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1434 lines
42 KiB
Plaintext
1434 lines
42 KiB
Plaintext
/*
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* test9500.trigeq - test of trigonometric identities for test 95dd
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*
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* We test over a wide variety of real (NUMBER) and complex (COMPLEX)
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* values, that various trigonometric identities hold for all calc
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* builtin trigonometric functions.
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*
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* We assume that the value produced by sin() (trigonometric sine)
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* and cos() (trigonometric cosine) are correct. We can reasonably
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* assume this because of the calc regression test suite:
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*
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* (such as test 34dd and in particular cal/test3400.trig.cal and
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* such as test 89dd and in particular cal/test8900.special.cal)
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*
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* will test such those function beforehand.
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*
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* We use various trigonometric identity to verify the non-inverse
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* trigonometric functions other than sin() and cos().
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*
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* we verify that it is true within the error tolerance of the eps
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* (epsilon) argument.
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*
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* Copyright (C) 2023 Landon Curt Noll
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*
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* Primary author: Landon Curt Noll
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*
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* Calc is open software; you can redistribute it and/or modify it under
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* the terms of the version 2.1 of the GNU Lesser General Public License
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* as published by the Free Software Foundation.
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*
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* Calc is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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* Public License for more details.
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*
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* A copy of version 2.1 of the GNU Lesser General Public License is
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* distributed with calc under the filename COPYING-LGPL. You should have
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* received a copy with calc; if not, write to Free Software Foundation, Inc.
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*
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* Under source code control: 2023/09/10 14:33:06
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* File existed as early as: 2023
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*
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* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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*/
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/*
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* base_tval - base set of test values
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*
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* Our 16 base test values must be > 0 and <= 1.
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* We use these fractions because, when multiplied
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* by pi() will give values that are commonly used.
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*
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* NOTE: There is no reason to sort these values other than ascetics. :-)
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*/
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static base_tval = list(
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1/12, /* ~ 0.08333333333333333333 */
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1/8, /* 0.12500000000000000000 */
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1/6, /* ~ 0.16666666666666666667 */
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1/5, /* 0.20000000000000000000 */
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1/4, /* 0.25000000000000000000 */
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1/3, /* ~ 0.33333333333333333333 */
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3/8, /* 0.37500000000000000000 */
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5/12, /* ~ 0.41666666666666666667 */
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1/2, /* 0.50000000000000000000 */
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2/3, /* ~ 0.66666666666666666667 */
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3/4, /* 0.75000000000000000000 */
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4/5, /* 0.80000000000000000000 */
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5/6, /* ~ 0.83333333333333333333 */
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7/8, /* 0.87500000000000000000 */
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11/12, /* ~ 0.91666666666666666667 */
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1 /* 1.00000000000000000000 */
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);
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/*
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* tval - full test list
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*
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* This long list is formed via the form_tval() function from the base_tval list.
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*
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* When the form_tval() function forms the full test test values
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* we will have 1025 values of various real and complex
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* values that also include random values added or subtracted.
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*
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* See the form_tval() function for details.
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*/
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tval = list();
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/*
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* Lists that hold precomputed trigonometric functions on the tval full test list
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*
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* The precompute_trig() function will fill out these lists.
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* They will be the same size as size as the full test list.
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*/
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sin_tval = list(); /* trigonometric sine of each test test value */
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cos_tval = list(); /* trigonometric cosine of each test test value */
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/*
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* seed_rand - seed the subtractive 100 shuffle pseudo-random number generator
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*
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* We want to seed the subtractive 100 shuffle pseudo-random number generator
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* with a constant so that the result of this test set will be deterministic.
