

Created:
9 years, 9 months ago by adonovan Modified:
9 years, 8 months ago Reviewers:
CC:
remyoudompheng, rsc, golangdev Visibility:
Public. 
Descriptionmath/big: add Rat.{,Set}Float64 methods for IEEE 754 conversions.
Added tests, using input data from strconv.ParseFloat.
Thanks to rsc for most of the test code.
math/big could use some good packagelevel documentation.
Patch Set 1 #Patch Set 2 : diff r 2888e5323790 https://code.google.com/p/go/ #
Total comments: 41
Patch Set 3 : diff r 2888e5323790 https://code.google.com/p/go/ #
Total comments: 19
Patch Set 4 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #
Total comments: 64
Patch Set 5 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #Patch Set 6 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #Patch Set 7 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #Patch Set 8 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #Patch Set 9 : diff r 3ef1c4fabb5f https://code.google.com/p/go/ #Patch Set 10 : diff r 601795ce6319 https://code.google.com/p/go/ #MessagesTotal messages: 19
Haven't thought through this is detail yet, but here some prelim. feedback. Please pay attention particularly to the reuse of the underlying slices by using the appropriate set functions. We have gone through a lot of pain to get meth/big to where it is. The reason for reusing the underlying memory is performance (the first implementation didn't do it and was _much_ slower overall). It may not matter for a single function, but it does matter overall when the function is used in a larger algorithm. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:35: panic("SetFloat requires finite value") SetFloat64 https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:35: panic("SetFloat requires finite value") on that note, I am wondering if this is a good choice. alternatively, one might return nil. as it is, a client will have to check anyway, so why not provide the result? also, if the client doesn't pay attention, it will die with a null ptr exception when the result is used. about the same. so: return nil ? https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:37: if f == 0.0 { f == 0 seems good enough  we are in Go after all https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:38: z.a, z.b = Int{}, *intOne that's not how we do this in this package  you throw away whatever memory is hanging of z by doing this use the appropriate Set function https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:43: const SmallestNormal = 2.2250738585072014e308 // 2**1022 this code is also in math/bits.go  should at least mention this in a comment (even better if we can find a way some of this can be shared)  it's subtle enough that we don't want to have random copies all over the place https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:52: mantissa := (1 << 52)  (bits & 0xFFFFFFFFFFFFF) The constants 52, 1023, etc. should be at least declared as constants (or perhaps computed from other constants) if we can't import them. same for 0x7ff. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:57: z.b = *intOne use Set function so we don't throw away underlying memory https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:60: z.b.abs = z.b.abs.shl(z.b.abs, uint(shift)) use set functions https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:69: // Preconditions: b is nonzero; a and b have no common factors. s/nonzero/nonzero/ https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:97: expt := alen  blen s/expt/exp/ please https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:117: if expt > 1024 { switch { case expt > 1024: ... case expt < 1023: if neg { return 1 } return 0 } https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:148: (uint64((expt+1023)&0x7FF) << 52)  mantissa) one line please https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:165: exact = false just return https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:172: exact = z2.Cmp(z) == 0 I'd do: if z2.Cmp(z) == 0 { exact = true } https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go File src/pkg/math/bits.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go#newcode40 src/pkg/math/bits.go:40: func IsFinite(f float64) bool { why not use IsInf?
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https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:53: exp := int((bits>>52)&0x7FF)  1023 mantissa := bits & (1<<521) (counting these F's is crazy) exp := int(bits>>52 & 0x7ff) switch exp { case 0x7ff: // NaN or infinite ... case 0: // denormal exp = 1023 default: mantissa = 1<<52 exp = 1023 } and remove the special cases above, and no need to change math package interface. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:82: // The result contains mantissa A/B and exponent e. Sorry but this algorithm is incorrect. It breaks at the simplest testcase: func TestFloat64(t *testing.T) { const U = 1<<60  1 z := new(Rat).SetInt64(U) v, _ := z.Float64() if v != 1<<60 { t.Errorf("got %b, expected %b", v, float64(1<<60)) } } https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:146: mantissa := uint64(q[0] & 0xfffffffffffff) // 52 bits This line doesn't compile at all. Here Word is 32 bit. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go... src/pkg/math/big/rat_test.go:508: // TODO(adonovan): is this ok? Or should I copy the file, or even I'm not sure testfp.txt is a good input file for tests. A table driven test + use testing/quick to check * z.SetFloat64(f).Float64() == f * x := z.Float64, x1, x2 = prevFloat64(x), nextFloat64(x) // use SetFloat64 and big.Rat arithmetic to check that x is closest to z as specified.
