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from
lpython
import
i8
,
i16
,
i32
,
f32
,
i64
,
f64
,
ccall
,
overload
pi
:
f64
=
3.141592653589793238462643383279502884197
e
:
f64
=
2.718281828459045235360287471352662497757
tau
:
f64
=
6.283185307179586
@
overload
def
modf
(
x
:
f64
)
->
tuple
[
f64
,
f64
]:
"""
Return fractional and integral parts of `x` as a pair.
Both results carry the sign of x and are floats.
"""
return
(
x
-
f64
(
int
(
x
)),
float
(
int
(
x
)))
@
overload
def
factorial
(
x
:
i32
)
->
i32
:
"""
Computes the factorial of `x`.
"""
result
:
i32
result
=
0
if
x
<
0
:
return
result
result
=
1
i
:
i32
for
i
in
range
(
1
,
x
+
1
):
result
*=
i
return
result
@
overload
def
factorial
(
x
:
i64
)
->
i64
:
"""
Computes the factorial of `x`.
"""
result
:
i64
result
=
i64
(
0
)
if
x
<
i64
(
0
):
return
result
result
=
i64
(
1
)
i
:
i64
for
i
in
range
(
i64
(
1
),
x
+
i64
(
1
)):
result
*=
i64
(
i
)
return
result
@
overload
def
floor
(
x
:
i32
)
->
i32
:
return
x
@
overload
def
floor
(
x
:
i64
)
->
i64
:
return
x
@
overload
def
floor
(
x
:
f64
)
->
i64
:
r
:
i64
r
=
int
(
x
)
if
x
>=
f64
(
0
)
or
x
==
f64
(
r
):
return
r
return
r
-
i64
(
1
)
@
overload
def
floor
(
x
:
f32
)
->
i32
:
r
:
i32
r
=
i32
(
x
)
if
x
>=
f32
(
0
)
or
x
==
f32
(
r
):
return
r
return
r
-
1
@
overload
def
ceil
(
x
:
i32
)
->
i32
:
return
x
@
overload
def
ceil
(
x
:
i64
)
->
i64
:
return
x
@
overload
def
ceil
(
x
:
f64
)
->
i64
:
r
:
i64
r
=
int
(
x
)
if
x
<=
f64
(
0
)
or
f64
(
r
)
==
x
:
return
r
return
r
+
i64
(
1
)
@
overload
def
ceil
(
x
:
f32
)
->
i32
:
r
:
i32
r
=
i32
(
x
)
if
x
<=
f32
(
0
)
or
f32
(
r
)
==
x
:
return
r
return
r
+
1
# fsum
# supported data types: i32, i64, f32, f64
@
overload
def
fsum
(
arr
:
list
[
i32
])
->
f64
:
"""
Floating-point sum of the elements of `arr`.
"""
sum
:
f64
sum
=
0.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
sum
+=
float
(
arr
[
i
])
return
sum
@
overload
def
fsum
(
arr
:
list
[
i64
])
->
f64
:
"""
Floating-point sum of the elements of `arr`.
"""
sum
:
f64
sum
=
0.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
sum
+=
float
(
arr
[
i
])
return
sum
@
overload
def
fsum
(
arr
:
list
[
f32
])
->
f64
:
"""
Floating-point sum of the elements of `arr`.
"""
sum
:
f64
sum
=
0.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
sum
+=
float
(
arr
[
i
])
return
sum
@
overload
def
fsum
(
arr
:
list
[
f64
])
->
f64
:
"""
Floating-point sum of the elements of `arr`.
"""
sum
:
f64
sum
=
0.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
sum
+=
arr
[
i
]
return
sum
# prod
# supported data types: i32, i64, f32, f64
@
overload
def
prod
(
arr
:
list
[
i32
])
->
f64
:
"""
Return the product of the elements of `arr`.
"""
result
:
f64
result
=
1.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
result
*=
float
(
arr
[
i
])
return
result
@
overload
def
prod
(
arr
:
list
[
i64
])
->
f64
:
"""
Return the product of the elements of `arr`.
"""
result
:
f64
result
=
1.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
result
*=
float
(
arr
[
i
])
return
result
@
overload
def
prod
(
arr
:
list
[
f32
])
->
f64
:
"""
Return the product of the elements of `arr`.
"""
result
:
f64
result
=
1.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
result
*=
float
(
arr
[
i
])
return
result
@
overload
def
prod
(
arr
:
list
[
f64
])
->
f64
:
"""
Return the product of the elements of `arr`.