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*
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* We seed the subtractive 100 shuffle pseudo-random number generator with
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* a 128-bit seed value. The 128-bit seed value was produced when a
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* Blum-Blum-Shub pseudo-random number generator was seeded with the
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* following 160-bit SHA1 hash of 3 calls to seed():
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*
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* sha1(sha1(seed(), seed()<<64, seed()<<128)) == 0x732fda50b1bf6e34b604b7c75b993e5c37a4ad97
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*
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* This produced the following 160-bit value that was used to seed
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* the Blum-Blum-Shub pseudo-random number:
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*
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* srandom(0x732fda50b1bf6e34b604b7c75b993e5c37a4ad97)
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*
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* The seeded Blum-Blum-Shub pseudo-random number generator was then
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* used to generate a 128-bit value:
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*
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* randombit(128) == 0x37301cf47204f7fababc2f32e39ab338
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*
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* We seed the subtractive 100 shuffle pseudo-random number generator
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* with the above mentioned 128-bit value:
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*
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* srand(0x37301cf47204f7fababc2f32e39ab338)
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*/
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define seed_rand()
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{
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return srand(0x37301cf47204f7fababc2f32e39ab338);
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}
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/*
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* epsilon_bits - number of bits in epsilon()
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*/
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static epsilon_bits = highbit(1/epsilon()) + 1;
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/*
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* epsilon_norm - norm of a epsilon()
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*/
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static epsilon_norm = norm(epsilon());
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/*
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* random_rational_value - compute a random rational value > 0 and < 1
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*
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* We compute a pseudo-random value in the range (0,1) with a prevision of epsilon().
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*
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* We compute two distinct non-zero pseudo-random integers (i.e., > 0), a and b,
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* that are epsilon_bits (see above) long and produced by the seeded
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* subtractive 100 shuffle pseudo-random number generator (see seed_rand()).
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*
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* Return the smaller of a,b divided by the larger of a,b.
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*/
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define random_rational_value()
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{
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local a; /* epsilon_bits pseudo-random integer > 0 */
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local b; /* epsilon_bits pseudo-random integer > 0 */
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/*
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* compute 1st non-zero pseudo-random epsilon_bits integer
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*/
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do {
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a = randbit(epsilon_bits);
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} while (a == 0);
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/*
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* compute 2nd non-zero pseudo-random epsilon_bits integer also != a
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*/
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do {
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b = randbit(epsilon_bits);
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} while (b == 0 || a == b);
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/*
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* return the min(a,b) / max(a,b): a value > 0 and < 1
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*/
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return min(a,b) / max(a,b);
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}
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/*
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* form_tval - form a full list of test values
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*
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* Given an initial list of 16 values, we form 1025 test values.
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*
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* From the test set starts with 16 values from the base_tval[] list:
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*
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* tval = base_tval;
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*
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* We form a list of 32 values by appending all of the above with:
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*
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* tval[i] + 1
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*
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* We form a list of 64 values by appending all of the above with:
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*
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* -tval[i]
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*
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* We form a list of 128 values by appending all of the above with:
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*
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* For values >= 0: tval[i] + random_rational_value
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* For values < 0: tval[i] - random_rational_value
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*
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* We form a list of 256 values by appending all of the above with:
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*
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* tval[i] * pi()
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*
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* We form a list of 512 values by appending all of the above with:
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*
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* tval[i] * 1i
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*
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* We for a list of 1024 values by appending new complex values where the
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* real part is a randomly selected real value (from the first 256 list values), and the
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* imaginary part is a randomly selected complex value (from the last 256 list values).
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*
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* Finally we append 0 to the list to form the full 1025 value list.
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*/
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define form_tval()
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{
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local tval_len; /* current length of the tval[] array */
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local real_cnt; /* number of real values in tval[] array */
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local imag_cnt; /* number of imaginary values in tval[] array */
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local i;
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/*
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* seed the subtractive 100 shuffle pseudo-random number generator
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*/
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seed_rand();
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/*
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* load base_tval[] array into tval[] array
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*/
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tval = base_tval;
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/*
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* expand all tval with tval+1
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*/
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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append(tval, tval[i] + 1);
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}
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/*
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* expand all tval with -tval
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*/
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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append(tval, -tval[i]);
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}
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/*
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* expand all tval with tval +/- random_rational_value
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*
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* For values we add random_rational_value if > 0
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* or we subtract crandom_rational_value if < 0.