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https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:82: // The result contains mantissa A/B and exponent e. After correcting please check that your function rounds correctly: 1<<253  1<<199 + 1 > 1<<253 1<<253  1<<199  1 > previous float64 before 1<<253 (1<<253  1<<200 I guess). And you should specify what happens when the rat is halfway.
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https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go... src/pkg/math/big/rat_test.go:508: // TODO(adonovan): is this ok? Or should I copy the file, or even You can read the file directly, that's fine. As for using it, what I had intended (but not expressed well) was to use the decimal > binary conversions as rat > binary conversions by building fractions with appropriate denominators. For example the file contains # Table 1: Stress Inputs for Conversion to 53bit Binary, < 1/2 ULP float64 %b 5e+125 6653062250012735p+365 float64 %b 69e+267 4705683757438170p+841 float64 %b 999e026 6798841691080350p129 In the strconv package that says to try strconv.ParseFloat("5e+125", 64) and make sure you get the 6653062250012735*2³⁶⁵. Here, though, you could create the fraction 5*10¹²⁵ / 1 and call .Float64 on it and make sure you get 5e+125 out (you can trust ParseFloat64, you don't need to look at the final field at all). Similarly, a few lines later, you could create the fraction 836168422905420598437 / 10²³⁴ and call .Float64 on it and make sure you get what ParseFloat says for 836168422905420598437e234. Do the same with the strings in the table in src/pkg/strconv/atof_test.go. If the code can pass both of those sets of cases, then I'll be pretty confident it's right.
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Thanks for the helpful review commentsthere were indeed a number of corner cases the tests hadn't touched. Still one testcase fails, for the exact same reason described in the Java blog post referenced. Suggestions welcome. Ready for another look. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:35: panic("SetFloat requires finite value") On 2012/12/13 01:52:06, gri wrote: > SetFloat64 Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:35: panic("SetFloat requires finite value") On 2012/12/13 01:52:06, gri wrote: > on that note, I am wondering if this is a good choice. alternatively, one might > return nil. as it is, a client will have to check anyway, so why not provide the > result? also, if the client doesn't pay attention, it will die with a null ptr > exception when the result is used. about the same. > > so: return nil ? Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:37: if f == 0.0 { On 2012/12/13 01:52:06, gri wrote: > f == 0 > > seems good enough  we are in Go after all Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:38: z.a, z.b = Int{}, *intOne On 2012/12/13 01:52:06, gri wrote: > that's not how we do this in this package  you throw away whatever memory is > hanging of z by doing this > > use the appropriate Set function Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:43: const SmallestNormal = 2.2250738585072014e308 // 2**1022 Per Remy's suggestion, this is gone. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:52: mantissa := (1 << 52)  (bits & 0xFFFFFFFFFFFFF) I tried that but it looked awful: long names everywhere, obscuring the meaning. 11, 52 and 1023 need no explanation. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:53: exp := int((bits>>52)&0x7FF)  1023 Very nice. Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:57: z.b = *intOne On 2012/12/13 01:52:06, gri wrote: > use Set function so we don't throw away underlying memory Done. This package could use some documentation explaining the proper use. I found I had to think quite hard about aliasing to avoid making even more mistakes. That you have to mention a value up to four times in a binary operation z = z.op(z, z) can be a cause for some headscratching. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:60: z.b.abs = z.b.abs.shl(z.b.abs, uint(shift)) On 2012/12/13 01:52:06, gri wrote: > use set functions Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:69: // Preconditions: b is nonzero; a and b have no common factors. On 2012/12/13 01:52:06, gri wrote: > s/nonzero/nonzero/ Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:82: // The result contains mantissa A/B and exponent e. You're right, it was always finding a value of equal or smaller magnitude, not the nearest. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:97: expt := alen  blen On 2012/12/13 01:52:06, gri wrote: > s/expt/exp/ please Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:117: if expt > 1024 { Done. (FWIW, that's "return 0.0" in effect.) https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:146: mantissa := uint64(q[0] & 0xfffffffffffff) // 52 bits On 2012/12/13 07:37:38, remyoudompheng wrote: > This line doesn't compile at all. > Here Word is 32 bit. Good catch; I'm testing on 64 bits. Fixed. