1
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{
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break-if-!=
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var curr/ebx: (addr byte) <- index buf, 0
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var one/edx: int <- copy 1
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copy-byte-to *curr, one
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n <- increment
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}
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return n
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}
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fn halve-array-of-decimal-digits _buf: (addr array byte), _n: int, _dp: int -> _/eax: int, _/edx: int {
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var buf/edi: (addr array byte) <- copy _buf
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var n/eax: int <- copy _n
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var dp/edx: int <- copy _dp
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# initialize one side
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{
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# if buf[n-1]%2 == 0, break
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var right-index/ecx: int <- copy n
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right-index <- decrement
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var right-a/ecx: (addr byte) <- index buf, right-index
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var right/ecx: byte <- copy-byte *right-a
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var right-int/ecx: int <- copy right
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var remainder/edx: int <- copy 0
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{
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var dummy/eax: int <- copy 0
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dummy, remainder <- integer-divide right-int, 2
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}
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compare remainder, 0
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break-if-=
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# buf[n] = 0
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var next-a/ecx: (addr byte) <- index buf, n
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var zero/edx: byte <- copy 0
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copy-byte-to *next-a, zero
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# n++
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n <- increment
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}
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# initialize the other
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var delta/ebx: int <- copy 0
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var x/esi: int <- copy 0
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{
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# if buf[0] >= 2, break
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var left/ecx: (addr byte) <- index buf, 0
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var src/ecx: byte <- copy-byte *left
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compare src, 2
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break-if->=
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# delta, x = 1, buf[0]
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delta <- copy 1
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x <- copy src
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# n--
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n <- decrement
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# dp--
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dp <- decrement
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}
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# loop
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var i/ecx: int <- copy 0
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{
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compare i, n
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break-if->=
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# x = x*10 + buf[i+delta]
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{
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var ten/edx: int <- copy 0xa
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x <- multiply ten
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var src-index/edx: int <- copy i
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src-index <- add delta
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var src-a/edx: (addr byte) <- index buf, src-index
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var src/edx: byte <- copy-byte *src-a
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x <- add src
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}
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# buf[i], x = x/2, x%2
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{
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var quotient/eax: int <- copy 0
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var remainder/edx: int <- copy 0
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quotient, remainder <- integer-divide x, 2
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x <- copy remainder
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var dest/edx: (addr byte) <- index buf, i
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copy-byte-to *dest, quotient
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}
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#
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i <- increment
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loop
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}
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return n, dp
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}
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fn _write-float-array-of-decimal-digits out: (addr stream byte), _buf: (addr array byte), n: int, dp: int, precision: int {
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var buf/edi: (addr array byte) <- copy _buf
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{
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compare dp, 0
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break-if->=
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_write-float-array-of-decimal-digits-in-scientific-notation out, buf, n, dp, precision
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return
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}
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{
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var dp2/eax: int <- copy dp
