Change division and modulus to use euclidean division, plus fix up a few

integer bugs

2 files changed, 64 insertions, 22 deletions

diff --git a/builtins/integers.c b/builtins/integers.c
index bb82fab6..0bf7dc22 100644
--- a/builtins/integers.c
+++ b/builtins/integers.c
@@ -152,17 +152,20 @@ public Int_t Int$slow_times(Int_t x, Int_t y) {
     return Int$from_mpz(result);
 }
 
-public Int_t Int$slow_divided_by(Int_t x, Int_t y) {
-    mpz_t result;
-    mpz_init_set_int(result, x);
-    if (y.small & 1) {
-        mpz_t y_mpz;
-        mpz_init_set_si(y_mpz, y.small >> 2);
-        mpz_cdiv_q(result, result, y_mpz);
-    } else {
-        mpz_cdiv_q(result, result, *y.big);
+public Int_t Int$slow_divided_by(Int_t dividend, Int_t divisor) {
+    // Euclidean division, see: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
+    mpz_t quotient, remainder;
+    mpz_init_set_int(quotient, dividend);
+    mpz_init_set_int(remainder, divisor);
+    mpz_tdiv_qr(quotient, remainder, quotient, remainder);
+    if (mpz_sgn(remainder) < 0) {
+        bool d_positive = __builtin_expect(divisor.small & 1, 1) ? divisor.small > 0x1 : mpz_sgn(*divisor.big) > 0;
+        if (d_positive)
+            mpz_sub_ui(quotient, quotient, 1);
+        else
+            mpz_add_ui(quotient, quotient, 1);
     }
-    return Int$from_mpz(result);
+    return Int$from_mpz(quotient);
 }
 
 public Int_t Int$slow_modulo(Int_t x, Int_t modulus)
@@ -359,7 +362,7 @@ public const TypeInfo $Int = {
     } \
     public CORD KindOfInt ## $format(c_type i, Int_t digits_int) { \
         int64_t digits = Int_to_Int64(digits_int, false); \
-        return CORD_asprintf("%0*" fmt, (int)digits, i); \
+        return CORD_asprintf("%0*ld", (int)digits, (int64_t)i); \
     } \
     public CORD KindOfInt ## $hex(c_type i, Int_t digits_int, bool uppercase, bool prefix) { \
         int64_t digits = Int_to_Int64(digits_int, false); \
@@ -427,7 +430,7 @@ public const TypeInfo $Int = {
         .CustomInfo={.compare=(void*)KindOfInt##$compare, .as_text=(void*)KindOfInt##$as_text}, \
     };
 
-DEFINE_INT_TYPE(int64_t,  Int64,  "ld",     INT64_MIN, INT64_MAX);
+DEFINE_INT_TYPE(int64_t,  Int64,  "ld_i64", INT64_MIN, INT64_MAX);
 DEFINE_INT_TYPE(int32_t,  Int32,  "d_i32",  INT32_MIN, INT32_MAX);
 DEFINE_INT_TYPE(int16_t,  Int16,  "d_i16",  INT16_MIN, INT16_MAX);
 DEFINE_INT_TYPE(int8_t,   Int8,   "d_i8",   INT8_MIN,  INT8_MAX);
diff --git a/builtins/integers.h b/builtins/integers.h
index 898469e2..e6b5b1fb 100644
--- a/builtins/integers.h
+++ b/builtins/integers.h
@@ -35,7 +35,26 @@
     Range_t type_name ## $to(c_type from, c_type to); \
     c_type type_name ## $from_text(CORD text, CORD *the_rest); \
     extern const c_type type_name ## $min, type_name##$max; \
-    extern const TypeInfo $ ## type_name;
+    extern const TypeInfo $ ## type_name; \
+    static inline c_type type_name ## $divided_by(c_type D, c_type d) { \
+        c_type q = D/d, r = D%d; \
+        if (r < 0) { \
+            if (d > 0) q = q-1; \
+            else q = q+1; \
+        } \
+        return q; \
+    } \
+    static inline c_type type_name ## $modulo(c_type D, c_type d) { \
+        c_type r = D%d; \
+        if (r < 0) { \
+            if (d > 0) r = r + d; \
+            else r = r - d; \
+        } \
+        return r; \
+    } \
+    static inline c_type type_name ## $modulo1(c_type D, c_type d) { \
+        return type_name ## $modulo(D-1, d) + 1; \
+    }
 
 DEFINE_INT_TYPE(int64_t, Int64);
 DEFINE_INT_TYPE(int32_t, Int32);
@@ -128,27 +147,47 @@ static inline Int_t Int$times(Int_t x, Int_t y) {
 
 static inline Int_t Int$divided_by(Int_t x, Int_t y) {
     if (__builtin_expect(((x.small & y.small) & 1) != 0, 1)) {
-        const int64_t z = ((x.small>>1) / (y.small>>1)) << 2;
-        if (__builtin_expect(z == (int32_t)z, 1))
-            return (Int_t){.small=z|1};
+        // Euclidean division, see: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
+        const int64_t D = (x.small>>2);
+        const int64_t d = (y.small>>2);
+        int64_t q = D/d;
+        int64_t r = D%d;
+        if (r < 0) {
+            if (d > 0) q = q-1;
+            else q = q+1;
+        }
+        if (__builtin_expect(q == (int32_t)q, 1))
+            return (Int_t){.small=(q<<2)|1};
     }
     return Int$slow_divided_by(x, y);
 }
 
 static inline Int_t Int$modulo(Int_t x, Int_t y) {
     if (__builtin_expect(((x.small & y.small) & 1) != 0, 1)) {
-        int64_t mod = (x.small>>2) % (y.small>>2);
-        if (mod < 0) mod += (y.small>>2);
-        return (Int_t){.small=(mod<<2)+1};
+        // Euclidean modulus, see: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
+        const int64_t D = (x.small>>2);
+        const int64_t d = (y.small>>2);
+        int64_t r = D%d;
+        if (r < 0) {
+            if (d > 0) r = r + d;
+            else r = r - d;
+        }
+        return (Int_t){.small=(r<<2)|1};
     }
     return Int$slow_modulo(x, y);
 }
 
 static inline Int_t Int$modulo1(Int_t x, Int_t y) {
     if (__builtin_expect(((x.small & y.small) & 1) != 0, 1)) {
-        int64_t mod = ((x.small>>2)-1) % (y.small>>2);
-        if (mod < 0) mod += (y.small>>2);
-        return (Int_t){.small=((mod+1)<<2)+1};
+        // Euclidean modulus, see: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
+        const int64_t D = (x.small>>2)-1;
+        const int64_t d = (y.small>>2);
+        int64_t r = D%d;
+        if (r < 0) {
+            if (d > 0) r = r + d;
+            else r = r - d;
+        }
+        return (Int_t){.small=((r+1)<<2)|1};
     }
     return Int$slow_modulo1(x, y);
 }