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:148: (uint64((expt+1023)&0x7FF) << 52)  mantissa) On 2012/12/13 01:52:06, gri wrote: > one line please Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:165: exact = false On 2012/12/13 01:52:06, gri wrote: > just return Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat.go#newc... src/pkg/math/big/rat.go:172: exact = z2.Cmp(z) == 0 On 2012/12/13 01:52:06, gri wrote: > I'd do: > > if z2.Cmp(z) == 0 { > exact = true > } Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/big/rat_test.go... src/pkg/math/big/rat_test.go:508: // TODO(adonovan): is this ok? Or should I copy the file, or even On 2012/12/13 14:41:58, rsc wrote: > You can read the file directly, that's fine. As for using it, what I had > intended (but not expressed well) was to use the decimal > binary conversions > as rat > binary conversions by building fractions with appropriate > denominators. For example the file contains > > # Table 1: Stress Inputs for Conversion to 53bit Binary, < 1/2 ULP > float64 %b 5e+125 6653062250012735p+365 > float64 %b 69e+267 4705683757438170p+841 > float64 %b 999e026 6798841691080350p129 > > In the strconv package that says to try strconv.ParseFloat("5e+125", 64) and > make sure you get the 6653062250012735*2³⁶⁵. Here, though, you could create the > fraction 5*10¹²⁵ / 1 and call .Float64 on it and make sure you get 5e+125 out > (you can trust ParseFloat64, you don't need to look at the final field at all). > > Similarly, a few lines later, you could create the fraction > 836168422905420598437 / 10²³⁴ and call .Float64 on it and make sure you get what > ParseFloat says for 836168422905420598437e234. > > Do the same with the strings in the table in src/pkg/strconv/atof_test.go. > > If the code can pass both of those sets of cases, then I'll be pretty confident > it's right. Done. https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go File src/pkg/math/bits.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go#newcode40 src/pkg/math/bits.go:40: func IsFinite(f float64) bool { On 2012/12/13 01:52:06, gri wrote: > why not use IsInf? This predicate is equivalent to !(IsNaN(f)  IsInf(f,0)) but faster than either arm. I've clarified this in the docstring.
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https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/nat.go File src/pkg/math/big/nat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/nat.go#new... src/pkg/math/big/nat.go:116: return uint64(z[1]<<32  z[0]) on 32 bits, z[1]<<32 is identically zero. Can you test your code with GOARCH=386 ? Also, from a very lowlevel point of view, adding a private method grows the method table of nat for no particular reason. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:94: switch { It's really not clear why you shift twice. // Determine A' and B', such A'/B' = A/B * (1<<shift) // is in the interval [1<<52, 1<<53). https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:105: default: // First we determine α/β where α and β are shifted values // of A and B such that 1 <= α/β < 2. // Here we only get 1/2 <= A/B*2^exp < 2. // If this is less than 1, decrement exp by 1 to get // back in interval [1, 2) https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:112: // Shift and divide. // Now we use A'/B' = α/β * 2^52 = A/B * 2^(52exp). // A'/B' is in the interval [2^52, 2^53). https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:114: var a2, b2 nat please reuse a2, b2 from above. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:127: if mantissa&^(1<<521) != 1<<52 { You want to check that mantissa>>52 == 1. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:139: if mantissa == 0x20000000000000 { 1<<53. I really don't want to count the zeroes. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:144: // After rounding, q*2^52 * 2^exp is a good approximation of A/B https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:151: I would write: switch { case exp > 1023: // infinity case exp >= 1022: // finite case exp < 102253: // zero default: // denormal or zero // q*2^(exp52) = q*2^(exp+1022)*2^(102252) shift := uint(1022exp) lostbits := mantissa & (1<<shift  1) mantissa >>= shift switch { case lostbits == 1<<(shift1): // halfway mantissa &^= 1 case lostbits>>(shift1) != 0: // round up mantissa++ default: // nothing to do } // Now mantissa is in [0, 1<<52] f = math.Float64frombits(mantissa) // valid even if mantissa == 1<<52 if neg { f = f } return f } https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:176: // can we tell which is closer? I'm not sure why it would oscillate. Denormalized/zero numbers are n * 2^(102252) where n is an integer in [0, 1<<52). The case n==1<<52 is exactly the next float64 so you just have to multiply by 1<<1074 and round to the nearest integer (even if the nearest is 1<<52). And the closest float64 is well defined. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:645: // smallest denormal Please add: * the exact half of smallest denormal (1p1075) > round to zero * a little more than the exact half of smallest denormal (let's say 1p1075 + 1p1100), rounding to 1p1074 * the exact halfway between smallest normal and largest denormal: 1p1022  1p1075, rounding to 1p1022 The decimal representation might be a bit long to write.
