[decimojo][fix] Enhance round() function and improve the performance + fix sqrt()

[forfudan]

This PR enhances the round() function and adds comprehensive benchmarks against Python's decimal package. The round() function now longer rely on scale_up and scale_down functions. Add checks on Decimal constructors to ensure that scale is between 0 and 28.

Fix wrong trailing zeros of sqrt().

[forfudan]

Before change: 57a7c56

=== DeciMojo Rounding Benchmark ===
Time: 2025-03-10T21:04:27.660441
System: Darwin 24.3.0
Processor: arm
Python version: 3.12.9
Python decimal precision: 28
Mojo decimal precision: 28

Running rounding benchmarks with 1000 iterations each

Benchmark:       Standard rounding to 2 places
Decimal:         123.456789
Round to:        2 places
Mojo result:     123.46
Python result:   123.46
Mojo Decimal:    232.0 ns per iteration
Python Decimal:  7298.0 ns per iteration
Speedup factor:  31.45689655172414

Benchmark:       Banker's rounding with even preceding digit
Decimal:         10.125
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    104.0 ns per iteration
Python Decimal:  7421.0 ns per iteration
Speedup factor:  71.35576923076923

Benchmark:       Banker's rounding with odd preceding digit
Decimal:         10.135
Round to:        2 places
Mojo result:     10.14
Python result:   10.14
Mojo Decimal:    89.0 ns per iteration
Python Decimal:  6963.0 ns per iteration
Speedup factor:  78.23595505617978

Benchmark:       Rounding with less than half
Decimal:         10.124
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    67.0 ns per iteration
Python Decimal:  6593.0 ns per iteration
Speedup factor:  98.40298507462687

Benchmark:       Rounding with more than half
Decimal:         10.126
Round to:        2 places
Mojo result:     10.13
Python result:   10.13
Mojo Decimal:    66.0 ns per iteration
Python Decimal:  7026.0 ns per iteration
Speedup factor:  106.45454545454545

Benchmark:       Rounding to whole number
Decimal:         123.456
Round to:        0 places
Mojo result:     123
Python result:   123
Mojo Decimal:    199.0 ns per iteration
Python Decimal:  6989.0 ns per iteration
Speedup factor:  35.120603015075375

Benchmark:       Rounding negative number
Decimal:         -123.456
Round to:        2 places
Mojo result:     -123.46
Python result:   -123.46
Mojo Decimal:    78.0 ns per iteration
Python Decimal:  6871.0 ns per iteration
Speedup factor:  88.08974358974359

Benchmark:       Rounding to tens (negative places)
Decimal:         123.456
Round to:        -1 places
Mojo result:     123
Python result:   123
Mojo Decimal:    210.0 ns per iteration
Python Decimal:  6865.0 ns per iteration
Speedup factor:  32.69047619047619

Benchmark:       Rounding to hundreds (negative places)
Decimal:         1234.56
Round to:        -2 places
Mojo result:     1235
Python result:   1235
Mojo Decimal:    139.0 ns per iteration
Python Decimal:  7055.0 ns per iteration
Speedup factor:  50.75539568345324

Benchmark:       Rounding very small number
Decimal:         0.0000001234
Round to:        10 places
Mojo result:     0.0000001234
Python result:   1.234E-7
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  6985.0 ns per iteration
Speedup factor:  6985.0

Benchmark:       Rounding already rounded number
Decimal:         123.45
Round to:        2 places
Mojo result:     123.45
Python result:   123.45
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  7057.0 ns per iteration
Speedup factor:  7057.0

Benchmark:       Rounding to high precision (20 places)
Decimal:         0.12345678901234567890123
Round to:        20 places
Mojo result:     0.12345678901234567890
Python result:   0.12345678901234567890
Mojo Decimal:    239.0 ns per iteration
Python Decimal:  7254.0 ns per iteration
Speedup factor:  30.351464435146443

Benchmark:       Rounding to more places than input (10)
Decimal:         123.456
Round to:        10 places
Mojo result:     123.4560000000
Python result:   123.4560000000
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  6848.0 ns per iteration
Speedup factor:  6848.0

Benchmark:       Rounding number with trailing 9's
Decimal:         9.999
Round to:        2 places
Mojo result:     10.00
Python result:   10.00
Mojo Decimal:    103.0 ns per iteration
Python Decimal:  7186.0 ns per iteration
Speedup factor:  69.76699029126213