"""
result
:
f64
result
=
1.0
i
:
i32
for
i
in
range
(
len
(
arr
)):
result
*=
arr
[
i
]
return
result
def
dist
(
x
:
list
[
f64
],
y
:
list
[
f64
])
->
f64
:
"""
Return euclidean distance between `x` and `y` points.
"""
if
len
(
x
)
!=
len
(
y
):
raise
ValueError
(
"Length of lists should be same"
)
res
:
f64
res
=
0.0
i
:
i32
for
i
in
range
(
len
(
x
)):
res
+=
(
x
[
i
]
-
y
[
i
])
*
(
x
[
i
]
-
y
[
i
])
return
res
**
0.5
def
comb
(
n
:
i32
,
k
:
i32
)
->
i32
:
"""
Computes the result of `nCk`, i.e, the number of ways to choose `k`
items from `n` items without repetition and without order.
"""
if
n
<
k
or
n
<
0
:
return
0
return
i32
(
factorial
(
n
)
//
(
factorial
(
k
)
*
factorial
(
n
-
k
)))
def
perm
(
n
:
i32
,
k
:
i32
)
->
i32
:
"""
Computes the result of `nPk`, i.e, the number of ways to choose `k` items
from `n` items without repetition and with order.
"""
if
n
<
k
or
n
<
0
:
return
0
return
i32
(
factorial
(
n
)
//
factorial
(
n
-
k
))
def
isqrt
(
n
:
i32
)
->
i32
:
"""
Computes the integer square root of the nonnegative integer `n`.
"""
if
n
<
0
:
raise
ValueError
(
'`n` should be nonnegative'
)
low
:
i32
mid
:
i32
high
:
i32
low
=
0
high
=
n
+
1
while
low
+
1
<
high
:
mid
=
i32
((
low
+
high
)
//
2
)
if
mid
*
mid
<=
n
:
low
=
mid
else
:
high
=
mid
return
low
# degrees
# supported data types: i8, i16, i32, i64, f32, f64
@
overload
def
degrees
(
x
:
i8
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
f64
(
x
)
*
180.0
/
pi
@
overload
def
degrees
(
x
:
i16
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
f64
(
x
)
*
180.0
/
pi
@
overload
def
degrees
(
x
:
i32
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
f64
(
x
)
*
180.0
/
pi
@
overload
def
degrees
(
x
:
i64
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
f64
(
x
)
*
180.0
/
pi
@
overload
def
degrees
(
x
:
f32
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
f64
(
x
)
*
180.0
/
pi
@
overload
def
degrees
(
x
:
f64
)
->
f64
:
"""
Convert angle `x` from radians to degrees.
"""
return
x
*
180.0
/
pi
# radians
# supported data types: i8, i16, i32, i64, f32, f64
@
overload
def
radians
(
x
:
i8
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
f64
(
x
)
*
pi
/
180.0
@
overload
def
radians
(
x
:
i16
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
f64
(
x
)
*
pi
/
180.0
@
overload
def
radians
(
x
:
i32
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
f64
(
x
)
*
pi
/
180.0
@
overload
def
radians
(
x
:
i64
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
f64
(
x
)
*
pi
/
180.0
@
overload
def
radians
(
x
:
f32
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
f64
(
x
)
*
pi
/
180.0
@
overload
def
radians
(
x
:
f64
)
->
f64
:
"""
Convert angle `x` from degrees to radians.
"""
return
x
*
pi
/
180.0
# fabs
# supported data types: i32, i64, f32, f64
@
overload
def
fabs
(
x
:
f32
)
->
f32
:
"""
Return the absolute value of `x`.
"""
if
x
<
f32
(
0.0
):
return
-
x
return
x
@
overload
def
fabs
(
x
:
f64
)
->
f64
:
"""
Return the absolute value of `x`.
"""
if
x
<
0.0
:
return
-
x
return
x
@
overload
def
fabs
(
x
:
i64
)
->
f64
:
"""
Return the absolute value of `x`.
"""
if
f64
(
x
)
<
0.0
:
return
-
float
(
x
)
return
float
(
x
)
@
overload
def
fabs
(
x
:
i32
)
->
f64
:
"""
Return the absolute value of `x`.
"""
if
f64
(
x
)
<
0.0
:
return
-
float
(
x
)
return
float
(
x
)
@
overload
def
fabs
(
x
:
i16
)
->
f64
:
"""
Return the absolute value of `x`.
"""
if
f64
(
x
)
<
0.0
:
return
-
float
(
x
)
return
float
(
x
)
@
overload
def
fabs
(
x
:
i8
)
->
f64
:
"""
Return the absolute value of `x`.
