math.bits: added missing functions and test

vlib/math/bits/bits.v

@@ -96,6 +96,7 @@ pub fn trailing_zeros_64(x u64) int {
 }
 
 // --- OnesCount ---
+
 // ones_count_8 returns the number of one bits ("population count") in x.
 pub fn ones_count_8(x byte) int {
 	return int(pop_8_tab[x])
@@ -142,6 +143,7 @@ pub fn ones_count_64(x u64) int {
 }
 
 // --- RotateLeft ---
+
 // rotate_left_8 returns the value of x rotated left by (k mod 8) bits.
 // To rotate x right by k bits, call rotate_left_8(x, -k).
 //
@@ -187,6 +189,7 @@ pub fn rotate_left_64(x u64, k int) u64 {
 }
 
 // --- Reverse ---
+
 // reverse_8 returns the value of x with its bits in reversed order.
 [inline]
 pub fn reverse_8(x byte) byte {
@@ -218,6 +221,7 @@ pub fn reverse_64(x u64) u64 {
 }
 
 // --- ReverseBytes ---
+
 // reverse_bytes_16 returns the value of x with its bytes in reversed order.
 //
 // This function's execution time does not depend on the inputs.
@@ -246,6 +250,7 @@ pub fn reverse_bytes_64(x u64) u64 {
 }
 
 // --- Len ---
+
 // len_8 returns the minimum number of bits required to represent x; the result is 0 for x == 0.
 pub fn len_8(x byte) int {
 	return int(len_8_tab[x])
@@ -296,3 +301,195 @@ pub fn len_64(x u64) int {
 	return n + int(len_8_tab[y])
 }
 
