Inline int_div_impl.inc

Author: mintsuki

divdi3.c

@@ -14,9 +14,12 @@
 
 // Returns: a / b
 
-#define fixint_t di_int
-#define fixuint_t du_int
-#define COMPUTE_UDIV(a, b) __udivmoddi4((a), (b), (du_int *)0)
-#include "int_div_impl.inc"
-
-COMPILER_RT_ABI di_int __divdi3(di_int a, di_int b) { return __divXi3(a, b); }
+COMPILER_RT_ABI di_int __divdi3(di_int a, di_int b) {
+  const int N = (int)(sizeof(di_int) * CHAR_BIT) - 1;
+  di_int s_a = a >> N;                            // s_a = a < 0 ? -1 : 0
+  di_int s_b = b >> N;                            // s_b = b < 0 ? -1 : 0
+  du_int a_u = (du_int)(a ^ s_a) + (-s_a);    // negate if s_a == -1
+  du_int b_u = (du_int)(b ^ s_b) + (-s_b);    // negate if s_b == -1
+  s_a ^= s_b;                                       // sign of quotient
+  return (__udivmoddi4(a_u, b_u, (du_int *)0) ^ s_a) + (-s_a);   // negate if s_a == -1
+}

divsi3.c

@@ -14,16 +14,20 @@
 
 // Returns: a / b
 
-#define fixint_t si_int
-#define fixuint_t su_int
 // On CPUs without unsigned hardware division support,
 //  this calls __udivsi3 (notice the cast to su_int).
 // On CPUs with unsigned hardware division support,
 //  this uses the unsigned division instruction.
-#define COMPUTE_UDIV(a, b) ((su_int)(a) / (su_int)(b))
-#include "int_div_impl.inc"
 
-COMPILER_RT_ABI si_int __divsi3(si_int a, si_int b) { return __divXi3(a, b); }
+COMPILER_RT_ABI si_int __divsi3(si_int a, si_int b) {
+  const int N = (int)(sizeof(si_int) * CHAR_BIT) - 1;
+  si_int s_a = a >> N;                            // s_a = a < 0 ? -1 : 0
+  si_int s_b = b >> N;                            // s_b = b < 0 ? -1 : 0
+  su_int a_u = (su_int)(a ^ s_a) + (-s_a);    // negate if s_a == -1
+  su_int b_u = (su_int)(b ^ s_b) + (-s_b);    // negate if s_b == -1
+  s_a ^= s_b;                                       // sign of quotient
+  return (((su_int)a_u / (su_int)b_u) ^ s_a) + (-s_a);   // negate if s_a == -1
+}
 
 #if defined(__ARM_EABI__)
 COMPILER_RT_ALIAS(__divsi3, __aeabi_idiv)

divti3.c

@@ -16,11 +16,14 @@
 
 // Returns: a / b
 
-#define fixint_t ti_int
-#define fixuint_t tu_int
-#define COMPUTE_UDIV(a, b) __udivmodti4((a), (b), (tu_int *)0)
-#include "int_div_impl.inc"
-
-COMPILER_RT_ABI ti_int __divti3(ti_int a, ti_int b) { return __divXi3(a, b); }
+COMPILER_RT_ABI ti_int __divti3(ti_int a, ti_int b) {
+  const int N = (int)(sizeof(ti_int) * CHAR_BIT) - 1;
+  ti_int s_a = a >> N;                            // s_a = a < 0 ? -1 : 0
+  ti_int s_b = b >> N;                            // s_b = b < 0 ? -1 : 0
+  tu_int a_u = (tu_int)(a ^ s_a) + (-s_a);    // negate if s_a == -1
+  tu_int b_u = (tu_int)(b ^ s_b) + (-s_b);    // negate if s_b == -1
+  s_a ^= s_b;                                       // sign of quotient
+  return (__udivmodti4(a_u, b_u, (tu_int *)0) ^ s_a) + (-s_a);   // negate if s_a == -1
+}
 