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*/
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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/* use the sign to determine if we add or subtract */
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if (tval[i] >= 0) {
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append(tval, tval[i] + random_rational_value());
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} else {
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append(tval, tval[i] - random_rational_value());
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}
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}
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/*
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* expand all tval with tval * pi()
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*/
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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append(tval, tval[i] * pi());
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}
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/*
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* expand all tval with tval * 1i
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*/
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tval_len = size(tval);
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/* tval[0] thru tval[real_cnt-1] are real values */
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real_cnt = tval_len;
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for (i=0; i < tval_len; ++i) {
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append(tval, tval[i] * 1i);
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}
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/*
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* expand tval with randomly selected real value
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* plus randomly selected complex value.
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*/
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tval_len = size(tval);
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/* tval[real_cnt] thru tval[real_cnt+imag_cnt-1] are complex values */
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imag_cnt = tval_len - real_cnt;
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for (i=0; i < tval_len; ++i) {
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append(tval, tval[rand(0,real_cnt)] + tval[real_cnt + rand(0,imag_cnt)]);
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}
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/*
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* last, append our final 0 value
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*/
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append(tval, 0);
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}
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/*
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* compute - form precomputed trigonometric value lists
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*/
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define precompute_trig()
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{
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local tval_len; /* current length of the tval[] array */
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local i;
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/*
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* firewall - be sure tval list is setup
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*/
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if (size(tval) <= 0) {
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form_tval();
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}
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tval_len = size(tval);
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if (tval_len <= 0) {
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quit "FATAL: tval_len is empty";
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}
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/*
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* compute trigonometric sine of the tval full test list
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*/
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for (i=0; i < tval_len; ++i) {
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append(sin_tval, sin(tval[i]));
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}
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if (size(tval) != size(sin_tval)) {
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print "****: size(tval):", size(tval), "!= size(sin_tval)", size(sin_tval);
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quit "FATAL: sin_tval not same size as tval_len";
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}
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/*
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* compute trigonometric cosine of the tval full test list
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*/
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for (i=0; i < tval_len; ++i) {
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append(cos_tval, cos(tval[i]));
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}
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if (size(tval) != size(cos_tval)) {
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print "****: size(tval):", size(tval), "!= size(cos_tval)", size(cos_tval);
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quit "FATAL: cos_tval not same size as tval_len";
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}
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}
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/*
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* compare - compare the trigonometric identity and the trigonometric function value
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*
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* given:
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* ident_val computed trig value trigonometric identity
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* trig_val computed value from the trigonometric function
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* name trig function name
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* index test index value
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* testnum regression test number being performed
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*
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* returns:
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* 0 ==> trigonometric identity and the trigonometric function value match
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* 1 ==> trigonometric identity and the trigonometric function value do NOT match
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*/
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define compare(ident_val, trig_val, name, index, testnum)
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{
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local abs_diff; /* absolute difference between ident_val and trig_val */
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/*
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* firewall
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*/
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if (!isnum(trig_val)) {
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printf("**** trig test %d-%d failed: %s(tval[%d]): ",
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testnum, index, name, index);
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printf("%d returned a non-numeric value\n", trig_val);
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return 1;
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}
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/*
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* compute absolute difference
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*/
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abs_diff = abs(ident_val - trig_val);
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/*
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* determine if ident_val within epsilon of trig_val
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*/
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if (near(norm(abs_diff), epsilon_norm) > 0) {
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printf("**** trig test %d-%d failed: %s(tval[%d]): ",
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testnum, index, name, index);
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printf("%d is not near trig identity value: %d\n",
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trig_val, ident_val);
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return 1;
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}