+// --- Add with carry ---
+
+// Add returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+
+// add_32 returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+fn add_32(x u32, y u32, carry u32) (u32, u32) {
+	sum64 := u64(x) + u64(y) + u64(carry)
+	sum := u32(sum64)
+	carry_out := u32(sum64>>32)
+	return sum, carry_out
+}
+
+// add_64 returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+fn add_64(x u64, y u64, carry u64) (u64, u64) {
+	sum := x + y + carry
+	// The sum will overflow if both top bits are set (x & y) or if one of them
+	// is (x | y), and a carry from the lower place happened. If such a carry
+	// happens, the top bit will be 1 + 0 + 1 = 0 (&^ sum).
+	carry_out := ((x & y) | ((x | y) & ~sum ))>>63
+	return sum, carry_out
+}
+
+// --- Subtract with borrow ---
+
+// Sub returns the difference of x, y and borrow: diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+
+// sub_32 returns the difference of x, y and borrow, diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+fn sub_32(x u32, y u32, borrow u32) (u32, u32) {
+	diff := x - y - borrow
+	// The difference will underflow if the top bit of x is not set and the top
+	// bit of y is set (^x & y) or if they are the same (^(x ^ y)) and a borrow
+	// from the lower place happens. If that borrow happens, the result will be
+	// 1 - 1 - 1 = 0 - 0 - 1 = 1 (& diff).
+	borrow_out := ((~x & y) | (~(x ^ y) & diff))>>31
+	return diff, borrow_out
+}
+
+// sub_64 returns the difference of x, y and borrow: diff = x - y - borrow.
+// The borrow input must be 0 or 1; otherwise the behavior is undefined.
+// The borrowOut output is guaranteed to be 0 or 1.
+//
+// This function's execution time does not depend on the inputs.
+fn sub_64(x u64, y u64, borrow u64) (u64, u64) {
+	diff := x - y - borrow
+	// See Sub32 for the bit logic.
+	borrow_out  := ((~x & y) | (~(x ^ y) & diff))>>63
+	return diff, borrow_out
+}
+
+// --- Full-width multiply ---
+
+const (
+	two32  = u64(0x1_0000_0000)
+	mask32 = two32 - 1
+	overflow_error = "Overflow Error"
+	divide_error = "Divide Error"
+)
+
+// mul_32 returns the 64-bit product of x and y: (hi, lo) = x * y
+// with the product bits' upper half returned in hi and the lower
+// half returned in lo.
+//
+// This function's execution time does not depend on the inputs.
+fn mul_32(x u32, y u32) (u32, u32) {
+	tmp := u64(x) * u64(y)
+	hi := u32(tmp>>32)
+	lo := u32(tmp)
+	return hi, lo
+}
+
+// mul_64 returns the 128-bit product of x and y: (hi, lo) = x * y
+// with the product bits' upper half returned in hi and the lower
+// half returned in lo.
+//
+// This function's execution time does not depend on the inputs.
+fn mul_64(x u64, y u64) (u64, u64) {
+	x0 := x & mask32
+	x1 := x>>32
+	y0 := y & mask32
+	y1 := y>>32
+	w0 := x0 * y0
+	t := x1*y0 + (w0>>32)
+	mut w1 := t & mask32
+	w2 := t>>32
+	w1 += x0 * y1
+	hi := x1*y1 + w2 + (w1>>32)
+	lo := x * y
+	return hi, lo
+}
+
+// --- Full-width divide ---
+
+// div_32 returns the quotient and remainder of (hi, lo) divided by y:
+// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
+// half in parameter hi and the lower half in parameter lo.
+// div_32 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
+fn div_32(hi u32, lo u32, y u32) (u32, u32) {
+	if y != 0 && y <= hi {
+		panic(overflow_error)
+	}
+	z := (u64(hi)<<32) | u64(lo)
+	quo := u32(z/u64(y))
+	rem := u32(z%u64(y))
+	return quo, rem
+}
+
+// div_64 returns the quotient and remainder of (hi, lo) divided by y:
+// quo = (hi, lo)/y, rem = (hi, lo)%y with the dividend bits' upper
+// half in parameter hi and the lower half in parameter lo.
+// div_64 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
+fn div_64(hi u64, lo u64, y1 u64) (u64, u64) {
+	mut y := y1
+	if y == 0 {
+		panic(overflow_error)
+	}
+	if y <= hi {
+		panic(overflow_error)
+	}
+
+	s := u32(leading_zeros_64(y))
+	y <<= s
+
+	yn1 := y>>32
+	yn0 := y & mask32
+	un32 := (hi<<s) | (lo>>(64-s))
+	un10 := lo<<s
+	un1 := un10>>32
+	un0 := un10 & mask32
+	mut q1 := un32 / yn1
+	mut rhat := un32 - q1*yn1
+
+	for q1 >= two32 || q1*yn0 > two32*rhat+un1 {
+		q1--
+		rhat += yn1
+		if rhat >= two32 {
+			break
+		}
+	}
+
+	un21 := un32*two32 + un1 - q1*y
+	mut q0 := un21 / yn1
+	rhat = un21 - q0*yn1
+
+	for q0 >= two32 || q0*yn0 > two32*rhat+un0 {
+		q0--
+		rhat += yn1
+		if rhat >= two32 {
+			break
+		}
+	}
+
+	return q1*two32 + q0, (un21*two32 + un0 - q0*y)>>s
+}
+
+// rem_32 returns the remainder of (hi, lo) divided by y. Rem32 panics
+// for y == 0 (division by zero) but, unlike Div32, it doesn't panic
+// on a quotient overflow.
+fn rem_32(hi u32, lo u32, y u32) u32 {
+	return u32((u64(hi)<<32 | u64(lo)) % u64(y))
+}
+
+// rem_64 returns the remainder of (hi, lo) divided by y. Rem64 panics
+// for y == 0 (division by zero) but, unlike div_64, it doesn't panic
+// on a quotient overflow.
+fn rem_64(hi, lo, y u64) u64 {
+	// We scale down hi so that hi < y, then use div_64 to compute the
+	// rem with the guarantee that it won't panic on quotient overflow.
+	// Given that
+	//   hi ≡ hi%y    (mod y)
+	// we have
+	//   hi<<64 + lo ≡ (hi%y)<<64 + lo    (mod y)
+	_, rem := div_64(hi%y, lo, y)
+	return rem
+}

vlib/math/bits/bits_test.v

@@ -1,8 +1,12 @@
+//
+// test suite for bits and bits math functions
+//
 module bits
 
