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Copyright 2013, 2014, 2018, 2019 Anton Krotov |
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This program is free software: you can redistribute it and/or modify |
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it under the terms of the GNU Lesser General Public License as published by |
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the Free Software Foundation, either version 3 of the License, or |
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(at your option) any later version. |
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This program is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU Lesser General Public License for more details. |
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You should have received a copy of the GNU Lesser General Public License |
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along with this program. If not, see . |
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*) |
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MODULE Math; |
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IMPORT SYSTEM; |
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CONST |
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pi* = 3.141592653589793; |
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e* = 2.718281828459045; |
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PROCEDURE IsNan* (x: REAL): BOOLEAN; |
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VAR |
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h, l: SET; |
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BEGIN |
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SYSTEM.GET(SYSTEM.ADR(x), l); |
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SYSTEM.GET(SYSTEM.ADR(x) + 4, h) |
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RETURN (h * {20..30} = {20..30}) & ((h * {0..19} # {}) OR (l * {0..31} # {})) |
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END IsNan; |
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PROCEDURE IsInf* (x: REAL): BOOLEAN; |
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RETURN ABS(x) = SYSTEM.INF() |
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END IsInf; |
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PROCEDURE Max (a, b: REAL): REAL; |
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VAR |
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res: REAL; |
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BEGIN |
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IF a > b THEN |
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res := a |
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ELSE |
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res := b |
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END |
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RETURN res |
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END Max; |
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PROCEDURE Min (a, b: REAL): REAL; |
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VAR |
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res: REAL; |
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BEGIN |
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IF a < b THEN |
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res := a |
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ELSE |
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res := b |
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END |
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RETURN res |
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END Min; |
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PROCEDURE SameValue (a, b: REAL): BOOLEAN; |
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VAR |
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eps: REAL; |
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res: BOOLEAN; |
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BEGIN |
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eps := Max(Min(ABS(a), ABS(b)) * 1.0E-12, 1.0E-12); |
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IF a > b THEN |
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res := (a - b) <= eps |
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ELSE |
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res := (b - a) <= eps |
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END |
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RETURN res |
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END SameValue; |
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PROCEDURE IsZero (x: REAL): BOOLEAN; |
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RETURN ABS(x) <= 1.0E-12 |
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END IsZero; |
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PROCEDURE [stdcall] sqrt* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0FAH, (* fsqrt *) |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END sqrt; |
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PROCEDURE [stdcall] sin* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0FEH, (* fsin *) |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END sin; |
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PROCEDURE [stdcall] cos* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0FFH, (* fcos *) |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END cos; |
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PROCEDURE [stdcall] tan* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0FBH, (* fsincos *) |
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0DEH, 0F9H, (* fdivp st1, st *) |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END tan; |
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PROCEDURE [stdcall] arctan2* (y, x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0DDH, 045H, 010H, (* fld qword [ebp + 10h] *) |
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0D9H, 0F3H, (* fpatan *) |
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0C9H, (* leave *) |
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0C2H, 010H, 000H (* ret 10h *) |
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) |
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RETURN 0.0 |
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END arctan2; |
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PROCEDURE [stdcall] ln* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0D9H, 0EDH, (* fldln2 *) |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0F1H, (* fyl2x *) |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END ln; |
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PROCEDURE [stdcall] log* (base, x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0D9H, 0E8H, (* fld1 *) |
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0DDH, 045H, 010H, (* fld qword [ebp + 10h] *) |
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0D9H, 0F1H, (* fyl2x *) |
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0D9H, 0E8H, (* fld1 *) |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0F1H, (* fyl2x *) |
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0DEH, 0F9H, (* fdivp st1, st *) |
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0C9H, (* leave *) |
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0C2H, 010H, 000H (* ret 10h *) |
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) |
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RETURN 0.0 |
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END log; |
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PROCEDURE [stdcall] exp* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0EAH, (* fldl2e *) |
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0DEH, 0C9H, 0D9H, 0C0H, |
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0D9H, 0FCH, 0DCH, 0E9H, |
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0D9H, 0C9H, 0D9H, 0F0H, |
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0D9H, 0E8H, 0DEH, 0C1H, |
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0D9H, 0FDH, 0DDH, 0D9H, |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END exp; |
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PROCEDURE [stdcall] round* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 07DH, 0F4H, 0D9H, |
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07DH, 0F6H, 066H, 081H, |
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04DH, 0F6H, 000H, 003H, |
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0D9H, 06DH, 0F6H, 0D9H, |
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0FCH, 0D9H, 06DH, 0F4H, |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END round; |
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PROCEDURE [stdcall] frac* (x: REAL): REAL; |
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BEGIN |
