examples: add pidigits.v; optimise math.big's Integer divide a bit (#21239)

examples/pidigits.v

@@ -0,0 +1,52 @@
+module main
+
+import os
+import math.big
+
+const digits_to_print = os.args[1] or { '1000' }.int()
+
+const zero = big.integer_from_int(0)
+const one = big.integer_from_int(1)
+const two = big.integer_from_int(2)
+const three = big.integer_from_int(3)
+const four = big.integer_from_int(4)
+const ten = big.integer_from_int(10)
+
+fn main() {
+	unbuffer_stdout()
+	mut digits_printed := 0
+	mut k := one
+	mut n1 := four
+	mut n2 := three
+	mut d := one
+	mut u := zero
+	mut v := zero
+	mut w := zero
+	for {
+		u = n1 / d
+		v = n2 / d
+		u_int := u.int()
+		v_int := v.int()
+		if u_int == v_int {
+			print(u_int)
+			digits_printed++
+			if digits_printed >= digits_to_print {
+				println('')
+				return
+			}
+			to_minus := u * ten * d
+			n1 = n1 * ten - to_minus
+			n2 = n2 * ten - to_minus
+		} else {
+			k2 := k * two
+			u = n1 * (k2 - one)
+			v = n2 * two
+			w = n1 * (k - one)
+			n1 = u + v
+			u = n2 * (k + two)
+			n2 = w + u
+			d = d * (k2 + one)
+			k += one
+		}
+	}
+}

vlib/math/big/array_ops.v

@@ -199,9 +199,7 @@ fn divide_digit_array(operand_a []u32, operand_b []u32, mut quotient []u32, mut
 	// a < b => q, r = 0, a
 	if cmp_result < 0 {
 		quotient.clear()
-		for index in 0 .. operand_a.len {
+		remainder << operand_a
-			remainder << operand_a[index]
-		}
 		return
 	}
 	if operand_b.len == 1 {

vlib/math/big/division_array_ops.v

@@ -6,9 +6,7 @@ import math.bits
 // Both quotient and remaider are allocated but of length 0
 @[direct_array_access]
 fn binary_divide_array_by_array(operand_a []u32, operand_b []u32, mut quotient []u32, mut remainder []u32) {
-	for index in 0 .. operand_a.len {
+	remainder << operand_a
-		remainder << operand_a[index]
-	}
 
 	len_diff := operand_a.len - operand_b.len
 	$if debug {
@@ -20,9 +18,7 @@ fn binary_divide_array_by_array(operand_a []u32, operand_b []u32, mut quotient [
 	for _ in 0 .. len_diff {
 		divisor << u32(0)
 	}
-	for index in 0 .. operand_b.len {
+	divisor << operand_b
-		divisor << operand_b[index]
-	}
 	for _ in 0 .. len_diff + 1 {
 		quotient << u32(0)
 	}

vlib/math/big/integer.v

@@ -615,12 +615,14 @@ pub fn (mut a Integer) dec() {
 }
 
 // == returns `true` if the integers `a` and `b` are equal in value and sign.
+@[inline]
 pub fn (a Integer) == (b Integer) bool {
 	return a.signum == b.signum && a.digits.len == b.digits.len && a.digits == b.digits
 }
 
 // abs_cmp returns the result of comparing the magnitudes of the integers `a` and `b`.
 // It returns a negative int if `|a| < |b|`, 0 if `|a| == |b|`, and a positive int if `|a| > |b|`.
+@[inline]
 pub fn (a Integer) abs_cmp(b Integer) int {
 	return compare_digit_array(a.digits, b.digits)
 }
@@ -921,6 +923,7 @@ fn u32_to_hex_with_lz(value u32) string {
 
 // int returns the integer value of the integer `a`.
 // NOTE: This may cause loss of precision.
+@[direct_array_access]
 pub fn (a Integer) int() int {
 	if a.signum == 0 {
 		return 0

vlib/math/big/special_array_ops.v

@@ -114,8 +114,8 @@ fn karatsuba_multiply_digit_array(operand_a []u32, operand_b []u32, mut storage
 
 	// thanks to the base cases we can pass zero-length arrays to the mult func
 	half := imax(operand_a.len, operand_b.len) / 2
-	a_l := operand_a[0..half]
+	a_l := unsafe { operand_a[0..half] }
-	a_h := operand_a[half..]
+	a_h := unsafe { operand_a[half..] }
 	mut b_l := []u32{}
 	mut b_h := []u32{}
 	if half <= operand_b.len {
@@ -169,15 +169,15 @@ fn toom3_multiply_digit_array(operand_a []u32, operand_b []u32, mut storage []u3
 
 	// Slices of a and b
 	a0 := Integer{
-		digits: operand_a[0..k]
+		digits: unsafe { operand_a[0..k] }
 		signum: 1
 	}
 	a1 := Integer{
-		digits: operand_a[k..k2]
+		digits: unsafe { operand_a[k..k2] }
 		signum: 1
 	}
 	a2 := Integer{
-		digits: operand_a[k2..]
+		digits: unsafe { operand_a[k2..] }
 		signum: 1
 	}