 fn test_bits(){
 	mut i := 0
 	mut i1:= u64(0)
+	
 	//
 	// --- LeadingZeros ---
 	//
@@ -10,26 +14,29 @@ fn test_bits(){
 	// 8 bit
 	i = 1
 	for x in 0..8 {
-		//C.printf("x:%02x lz: %d cmp: %d\n",i<<x,leading_zeros_8(i<<x), 7-x)
+		//C.printf("x:%02x lz: %d cmp: %d\n", i << x, leading_zeros_8(i << x), 7-x)
-		assert leading_zeros_8(byte(i<<x)) == 7 - x
+		assert leading_zeros_8(byte(i << x)) == 7 - x
 	}
+	
 	// 16 bit
 	i = 1
 	for x in 0..16 {
-		//C.printf("x:%04x lz: %d cmp: %d\n",u16(i)<<x,leading_zeros_16(u16(i)<<x), 15-x)
+		//C.printf("x:%04x lz: %d cmp: %d\n", u16(i) << x, leading_zeros_16(u16(i) << x), 15-x)
-		assert leading_zeros_16(u16(i)<<x) == 15 - x
+		assert leading_zeros_16(u16(i) << x) == 15 - x
 	}
+	
 	// 32 bit
 	i = 1
 	for x in 0..32 {
-		//C.printf("x:%08x lz: %d cmp: %d\n",u32(i)<<x,leading_zeros_32(u32(i)<<x), 31-x)
+		//C.printf("x:%08x lz: %d cmp: %d\n", u32(i) << x, leading_zeros_32(u32(i) << x), 31-x)
-		assert leading_zeros_32(u32(i)<<x) == 31 - x
+		assert leading_zeros_32(u32(i) << x) == 31 - x
 	}
+	
 	// 64 bit
 	i = 1
 	for x in 0..64 {
-		//C.printf("x:%016llx lz: %llu cmp: %d\n",u64(i)<<x,leading_zeros_64(u64(i)<<x), 63-x)
+		//C.printf("x:%016llx lz: %llu cmp: %d\n", u64(i) << x, leading_zeros_64(u64(i) << x), 63-x)
-		assert leading_zeros_64(u64(i)<<x) == 63 - x
+		assert leading_zeros_64(u64(i) << x) == 63 - x
 	}
 
 	//
@@ -39,29 +46,32 @@ fn test_bits(){
 	// 8 bit
 	i = 0
 	for x in 0..9 {
-		//C.printf("x:%02x lz: %llu cmp: %d\n",byte(i),ones_count_8(byte(i)), x)
+		//C.printf("x:%02x lz: %llu cmp: %d\n", byte(i), ones_count_8(byte(i)), x)
 		assert ones_count_8(byte(i)) == x
 		i = (i << 1) + 1
 	}
+	
 	// 16 bit
 	i = 0
 	for x in 0..17 {
-		//C.printf("x:%04x lz: %llu cmp: %d\n",u16(i),ones_count_16(u16(i)), x)
+		//C.printf("x:%04x lz: %llu cmp: %d\n", u16(i), ones_count_16(u16(i)), x)
 		assert ones_count_16(u16(i)) == x
 		i = (i << 1) + 1
 	}
+	
 	// 32 bit
 	i = 0
 	for x in 0..33 {
-		//C.printf("x:%08x lz: %llu cmp: %d\n",u32(i),ones_count_32(u32(i)), x)
+		//C.printf("x:%08x lz: %llu cmp: %d\n", u32(i), ones_count_32(u32(i)), x)
 		assert ones_count_32(u32(i)) == x
 		i = (i << 1) + 1
 	}
+	
 	// 64 bit
 	i1 = 0
 	for x in 0..65 {
-		//C.printf("x:%016llx lz: %llu cmp: %d\n",u64(i1),ones_count_64(u64(i1)), x)
+		//C.printf("x:%016llx lz: %llu cmp: %d\n", u64(i1), ones_count_64(u64(i1)), x)
-		assert ones_count_64(u64(i1)) == x
+		assert ones_count_64(i1) == x
 		i1 = (i1 << 1) + 1
 	}
 
