Tree Text Locality of Reference Timing Test

# Hash-Based Erase Memory-Use Test

## Description

This test inserts a number of uniform i.i.d. integer keys into a container, then erases all keys except one. It measures the final size of the container.

(The test was executed with `hash_random_int_erase_mem_usage.cc` 2000 2000 2100)

## Purpose

The test checks how containers adjust internally as their logical size decreases (see Motivation::Associative Containers::Slightly Different Methods::Methods Related to Erase).

## Results

Figures NHG, NHM and NHL show the results for the native and collision-chaining types in g++, msvc++ and local, respectively.

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NHG: Native, collision-chaing, and probing, hash random int erase test - g++

In the above figure, the names in the legends have the following meaning:

1. n_hash_set_ncah- `std::tr1::unordered_set` with `cache_hash_code` = `false`
2. gp_hash_mask_linp_exp_nea_lc_1div8_1div2_nsth_set- `gp_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2, and `Probe_Fn` = `linear_probe_fn`
3. cc_hash_mod_prime_nea_lc_1div8_1div1_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mod_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_prime_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/1
4. cc_hash_mask_exp_nea_lc_1div8_1div2_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2

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NHM: Native, collision-chaing, and probing, hash random int erase test - msvc++

In the above figure, the names in the legends have the following meaning:

1. n_hash_set_ncah- `stdext::hash_set`
2. gp_hash_mask_linp_exp_nea_lc_1div8_1div2_nsth_set- `gp_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2, and `Probe_Fn` = `linear_probe_fn`
3. cc_hash_mod_prime_nea_lc_1div8_1div1_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mod_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_prime_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/1
4. cc_hash_mask_exp_nea_lc_1div8_1div2_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2

######

NHM: Native, collision-chaing, and probing, hash random int erase test - msvc++

In the above figure, the names in the legends have the following meaning:

1. n_hash_set_ncah- `stdext::hash_set`
2. gp_hash_mask_linp_exp_nea_lc_1div8_1div2_nsth_set- `gp_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2, and `Probe_Fn` = `linear_probe_fn`
3. cc_hash_mod_prime_nea_lc_1div8_1div1_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mod_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_prime_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/1
4. cc_hash_mask_exp_nea_lc_1div8_1div2_nsth_set- `cc_hash_table` with `Comb_Hash_Fn` = `direct_mask_range_hashing` , and `Resize_Policy` = `hash_standard_resize_policy` with `Size_Policy` = `hash_exponential_size_policy` , and `Trigger_Policy` = `hash_load_check_resize_trigger` with αmin = 1/8 and αmax = 1/2

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NHL: Native, collision-chaing, and probing, hash random int erase test - local

## Observations

STL hash-based containers act very differently than trees in this respect. When erasing numerous keys from an STL associative-container, the resulting memory user varies greatly depending on whether the container is tree-based or hash-based. As noted in Motivation::Choice of Methods , this is a fundamental consequence of the STL's associative containers' interface, it is not due to a specific implementation.

(See Priority Queue Text `pop` Memory Use Test for a similar phenomenon regarding priority queues.)