Fuzion • Idioms • Idiom # 32: Integer exponentiation by squaring

Idiom # 32: Integer exponentiation by squaring

Code

# for an explict type like i32
#
exp(x, n i32) => x**n


# using a type parameter to work for any integer type
#
exp(T type : integer T, x, n T) => x**n

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# for an explict type like i32
#
exp(x, n i32) => x**n
# using a type parameter to work for any integer type
#
exp(T type : integer T, x, n T) => x**n
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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What are effects?

Running Example

idiom32ex is

  exp(T type : integer, x, n T) => x**n

  for i in 1..5 do
    for j in 1..5 do
      say "exp $i $j is {exp i j}"

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idiom32ex is
  exp(T type : integer, x, n T) => x**n
  for i in 1..5 do
    for j in 1..5 do
      say "exp $i $j is {exp i j}"
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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What are effects?

Another version showing more results using wrap-around, saturating and overflow-checking versions:

idiom32ex2 is

  exp     (T type : integer, x, n T) => x **  n
  exp_wrap (T type : num.wrap_around, x, n T) => x **° n
  exp_max  (T type : integer, x, n T) => x **^ n
  exp_check(T type : integer, x, n T) => x **? n

  for i in 0..15 do
    for j in 0..15 do
      say "exp $i $j is {exp_wrap i j} {exp_max i j} {exp_check i j}"

  for i in -15 .. -1 do
    for j in 0..15 do
      say "exp $i $j is {exp_wrap i j} {exp_max i j} {exp_check i j}"

  # using the standard exp will eventually cause an error:
  for i in 0..15 do
    for j in 0..15 do
      say "exp $i $j is {exp i j}"

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idiom32ex2 is
  exp     (T type : integer, x, n T) => x **  n
  exp_wrap (T type : num.wrap_around, x, n T) => x **° n
  exp_max  (T type : integer, x, n T) => x **^ n
  exp_check(T type : integer, x, n T) => x **? n
  for i in 0..15 do
    for j in 0..15 do
      say "exp $i $j is {exp_wrap i j} {exp_max i j} {exp_check i j}"
  for i in -15 .. -1 do
    for j in 0..15 do
      say "exp $i $j is {exp_wrap i j} {exp_max i j} {exp_check i j}"
  # using the standard exp will eventually cause an error:
  for i in 0..15 do
    for j in 0..15 do
      say "exp $i $j is {exp i j}"
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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What are effects?

last changed: 2025-05-13

next: Idiom # 33: Atomically read and update variable