 #endif // CRT_HAS_128BIT

int_div_impl.inc

@@ -14,9 +14,13 @@
 
 // Returns: a % b
 
-#define fixint_t di_int
-#define fixuint_t du_int
-#define ASSIGN_UMOD(res, a, b) __udivmoddi4((a), (b), &(res))
-#include "int_div_impl.inc"
-
-COMPILER_RT_ABI di_int __moddi3(di_int a, di_int b) { return __modXi3(a, b); }
+COMPILER_RT_ABI di_int __moddi3(di_int a, di_int b) {
+  const int N = (int)(sizeof(di_int) * CHAR_BIT) - 1;
+  di_int s = b >> N;                              // s = b < 0 ? -1 : 0
+  du_int b_u = (du_int)(b ^ s) + (-s);        // negate if s == -1
+  s = a >> N;                                       // s = a < 0 ? -1 : 0
+  du_int a_u = (du_int)(a ^ s) + (-s);        // negate if s == -1
+  du_int res;
+  __udivmoddi4(a_u, b_u, &res);
+  return (res ^ s) + (-s);                          // negate if s == -1
+}

moddi3.c

@@ -16,11 +16,15 @@
 
 // Returns: a % b
 
-#define fixint_t ti_int
-#define fixuint_t tu_int
-#define ASSIGN_UMOD(res, a, b) __udivmodti4((a), (b), &(res))
-#include "int_div_impl.inc"
-
-COMPILER_RT_ABI ti_int __modti3(ti_int a, ti_int b) { return __modXi3(a, b); }
+COMPILER_RT_ABI ti_int __modti3(ti_int a, ti_int b) {
+  const int N = (int)(sizeof(ti_int) * CHAR_BIT) - 1;
+  ti_int s = b >> N;                              // s = b < 0 ? -1 : 0
+  tu_int b_u = (tu_int)(b ^ s) + (-s);        // negate if s == -1
+  s = a >> N;                                       // s = a < 0 ? -1 : 0
+  tu_int a_u = (tu_int)(a ^ s) + (-s);        // negate if s == -1
+  tu_int res;
+  __udivmodti4(a_u, b_u, &res);
+  return (res ^ s) + (-s);                          // negate if s == -1
+}
 
 #endif // CRT_HAS_128BIT

modti3.c

@@ -12,12 +12,36 @@
 
 #include "int_lib.h"
 
-typedef du_int fixuint_t;
-typedef di_int fixint_t;
-#include "int_div_impl.inc"
-
 // Returns: a / b
 
-COMPILER_RT_ABI du_int __udivdi3(du_int a, du_int b) {
-  return __udivXi3(a, b);
+#undef clz
+#define clz(a) (sizeof(a) == sizeof(unsigned long long) ? __builtin_clzll(a) : clzsi(a))
+
+// Adapted from Figure 3-40 of The PowerPC Compiler Writer's Guide
+COMPILER_RT_ABI du_int __udivdi3(du_int n, du_int d) {
+  const unsigned N = sizeof(du_int) * CHAR_BIT;
+  // d == 0 cases are unspecified.
+  unsigned sr = (d ? clz(d) : N) - (n ? clz(n) : N);
+  // 0 <= sr <= N - 1 or sr is very large.
+  if (sr > N - 1) // n < d
+    return 0;
+  if (sr == N - 1) // d == 1
+    return n;
+  ++sr;
+  // 1 <= sr <= N - 1. Shifts do not trigger UB.
+  du_int r = n >> sr;
+  n <<= N - sr;
+  du_int carry = 0;
+  for (; sr > 0; --sr) {
+    r = (r << 1) | (n >> (N - 1));
+    n = (n << 1) | carry;
+    // Branch-less version of:
+    // carry = 0;
+    // if (r >= d) r -= d, carry = 1;
+    const di_int s = (di_int)(d - r - 1) >> (N - 1);
+    carry = s & 1;
+    r -= d & s;
+  }
+  n = (n << 1) | carry;
+  return n;
 }

udivdi3.c

@@ -12,14 +12,38 @@
 
 #include "int_lib.h"
 
-typedef su_int fixuint_t;
-typedef si_int fixint_t;
-#include "int_div_impl.inc"
-
 // Returns: a / b
 