@@ -88,10 +98,11 @@ fn test_bits(){
 			bc++
 			n = n >> 1
 		}
-		//C.printf("x:%02x lz: %llu cmp: %d\n",byte(i),reverse_8(byte(i)), rv)
+		//C.printf("x:%02x lz: %llu cmp: %d\n", byte(i), reverse_8(byte(i)), rv)
 		assert reverse_8(byte(i)) == rv
 		i = (i << 1) + 1
 	}
+	
 	// 16 bit
 	i = 0
 	for x in 0..17 {
@@ -103,10 +114,11 @@ fn test_bits(){
 			bc++
 			n = n >> 1
 		}
-		//C.printf("x:%04x lz: %llu cmp: %d\n",u16(i),reverse_16(u16(i)), rv)
+		//C.printf("x:%04x lz: %llu cmp: %d\n", u16(i), reverse_16(u16(i)), rv)
 		assert reverse_16(u16(i)) == rv
 		i = (i << 1) + 1
 	}
+	
 	// 32 bit
 	i = 0
 	for x in 0..33 {
@@ -118,10 +130,11 @@ fn test_bits(){
 			bc++
 			n = n >> 1
 		}
-		//C.printf("x:%08x lz: %llu cmp: %d\n",u32(i),reverse_32(u32(i)), rv)
+		//C.printf("x:%08x lz: %llu cmp: %d\n", u32(i), reverse_32(u32(i)), rv)
 		assert reverse_32(u32(i)) == rv
 		i = (i << 1) + 1
 	}
+	
 	// 64 bit
 	i1 = 0
 	for x in 0..64 {
@@ -133,8 +146,144 @@ fn test_bits(){
 			bc++
 			n = n >> 1
 		}
-		//C.printf("x:%016llx lz: %016llx cmp: %016llx\n",u64(i1),reverse_64(u64(i1)), rv)
+		//C.printf("x:%016llx lz: %016llx cmp: %016llx\n", u64(i1), reverse_64(u64(i1)), rv)
-		assert reverse_64(u64(i1)) == rv
+		assert reverse_64(i1) == rv
 		i1 = (i1 << 1) + 1
 	}
-}
+
+	//
+	// --- add ---
+	//
+
+	// 32 bit
+	i = 1
+	for x in 0..32 {
+		v := u32(i) << x
+		sum,carry := add_32(v, v, u32(0))
+		//C.printf("x:%08x [%llu,%llu] %llu\n", u32(i) << x, sum, carry, u64(v) + u64(v))
+		assert ((u64(carry) << 32) | u64(sum)) == u64(v) + u64(v)
+	}
+	mut sum_32t, mut carry_32t := add_32(0x8000_0000, 0x8000_0000, u32(0))
+	assert sum_32t == u32(0)
+	assert carry_32t == u32(1)
+
+	sum_32t, carry_32t = add_32(0xFFFF_FFFF, 0xFFFF_FFFF, u32(1))
+	assert sum_32t == 0xFFFF_FFFF
+	assert carry_32t == u32(1)
+
+	// 64 bit
+	i = 1
+	for x in 0..63 {
+		v := u64(i) << x
+		sum,carry := add_64(v, v, u64(0))
+		//C.printf("x:%16x [%llu,%llu] %llu\n", u64(i) << x, sum, carry, u64(v >> 32) + u64(v >> 32))
+		assert ((carry << 32) | sum) == v + v
+	}
+	mut sum_64t, mut carry_64t := add_64(0x8000_0000_0000_0000, 0x8000_0000_0000_0000, u64(0))
+	assert sum_64t == u64(0)
+	assert carry_64t == u64(1)
+
+	sum_64t, carry_64t = add_64(0xFFFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF, u64(1))
+	assert sum_64t == 0xFFFF_FFFF_FFFF_FFFF
+	assert carry_64t == u64(1)
+
+	//
+	// --- sub ---
+	//
+	
+	// 32 bit
+	i = 1
+	for x in 1..32 {
+		v0 := u32(i) << x
+		v1 := v0 >> 1
