util/tests/fast_idiv_by_const_test.cpp

/*
 * Copyright © 2018 Intel Corporation
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice (including the next
 * paragraph) shall be included in all copies or substantial portions of the
 * Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
 * IN THE SOFTWARE.
 */

#undef NDEBUG

#include <gtest/gtest.h>
#include "util/bigmath.h"
#include "util/fast_idiv_by_const.h"
#include "util/u_math.h"

#define RAND_TEST_ITERATIONS 100000

static inline uint64_t
utrunc(uint64_t x, unsigned num_bits)
{
   if (num_bits == 64)
      return x;

   return (x << (64 - num_bits)) >> (64 - num_bits);
}

static inline int64_t
strunc(int64_t x, unsigned num_bits)
{
   if (num_bits == 64)
      return x;

   return (int64_t)((uint64_t)x << (64 - num_bits)) >> (64 - num_bits);
}

static inline bool
uint_is_in_range(uint64_t x, unsigned num_bits)
{
   if (num_bits == 64)
      return true;

   return x < (1ull << num_bits);
}

static inline bool
sint_is_in_range(int64_t x, unsigned num_bits)
{
   if (num_bits == 64)
      return true;

   return x >= -(1ll << (num_bits - 1)) &&
          x < (1ll << (num_bits - 1));
}

static inline uint64_t
uadd_sat(uint64_t a, uint64_t b, unsigned num_bits)
{
   assert(uint_is_in_range(a, num_bits));
   assert(uint_is_in_range(b, num_bits));

   uint64_t sum = a + b;
   if (num_bits == 64) {
      /* Standard overflow check */
      return sum < a ? UINT64_MAX : sum;
   } else {
      /* Check if sum is more than num_bits */
      return (sum >> num_bits) ? u_uintN_max(num_bits) : sum;
   }
}

static inline uint64_t
umul_add_high(uint64_t a, uint64_t b, uint64_t c, unsigned num_bits)
{
   assert(uint_is_in_range(a, num_bits));
   assert(uint_is_in_range(b, num_bits));
   assert(uint_is_in_range(c, num_bits));

   if (num_bits == 64) {
      uint32_t a32[2] = { (uint32_t)a, (uint32_t)(a >> 32) };
      uint32_t b32[2] = { (uint32_t)b, (uint32_t)(b >> 32) };
      uint32_t c32[2] = { (uint32_t)c, (uint32_t)(c >> 32) };

      uint32_t ab32[4];
      ubm_mul_u32arr(ab32, a32, b32);

      uint32_t abc32[4];
      ubm_add_u32arr(abc32, ab32, c32);

      return abc32[2] | ((uint64_t)abc32[3] << 32);
   } else {
      assert(num_bits <= 32);
      return utrunc(((a * b) + c) >> num_bits, num_bits);
   }
}

static inline int64_t
smul_high(int64_t a, int64_t b, unsigned num_bits)
{
   assert(sint_is_in_range(a, num_bits));
   assert(sint_is_in_range(b, num_bits));

   if (num_bits == 64) {
      uint32_t a32[4] = {
         (uint32_t)a,
         (uint32_t)(a >> 32),
         (uint32_t)(a >> 63), /* sign extend */
         (uint32_t)(a >> 63), /* sign extend */
      };
      uint32_t b32[4] = {
         (uint32_t)b,
         (uint32_t)(b >> 32),
         (uint32_t)(b >> 63), /* sign extend */
         (uint32_t)(b >> 63), /* sign extend */
      };

      uint32_t ab32[4];
      ubm_mul_u32arr(ab32, a32, b32);

      return ab32[2] | ((uint64_t)ab32[3] << 32);
   } else {
      assert(num_bits <= 32);
      return strunc((a * b) >> num_bits, num_bits);
   }
}

static inline uint64_t
fast_udiv_add_sat(uint64_t n, struct util_fast_udiv_info m, unsigned num_bits)
{
   assert(uint_is_in_range(n, num_bits));
   assert(uint_is_in_range(m.multiplier, num_bits));

   n = n >> m.pre_shift;
   n = uadd_sat(n, m.increment, num_bits);
   n = umul_add_high(n, m.multiplier, 0, num_bits);
   n = n >> m.post_shift;

   return n;
}

static inline uint64_t
fast_udiv_mul_add(uint64_t n, struct util_fast_udiv_info m, unsigned num_bits)
{
   assert(uint_is_in_range(n, num_bits));
   assert(uint_is_in_range(m.multiplier, num_bits));

   n = n >> m.pre_shift;
   n = umul_add_high(n, m.multiplier,
                     m.increment ? m.multiplier : 0,
                     num_bits);
   n = n >> m.post_shift;