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Once Remy is happy I'll be happy. :) https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go File src/pkg/math/bits.go (right): https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go#newcode40 src/pkg/math/bits.go:40: func IsFinite(f float64) bool { To add new API we need more widespread use cases than just one package. Please put this in your new code (unexported) instead of here. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:171: if mantissa == 0x10000000000000 { 1<<52
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Thanks again for the great review comments, and apologies for the lack of polish. If it wasn't obvious, f.p. code is not my comfort zone and I was just trying to solicit an extra round of review feedback before checking out for the weekend. On 14 December 2012 21:49, <rsc@golang.org> wrote: > Once Remy is happy I'll be happy. :) > > > > > https://codereview.appspot.**com/6930059/diff/2001/src/pkg/**math/bits.go<htt... > File src/pkg/math/bits.go (right): > > https://codereview.appspot.**com/6930059/diff/2001/src/pkg/** > math/bits.go#newcode40<https://codereview.appspot.com/6930059/diff/2001/src/pkg/math/bits.go#newcode40> > src/pkg/math/bits.go:40: func IsFinite(f float64) bool { > To add new API we need more widespread use cases than just one package. > Please put this in your new code (unexported) instead of here. > > > https://codereview.appspot.**com/6930059/diff/11001/src/** > pkg/math/big/rat.go<https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go> > File src/pkg/math/big/rat.go (right): > > https://codereview.appspot.**com/6930059/diff/11001/src/** > pkg/math/big/rat.go#newcode171<https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#newcode171> > src/pkg/math/big/rat.go:171: if mantissa == 0x10000000000000 { > 1<<52 > > https://codereview.appspot.**com/6930059/<https://codereview.appspot.com/6930... >
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I am a little worried about the double rounding. I think it would be more clearly correct to tweak the algorithm a little bit. The state you care about for rounding floating point numbers accurately is: 1) The bits of computed mantissa. 2) The first bit of the remainder fraction. 3) Whether any of the rest of the bits in the remainder are zero. My suggestion is to generate 54 bits of mantissa, a combination of 1+2. (That is, the low bit of the quotient is going to be used for rounding and then thrown away.) Choose q, r, exp such that (q + r/b) * 2^(exp1) = a/b q in [1<<53, 1<<54) // Handle denormal loss of precision by moving more into remainder. haveR := r > 0 if denormal { n := bits to drop haveR = haveR  (q & (1<<n1)) != 0 q >>= n } // Round q, dropping the low bit we've been carrying. if q&1 != 0 && haveR  q&2 == 0 { q++ } q >>= 1 f := math.Ldexp(float64(q), exp) if neg { f = f } return f https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:94: switch { On 2012/12/15 00:17:48, remyoudompheng wrote: > It's really not clear why you shift twice. > > // Determine A' and B', such A'/B' = A/B * (1<<shift) > // is in the interval [1<<52, 1<<53). The first shift makes it possible to use cmp directly. Otherwise we'd need a custom compare function. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:122: // REVIEWERS: what's the recommended memory discipline here? This is fine for now. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:193: // exact is true iff no approximation was involved. we tend not to use iff in docs. // If z is exactly representable as a float64, Float64 returns exact=true.
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3) should say ... are nonzero.
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Hello remyoudompheng@gmail.com, rsc@golang.org (cc: golangdev@googlegroups.com), I'd like you to review this change to https://code.google.com/p/go/
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https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/nat.go File src/pkg/math/big/nat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/nat.go#new... src/pkg/math/big/nat.go:116: return uint64(z[1]<<32  z[0]) On 2012/12/15 00:17:48, remyoudompheng wrote: > on 32 bits, z[1]<<32 is identically zero. > > Can you test your code with GOARCH=386 ? > > Also, from a very lowlevel point of view, adding a private method grows the > method table of nat for no particular reason. Done. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:105: default: On 2012/12/15 00:17:48, remyoudompheng wrote: > // First we determine α/β where α and β are shifted values > // of A and B such that 1 <= α/β < 2. > > // Here we only get 1/2 <= A/B*2^exp < 2. > // If this is less than 1, decrement exp by 1 to get > // back in interval [1, 2) Done. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:139: if mantissa == 0x20000000000000 { On 2012/12/15 00:17:48, remyoudompheng wrote: > 1<<53. I really don't want to count the zeroes. Done. https://codereview.appspot.com/6930059/diff/11001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:144: On 2012/12/15 00:17:48, remyoudompheng wrote: > // After rounding, q*2^52 * 2^exp is a good approximation of A/B Done.
