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Enhanced RDoc for Float#next_float (#5160)

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* Enhanced RDoc for Float#next_float
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Burdette Lamar 2021-11-23 15:38:28 -06:00 committed by GitHub
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Notes: git 2021-11-24 06:38:49 +09:00 
Merged-By: BurdetteLamar <BurdetteLamar@Yahoo.com>
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@ -1975,53 +1975,61 @@ flo_nextafter(VALUE flo, double value)
* call-seq:
* next_float -> float
*
* Returns the next representable floating point number.
* Returns the next-larger representable \Float.
*
* Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY.
* These examples show the internally stored values (64-bit hexadecimal)
* for each \Float +f+ and for the corresponding <tt>f.next_float</tt>:
*
* Float::NAN.next_float is Float::NAN.
* f = 0.0 # 0x0000000000000000
* f.next_float # 0x0000000000000001
*
* For example:
* f = 0.01 # 0x3f847ae147ae147b
* f.next_float # 0x3f847ae147ae147c
*
* 0.01.next_float #=> 0.010000000000000002
* 1.0.next_float #=> 1.0000000000000002
* 100.0.next_float #=> 100.00000000000001
* In the remaining examples here, the output is shown in the usual way
* (result +to_s+);
*
* 0.01.next_float - 0.01 #=> 1.734723475976807e-18
* 1.0.next_float - 1.0 #=> 2.220446049250313e-16
* 100.0.next_float - 100.0 #=> 1.4210854715202004e-14
* Float::MAX.next_float # => Infinity
*
* f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
* #=> 0x1.47ae147ae147bp-7 0.01
* # 0x1.47ae147ae147cp-7 0.010000000000000002
* # 0x1.47ae147ae147dp-7 0.010000000000000004
* # 0x1.47ae147ae147ep-7 0.010000000000000005
* # 0x1.47ae147ae147fp-7 0.010000000000000007
* # 0x1.47ae147ae148p-7 0.010000000000000009
* # 0x1.47ae147ae1481p-7 0.01000000000000001
* # 0x1.47ae147ae1482p-7 0.010000000000000012
* # 0x1.47ae147ae1483p-7 0.010000000000000014
* # 0x1.47ae147ae1484p-7 0.010000000000000016
* # 0x1.47ae147ae1485p-7 0.010000000000000018
* # 0x1.47ae147ae1486p-7 0.01000000000000002
* # 0x1.47ae147ae1487p-7 0.010000000000000021
* # 0x1.47ae147ae1488p-7 0.010000000000000023
* # 0x1.47ae147ae1489p-7 0.010000000000000024
* # 0x1.47ae147ae148ap-7 0.010000000000000026
* # 0x1.47ae147ae148bp-7 0.010000000000000028
* # 0x1.47ae147ae148cp-7 0.01000000000000003
* # 0x1.47ae147ae148dp-7 0.010000000000000031
* # 0x1.47ae147ae148ep-7 0.010000000000000033
* 0.01.next_float # => 0.010000000000000002
* 1.0.next_float # => 1.0000000000000002
* 100.0.next_float # => 100.00000000000001
*
* f = 0.01
* (0..19).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float }
*
* Output:
*
* 0 0x1.47ae147ae147bp-7 0.01
* 1 0x1.47ae147ae147cp-7 0.010000000000000002
* 2 0x1.47ae147ae147dp-7 0.010000000000000004
* 3 0x1.47ae147ae147ep-7 0.010000000000000005
* 4 0x1.47ae147ae147fp-7 0.010000000000000007
* 5 0x1.47ae147ae148p-7 0.010000000000000009
* 6 0x1.47ae147ae1481p-7 0.01000000000000001
* 7 0x1.47ae147ae1482p-7 0.010000000000000012
* 8 0x1.47ae147ae1483p-7 0.010000000000000014
* 9 0x1.47ae147ae1484p-7 0.010000000000000016
* 10 0x1.47ae147ae1485p-7 0.010000000000000018
* 11 0x1.47ae147ae1486p-7 0.01000000000000002
* 12 0x1.47ae147ae1487p-7 0.010000000000000021
* 13 0x1.47ae147ae1488p-7 0.010000000000000023
* 14 0x1.47ae147ae1489p-7 0.010000000000000024
* 15 0x1.47ae147ae148ap-7 0.010000000000000026
* 16 0x1.47ae147ae148bp-7 0.010000000000000028
* 17 0x1.47ae147ae148cp-7 0.01000000000000003
* 18 0x1.47ae147ae148dp-7 0.010000000000000031
* 19 0x1.47ae147ae148ep-7 0.010000000000000033
*
* f = 0.0; 100.times { f += 0.1 }
* f # => 9.99999999999998 # should be 10.0 in the ideal world.
* 10-f # => 1.9539925233402755e-14 # the floating point error.
* 10.0.next_float-10 # => 1.7763568394002505e-15 # 1 ulp (unit in the last place).
* (10-f)/(10.0.next_float-10) # => 11.0 # the error is 11 ulp.
* (10-f)/(10*Float::EPSILON) # => 8.8 # approximation of the above.
* "%a" % 10 # => "0x1.4p+3"
* "%a" % f # => "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp.
*
* f = 0.0
* 100.times { f += 0.1 }
* f #=> 9.99999999999998 # should be 10.0 in the ideal world.
* 10-f #=> 1.9539925233402755e-14 # the floating point error.
* 10.0.next_float-10 #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place).
* (10-f)/(10.0.next_float-10) #=> 11.0 # the error is 11 ulp.
* (10-f)/(10*Float::EPSILON) #=> 8.8 # approximation of the above.
* "%a" % 10 #=> "0x1.4p+3"
* "%a" % f #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5. 16 - 5 = 11 ulp.
*/
static VALUE
flo_next_float(VALUE vx)