Benchmark:       Rounding requiring carry propagation
Decimal:         9.99
Round to:        1 places
Mojo result:     10.0
Python result:   10.0
Mojo Decimal:    76.0 ns per iteration
Python Decimal:  6987.0 ns per iteration
Speedup factor:  91.9342105263158

Benchmark:       Rounding exactly half with even preceding digit
Decimal:         2.5
Round to:        0 places
Mojo result:     2
Python result:   2
Mojo Decimal:    83.0 ns per iteration
Python Decimal:  6967.0 ns per iteration
Speedup factor:  83.93975903614458

Benchmark:       Rounding exactly half with odd preceding digit
Decimal:         3.5
Round to:        0 places
Mojo result:     4
Python result:   4
Mojo Decimal:    79.0 ns per iteration
Python Decimal:  7376.0 ns per iteration
Speedup factor:  93.36708860759494

Benchmark:       Rounding value close to MAX
Decimal:         12345678901234567889.87655
Round to:        2 places
Mojo result:     12345678901234567889.88
Python result:   12345678901234567889.88
Mojo Decimal:    226.0 ns per iteration
Python Decimal:  7221.0 ns per iteration
Speedup factor:  31.951327433628318

Benchmark:       Rounding minimum positive value
Decimal:         0.0000000000000000000000000001
Round to:        28 places
Mojo result:     0.0000000000000000000000000001
Python result:   1E-28
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  7484.0 ns per iteration
Speedup factor:  7484.0

Benchmark:       Rounding engineering notation value
Decimal:         123.456789
Round to:        4 places
Mojo result:     123.4568
Python result:   123.4568
Mojo Decimal:    136.0 ns per iteration
Python Decimal:  7169.0 ns per iteration
Speedup factor:  52.713235294117645

Benchmark:       Rounding number with long integer part
Decimal:         12345678901234567.8901
Round to:        2 places
Mojo result:     12345678901234567.89
Python result:   12345678901234567.89
Mojo Decimal:    132.0 ns per iteration
Python Decimal:  7057.0 ns per iteration
Speedup factor:  53.46212121212121

Benchmark:       Rounding number just below half
Decimal:         10.12499999999999999
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    371.0 ns per iteration
Python Decimal:  7216.0 ns per iteration
Speedup factor:  19.450134770889488

Benchmark:       Rounding number just above half
Decimal:         10.12500000000000001
Round to:        2 places
Mojo result:     10.13
Python result:   10.13
Mojo Decimal:    380.0 ns per iteration
Python Decimal:  6932.0 ns per iteration
Speedup factor:  18.242105263157896

Benchmark:       Rounding to maximum precision (28)
Decimal:         0.1111111111111111111111111111
Round to:        28 places
Mojo result:     0.1111111111111111111111111111
Python result:   0.1111111111111111111111111111
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  7827.0 ns per iteration
Speedup factor:  7827.0

Benchmark:       Rounding zero
Decimal:         0
Round to:        10 places
Mojo result:     0.0000000000
Python result:   0E-10
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  7371.0 ns per iteration
Speedup factor:  7371.0

Benchmark:       Rounding Pi to various places
Decimal:         3.141592653589793238462643383
Round to:        15 places
Mojo result:     3.141592653589793
Python result:   3.141592653589793
Mojo Decimal:    493.0 ns per iteration
Python Decimal:  7105.0 ns per iteration
Speedup factor:  14.411764705882353

Benchmark:       Rounding negative with carry propagation
Decimal:         -9.99
Round to:        1 places
Mojo result:     -10.0
Python result:   -10.0
Mojo Decimal:    76.0 ns per iteration
Python Decimal:  7324.0 ns per iteration
Speedup factor:  96.36842105263158

Benchmark:       Rounding with exact .5 and zeros after
Decimal:         1.5000000000000000000
Round to:        0 places
Mojo result:     2
Python result:   2
Mojo Decimal:    522.0 ns per iteration
Python Decimal:  7193.0 ns per iteration
Speedup factor:  13.779693486590038

Benchmark:       Rounding with exact .5 and non-zeros after
Decimal:         1.50000000000000000001
Round to:        0 places
Mojo result:     2
Python result:   2
Mojo Decimal:    532.0 ns per iteration
Python Decimal:  7492.0 ns per iteration
Speedup factor:  14.082706766917294