+		mut diff, mut borrow_out := sub_32(v0, v1, u32(0))
+		//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v0 - v1)
+		assert diff == v1
+
+		diff, borrow_out = sub_32(v0, v1, u32(1))
+		//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v0 - v1)
+		assert diff == (v1 - 1) 
+		assert borrow_out == u32(0)
+
+		diff, borrow_out = sub_32(v1, v0, u32(1))
+		//C.printf("x:%08x [%llu,%llu] %08x\n", u32(i) << x, diff, borrow_out, v1 - v0)
+		assert borrow_out == u32(1)
+	}
+
+	// 64 bit
+	i = 1
+	for x in 1..64 {
+		v0 := u64(i) << x
+		v1 := v0 >> 1
+		mut diff, mut borrow_out := sub_64(v0, v1, u64(0))
+		//C.printf("x:%08x [%llu,%llu] %08x\n", u64(i) << x, diff, borrow_out, v0 - v1)
+		assert diff == v1
+
+		diff, borrow_out = sub_64(v0, v1, u64(1))
+		//C.printf("x:%08x [%llu,%llu] %08x\n", u64(i) << x, diff, borrow_out, v0 - v1)
+		assert diff == (v1 - 1) 
+		assert borrow_out == u64(0)
+
+		diff, borrow_out = sub_64(v1, v0, u64(1))
+		//C.printf("x:%08x [%llu,%llu] %08x\n",u64(i) << x, diff, borrow_out, v1 - v0)
+		assert borrow_out == u64(1)
+	}
+
+	//
+	// --- mul ---
+	//
+
+	// 32 bit
+	i = 1
+	for x in 0..32 {
+		v0 := u32(i) << x
+		v1 := v0 - 1
+		hi, lo := mul_32(v0, v1)
+		//C.printf("x:%08x [%llu,%llu] %llu\n", v0, hi, lo, u64(v0 * v1))
+		assert (u64(hi) << 32) | (u64(lo)) == u64(v0 * v1)
+	}
+
+	// 64 bit
+	i = 1
+	for x in 0..64 {
+		v0 := u64(i) << x
+		v1 := v0 - 1
+		hi, lo := mul_64(v0, v1)
+		//C.printf("v0: %llu v1: %llu [%llu,%llu] tt: %llu\n", v0, v1, hi, lo, (v0 >> 32) * (v1 >> 32))
+		assert (hi & 0xFFFF_FFFF_0000_0000) == (((v0 >> 32)*(v1 >> 32)) & 0xFFFF_FFFF_0000_0000)
+		assert (lo & 0x0000_0000_FFFF_FFFF) == (((v0 & 0x0000_0000_FFFF_FFFF) * (v1 & 0x0000_0000_FFFF_FFFF)) & 0x0000_0000_FFFF_FFFF)
+	}
+
+	//
+	// --- div ---
+	//
+
+	// 32 bit
+	i = 1
+	for x in 0..31 {
+		hi := u32(i) << x
+		lo := hi - 1
+		y  := u32(3) << x
+		quo, rem := div_32(hi, lo, y)
+		//C.printf("[%08x_%08x] %08x (%08x,%08x)\n", hi, lo, y, quo, rem)
+		tst := ((u64(hi) << 32) | u64(lo))
+		assert quo == (tst / u64(y))
+		assert rem == (tst % u64(y))
+		assert rem == rem_32(hi, lo, y)
+	}
+
+	// 64 bit
+	i = 1
+	for x in 0..62 {
+		hi := u64(i) << x
+		lo := u64(2) //hi - 1
+		y  := 0x4000_0000_0000_0000
+		quo, rem := div_64(hi, lo, y)
+		//C.printf("[%016llx_%016llx] %016llx (%016llx,%016llx)\n", hi, lo, y, quo, rem)
+		assert quo == u64(2)<<(x+1)
+		_, rem1 := div_64(hi%y, lo, y)
+		assert rem == rem1
+		assert rem == rem_64(hi, lo, y)
+	}
+	
+}