-COMPILER_RT_ABI su_int __udivsi3(su_int a, su_int b) {
-  return __udivXi3(a, b);
+#undef clz
+#define clz(a) (sizeof(a) == sizeof(unsigned long long) ? __builtin_clzll(a) : clzsi(a))
+
+// Adapted from Figure 3-40 of The PowerPC Compiler Writer's Guide
+COMPILER_RT_ABI su_int __udivsi3(su_int n, su_int d) {
+  const unsigned N = sizeof(su_int) * CHAR_BIT;
+  // d == 0 cases are unspecified.
+  unsigned sr = (d ? clz(d) : N) - (n ? clz(n) : N);
+  // 0 <= sr <= N - 1 or sr is very large.
+  if (sr > N - 1) // n < d
+    return 0;
+  if (sr == N - 1) // d == 1
+    return n;
+  ++sr;
+  // 1 <= sr <= N - 1. Shifts do not trigger UB.
+  su_int r = n >> sr;
+  n <<= N - sr;
+  su_int carry = 0;
+  for (; sr > 0; --sr) {
+    r = (r << 1) | (n >> (N - 1));
+    n = (n << 1) | carry;
+    // Branch-less version of:
+    // carry = 0;
+    // if (r >= d) r -= d, carry = 1;
+    const si_int s = (si_int)(d - r - 1) >> (N - 1);
+    carry = s & 1;
+    r -= d & s;
+  }
+  n = (n << 1) | carry;
+  return n;
 }
 
 #if defined(__ARM_EABI__)

udivsi3.c

@@ -12,12 +12,35 @@
 
 #include "int_lib.h"
 
-typedef du_int fixuint_t;
-typedef di_int fixint_t;
-#include "int_div_impl.inc"
-
 // Returns: a % b
 
-COMPILER_RT_ABI du_int __umoddi3(du_int a, du_int b) {
-  return __umodXi3(a, b);
+#undef clz
+#define clz(a) (sizeof(a) == sizeof(unsigned long long) ? __builtin_clzll(a) : clzsi(a))
+
+// Mostly identical to __udivdi3 but the return values are different.
+COMPILER_RT_ABI du_int __umoddi3(du_int n, du_int d) {
+  const unsigned N = sizeof(du_int) * CHAR_BIT;
+  // d == 0 cases are unspecified.
+  unsigned sr = (d ? clz(d) : N) - (n ? clz(n) : N);
+  // 0 <= sr <= N - 1 or sr is very large.
+  if (sr > N - 1) // n < d
+    return n;
+  if (sr == N - 1) // d == 1
+    return 0;
+  ++sr;
+  // 1 <= sr <= N - 1. Shifts do not trigger UB.
+  du_int r = n >> sr;
+  n <<= N - sr;
+  du_int carry = 0;
+  for (; sr > 0; --sr) {
+    r = (r << 1) | (n >> (N - 1));
+    n = (n << 1) | carry;
+    // Branch-less version of:
+    // carry = 0;
+    // if (r >= d) r -= d, carry = 1;
+    const di_int s = (di_int)(d - r - 1) >> (N - 1);
+    carry = s & 1;
+    r -= d & s;
+  }
+  return r;
 }

umoddi3.c

@@ -12,12 +12,35 @@
 
 #include "int_lib.h"
 
-typedef su_int fixuint_t;
-typedef si_int fixint_t;
-#include "int_div_impl.inc"
-
 // Returns: a % b
 
-COMPILER_RT_ABI su_int __umodsi3(su_int a, su_int b) {
-  return __umodXi3(a, b);
+#undef clz
+#define clz(a) (sizeof(a) == sizeof(unsigned long long) ? __builtin_clzll(a) : clzsi(a))
+
+// Mostly identical to __udivsi3 but the return values are different.
+COMPILER_RT_ABI su_int __umodsi3(su_int n, su_int d) {
+  const unsigned N = sizeof(su_int) * CHAR_BIT;
+  // d == 0 cases are unspecified.
+  unsigned sr = (d ? clz(d) : N) - (n ? clz(n) : N);
+  // 0 <= sr <= N - 1 or sr is very large.
+  if (sr > N - 1) // n < d
+    return n;
+  if (sr == N - 1) // d == 1
+    return 0;
+  ++sr;
+  // 1 <= sr <= N - 1. Shifts do not trigger UB.
+  su_int r = n >> sr;
+  n <<= N - sr;
+  su_int carry = 0;
+  for (; sr > 0; --sr) {
+    r = (r << 1) | (n >> (N - 1));
+    n = (n << 1) | carry;
+    // Branch-less version of:
+    // carry = 0;
+    // if (r >= d) r -= d, carry = 1;
+    const si_int s = (si_int)(d - r - 1) >> (N - 1);
+    carry = s & 1;
+    r -= d & s;
+  }
+  return r;
 }