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Looks correct to me! https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:32: // If f is not finite, SetFloat simply returns nil. s/simply // https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:34: const expMask = (1 << 11)  1 drop ( ) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:36: mantissa := bits & ((1 << 52)  1) drop inner ( ) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:47: z.a.SetUint64(mantissa) Before this, I would suggest for mantissa&1 == 0 && shift < 0 { mantissa >>= 1 shift++ } Then things like 1.0 will give 1/1 instead of 2^52/2^52. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:52: // REVIEWERS: what's the correct memory discipline here? This is fine but you can also let the Int routines worry about it. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:53: z.b.abs = z.b.abs.shl(z.b.abs, uint(shift)) z.b.Lsh(&z.b, uint(shift)) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:55: z.a.abs = z.a.abs.shl(z.a.abs, uint(shift)) z.a.Lsh(&z.a, uint(shift)) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:60: // isFinite returns whether f represents a finite rational value. s/returns/reports/ https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:127: haveRem := len(r) > 0 // m[0]&1 && !haveRem => remainder is exactly half If you move this up after the mantissa := low64(q) at line 113, then you can change the r = r.add(r, b2) at line 119 to haveRem = true https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:139: if mantissa&1 != 0 && haveRem  mantissa&2 != 0 { Perhaps you meant if mantissa&1 != 0 && (haveRem  mantissa&2 != 0) { The condition you've got triggers for mantissa&1 == 0 && mantissa&2 != 0. Luckily, in that case the ++ only touches the low bit, which is about to be shifted away, so it's actually correct, just probably not what you meant. If you track exactness the bug goes away because you have to split the expression anyway: exact := !haveRem if mantissa&1 != 0 { exact = false if haveRem  mantissa&2 != 0 { if mantissa++; mantissa >= 1<<54 { // Complete rollover 11...1 => 100...0, so shift is safe. mantissa >>= 1 exp++ } } } mantissa >>= 1 if exp > 1023 { exact = false if neg { f = math.Inf(1) } f = math.Inf(+1) } else { f = math.Ldexp(float64(mantissa), exp53) } https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:140: mantissa++ // may carry into exponent I know what you mean, but there's no exponent in a mantissa. // may create 55bit number https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:142: mantissa >>= 1 // discard extra rounding bit. 53 bits left. // discard rounding bit. Mantissa now scaled by 2^53. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:164: // Inefficient! You might as well figure this out in quotToFloat. See comment above. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:503: var inputs = []string{ float64inputs https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:695: if expected != x { x != expected The same way you'd write x != nil. Not the same way xUnit programmers write 0 != f(). https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:696: t.Errorf("string > Rat > float64 yielded wrong value; input=%s expected=%g actual=%g error=%g", input, expected, x, (xexpected)/expected) Use Go syntax to describe values; show x first, like in x != expected. The general form is: expression = value, want expectedvalue Also, %b will print a float64 using 1p+4 notation, which is usually helpful: t.Errorf("Rat.SetString(%s).Float64() = %g (%b), want %g (%b); delta=%b", input, x, x, expected, expected, xexpected) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:712: t.Error("SetFloat64 returned nil for a finite value", f) t.Errorf("Rat.SetFloat64(%g) = nil", f) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:716: if f != f2 { f2 != f But really you can do both here: if f2 != f  exact != true { https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:717: t.Error("float64>Rat>float64 roundtrip was lossy", f, f2, (f2f)/f) t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta=%b", f, f2, f2, exact, f, f, true, f2f) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:719: if !exact { Can drop (now handled above) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:730: t.Errorf("SetFloat64(%g) returned nonnil value: %v", f, r2) Rat.SetFloat64(%g) = %v, want nil https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:745: {"1.23456788e1234", 0.0}, s/.0// https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:746: {"1.23456788e1234", 0.0}, // 0.0, actually s/0.0/math.Copysign(0, 1)/ and then drop the comment https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:747: {"1152921504606846975", float64(1<<60  1)}, The conversions here should be unnecessary. 