7719 - baremetal: print floats
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== code
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integer-divide: # a: int, b: int -> quotient/eax: int, remainder/edx: int
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# . prologue
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55/push-ebp
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89/<- %ebp 4/r32/esp
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# eax = a
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8b/-> *(ebp+8) 0/r32/eax
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# edx = all 0s or all 1s
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99/sign-extend-eax-into-edx
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# quotient, remainder = divide eax by b
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f7 7/subop/divide-eax-edx-by *(ebp+0xc)
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$integer-divide:end:
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# . epilogue
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89/<- %esp 5/r32/ebp
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5d/pop-to-ebp
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c3/return
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@ -57,3 +57,5 @@ sig to-decimal-digit in: grapheme -> _/eax: int
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sig next-word line: (addr stream byte), out: (addr slice) # skips '#' comments
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sig next-raw-word line: (addr stream byte), out: (addr slice) # does not skip '#' comments
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sig stream-empty? s: (addr stream _) -> _/eax: boolean
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sig integer-divide a: int, b: int -> _/eax: int, _/edx: int
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@ -0,0 +1,23 @@
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# Some quick-n-dirty ways to create floats.
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fn fill-in-rational _out: (addr float), nr: int, dr: int {
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var out/edi: (addr float) <- copy _out
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var result/xmm0: float <- convert nr
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var divisor/xmm1: float <- convert dr
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result <- divide divisor
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copy-to *out, result
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}
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fn fill-in-sqrt _out: (addr float), n: int {
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var out/edi: (addr float) <- copy _out
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var result/xmm0: float <- convert n
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result <- square-root result
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copy-to *out, result
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}
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fn rational nr: int, dr: int -> _/xmm0: float {
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var result/xmm0: float <- convert nr
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var divisor/xmm1: float <- convert dr
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result <- divide divisor
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return result
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}
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@ -0,0 +1,604 @@
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# 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-render-float-decimal-normal {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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# 0.5
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var half/xmm0: float <- rational 1, 2
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var dummy/eax: int <- render-float-decimal screen, half, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "0.5 ", "F - test-render-float-decimal-normal 0.5"
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# 0.25
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clear-screen screen
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var quarter/xmm0: float <- rational 1, 4
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var dummy/eax: int <- render-float-decimal screen, quarter, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "0.25 ", "F - test-render-float-decimal-normal 0.25"
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# 0.75
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clear-screen screen
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var three-quarters/xmm0: float <- rational 3, 4
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var dummy/eax: int <- render-float-decimal screen, three-quarters, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "0.75 ", "F - test-render-float-decimal-normal 0.75"
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# 0.125
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clear-screen screen
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var eighth/xmm0: float <- rational 1, 8
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var dummy/eax: int <- render-float-decimal screen, eighth, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "0.125 ", "F - test-render-float-decimal-normal 0.125"
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# 0.0625; start using scientific notation
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clear-screen screen
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var sixteenth/xmm0: float <- rational 1, 0x10
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var dummy/eax: int <- render-float-decimal screen, sixteenth, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "6.25e-2 ", "F - test-render-float-decimal-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-screen screen
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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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var dummy/eax: int <- render-float-decimal screen, sqrt-2, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "1.414 ", "F - test-render-float-decimal-normal √2"