"""
if
f64
(
x
)
<
0.0
:
return
-
float
(
x
)
return
float
(
x
)
# pow
# supported data types: i32, i64, f32, f64
@
overload
def
pow
(
x
:
f64
,
y
:
f64
)
->
f64
:
"""
Return `x` raised to the power `y`.
"""
if
y
<
0.0
:
raise
ValueError
(
'y should be nonnegative'
)
result
:
f64
result
=
x
**
y
return
result
@
overload
def
pow
(
x
:
i64
,
y
:
i64
)
->
i64
:
"""
Return `x` raised to the power `y`.
"""
if
y
<
i64
(
0
):
raise
ValueError
(
'y should be nonnegative'
)
return
i64
(
x
**
y
)
@
overload
def
pow
(
x
:
f32
,
y
:
f32
)
->
f64
:
"""
Return `x` raised to the power `y`.
"""
if
y
<
f32
(
0
):
raise
ValueError
(
'y should be nonnegative'
)
return
f64
(
x
**
y
)
@
overload
def
pow
(
x
:
i32
,
y
:
i32
)
->
i32
:
"""
Return `x` raised to the power `y`.
"""
if
y
<
0
:
raise
ValueError
(
'y should be nonnegative'
)
result
:
i32
result
=
x
**
y
return
result
@
overload
def
ldexp
(
x
:
f64
,
i
:
i32
)
->
f64
:
result
:
f64
result
=
x
*
f64
(
2
**
i
)
return
result
def
mod
(
a
:
i32
,
b
:
i32
)
->
i32
:
"""
Returns a%b
"""
return
a
-
i32
(
a
//
b
)
*
b
def
gcd
(
a
:
i32
,
b
:
i32
)
->
i32
:
"""
Returns greatest common divisor of `a` and `b`
"""
temp
:
i32
a_
:
i32
b_
:
i32
a_
=
a
b_
=
b
if
a_
<
0
:
a_
=
-
a_
if
b_
<
0
:
b_
=
-
b_
while
b_
!=
0
:
a_
=
mod
(
a_
,
b_
)
temp
=
a_
a_
=
b_
b_
=
temp
return
a_
def
lcm
(
a
:
i32
,
b
:
i32
)
->
i32
:
"""
Returns least common multiple of `a` and `b`
"""
a_
:
i32
b_
:
i32
a_
=
a
b_
=
b
if
a_
<
0
:
a_
=
-
a_
if
b_
<
0
:
b_
=
-
b_
if
a_
*
b_
==
0
:
return
0
return
i32
((
a_
*
b_
)
//
gcd
(
a_
,
b_
))
def
copysign
(
x
:
f64
,
y
:
f64
)
->
f64
:
"""
Return `x` with the sign of `y`.
"""
if
y
>
0.0
or
(
y
==
0.0
and
atan2
(
y
,
-
1.0
)
>
0.0
):
return
fabs
(
x
)
else
:
return
-
fabs
(
x
)
def
hypot
(
x
:
i32
,
y
:
i32
)
->
f64
:
"""
Returns the hypotenuse of the right triangle with sides `x` and `y`.
"""
return
sqrt
(
f64
(
1.0
)
*
f64
(
x
**
2
+
y
**
2
))
@
overload
def
trunc
(
x
:
f64
)
->
i64
:
"""
Return x with the fractional part removed, leaving the integer part.
"""
if
x
>
f64
(
0
):
return
floor
(
x
)
else
:
return
ceil
(
x
)
@
overload
def
trunc
(
x
:
f32
)
->
i32
:
"""
Return x with the fractional part removed, leaving the integer part.