1<<60  1 (1<<60 1) and so on https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:759: if s.expected != f { if f != s.expected Although here I think you should probably do if !sameFloat(f, s.expected)  exact != false { And define // f1==f2 but treats 0, +0 as distinct. func sameFloat(f1, f2 float64) { return math.Float64bits(f1) == math.Float64bits(f2) } https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:760: t.Errorf("Rat.Float64() returned incorrect value; literal=%v value=%b expected=%b delta=%g", s.rat, f, s.expected, fs.expected) Rat.SetString(%s).Float64() = %g (%b), %v, want %g (%b), %v; delta=%b https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:829: if r.Cmp(rf0) <= 0  r.Cmp(rf1) >= 0 { Maybe you can drop this entirely. The closeness checks will handle this (and arguably give better messages). https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:836: df0 := new(Rat).Sub(r, rf0) // known > 0 .Abs(new(Rat)) and drop comment https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:837: df1 := new(Rat).Sub(rf1, r) // known > 0 same https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:839: t.Errorf("%b (approx. of %v) is not as close as previous float %b", f, r, f0) "Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer" https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:847: t.Errorf("%b (approx. of %v) should round halfway to previous (even) float %b ", f, r, f0) "Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead" https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:861: 1 / 3, 1.0 / 3 maybe (1/3 = 0)
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PTAL. Russ, thanks again for the patient and thorough review during which you effectively wrote the entire change (production code and tests) much better than I was evidently doing. P.S. One discovery I made is that 'aptget install gnomegenius' gives you a nice infiniteprecision calculator: what I wish bc(1) had been. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:32: // If f is not finite, SetFloat simply returns nil. On 2013/01/25 22:23:50, rsc wrote: > s/simply // Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:34: const expMask = (1 << 11)  1 On 2013/01/25 22:23:50, rsc wrote: > drop ( ) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:36: mantissa := bits & ((1 << 52)  1) On 2013/01/25 22:23:50, rsc wrote: > drop inner ( ) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:47: z.a.SetUint64(mantissa) On 2013/01/25 22:23:50, rsc wrote: > Before this, I would suggest > > for mantissa&1 == 0 && shift < 0 { > mantissa >>= 1 > shift++ > } > > Then things like 1.0 will give 1/1 instead of 2^52/2^52. Done. (I think you had the sense of < and ++ backwards.) It's not clear to me that 52 iterations of this loop is saving us much in the common case of 1.0. Is there a good Go definition of ntz(uint64) somewhere? Hacker's Delight has four candidates but none is a oneliner, and I don't think it merits an inline implementation. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:52: // REVIEWERS: what's the correct memory discipline here? On 2013/01/25 22:23:50, rsc wrote: > This is fine but you can also let the Int routines worry about it. Right. Sorry for the dumb questionby the time of this review iteration I has already discovered the answer. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:53: z.b.abs = z.b.abs.shl(z.b.abs, uint(shift)) On 2013/01/25 22:23:50, rsc wrote: > z.b.Lsh(&z.b, uint(shift)) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:55: z.a.abs = z.a.abs.shl(z.a.abs, uint(shift)) On 2013/01/25 22:23:50, rsc wrote: > z.a.Lsh(&z.a, uint(shift)) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:60: // isFinite returns whether f represents a finite rational value. On 2013/01/25 22:23:50, rsc wrote: > s/returns/reports/ Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:127: haveRem := len(r) > 0 // m[0]&1 && !haveRem => remainder is exactly half On 2013/01/25 22:23:50, rsc wrote: > If you move this up after the mantissa := low64(q) at line 113, then you can > change the r = r.add(r, b2) at line 119 to haveRem = true That's better. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:139: if mantissa&1 != 0 && haveRem  mantissa&2 != 0 { On 2013/01/25 22:23:50, rsc wrote: > Perhaps you meant > if mantissa&1 != 0 && (haveRem  mantissa&2 != 0) { > > The condition you've got triggers for mantissa&1 == 0 && mantissa&2 != 0. > Luckily, in that case the ++ only touches the low bit, which is about to be > shifted away, so it's actually correct, just probably not what you meant. You're absolutely right, I misassociated the expression. > If you track exactness the bug goes away because you have to split the > expression anyway: > > exact := !haveRem > if mantissa&1 != 0 { > exact = false > if haveRem  mantissa&2 != 0 { > if mantissa++; mantissa >= 1<<54 { > // Complete rollover 11...1 => 100...0, so shift is safe. > mantissa >>= 1 > exp++ > } > } > } > mantissa >>= 1 > > if exp > 1023 { > exact = false > if neg { > f = math.Inf(1) > } > f = math.Inf(+1) > } else { > f = math.Ldexp(float64(mantissa), exp53) > } > Much better; this saves the expensive exactness check. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.go File src/pkg/math/big/rat_test.