106 lines
4.1 KiB
C++
106 lines
4.1 KiB
C++
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/*============================================================================
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This source file is an extension to the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2b, written for Bochs (x86 achitecture simulator)
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floating point emulation.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
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been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
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RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
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AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
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COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
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EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
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INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
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OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) the source code for the derivative work includes prominent notice that
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the work is derivative, and (2) the source code includes prominent notice with
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these four paragraphs for those parts of this code that are retained.
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=============================================================================*/
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/*============================================================================
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* Written for Bochs (x86 achitecture simulator) by
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* Stanislav Shwartsman (gate at fidonet.org.il)
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* ==========================================================================*/
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#define FLOAT128
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#include <assert.h>
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#include "softfloat.h"
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// 2 3 4 n
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// f(x) ~ C + (C * x) + (C * x) + (C * x) + (C * x) + ... + (C * x)
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// 0 1 2 3 4 n
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//
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// -- 2k -- 2k+1
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// p(x) = > C * x q(x) = > C * x
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// -- 2k -- 2k+1
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//
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// f(x) ~ [ p(x) + x * q(x) ]
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//
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float128 EvalPoly(float128 x, float128 *arr, unsigned n, float_status_t &status)
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{
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float128 x2 = float128_mul(x, x, status);
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unsigned i;
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assert(n > 1);
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float128 r1 = arr[--n];
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i = n;
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while(i >= 2) {
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r1 = float128_mul(r1, x2, status);
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i -= 2;
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r1 = float128_add(r1, arr[i], status);
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}
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if (i) r1 = float128_mul(r1, x, status);
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float128 r2 = arr[--n];
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i = n;
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while(i >= 2) {
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r2 = float128_mul(r2, x2, status);
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i -= 2;
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r2 = float128_add(r2, arr[i], status);
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}
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if (i) r2 = float128_mul(r2, x, status);
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return float128_add(r1, r2, status);
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}
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// 2 4 6 8 2n
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// f(x) ~ C + (C * x) + (C * x) + (C * x) + (C * x) + ... + (C * x)
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// 0 1 2 3 4 n
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//
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// -- 4k -- 4k+2
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// p(x) = > C * x q(x) = > C * x
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// -- 2k -- 2k+1
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//
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// 2
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// f(x) ~ [ p(x) + x * q(x) ]
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//
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float128 EvenPoly(float128 x, float128 *arr, unsigned n, float_status_t &status)
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{
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return EvalPoly(float128_mul(x, x, status), arr, n, status);
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}
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// 3 5 7 9 2n+1
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// f(x) ~ (C * x) + (C * x) + (C * x) + (C * x) + (C * x) + ... + (C * x)
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// 0 1 2 3 4 n
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// 2 4 6 8 2n
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// = x * [ C + (C * x) + (C * x) + (C * x) + (C * x) + ... + (C * x)
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// 0 1 2 3 4 n
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//
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// -- 4k -- 4k+2
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// p(x) = > C * x q(x) = > C * x
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// -- 2k -- 2k+1
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//
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// 2
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// f(x) ~ x * [ p(x) + x * q(x) ]
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//
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float128 OddPoly(float128 x, float128 *arr, unsigned n, float_status_t &status)
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{
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return float128_mul(x, EvenPoly(x, arr, n, status), status);
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}
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