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Fix BigDecimal#round for large digit counts in base 10 #13811

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Sep 20, 2023
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Fix BigDecimal#round for large digit counts in base 10 #13811

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105 changes: 105 additions & 0 deletions spec/std/big/big_decimal_spec.cr
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Original file line number Diff line number Diff line change
Expand Up @@ -818,6 +818,23 @@ describe BigDecimal do
"-12.345".to_big_d.round(0, mode: :to_zero).should eq "-12".to_big_d
"-12.345".to_big_d.round(1, mode: :to_zero).should eq "-12.3".to_big_d
"-12.345".to_big_d.round(2, mode: :to_zero).should eq "-12.34".to_big_d

# 1 + 3.0000e-200 -> 1 + 3.0e-200 (ditto for others)
(1.to_big_d + BigDecimal.new(30000, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(30001, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(39999, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(40000, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40001, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(49999, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(50000, 204)).round(200, mode: :to_zero).should eq(1.to_big_d + BigDecimal.new(5, 200))

(-1.to_big_d - BigDecimal.new(30000, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(30001, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(39999, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(40000, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40001, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(49999, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(50000, 204)).round(200, mode: :to_zero).should eq(-1.to_big_d - BigDecimal.new(5, 200))
end

it "to_positive" do
Expand All @@ -829,6 +846,23 @@ describe BigDecimal do
"-12.345".to_big_d.round(0, mode: :to_positive).should eq "-12".to_big_d
"-12.345".to_big_d.round(1, mode: :to_positive).should eq "-12.3".to_big_d
"-12.345".to_big_d.round(2, mode: :to_positive).should eq "-12.34".to_big_d

# 1 + 3.0000e-200 -> 1 + 3.0e-200 (ditto for others)
(1.to_big_d + BigDecimal.new(30000, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(30001, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(39999, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40000, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40001, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(5, 200))
(1.to_big_d + BigDecimal.new(49999, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(5, 200))
(1.to_big_d + BigDecimal.new(50000, 204)).round(200, mode: :to_positive).should eq(1.to_big_d + BigDecimal.new(5, 200))

(-1.to_big_d - BigDecimal.new(30000, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(30001, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(39999, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(40000, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40001, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(49999, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(50000, 204)).round(200, mode: :to_positive).should eq(-1.to_big_d - BigDecimal.new(5, 200))
end

it "to_negative" do
Expand All @@ -840,6 +874,23 @@ describe BigDecimal do
"-12.345".to_big_d.round(0, mode: :to_negative).should eq "-13".to_big_d
"-12.345".to_big_d.round(1, mode: :to_negative).should eq "-12.4".to_big_d
"-12.345".to_big_d.round(2, mode: :to_negative).should eq "-12.35".to_big_d

# 1 + 3.0000e-200 -> 1 + 3.0e-200 (ditto for others)
(1.to_big_d + BigDecimal.new(30000, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(30001, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(39999, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(40000, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40001, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(49999, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(50000, 204)).round(200, mode: :to_negative).should eq(1.to_big_d + BigDecimal.new(5, 200))

(-1.to_big_d - BigDecimal.new(30000, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(30001, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(39999, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40000, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40001, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(5, 200))
(-1.to_big_d - BigDecimal.new(49999, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(5, 200))
(-1.to_big_d - BigDecimal.new(50000, 204)).round(200, mode: :to_negative).should eq(-1.to_big_d - BigDecimal.new(5, 200))
end

it "ties_away" do
Expand All @@ -851,6 +902,33 @@ describe BigDecimal do
"-13.825".to_big_d.round(0, mode: :ties_away).should eq "-14".to_big_d
"-13.825".to_big_d.round(1, mode: :ties_away).should eq "-13.8".to_big_d
"-13.825".to_big_d.round(2, mode: :ties_away).should eq "-13.83".to_big_d

# 1 + 3.0000e-200 -> 1 + 3.0e-200 (ditto for others)
(1.to_big_d + BigDecimal.new(30000, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(30001, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(34999, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(35000, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(35001, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(39999, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40000, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40001, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(44999, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(45000, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(5, 200))
(1.to_big_d + BigDecimal.new(45001, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(5, 200))
(1.to_big_d + BigDecimal.new(50000, 204)).round(200, mode: :ties_away).should eq(1.to_big_d + BigDecimal.new(5, 200))