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:503: var inputs = []string{ On 2013/01/25 22:23:50, rsc wrote: > float64inputs Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:695: if expected != x { On 2013/01/25 22:23:50, rsc wrote: > x != expected > > The same way you'd write x != nil. > Not the same way xUnit programmers write 0 != f(). > Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:696: t.Errorf("string > Rat > float64 yielded wrong value; input=%s expected=%g actual=%g error=%g", input, expected, x, (xexpected)/expected) On 2013/01/25 22:23:50, rsc wrote: > Use Go syntax to describe values; show x first, like in x != expected. > The general form is: > expression = value, want expectedvalue > > Also, %b will print a float64 using 1p+4 notation, which is usually helpful: > > t.Errorf("Rat.SetString(%s).Float64() = %g (%b), want %g (%b); delta=%b", input, > x, x, expected, expected, xexpected) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:712: t.Error("SetFloat64 returned nil for a finite value", f) On 2013/01/25 22:23:50, rsc wrote: > t.Errorf("Rat.SetFloat64(%g) = nil", f) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:716: if f != f2 { On 2013/01/25 22:23:50, rsc wrote: > f2 != f > But really you can do both here: > > if f2 != f  exact != true { Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:717: t.Error("float64>Rat>float64 roundtrip was lossy", f, f2, (f2f)/f) On 2013/01/25 22:23:50, rsc wrote: > t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; > delta=%b", f, f2, f2, exact, f, f, true, f2f) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:719: if !exact { On 2013/01/25 22:23:50, rsc wrote: > Can drop (now handled above) Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:730: t.Errorf("SetFloat64(%g) returned nonnil value: %v", f, r2) On 2013/01/25 22:23:50, rsc wrote: > Rat.SetFloat64(%g) = %v, want nil Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:745: {"1.23456788e1234", 0.0}, On 2013/01/25 22:23:50, rsc wrote: > s/.0// Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:746: {"1.23456788e1234", 0.0}, // 0.0, actually On 2013/01/25 22:23:50, rsc wrote: > s/0.0/math.Copysign(0, 1)/ > and then drop the comment +0.0 and 0.0 are equivalent anyway so this was merely documentation; the test is not comparing bitpatterns or signs. In any case I realised that all of these testcases (with the exception of "1/3") are all subsumed by the existing float64inputs test as recently augumented. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:747: {"1152921504606846975", float64(1<<60  1)}, On 2013/01/25 22:23:50, rsc wrote: > The conversions here should be unnecessary. > 1<<60  1 > (1<<60 1) > and so on Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:747: {"1152921504606846975", float64(1<<60  1)}, On 2013/01/25 22:23:50, rsc wrote: > The conversions here should be unnecessary. > 1<<60  1 > (1<<60 1) > and so on Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:759: if s.expected != f { On 2013/01/25 22:23:50, rsc wrote: > if f != s.expected > > Although here I think you should probably do > > if !sameFloat(f, s.expected)  exact != false { > > And define > > // f1==f2 but treats 0, +0 as distinct. > func sameFloat(f1, f2 float64) { > return math.Float64bits(f1) == math.Float64bits(f2) > } We need to make a special exception for Rat.SetString("0"): we can't expect Rat to retain the sign, but we do want to ensure that very small negative rationals map to 0.0. Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:760: t.Errorf("Rat.Float64() returned incorrect value; literal=%v value=%b expected=%b delta=%g", s.rat, f, s.expected, fs.expected) On 2013/01/25 22:23:50, rsc wrote: > Rat.SetString(%s).Float64() = %g (%b), %v, want %g (%b), %v; delta=%b Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:829: if r.Cmp(rf0) <= 0  r.Cmp(rf1) >= 0 { On 2013/01/25 22:23:50, rsc wrote: > Maybe you can drop this entirely. The closeness checks will handle this (and > arguably give better messages). Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:836: df0 := new(Rat).Sub(r, rf0) // known > 0 On 2013/01/25 22:23:50, rsc wrote: > .Abs(new(Rat)) and drop comment I think you meant: df0 := new(Rat).Sub(r, rf0) df0.Abs(df0) (This took me a good while to find. I find this calling convention endlessly burdensome despite being aware of its motivation. libgmp suffers from a similar affliction.) https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:837: df1 := new(Rat).Sub(rf1, r) // known > 0 On 2013/01/25 22:23:50, rsc wrote: > same Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:839: t.Errorf("%b (approx. of %v) is not as close as previous float %b", f, r, f0) On 2013/01/25 22:23:50, rsc wrote: > "Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer" Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:847: t.Errorf("%b (approx. of %v) should round halfway to previous (even) float %b ", f, r, f0) On 2013/01/25 22:23:50, rsc wrote: > "Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead" Done. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat_test.g... src/pkg/math/big/rat_test.go:861: 1 / 3, On 2013/01/25 22:23:50, rsc wrote: > 1.0 / 3 maybe > (1/3 = 0) Ouch. That is quite a surprise.