   return n;
}

static inline uint64_t
fast_sdiv(int64_t n, int64_t d, struct util_fast_sdiv_info m, unsigned num_bits)
{
   assert(sint_is_in_range(n, num_bits));
   assert(sint_is_in_range(d, num_bits));
   assert(sint_is_in_range(m.multiplier, num_bits));

   int64_t res;
   res = smul_high(n, m.multiplier, num_bits);
   if (d > 0 && m.multiplier < 0)
      res = strunc(res + n, num_bits);
   if (d < 0 && m.multiplier > 0)
      res = strunc(res - n, num_bits);
   res = res >> m.shift;
   res = res - (res >> (num_bits - 1));

   return res;
}

static uint64_t
rand_uint(unsigned bits, unsigned min)
{
   assert(bits >= 4);

   /* Make sure we get some small and large numbers and powers of two every
    * once in a while
    */
   int k = rand() % 64;
   if (k == 17) {
      return min + (rand() % 16);
   } else if (k == 42) {
      return u_uintN_max(bits) - (rand() % 16);
   } else if (k == 9) {
      uint64_t r;
      do {
         r = 1ull << (rand() % bits);
      } while (r < min);
      return r;
   }

   if (min == 0) {
      assert(bits <= 64);
      uint64_t r = 0;
      for (unsigned i = 0; i < 8; i++)
         r |= ((uint64_t)rand() & 0xf) << i * 8;
      return r >> (63 - (rand() % bits));
   } else {
      uint64_t r;
      do {
         r = rand_uint(bits, 0);
      } while (r < min);
      return r;
   }
}

static int64_t
rand_sint(unsigned bits, unsigned min_abs)
{
   /* Make sure we hit MIN_INT every once in a while */
   if (rand() % 64 == 37)
      return u_intN_min(bits);

   int64_t s = rand_uint(bits - 1, min_abs);
   return rand() & 1 ? s : -s;
}

static uint64_t
udiv(uint64_t a, uint64_t b, unsigned bit_size)
{
   switch (bit_size) {
   case 64: return (uint64_t)a / (uint64_t)b;
   case 32: return (uint32_t)a / (uint32_t)b;
   case 16: return (uint16_t)a / (uint16_t)b;
   case 8:  return  (uint8_t)a / (uint8_t)b;
   default:
      assert(!"Invalid bit size");
      return 0;
   }
}

static int64_t
sdiv(int64_t a, int64_t b, unsigned bit_size)
{
   switch (bit_size) {
   case 64: return (int64_t)a / (int64_t)b;
   case 32: return (int32_t)a / (int32_t)b;
   case 16: return (int16_t)a / (int16_t)b;
   case 8:  return  (int8_t)a / (int8_t)b;
   default:
      assert(!"Invalid bit size");
      return 0;
   }
}

static void
random_udiv_add_sat_test(unsigned bits, bool bounded)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      uint64_t n = rand_uint(bits, 0);
      uint64_t d = rand_uint(bits, 2);
      assert(uint_is_in_range(n, bits));
      assert(uint_is_in_range(d, bits) && d >= 2);

      unsigned n_bits = bounded ? util_logbase2_64(MAX2(n, 1)) + 1 : bits;

      struct util_fast_udiv_info m =
         util_compute_fast_udiv_info(d, n_bits, bits);
      EXPECT_EQ(fast_udiv_add_sat(n, m, bits), udiv(n, d, bits));
   }
}

static void
random_udiv_mul_add_test(unsigned bits, bool bounded)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      uint64_t n = rand_uint(bits, 0);
      uint64_t d = rand_uint(bits, 1);
      assert(uint_is_in_range(n, bits));
      assert(uint_is_in_range(d, bits) && d >= 1);

      unsigned n_bits = bounded ? util_logbase2_64(MAX2(n, 1)) + 1: bits;

      struct util_fast_udiv_info m =
         util_compute_fast_udiv_info(d, n_bits, bits);
      EXPECT_EQ(fast_udiv_mul_add(n, m, bits), udiv(n, d, bits));
   }
}

static void
random_sdiv_test(unsigned bits)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      int64_t n = rand_sint(bits, 0);
      int64_t d;
      do {
         d = rand_sint(bits, 2);
      } while (d == INT64_MIN || util_is_power_of_two_or_zero64(llabs(d)));

      assert(sint_is_in_range(n, bits));
      assert(sint_is_in_range(d, bits) && llabs(d) >= 2);

      struct util_fast_sdiv_info m =
         util_compute_fast_sdiv_info(d, bits);
      EXPECT_EQ(fast_sdiv(n, d, m, bits), sdiv(n, d, bits));
   }
}

