Implement floored / and divisor-sign % operators (#745)

Fixes #703

src/asm/rgbasm.5

@@ -143,9 +143,16 @@ A great number of operators you can use in expressions are available (listed fro
 complements a value by inverting all its bits.
 .Pp
 .Ic %
-is used to get the remainder of the corresponding division.
-.Sq 5 % 2
-is 1.
+is used to get the remainder of the corresponding division, so that
+.Sq a / b * b + a % b == a
+is always true.
+The result has the same sign as the divisor.
+This makes
+.Sq a % b .
+equal to
+.Sq (a + b) % b
+or
+.Sq (a - b) % b .
 .Pp
 Shifting works by shifting all bits in the left operand either left
 .Pq Sq <<
@@ -168,7 +175,8 @@ still evaluates both operands of
 and
 .Sq || .
 .Pp
-! returns 1 if the operand was 0, and 0 otherwise.
+.Ic \&!
+returns 1 if the operand was 0, and 0 otherwise.
 .Ss Fixed‐point Expressions
 Fixed-point numbers are basically normal (32-bit) integers, which count 65536th's instead of entire units, offering better precision than integers but limiting the range of values.
 The upper 16 bits are used for the integer part and the lower 16 bits are used for the fraction (65536ths).

src/asm/rpn.c

@@ -283,6 +283,22 @@ static int32_t shift(int32_t shiftee, int32_t amount)
 	}
 }
 
+static int32_t divide(int32_t dividend, int32_t divisor)
+{
+	// Adjust division to floor toward negative infinity,
+	// not truncate toward zero
+	return dividend / divisor - ((dividend % divisor < 0) != (divisor < 0));
+}
+
+static int32_t modulo(int32_t dividend, int32_t divisor)
+{
+	int32_t remainder = dividend % divisor;
+
+	// Adjust modulo to have the sign of the divisor,
+	// not the sign of the dividend
+	return remainder + divisor * ((remainder < 0) != (divisor < 0));
+}
+
 static int32_t exponent(int32_t base, uint32_t power)
 {
 	int32_t result = 1;
@@ -410,17 +426,17 @@ void rpn_BinaryOp(enum RPNCommand op, struct Expression *expr,
 					PRId32 "\n", INT32_MIN, INT32_MIN);
 				expr->nVal = INT32_MIN;
 			} else {
-				expr->nVal = src1->nVal / src2->nVal;
+				expr->nVal = divide(src1->nVal, src2->nVal);
 			}
 			break;
 		case RPN_MOD:
 			if (src2->nVal == 0)
-				fatalerror("Division by zero\n");
+				fatalerror("Modulo by zero\n");
 
 			if (src1->nVal == INT32_MIN && src2->nVal == -1)
 				expr->nVal = 0;
 			else
-				expr->nVal = src1->nVal % src2->nVal;
+				expr->nVal = modulo(src1->nVal, src2->nVal);
 			break;
 		case RPN_EXP:
 			if (src2->nVal < 0)

src/link/patch.c

@@ -21,6 +21,22 @@
 
 #include "extern/err.h"
 
+static int32_t divide(int32_t dividend, int32_t divisor)
+{
+	// Adjust division to floor toward negative infinity,
+	// not truncate toward zero
+	return dividend / divisor - ((dividend % divisor < 0) != (divisor < 0));
+}
+
+static int32_t modulo(int32_t dividend, int32_t divisor)
+{
+	int32_t remainder = dividend % divisor;
+
+	// Adjust modulo to have the sign of the divisor,
+	// not the sign of the dividend
+	return remainder + divisor * ((remainder < 0) != (divisor < 0));
+}
+
 static int32_t exponent(int32_t base, uint32_t power)
 {
 	int32_t result = 1;
@@ -235,7 +251,7 @@ static int32_t computeRPNExpr(struct Patch const *patch,
 				popRPN();
 				value = INT32_MAX;
 			} else {
-				value = popRPN() / value;
+				value = divide(popRPN(), value);
 			}
 			break;
 		case RPN_MOD:
@@ -247,7 +263,7 @@ static int32_t computeRPNExpr(struct Patch const *patch,
 				popRPN();
 				value = 0;
 			} else {
-				value = popRPN() % value;
+				value = modulo(popRPN(), value);
 			}
 			break;
 		case RPN_UNSUB:

test/asm/div-mod.asm

@@ -0,0 +1,36 @@
+_ASM equ 0
+
+test: MACRO
+; Test RGBASM
+V equs "_ASM +"
+	static_assert \#
+	PURGE V
+; Test RGBLINK
+V equs "_LINK +"
+	assert \#
+	PURGE V
+ENDM
+
+for x, -300, 301
+  for y, -x - 1, x + 2
+    if y != 0
+q = x / y
+r = x % y
+      test (V (q * y + r)) == (V x)
+      test (V (x + y) % y) == (V r)
+      test (V (x - y) % y) == (V r)
+    endc
+  endr
+endr
+
+for x, -300, 301
+  for p, 31
+y = 2 ** p
+r = x % y
+m = x & (y - 1)
+    test (V r) == (V m)
+  endr
+endr
+
+SECTION "LINK", ROM0
+_LINK::