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SYSTEM.CODE( |
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050H, |
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0DDH, 045H, 008H, (* fld qword [ebp + 08h] *) |
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0D9H, 0C0H, 0D9H, 03CH, |
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024H, 0D9H, 07CH, 024H, |
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002H, 066H, 081H, 04CH, |
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024H, 002H, 000H, 00FH, |
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0D9H, 06CH, 024H, 002H, |
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0D9H, 0FCH, 0D9H, 02CH, |
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024H, 0DEH, 0E9H, |
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0C9H, (* leave *) |
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0C2H, 008H, 000H (* ret 08h *) |
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) |
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RETURN 0.0 |
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END frac; |
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PROCEDURE arcsin* (x: REAL): REAL; |
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RETURN arctan2(x, sqrt(1.0 - x * x)) |
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END arcsin; |
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PROCEDURE arccos* (x: REAL): REAL; |
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RETURN arctan2(sqrt(1.0 - x * x), x) |
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END arccos; |
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PROCEDURE arctan* (x: REAL): REAL; |
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RETURN arctan2(x, 1.0) |
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END arctan; |
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PROCEDURE sinh* (x: REAL): REAL; |
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BEGIN |
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x := exp(x) |
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RETURN (x - 1.0 / x) * 0.5 |
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END sinh; |
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PROCEDURE cosh* (x: REAL): REAL; |
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BEGIN |
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x := exp(x) |
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RETURN (x + 1.0 / x) * 0.5 |
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END cosh; |
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PROCEDURE tanh* (x: REAL): REAL; |
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BEGIN |
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IF x > 15.0 THEN |
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x := 1.0 |
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ELSIF x < -15.0 THEN |
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x := -1.0 |
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ELSE |
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x := exp(2.0 * x); |
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x := (x - 1.0) / (x + 1.0) |
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END |
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RETURN x |
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END tanh; |
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PROCEDURE arsinh* (x: REAL): REAL; |
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RETURN ln(x + sqrt(x * x + 1.0)) |
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END arsinh; |
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PROCEDURE arcosh* (x: REAL): REAL; |
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RETURN ln(x + sqrt(x * x - 1.0)) |
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END arcosh; |
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PROCEDURE artanh* (x: REAL): REAL; |
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VAR |
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res: REAL; |
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BEGIN |
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IF SameValue(x, 1.0) THEN |
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res := SYSTEM.INF() |
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ELSIF SameValue(x, -1.0) THEN |
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res := -SYSTEM.INF() |
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ELSE |
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res := 0.5 * ln((1.0 + x) / (1.0 - x)) |
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END |
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RETURN res |
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END artanh; |
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PROCEDURE floor* (x: REAL): REAL; |
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VAR |
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f: REAL; |
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BEGIN |
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f := frac(x); |
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x := x - f; |
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IF f < 0.0 THEN |
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x := x - 1.0 |
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END |
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RETURN x |
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END floor; |
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PROCEDURE ceil* (x: REAL): REAL; |
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VAR |
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f: REAL; |
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BEGIN |
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f := frac(x); |
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x := x - f; |
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IF f > 0.0 THEN |
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x := x + 1.0 |
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END |
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RETURN x |
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END ceil; |
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PROCEDURE power* (base, exponent: REAL): REAL; |
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VAR |
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res: REAL; |
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BEGIN |
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IF exponent = 0.0 THEN |
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res := 1.0 |
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ELSIF (base = 0.0) & (exponent > 0.0) THEN |
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res := 0.0 |
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ELSE |
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res := exp(exponent * ln(base)) |
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END |
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RETURN res |
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END power; |
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PROCEDURE sgn* (x: REAL): INTEGER; |
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VAR |
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res: INTEGER; |
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BEGIN |
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IF x > 0.0 THEN |
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res := 1 |
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ELSIF x < 0.0 THEN |
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res := -1 |
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ELSE |
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res := 0 |
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END |
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RETURN res |
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END sgn; |
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PROCEDURE fact* (n: INTEGER): REAL; |
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VAR |
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res: REAL; |
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BEGIN |
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res := 1.0; |
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WHILE n > 1 DO |
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res := res * FLT(n); |
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DEC(n) |
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END |
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RETURN res |
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END fact; |
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END Math. |