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I think you should decide whether you want the Float64 method to ever return 0. If so, you should test for it. If not, you should test for its absence. I believe reasonable arguments can be made either way, and as long as you define the answer, I'm happy. It is true that +0 and 0 behave mostly the same in floating point arithmetic, but they are not completely identical. For example: http://play.golang.org/p/eb6pInQoyH. And of course they print differently. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:47: z.a.SetUint64(mantissa) On 2013/01/28 18:05:46, adonovan wrote: > On 2013/01/25 22:23:50, rsc wrote: > > Before this, I would suggest > > > > for mantissa&1 == 0 && shift < 0 { > > mantissa >>= 1 > > shift++ > > } > > > > Then things like 1.0 will give 1/1 instead of 2^52/2^52. > > Done. (I think you had the sense of < and ++ backwards.) > > It's not clear to me that 52 iterations of this loop is saving us much in the > common case of 1.0. Is there a good Go definition of ntz(uint64) somewhere? > Hacker's Delight has four candidates but none is a oneliner, and I don't think > it merits an inline implementation. 52 loop iterations is nothing compared to the rest of the stuff going on. I missed the z.norm at the end, though, so maybe it's not actually interesting. Does this function handle 0 correctly now?
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On 2013/01/28 18:15:07, rsc wrote: > I think you should decide whether you want the Float64 method to ever return 0. > If so, you should test for it. I think it should return 0 in the case of small but nonzero negative numbers, as indeed it does. All that was lacking was a test case, which I thought was already present but was not. ("1e350") Done. > It is true that +0 and 0 behave mostly the same in floating point arithmetic, > but they are not completely identical. Yes, no argument there.
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I think Float64() should return 0 in the case of small but nonzero negative numbers, as indeed it does. All that was lacking was a test case, which I thought was already present but was not ("1e350"). Added now. > It is true that +0 and 0 behave mostly the same in floating point arithmetic, > but they are not completely identical. Yes, no argument there. https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go File src/pkg/math/big/rat.go (right): https://codereview.appspot.com/6930059/diff/18001/src/pkg/math/big/rat.go#new... src/pkg/math/big/rat.go:47: z.a.SetUint64(mantissa) On 2013/01/28 18:15:08, rsc wrote: > On 2013/01/28 18:05:46, adonovan wrote: > > On 2013/01/25 22:23:50, rsc wrote: > > > Before this, I would suggest > > > > > > for mantissa&1 == 0 && shift < 0 { > > > mantissa >>= 1 > > > shift++ > > > } > > > > > > Then things like 1.0 will give 1/1 instead of 2^52/2^52. > > > > Done. (I think you had the sense of < and ++ backwards.) > > > > It's not clear to me that 52 iterations of this loop is saving us much in the > > common case of 1.0. Is there a good Go definition of ntz(uint64) somewhere? > > Hacker's Delight has four candidates but none is a oneliner, and I don't > think > > it merits an inline implementation. > > 52 loop iterations is nothing compared to the rest of the stuff going on. I > missed the z.norm at the end, though, so maybe it's not actually interesting. > Does this function handle 0 correctly now? Yes.
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*** Submitted as https://code.google.com/p/go/source/detail?r=ca5e5de48173 *** math/big: add Rat.{,Set}Float64 methods for IEEE 754 conversions. Added tests, using input data from strconv.ParseFloat. Thanks to rsc for most of the test code. math/big could use some good packagelevel documentation. R=remyoudompheng, rsc CC=golangdev https://codereview.appspot.com/6930059
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