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return 0;
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}
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/*
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* not_near_zero - determine if a value is within epsilon() of 0
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*
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* given:
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* value real or complex value
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*
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* returns:
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* 1 ==> value is farther from 0 than epsilon (not near zero)
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* 0 ==> value is within epsilon of 0 (near zero)
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*/
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define not_near_zero(value)
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{
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if (near(norm(value), epsilon_norm) > 0) {
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/* value is farther from 0 than epsilon */
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return 1;
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}
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/* value is within epsilon of 0 */
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return 0;
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}
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/*
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* verify_tan - verify trigonometric tangent
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*
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* We use the following trigonometric identity:
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*
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* tan(x) = sin(x) / cos(x)
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*
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* given:
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* testnum regression test number being performed
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*
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* returns:
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* number of tests that failed
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*/
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define verify_tan(testnum)
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{
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local tval_len; /* current length of the tval[] array */
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local ident_val; /* computed trig value trigonometric identity */
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local trig_val; /* computed value from the trigonometric function */
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local error_count; /* number of compare errors detected */
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local i;
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/*
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* firewall
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*/
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if (size(sin_tval) <= 0 || size(cos_tval) <= 0) {
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precompute_trig();
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}
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/*
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* for each test value, verify the trigonometric identity within epsilon
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*/
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error_count = 0;
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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/* skip test when cos(x) within epsilon of 0 */
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if (not_near_zero(cos_tval[i])) {
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/* compute trigonometric identity */
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ident_val = sin_tval[i] / cos_tval[i];
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/* compute trigonometric function */
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trig_val = tan(tval[i]);
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/* compare trigonometric identity with trigonometric function value */
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if (compare(ident_val, trig_val, "tan", i, testnum)) {
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++error_count;
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}
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}
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}
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/*
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* report test results
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*/
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if (error_count != 0) {
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print '**** test', testnum : ': tan test failure count:', error_count;
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}
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return error_count;
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}
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|
|
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/*
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* verify_cot - verify trigonometric cotangent
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*
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* We use the following trigonometric identity:
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*
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* cot(x) = cos(x) / sin(x)
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*
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|
* given:
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* testnum regression test number being performed
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*
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* returns:
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* number of tests that failed
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*/
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define verify_cot(testnum)
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{
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local tval_len; /* current length of the tval[] array */
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local ident_val; /* computed trig value trigonometric identity */
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local trig_val; /* computed value from the trigonometric function */
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local error_count; /* number of compare errors detected */
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local i;
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/*
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* firewall
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*/
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if (size(sin_tval) <= 0 || size(cos_tval) <= 0) {
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precompute_trig();
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}
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/*
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* for each test value, verify the trigonometric identity within epsilon
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*/
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tval_len = size(tval);
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for (i=0; i < tval_len; ++i) {
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/* skip test when sin(x) within epsilon of 0 */
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if (not_near_zero(sin_tval[i])) {
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/* compute trigonometric identity */
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ident_val = cos_tval[i] / sin_tval[i];
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/* compute trigonometric function */
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trig_val = cot(tval[i]);
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/* compare trigonometric identity with trigonometric function value */
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if (compare(ident_val, trig_val, "cot", i, testnum)) {
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++error_count;
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}
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}
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}
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/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': cot test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_sec - verify trigonometric secant