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}
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# print whole integers without decimals
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fn test-render-float-decimal-integer {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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# 1
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var one-f/xmm0: float <- rational 1, 1
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var dummy/eax: int <- render-float-decimal screen, one-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "1 ", "F - test-render-float-decimal-integer 1"
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# 2
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clear-screen screen
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var two-f/xmm0: float <- rational 2, 1
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var dummy/eax: int <- render-float-decimal screen, two-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "2 ", "F - test-render-float-decimal-integer 2"
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# 10
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clear-screen screen
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var ten-f/xmm0: float <- rational 0xa, 1
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var dummy/eax: int <- render-float-decimal screen, ten-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "10 ", "F - test-render-float-decimal-integer 10"
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# -10
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clear-screen screen
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var minus-ten-f/xmm0: float <- rational -0xa, 1
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var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "-10 ", "F - test-render-float-decimal-integer -10"
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# 999
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clear-screen screen
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var minus-ten-f/xmm0: float <- rational 0x3e7, 1
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var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "999 ", "F - test-render-float-decimal-integer 1000"
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# 1000 - start using scientific notation
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clear-screen screen
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var minus-ten-f/xmm0: float <- rational 0x3e8, 1
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var dummy/eax: int <- render-float-decimal screen, minus-ten-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "1.00e3 ", "F - test-render-float-decimal-integer 1000"
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# 100,000
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clear-screen screen
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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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var dummy/eax: int <- render-float-decimal screen, hundred-thousand-f, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "1.00e5 ", "F - test-render-float-decimal-integer 100,000"
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}
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fn test-render-float-decimal-zero {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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var zero: float
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var dummy/eax: int <- render-float-decimal screen, zero, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "0 ", "F - test-render-float-decimal-zero"
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}
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fn test-render-float-decimal-negative-zero {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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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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var dummy/eax: int <- render-float-decimal screen, negative-zero, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "-0 ", "F - test-render-float-decimal-negative-zero"
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}
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fn test-render-float-decimal-infinity {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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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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var dummy/eax: int <- render-float-decimal screen, infinity, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "Inf ", "F - test-render-float-decimal-infinity"
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}
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fn test-render-float-decimal-negative-infinity {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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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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var dummy/eax: int <- render-float-decimal screen, negative-infinity, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "-Inf ", "F - test-render-float-decimal-negative-infinity"
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}
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fn test-render-float-decimal-not-a-number {
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var screen-on-stack: screen
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var screen/esi: (addr screen) <- address screen-on-stack
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initialize-screen screen, 0x20, 5 # 32 columns should be more than enough
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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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var dummy/eax: int <- render-float-decimal screen, nan, 3/precision, 0, 0, 3/fg, 0/bg
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check-screen-row screen, 0/y, "NaN ", "F - test-render-float-decimal-not-a-number"