Benchmark:       Rounding extremely close to MAX
Decimal:         123456789012345677.999999999
Round to:        8 places
Mojo result:     123456789012345678.00000000
Python result:   123456789012345678.00000000
Mojo Decimal:    105.0 ns per iteration
Python Decimal:  7490.0 ns per iteration
Speedup factor:  71.33333333333333

Benchmark:       Random decimal with various digits
Decimal:         7.389465718934026719043
Round to:        12 places
Mojo result:     7.389465718934
Python result:   7.389465718934
Mojo Decimal:    482.0 ns per iteration
Python Decimal:  6721.0 ns per iteration
Speedup factor:  13.943983402489627

Benchmark:       Number with alternating digits
Decimal:         1.010101010101010101010101
Round to:        18 places
Mojo result:     1.010101010101010101
Python result:   1.010101010101010101
Mojo Decimal:    283.0 ns per iteration
Python Decimal:  7160.0 ns per iteration
Speedup factor:  25.300353356890458

=== Rounding Benchmark Summary ===
Benchmarked:      32 different rounding cases
Each case ran:    1000 iterations
Average speedup:  1192.78×

Individual speedup factors:
Case 1: 31.46×
Case 2: 71.36×
Case 3: 78.24×
Case 4: 98.40×
Case 5: 106.45×
Case 6: 35.12×
Case 7: 88.09×
Case 8: 32.69×
Case 9: 50.76×
Case 10: 6985.00×
Case 11: 7057.00×
Case 12: 30.35×
Case 13: 6848.00×
Case 14: 69.77×
Case 15: 91.93×
Case 16: 83.94×
Case 17: 93.37×
Case 18: 31.95×
Case 19: 7484.00×
Case 20: 52.71×
Case 21: 53.46×
Case 22: 19.45×
Case 23: 18.24×
Case 24: 7827.00×
Case 25: 7371.00×
Case 26: 14.41×
Case 27: 96.37×
Case 28: 13.78×
Case 29: 14.08×
Case 30: 71.33×
Case 31: 13.94×
Case 32: 25.30×

[forfudan]

After change c2823a4

=== DeciMojo Rounding Benchmark ===
Time: 2025-03-11T20:54:09.147735
System: Darwin 24.3.0
Processor: arm
Python version: 3.12.9
Python decimal precision: 28
Mojo decimal precision: 28

Running rounding benchmarks with 1000 iterations each

Benchmark:       Standard rounding to 2 places
Decimal:         123.456789
Round to:        2 places
Mojo result:     123.46
Python result:   123.46
Mojo Decimal:    97.0 ns per iteration
Python Decimal:  15665.0 ns per iteration
Speedup factor:  161.49484536082474

Benchmark:       Banker's rounding with even preceding digit
Decimal:         10.125
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    39.0 ns per iteration
Python Decimal:  12446.0 ns per iteration
Speedup factor:  319.12820512820514

Benchmark:       Banker's rounding with odd preceding digit
Decimal:         10.135
Round to:        2 places
Mojo result:     10.14
Python result:   10.14
Mojo Decimal:    32.0 ns per iteration
Python Decimal:  11304.0 ns per iteration
Speedup factor:  353.25

Benchmark:       Rounding with less than half
Decimal:         10.124
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    28.0 ns per iteration
Python Decimal:  10738.0 ns per iteration
Speedup factor:  383.5

Benchmark:       Rounding with more than half
Decimal:         10.126
Round to:        2 places
Mojo result:     10.13
Python result:   10.13
Mojo Decimal:    31.0 ns per iteration
Python Decimal:  9852.0 ns per iteration
Speedup factor:  317.80645161290323

Benchmark:       Rounding to whole number
Decimal:         123.456
Round to:        0 places
Mojo result:     123
Python result:   123
Mojo Decimal:    32.0 ns per iteration
Python Decimal:  9552.0 ns per iteration
Speedup factor:  298.5

Benchmark:       Rounding negative number
Decimal:         -123.456
Round to:        2 places
Mojo result:     -123.46
Python result:   -123.46
Mojo Decimal:    34.0 ns per iteration
Python Decimal:  9445.0 ns per iteration
Speedup factor:  277.79411764705884