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* sec(x) = 1 / cos(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_sec(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 / cos_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = sec(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "sec", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': sec test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_csc - verify trigonometric cosecant
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* csc(x) = 1 / sin(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_csc(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when sin(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 / sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = csc(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "csc", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': csc test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_versin - verify versed trigonometric sine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* versin(x) = 1 - cos(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_versin(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 - cos_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = versin(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "versin", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': versin test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_coversin - verify coversed trigonometric sine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* coversin(x) = 1 - sin(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_coversin(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when sin(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 - sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = coversin(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "coversin", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': coversin test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_vercos - verify versed trigonometric cosine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* vercos(x) = 1 + cos(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_vercos(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 + cos_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = vercos(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "vercos", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': vercos test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_covercos - verify coversed trigonometric cosine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* covercos(x) = 1 + sin(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_covercos(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when sin(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 1 + sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = covercos(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "covercos", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': covercos test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_haversin - verify half versed trigonometric sine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* haversin(x) = versin(x) / 2 = (1 - cos(x)) / 2
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_haversin(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 - cos_tval[i]) / 2;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = haversin(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "haversin", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': haversin test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_hacoversin - verify half versed trigonometric cosine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* hacoversin(x) = coversin(x) / 2 = (1 - sin(x)) / 2
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_hacoversin(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 - sin_tval[i]) / 2;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = hacoversin(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "hacoversin", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': hacoversin test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_havercos - verify half versed trigonometric cosine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* havercos(x) = vercos(x) / 2 = (1 + cos(x)) / 2
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_havercos(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 + cos_tval[i]) / 2;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = havercos(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "havercos", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': havercos test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_hacovercos - verify half coversed trigonometric cosine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* hacovercos(x) = covercos(x) / 2 = (1 + sin(x)) / 2
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_hacovercos(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when sin(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 + sin_tval[i]) / 2;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = hacovercos(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "hacovercos", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': hacovercos test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_exsec - exterior trigonometric secant
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* exsec(x) = sec(x) - 1 = (1 / cos(x)) - 1
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_exsec(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when cos(x) within epsilon of 0 */
|
|
if (not_near_zero(cos_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 / cos_tval[i]) - 1;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = exsec(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "exsec", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': exsec test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_excsc - verify trigonometric cosecant
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* excsc(x) = csc(x) - 1 = (1 / sin(x)) - 1
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_excsc(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* skip test when sin(x) within epsilon of 0 */
|
|
if (not_near_zero(sin_tval[i])) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = (1 / sin_tval[i]) - 1;
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = excsc(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "excsc", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': excsc test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_crd - verify trigonometric chord of a unit circle
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* crd(x) = 2 * sin(x / 2)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_crd(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* NOTE: We actually check the identity: crd(x*2) = 2 * sin(x) */
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = 2 * sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = crd(tval[i] * 2);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "crd", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': crd test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_cas - verify cosine plus sine
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* cas(x) = cos(x) + sin(x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_cas(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = cos_tval[i] + sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = cas(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "cas", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': cas test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|
|
|
|
|
|
/*
|
|
* verify_cis - verify Euler's formula
|
|
*
|
|
* We use the following trigonometric identity:
|
|
*
|
|
* cis(x) = cos(x) + i*sin(x)
|
|
* cis(x) = exp(1i * x)
|
|
*
|
|
* given:
|
|
* testnum regression test number being performed
|
|
*
|
|
* returns:
|
|
* number of tests that failed
|
|
*/
|
|
define verify_cis(testnum)
|
|
{
|
|
local tval_len; /* current length of the tval[] array */
|
|
local ident_val; /* computed trig value trigonometric identity */
|
|
local trig_val; /* computed value from the trigonometric function */
|
|
local error_count; /* number of compare errors detected */
|
|
local i;
|
|
|
|
/*
|
|
* firewall
|
|
*/
|
|
if (size(sin_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
if (size(cos_tval) <= 0) {
|
|
precompute_trig();
|
|
}
|
|
|
|
/*
|
|
* for each test value, verify the trigonometric identity within epsilon
|
|
*/
|
|
tval_len = size(tval);
|
|
for (i=0; i < tval_len; ++i) {
|
|
|
|
/* compute trigonometric identity */
|
|
ident_val = cos_tval[i] + 1i*sin_tval[i];
|
|
|
|
/* compute trigonometric function */
|
|
trig_val = cis(tval[i]);
|
|
|
|
/* compare trigonometric identity with trigonometric function value */
|
|
if (compare(ident_val, trig_val, "cis", i, testnum)) {
|
|
++error_count;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* report test results
|
|
*/
|
|
if (error_count != 0) {
|
|
print '**** test', testnum : ': cis test failure count:', error_count;
|
|
}
|
|
return error_count;
|
|
}
|