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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 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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# - 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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var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "0", x, y, color, background-color
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return new-x
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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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var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "-0", x, y, color, background-color
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return new-x
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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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var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "Inf", x, y, color, background-color
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return new-x
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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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var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "-Inf", x, y, color, background-color
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return new-x
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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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var new-x/eax: int <- draw-text-rightward-over-full-screen screen, "NaN", x, y, color, background-color
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return new-x
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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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draw-code-point screen, 0x2d/minus, x, y, color, background-color
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increment x
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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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var new-x/eax: int <- render-float-buffer screen, buf, n, dp, precision, x, y, color, background-color
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return new-x
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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
|
||||
var delta/ebx: int <- copy 0
|
||||
var x/esi: int <- copy 0
|
||||
{
|
||||
# if buf[0] >= 2, break
|
||||
var left/ecx: (addr byte) <- index buf, 0
|
||||
var src/ecx: byte <- copy-byte *left
|
||||
compare src, 2
|
||||
break-if->=
|
||||
# delta, x = 1, buf[0]
|
||||
delta <- copy 1
|
||||
x <- copy src
|
||||
# n--
|
||||
n <- decrement
|
||||
# dp--
|
||||
dp <- decrement
|
||||
}
|
||||
# loop
|
||||
var i/ecx: int <- copy 0
|
||||
{
|
||||
compare i, n
|
||||
break-if->=
|
||||
# x = x*10 + buf[i+delta]
|
||||
{
|
||||
var ten/edx: int <- copy 0xa
|
||||
x <- multiply ten
|
||||
var src-index/edx: int <- copy i
|
||||
src-index <- add delta
|
||||
var src-a/edx: (addr byte) <- index buf, src-index
|
||||
var src/edx: byte <- copy-byte *src-a
|
||||
x <- add src
|
||||
}
|
||||
# buf[i], x = x/2, x%2
|
||||
{
|
||||
var quotient/eax: int <- copy 0
|
||||
var remainder/edx: int <- copy 0
|
||||
quotient, remainder <- integer-divide x, 2
|
||||
x <- copy remainder
|
||||
var dest/edx: (addr byte) <- index buf, i
|
||||
copy-byte-to *dest, quotient
|
||||
}
|
||||
#
|
||||
i <- increment
|
||||
loop
|
||||
}
|
||||
return n, dp
|
||||
}
|
||||
|
||||
fn render-float-buffer screen: (addr screen), _buf: (addr array byte), n: int, dp: int, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
|
||||
var buf/edi: (addr array byte) <- copy _buf
|
||||
{
|
||||
compare dp, 0
|
||||
break-if->=
|
||||
var new-x/eax: int <- render-float-buffer-in-scientific-notation screen, buf, n, dp, precision, x, y, color, background-color
|
||||
return new-x
|
||||
}
|
||||
{
|
||||
var dp2/eax: int <- copy dp
|
||||
compare dp2, precision
|
||||
break-if-<=
|
||||
var new-x/eax: int <- render-float-buffer-in-scientific-notation screen, buf, n, dp, precision, x, y, color, background-color
|
||||
return new-x
|
||||
}
|
||||
{
|
||||
compare dp, 0
|
||||
break-if-!=
|
||||
draw-code-point screen, 0x30/0, x, y, color, background-color
|
||||
increment x
|
||||
}
|
||||
var i/eax: int <- copy 0
|
||||
# bounds = min(n, dp+3)
|
||||
var limit/edx: int <- copy dp
|
||||
limit <- add 3
|
||||
{
|
||||
compare limit, n
|
||||
break-if-<=
|
||||
limit <- copy n
|
||||
}
|
||||
{
|
||||
compare i, limit
|
||||
break-if->=
|
||||
# print '.' if necessary
|
||||
compare i, dp
|
||||
{
|
||||
break-if-!=
|
||||
draw-code-point screen, 0x2e/decimal-point, x, y, color, background-color
|
||||
increment x
|
||||
}
|
||||
var curr-a/ecx: (addr byte) <- index buf, i
|
||||
var curr/ecx: byte <- copy-byte *curr-a
|
||||
curr <- add 0x30/0
|
||||
var curr-grapheme/ecx: grapheme <- copy curr
|
||||
draw-grapheme screen, curr-grapheme, x, y, color, background-color
|
||||
increment x
|
||||
i <- increment
|
||||
loop
|
||||
}
|
||||
return x
|
||||
}
|
||||
|
||||
fn render-float-buffer-in-scientific-notation screen: (addr screen), _buf: (addr array byte), n: int, dp: int, precision: int, x: int, y: int, color: int, background-color: int -> _/eax: int {
|
||||
var buf/edi: (addr array byte) <- copy _buf
|
||||
var i/eax: int <- copy 0
|
||||
{
|
||||
compare i, n
|
||||
break-if->=
|
||||
compare i, precision
|
||||
break-if->=
|
||||
compare i, 1
|
||||
{
|
||||
break-if-!=
|
||||
draw-code-point screen, 0x2e/decimal-point, x, y, color, background-color
|
||||
increment x
|
||||
}
|
||||
var curr-a/ecx: (addr byte) <- index buf, i
|
||||
var curr/ecx: byte <- copy-byte *curr-a
|
||||
curr <- add 0x30/0
|
||||
var curr-grapheme/ecx: grapheme <- copy curr
|
||||
draw-grapheme screen, curr-grapheme, x, y, color, background-color
|
||||
increment x
|
||||
#
|
||||
i <- increment
|
||||
loop
|
||||
}
|
||||
draw-code-point screen, 0x65/e, x, y, color, background-color
|
||||
increment x
|
||||
decrement dp
|
||||
var new-x/eax: int <- copy 0
|
||||
var new-y/ecx: int <- copy 0
|
||||
new-x, new-y <- draw-int32-decimal-wrapping-right-then-down-over-full-screen screen, dp, x, y, color, background-color
|
||||
return new-x
|
||||
}
|
||||
|
||||
# follows the structure of render-float-decimal
|
||||
# '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
|
||||
}
|
Loading…
Reference in New Issue