Benchmark:       Rounding to tens (negative places)
Decimal:         123.456
Round to:        -1 places
Mojo result:     120
Python result:   1.2E+2
Mojo Decimal:    36.0 ns per iteration
Python Decimal:  8793.0 ns per iteration
Speedup factor:  244.25

Benchmark:       Rounding to hundreds (negative places)
Decimal:         1234.56
Round to:        -2 places
Mojo result:     1200
Python result:   1.2E+3
Mojo Decimal:    34.0 ns per iteration
Python Decimal:  8781.0 ns per iteration
Speedup factor:  258.2647058823529

Benchmark:       Rounding very small number
Decimal:         0.0000001234
Round to:        10 places
Mojo result:     0.0000001234
Python result:   1.234E-7
Mojo Decimal:    2.0 ns per iteration
Python Decimal:  8530.0 ns per iteration
Speedup factor:  4265.0

Benchmark:       Rounding already rounded number
Decimal:         123.45
Round to:        2 places
Mojo result:     123.45
Python result:   123.45
Mojo Decimal:    2.0 ns per iteration
Python Decimal:  8649.0 ns per iteration
Speedup factor:  4324.5

Benchmark:       Rounding to high precision (20 places)
Decimal:         0.12345678901234567890123
Round to:        20 places
Mojo result:     0.12345678901234567890
Python result:   0.12345678901234567890
Mojo Decimal:    153.0 ns per iteration
Python Decimal:  8384.0 ns per iteration
Speedup factor:  54.79738562091503

Benchmark:       Rounding to more places than input (10)
Decimal:         123.456
Round to:        10 places
Mojo result:     123.4560000000
Python result:   123.4560000000
Mojo Decimal:    18.0 ns per iteration
Python Decimal:  8855.0 ns per iteration
Speedup factor:  491.94444444444446

Benchmark:       Rounding number with trailing 9's
Decimal:         9.999
Round to:        2 places
Mojo result:     10.00
Python result:   10.00
Mojo Decimal:    25.0 ns per iteration
Python Decimal:  8687.0 ns per iteration
Speedup factor:  347.48

Benchmark:       Rounding requiring carry propagation
Decimal:         9.99
Round to:        1 places
Mojo result:     10.0
Python result:   10.0
Mojo Decimal:    20.0 ns per iteration
Python Decimal:  8783.0 ns per iteration
Speedup factor:  439.15

Benchmark:       Rounding exactly half with even preceding digit
Decimal:         2.5
Round to:        0 places
Mojo result:     2
Python result:   2
Mojo Decimal:    15.0 ns per iteration
Python Decimal:  8783.0 ns per iteration
Speedup factor:  585.5333333333333

Benchmark:       Rounding exactly half with odd preceding digit
Decimal:         3.5
Round to:        0 places
Mojo result:     4
Python result:   4
Mojo Decimal:    14.0 ns per iteration
Python Decimal:  8627.0 ns per iteration
Speedup factor:  616.2142857142857

Benchmark:       Rounding value close to MAX
Decimal:         12345678901234567889.87655
Round to:        2 places
Mojo result:     12345678901234567889.88
Python result:   12345678901234567889.88
Mojo Decimal:    166.0 ns per iteration
Python Decimal:  8730.0 ns per iteration
Speedup factor:  52.59036144578313

Benchmark:       Rounding minimum positive value
Decimal:         0.0000000000000000000000000001
Round to:        28 places
Mojo result:     0.0000000000000000000000000001
Python result:   1E-28
Mojo Decimal:    2.0 ns per iteration
Python Decimal:  8991.0 ns per iteration
Speedup factor:  4495.5

Benchmark:       Rounding engineering notation value
Decimal:         123.456789
Round to:        4 places
Mojo result:     123.4568
Python result:   123.4568
Mojo Decimal:    53.0 ns per iteration
Python Decimal:  9388.0 ns per iteration
Speedup factor:  177.1320754716981

Benchmark:       Rounding number with long integer part
Decimal:         12345678901234567.8901
Round to:        2 places
Mojo result:     12345678901234567.89
Python result:   12345678901234567.89
Mojo Decimal:    160.0 ns per iteration
Python Decimal:  8600.0 ns per iteration
Speedup factor:  53.75

Benchmark:       Rounding number just below half
Decimal:         10.12499999999999999
Round to:        2 places
Mojo result:     10.12
Python result:   10.12
Mojo Decimal:    130.0 ns per iteration
Python Decimal:  8876.0 ns per iteration
Speedup factor:  68.27692307692308