(-1.to_big_d - BigDecimal.new(30000, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(30001, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(34999, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(35000, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(35001, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(39999, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40000, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40001, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(44999, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(45000, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(5, 200))
(-1.to_big_d - BigDecimal.new(45001, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(5, 200))
(-1.to_big_d - BigDecimal.new(50000, 204)).round(200, mode: :ties_away).should eq(-1.to_big_d - BigDecimal.new(5, 200))
end

it "ties_even" do
Expand All @@ -862,6 +940,33 @@ describe BigDecimal do
"-15.255".to_big_d.round(0, mode: :ties_even).should eq "-15".to_big_d
"-15.255".to_big_d.round(1, mode: :ties_even).should eq "-15.3".to_big_d
"-15.255".to_big_d.round(2, mode: :ties_even).should eq "-15.26".to_big_d

# 1 + 3.0000e-200 -> 1 + 3.0e-200 (ditto for others)
(1.to_big_d + BigDecimal.new(30000, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(30001, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(34999, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(3, 200))
(1.to_big_d + BigDecimal.new(35000, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(35001, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(39999, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40000, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(40001, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(44999, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(45000, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(4, 200))
(1.to_big_d + BigDecimal.new(45001, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(5, 200))
(1.to_big_d + BigDecimal.new(50000, 204)).round(200, mode: :ties_even).should eq(1.to_big_d + BigDecimal.new(5, 200))

(-1.to_big_d - BigDecimal.new(30000, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(30001, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(34999, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(3, 200))
(-1.to_big_d - BigDecimal.new(35000, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(35001, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(39999, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40000, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(40001, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(44999, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(45000, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(4, 200))
(-1.to_big_d - BigDecimal.new(45001, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(5, 200))
(-1.to_big_d - BigDecimal.new(50000, 204)).round(200, mode: :ties_even).should eq(-1.to_big_d - BigDecimal.new(5, 200))
end
end
end
Expand Down
51 changes: 35 additions & 16 deletions src/big/big_decimal.cr
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Original file line number Diff line number Diff line change
Expand Up @@ -460,27 +460,37 @@ struct BigDecimal < Number
end

def round(digits : Number, base = 10, *, mode : RoundingMode = :ties_even) : BigDecimal
return self if (base == 10 && @scale <= digits) || zero?
return self if zero?

# the following is same as the overload in `Number` except `base.to_f`
# becomes `.to_big_d`
if digits < 0
multiplier = base.to_big_d ** digits.abs
shifted = self / multiplier
if base == 10
return self if @scale <= digits

# optimized version that skips `#div` completely, always exact
shifted = mul_power_of_ten(digits)
rounded = shifted.round(mode)
rounded.mul_power_of_ten(-digits)
else
multiplier = base.to_big_d ** digits
shifted = self * multiplier
end
# the following is same as the overload in `Number` except `base.to_f`
# becomes `base.to_big_d`; note that the `#/` calls always use
# `DEFAULT_PRECISION`
if digits < 0
multiplier = base.to_big_d ** digits.abs
shifted = self / multiplier
else
multiplier = base.to_big_d ** digits
shifted = self * multiplier
end

rounded = shifted.round(mode)
rounded = shifted.round(mode)

if digits < 0
result = rounded * multiplier
else
result = rounded / multiplier
end
if digits < 0
result = rounded * multiplier
else
result = rounded / multiplier
end

BigDecimal.new result
BigDecimal.new result
end
end

def to_s(io : IO) : Nil
Expand Down Expand Up @@ -759,6 +769,15 @@ struct BigDecimal < Number
TEN_I ** x
end

# returns `self * 10 ** exponent`
protected def mul_power_of_ten(exponent : Int)
if exponent <= scale
BigDecimal.new(@value, @scale - exponent)
else
BigDecimal.new(@value * power_ten_to(exponent - scale), 0_u64)
end
end

# Factors out any extra powers of ten in the internal representation.
# For instance, value=100 scale=2 => value=1 scale=0
protected def factor_powers_of_ten
Expand Down
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