"""
if
x
>
f32
(
0
):
return
floor
(
x
)
else
:
return
ceil
(
x
)
def
sqrt
(
x
:
f64
)
->
f64
:
"""
Returns square root of a number x
"""
return
x
**
(
1
/
2
)
def
cbrt
(
x
:
f64
)
->
f64
:
"""
Returns cube root of a number x
"""
return
x
**
(
1
/
3
)
@
ccall
def
_lfortran_dsin
(
x
:
f64
)
->
f64
:
pass
def
sin
(
x
:
f64
)
->
f64
:
return
_lfortran_dsin
(
x
)
@
ccall
def
_lfortran_dcos
(
x
:
f64
)
->
f64
:
pass
def
cos
(
x
:
f64
)
->
f64
:
return
_lfortran_dcos
(
x
)
@
ccall
def
_lfortran_dtan
(
x
:
f64
)
->
f64
:
pass
def
tan
(
x
:
f64
)
->
f64
:
return
_lfortran_dtan
(
x
)
@
ccall
def
_lfortran_dlog
(
x
:
f64
)
->
f64
:
pass
def
log
(
x
:
f64
)
->
f64
:
return
_lfortran_dlog
(
x
)
@
ccall
def
_lfortran_dlog10
(
x
:
f64
)
->
f64
:
pass
def
log10
(
x
:
f64
)
->
f64
:
return
_lfortran_dlog10
(
x
)
def
log2
(
x
:
f64
)
->
f64
:
return
_lfortran_dlog
(
x
)
/
_lfortran_dlog
(
2.0
)
@
ccall
def
_lfortran_derf
(
x
:
f64
)
->
f64
:
pass
def
erf
(
x
:
f64
)
->
f64
:
return
_lfortran_derf
(
x
)
@
ccall
def
_lfortran_derfc
(
x
:
f64
)
->
f64
:
pass
def
erfc
(
x
:
f64
)
->
f64
:
return
_lfortran_derfc
(
x
)
@
ccall
def
_lfortran_dgamma
(
x
:
f64
)
->
f64
:
pass
def
gamma
(
x
:
f64
)
->
f64
:
return
_lfortran_dgamma
(
x
)
@
ccall
def
_lfortran_dlog_gamma
(
x
:
f64
)
->
f64
:
pass
def
lgamma
(
x
:
f64
)
->
f64
:
return
_lfortran_dlog_gamma
(
x
)
@
ccall
def
_lfortran_dasin
(
x
:
f64
)
->
f64
:
pass
def
asin
(
x
:
f64
)
->
f64
:
return
_lfortran_dasin
(
x
)
@
ccall
def
_lfortran_dacos
(
x
:
f64
)
->
f64
:
pass
def
acos
(
x
:
f64
)
->
f64
:
return
_lfortran_dacos
(
x
)
@
ccall
def
_lfortran_datan
(
x
:
f64
)
->
f64
:
pass
def
atan
(
x
:
f64
)
->
f64
:
return
_lfortran_datan
(
x
)
@
ccall
def
_lfortran_datan2
(
y
:
f64
,
x
:
f64
)
->
f64
:
pass
def
atan2
(
y
:
f64
,
x
:
f64
)
->
f64
:
return
_lfortran_datan2
(
y
,
x
)
@
ccall
def
_lfortran_dsinh
(
x
:
f64
)
->
f64
:
pass
def
sinh
(
x
:
f64
)
->
f64
:
return
_lfortran_dsinh
(
x
)
@
ccall
def
_lfortran_dcosh
(
x
:
f64
)
->
f64
:
pass
def
cosh
(
x
:
f64
)
->
f64
:
return
_lfortran_dcosh
(
x
)
@
ccall
def
_lfortran_dtanh
(
x
:
f64
)
->
f64
:
pass
def
tanh
(
x
:
f64
)
->
f64
:
return
_lfortran_dtanh
(
x
)
@
ccall
def
_lfortran_dasinh
(
x
:
f64
)
->
f64
:
pass
def
asinh
(
x
:
f64
)
->
f64
:
return
_lfortran_dasinh
(
x
)
@
ccall
def
_lfortran_dacosh
(
x
:
f64
)
->
f64
:
pass
def
acosh
(
x
:
f64
)
->
f64
:
return
_lfortran_dacosh
(
x
)
@
ccall
def
_lfortran_datanh
(
x
:
f64
)
->
f64
:
pass
def
atanh
(
x
:
f64
)
->
f64
:
return
_lfortran_datanh
(
x
)
def
log1p
(
x
:
f64
)
->
f64
:
return
log
(
1.0
+
x
)
def
fmod
(
x
:
f64
,
y
:
f64
)
->
f64
:
if
y
==
0.0
:
raise
ValueError
(
'math domain error'
)
return
_lfortran_dfmod
(
x
,
y
)
@
ccall
def
_lfortran_dfmod
(
x
:
f64
,
y
:
f64
)
->
f64
:
pass
def
remainder
(
x
:
f64
,
y
:
f64
)
->
f64
:
q
:
i64
q
=
int
(
x
/
y
)
if
x
-
y
*
f64
(
q
)
>
y
*
f64
(
q
+
i64
(
1
))
-
x
:
return
x
-
y
*
f64
(
q
+
i64
(
1
))
return
x
-
y
*
f64
(
q
)
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