Benchmark:       Rounding number just above half
Decimal:         10.12500000000000001
Round to:        2 places
Mojo result:     10.13
Python result:   10.13
Mojo Decimal:    126.0 ns per iteration
Python Decimal:  8896.0 ns per iteration
Speedup factor:  70.60317460317461

Benchmark:       Rounding to maximum precision (28)
Decimal:         0.1111111111111111111111111111
Round to:        28 places
Mojo result:     0.1111111111111111111111111111
Python result:   0.1111111111111111111111111111
Mojo Decimal:    1.0 ns per iteration
Python Decimal:  8980.0 ns per iteration
Speedup factor:  8980.0

Benchmark:       Rounding zero
Decimal:         0
Round to:        10 places
Mojo result:     0.0000000000
Python result:   0E-10
Mojo Decimal:    8.0 ns per iteration
Python Decimal:  8816.0 ns per iteration
Speedup factor:  1102.0

Benchmark:       Rounding Pi to various places
Decimal:         3.141592653589793238462643383
Round to:        15 places
Mojo result:     3.141592653589793
Python result:   3.141592653589793
Mojo Decimal:    213.0 ns per iteration
Python Decimal:  9174.0 ns per iteration
Speedup factor:  43.070422535211264

Benchmark:       Rounding negative with carry propagation
Decimal:         -9.99
Round to:        1 places
Mojo result:     -10.0
Python result:   -10.0
Mojo Decimal:    18.0 ns per iteration
Python Decimal:  9257.0 ns per iteration
Speedup factor:  514.2777777777778

Benchmark:       Rounding with exact .5 and zeros after
Decimal:         1.5000000000000000000
Round to:        0 places
Mojo result:     2
Python result:   2
Mojo Decimal:    145.0 ns per iteration
Python Decimal:  8850.0 ns per iteration
Speedup factor:  61.03448275862069

Benchmark:       Rounding with exact .5 and non-zeros after
Decimal:         1.50000000000000000001
Round to:        0 places
Mojo result:     1
Python result:   2
Mojo Decimal:    172.0 ns per iteration
Python Decimal:  9255.0 ns per iteration
Speedup factor:  53.80813953488372

Benchmark:       Rounding extremely close to MAX
Decimal:         123456789012345677.999999999
Round to:        8 places
Mojo result:     123456789012345678.00000000
Python result:   123456789012345678.00000000
Mojo Decimal:    185.0 ns per iteration
Python Decimal:  8906.0 ns per iteration
Speedup factor:  48.14054054054054

Benchmark:       Random decimal with various digits
Decimal:         7.389465718934026719043
Round to:        12 places
Mojo result:     7.389465718934
Python result:   7.389465718934
Mojo Decimal:    162.0 ns per iteration
Python Decimal:  9073.0 ns per iteration
Speedup factor:  56.00617283950617

Benchmark:       Number with alternating digits
Decimal:         1.010101010101010101010101
Round to:        18 places
Mojo result:     1.010101010101010101
Python result:   1.010101010101010101
Mojo Decimal:    176.0 ns per iteration
Python Decimal:  8894.0 ns per iteration
Speedup factor:  50.53409090909091

=== Rounding Benchmark Summary ===
Benchmarked:      32 different rounding cases
Each case ran:    1000 iterations
Average speedup:  923.9166230074229×

Individual speedup factors:
Case 1: 161.49×
Case 2: 319.13×
Case 3: 353.25×
Case 4: 383.5×
Case 5: 317.81×
Case 6: 298.5×
Case 7: 277.79×
Case 8: 244.25×
Case 9: 258.26×
Case 10: 4265.0×
Case 11: 4324.5×
Case 12: 54.8×
Case 13: 491.94×
Case 14: 347.48×
Case 15: 439.15×
Case 16: 585.53×
Case 17: 616.21×
Case 18: 52.59×
Case 19: 4495.5×
Case 20: 177.13×
Case 21: 53.75×
Case 22: 68.28×
Case 23: 70.6×
Case 24: 8980.0×
Case 25: 1102.0×
Case 26: 43.07×
Case 27: 514.28×
Case 28: 61.03×
Case 29: 53.81×
Case 30: 48.14×
Case 31: 56.01×
Case 32: 50.53×