Floating-point number

Check a number class of floating point numbers

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (<predicate> <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “<output>”.

Examples

predicate	value	output
number?	3.14	A
number?	-42.2045	A
complex?	3.14	A
complex?	-42.2045	A
real?	3.14	A
real?	-42.2045	A
rational?	0	A
rational?	1	A
rational?	-42	A
rational?	3.14	A
rational?	-42.2045	A
rational?	(exp 1)	A
integer?	3.14	B
integer?	-42.2045	B

Check if a number is exact

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (exact? <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “<output>”.

Examples

value	output
-42	A
-3.14	B
0	A
3.14	B
42	A

Check if a number is inexact

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (inexact? <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “<output>”.

Examples

value	output
-42	B
-3.14	A
0	B
3.14	A
42	B

Check if a number is an exact integer

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (exact-integer? <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “<output>”.

Examples

value	output
-42	A
-3.14	B
0	A
3.14	B
42	A

Calculate an exponentiation

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (< (abs (- (expt 2 3) (exp (* (log 2) 3)))) 0.000001) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Calculate a logarithm

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (< (abs (- (log 2 3) (/ (log 2) (log 3)))) 0.000001) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Truncate a number

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (truncate <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
0	0
0.1	0
0.9	0
1	1
1.1	1
1.9	1
2	2
-0.9	0
-1	-1
-1.9	-1
-2	-2
-2.1	-2

Calculate a floor

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (floor <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
0	0
0.1	0
0.9	0
1	1
1.1	1
1.9	1
2	2
-0.9	-1
-1	-1
-1.9	-2
-2	-2
-2.1	-3

Calculate a ceiling

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (ceiling <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
0	0
0.1	1
0.9	1
1	1
1.1	2
1.9	2
2	2
-0.9	0
-1	-1
-1.9	-1
-2	-2
-2.1	-2

Round a number

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (round <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
0	0
0.1	0
0.49	0
0.5	0
0.9	1
1	1
1.1	1
1.49	1
1.5	2
1.9	2
2	2
2.5	2
3.5	4
-0.5	0
-1	-1
-0.9	-1
-1.5	-2
-1.51	-2
-1.9	-2
-2.5	-2
-3.5	-4

Rationalize a number

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (rationalize <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
0 0	0
42 0	42
42 (/ 1 10)	42
0.1 0	0.1

Convert a floating point number to a string

Given a file named “main.scm” with:

(import (scheme base))

(write-string (number->string <value>))

When I successfully run stak main.scm

Then the stdout should contain exactly “<value>”.

Examples

value
0.5
0.125
1.2
3.14
-3.14
3.141592653589793
2.718281828459045
0.999999999999

Convert a non-finite floating point number to a string

Given a file named “main.scm” with:

(import (scheme base))

(write-string (number->string <value>))

When I successfully run stak main.scm

Then the stdout should contain “<output>”.

Examples

value	output
(/ 0 0)	nan
(/ 1 0)	infinity
(/ -1 0)	-infinity

Convert a string to a floating point number

Given a file named “main.scm” with:

(import (scheme base))

(write-string (number->string (string->number "<value>")))

When I successfully run stak main.scm

Then the stdout should contain exactly “<value>”.

Examples

value
0.5
0.125
1.2
3.14
-3.14
3.141592653589793
2.718281828459045
0.999999999999

Calculate a square root

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8
  (if (< (abs (- (expt (sqrt <value>) 2) <value>)) 0.001)
    65
    66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

value
0
1
2
42

Use trigonometric functions

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8
  (if (< (abs (- (/ (sin <value>) (cos <value>)) (tan <value>))) 0.001)
    65
    66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

value
-2
-1
0
1
2

Use inverse trigonometric functions

Given a file named “main.scm” with:

(import (scheme base) (scheme complex) (scheme inexact))

(write-u8
  (if (= (round (real-part (<normal> (<inverse> 1)))) 1)
    65
    66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

normal	inverse
cos	acos
sin	asin
tan	atan

IEEE 754

Keep the precision of a literal

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (< 3.1415926534 3.1415926535 3.1415926536) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Keep a large mantissa of a literal

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (= <literal> <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

literal	value
137438953471.5	(- (* 65536.0 2097152.0) 0.5)
2251799813685247.5	(- (* 2097152.0 1073741824.0) 0.5)
4503599627370495.5	(- (* 67108864.0 67108864.0) 0.5)
9007199254740991.0	(- (* 134217728.0 67108864.0) 1.0)

Keep an exact literal

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (= <literal> <value>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

literal	value
0.5	(/ 1.0 2.0)
1.5	(/ 3.0 2.0)
0.125	(/ 1.0 8.0)
12.5	(/ 25.0 2.0)
0.001953125	(/ 1.0 512.0)
0.1	(/ 1.0 10.0)
0.6	(/ 6.0 10.0)

Round a large number

Given a file named “main.scm” with:

(import (scheme base) (scheme inexact))

(write-u8 (if (= (round <input>) <output>) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Examples

input	output
(+ (* 67108864.0 67108864.0) 1.0)	(+ (* 67108864.0 67108864.0) 1.0)
(- (* 134217728.0 67108864.0) 1.0)	(- (* 134217728.0 67108864.0) 1.0)
(- 1.0 (* 134217728.0 67108864.0))	(- 1.0 (* 134217728.0 67108864.0))
(- (* 67108864.0 67108864.0) 0.5)	(* 67108864.0 67108864.0)
(- (* 67108864.0 67108864.0) 1.5)	(- (* 67108864.0 67108864.0) 2.0)
(- 0.5 (* 67108864.0 67108864.0))	(- 0.0 (* 67108864.0 67108864.0))

Underflow a tiny literal gradually

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (< (* 0.9 (expt 10.0 -300)) 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (* 1.1 (expt 10.0 -300))) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.

Flush a subnormal literal to zero

Given a file named “main.scm” with:

(import (scheme base))

(write-u8 (if (= 0.0 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001) 65 66))

When I successfully run stak main.scm

Then the stdout should contain exactly “A”.