TEST(fast_idiv_by_const, uint8_add_sat)
{
   /* 8-bit is small enough we can brute-force the entire space */
   for (unsigned d = 2; d < 256; d++) {
      for (unsigned n_bits = 1; n_bits <= 8; n_bits++) {
         struct util_fast_udiv_info m =
            util_compute_fast_udiv_info(d, n_bits, 8);

         for (unsigned n = 0; n < (1u << n_bits); n++)
            EXPECT_EQ(fast_udiv_add_sat(n, m, 8), udiv(n, d, 8));
      }
   }
}

TEST(fast_idiv_by_const, uint8_mul_add)
{
   /* 8-bit is small enough we can brute-force the entire space */
   for (unsigned d = 2; d < 256; d++) {
      for (unsigned n_bits = 1; n_bits <= 8; n_bits++) {
         struct util_fast_udiv_info m =
            util_compute_fast_udiv_info(d, n_bits, 8);

         for (unsigned n = 0; n < (1u << n_bits); n++)
            EXPECT_EQ(fast_udiv_mul_add(n, m, 8), udiv(n, d, 8));
      }
   }
}

TEST(fast_idiv_by_const, int8)
{
   /* 8-bit is small enough we can brute-force the entire space */
   for (int n = -128; n < 128; n++) {
      for (int d = -128; d < 128; d++) {
         if (util_is_power_of_two_or_zero(abs(d)))
            continue;

         struct util_fast_sdiv_info m =
            util_compute_fast_sdiv_info(d, 8);
         EXPECT_EQ(fast_sdiv(n, d, m, 8), sdiv(n, d, 8));
      }
   }
}

TEST(fast_idiv_by_const, uint16_add_sat_bounded)
{
   random_udiv_add_sat_test(16, true);
}

TEST(fast_idiv_by_const, uint16_add_sat_full)
{
   random_udiv_add_sat_test(16, false);
}

TEST(fast_idiv_by_const, uint16_mul_add_bounded)
{
   random_udiv_mul_add_test(16, true);
}

TEST(fast_idiv_by_const, uint16_mul_add_full)
{
   random_udiv_mul_add_test(16, false);
}

TEST(fast_idiv_by_const, int16)
{
   random_sdiv_test(16);
}

TEST(fast_idiv_by_const, uint32_add_sat_bounded)
{
   random_udiv_add_sat_test(32, true);
}

TEST(fast_idiv_by_const, uint32_add_sat_full)
{
   random_udiv_add_sat_test(32, false);
}

TEST(fast_idiv_by_const, uint32_mul_add_bounded)
{
   random_udiv_mul_add_test(32, true);
}

TEST(fast_idiv_by_const, uint32_mul_add_full)
{
   random_udiv_mul_add_test(32, false);
}

TEST(fast_idiv_by_const, int32)
{
   random_sdiv_test(32);
}

TEST(fast_idiv_by_const, util_fast_udiv32)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      uint32_t n = rand_uint(32, 0);
      uint32_t d = rand_uint(32, 1);

      struct util_fast_udiv_info m =
         util_compute_fast_udiv_info(d, 32, 32);
      EXPECT_EQ(util_fast_udiv32(n, m), n / d);
   }
}

TEST(fast_idiv_by_const, util_fast_udiv32_nuw)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      uint32_t n = rand_uint(32, 0);
      if (n == UINT32_MAX)
         continue;
      uint32_t d = rand_uint(32, 1);

      struct util_fast_udiv_info m =
         util_compute_fast_udiv_info(d, 32, 32);
      EXPECT_EQ(util_fast_udiv32_nuw(n, m), n / d);
   }
}

TEST(fast_idiv_by_const, util_fast_udiv32_u31_d_not_one)
{
   for (unsigned i = 0; i < RAND_TEST_ITERATIONS; i++) {
      uint32_t n = rand_uint(31, 0);
      uint32_t d = rand_uint(31, 2);

      struct util_fast_udiv_info m =
         util_compute_fast_udiv_info(d, 31, 32);
      EXPECT_EQ(util_fast_udiv32_u31_d_not_one(n, m), n / d);
   }
}

TEST(fast_idiv_by_const, uint64_add_sat_bounded)
{
   random_udiv_add_sat_test(64, true);
}

TEST(fast_idiv_by_const, uint64_add_sat_full)
{
   random_udiv_add_sat_test(64, false);
}

TEST(fast_idiv_by_const, uint64_mul_add_bounded)
{
   random_udiv_mul_add_test(64, true);
}

TEST(fast_idiv_by_const, uint64_mul_add_full)
{
   random_udiv_mul_add_test(64, false);
}

TEST(fast_idiv_by_const, int64)
{
   random_sdiv_test(64);
}