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compare dp2, precision
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break-if-<=
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_write-float-array-of-decimal-digits-in-scientific-notation out, buf, n, dp, precision
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return
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}
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{
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compare dp, 0
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break-if-!=
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append-byte out, 0x30/0
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}
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var i/eax: int <- copy 0
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# bounds = min(n, dp+3)
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var limit/edx: int <- copy dp
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limit <- add 3
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{
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compare limit, n
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break-if-<=
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limit <- copy n
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}
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{
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compare i, limit
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break-if->=
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# print '.' if necessary
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compare i, dp
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{
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break-if-!=
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append-byte out, 0x2e/decimal-point
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}
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var curr-a/ecx: (addr byte) <- index buf, i
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var curr/ecx: byte <- copy-byte *curr-a
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var curr-int/ecx: int <- copy curr
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curr-int <- add 0x30/0
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append-byte out, curr-int
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#
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i <- increment
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loop
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}
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}
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fn _write-float-array-of-decimal-digits-in-scientific-notation out: (addr stream byte), _buf: (addr array byte), n: int, dp: int, precision: int {
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var buf/edi: (addr array byte) <- copy _buf
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var i/eax: int <- copy 0
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{
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compare i, n
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break-if->=
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compare i, precision
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break-if->=
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compare i, 1
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{
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break-if-!=
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append-byte out, 0x2e/decimal-point
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}
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var curr-a/ecx: (addr byte) <- index buf, i
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var curr/ecx: byte <- copy-byte *curr-a
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var curr-int/ecx: int <- copy curr
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curr-int <- add 0x30/0
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append-byte out, curr-int
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#
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i <- increment
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loop
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}
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append-byte out, 0x65/e
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decrement dp
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write-int32-decimal out, dp
|
|
}
|
|
|
|
# follows the structure of write-float-decimal-approximate
|
|
# 'precision' controls the maximum width past which we resort to scientific notation
|
|
fn float-size in: float, precision: int -> _/eax: int {
|
|
# - special names
|
|
var bits/eax: int <- reinterpret in
|
|
compare bits, 0
|
|
{
|
|
break-if-!=
|
|
return 1 # for "0"
|
|
}
|
|
compare bits, 0x80000000
|
|
{
|
|
break-if-!=
|
|
return 2 # for "-0"
|
|
}
|
|
compare bits, 0x7f800000
|
|
{
|
|
break-if-!=
|
|
return 3 # for "Inf"
|
|
}
|
|
compare bits, 0xff800000
|
|
{
|
|
break-if-!=
|
|
return 4 # for "-Inf"
|
|
}
|
|
var exponent/ecx: int <- copy bits
|
|
exponent <- shift-right 0x17 # 23 bits of mantissa
|
|
exponent <- and 0xff
|
|
exponent <- subtract 0x7f
|
|
compare exponent, 0x80
|
|
{
|
|
break-if-!=
|
|
return 3 # for "NaN"
|
|
}
|
|
# - regular numbers
|
|
# v = 1.mantissa (in base 2) << 0x17
|
|
var v/ebx: int <- copy bits
|
|
v <- and 0x7fffff
|
|
v <- or 0x00800000 # insert implicit 1
|
|
# e = exponent - 0x17
|
|
var e/ecx: int <- copy exponent
|
|
e <- subtract 0x17 # move decimal place from before mantissa to after
|
|
|
|
# initialize buffer with decimal representation of v
|
|
var buf-storage: (array byte 0x7f)
|
|
var buf/edi: (addr array byte) <- address buf-storage
|
|
var n/eax: int <- decimal-digits v, buf
|
|
reverse-digits buf, n
|
|
|
|
# loop if e > 0
|
|
{
|
|
compare e, 0
|
|
break-if-<=
|
|
n <- double-array-of-decimal-digits buf, n
|
|
e <- decrement
|
|
loop
|
|
}
|
|
|
|
var dp/edx: int <- copy n
|
|
|
|
# loop if e < 0
|
|
{
|
|
compare e, 0
|
|
break-if->=
|
|
n, dp <- halve-array-of-decimal-digits buf, n, dp
|
|
e <- increment
|
|
loop
|
|
}
|
|
|
|
compare dp, 0
|
|
{
|
|
break-if->=
|
|
return 8 # hacky for scientific notation
|
|
}
|
|
{
|
|
var dp2/eax: int <- copy dp
|
|
compare dp2, precision
|
|
break-if-<=
|
|
return 8 # hacky for scientific notation
|
|
}
|
|
|
|
# result = min(n, dp+3)
|
|
var result/ecx: int <- copy dp
|
|
result <- add 3
|
|
{
|
|
compare result, n
|
|
break-if-<=
|
|
result <- copy n
|
|
}
|
|
|
|
# account for decimal point
|
|
compare dp, n
|
|
{
|
|
break-if->=
|
|
result <- increment
|
|
}
|
|
|
|
# account for sign
|
|
var sign/edx: int <- reinterpret in
|
|
sign <- shift-right 0x1f
|
|
{
|
|
compare sign, 1
|
|
break-if-!=
|
|
result <- increment
|
|
}
|
|
return result
|
|
}
|