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dos_compilers/Artek Ada v125/MATH.ADA
davidly c8dcd3cb13 Artek Ada v1.25
2024-07-08 09:31:49 -07:00

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--
-- MATH.ADA
--
-- Mathematical routines for Artek Ada
--
-- Package body Copyright (C) 1986 Artek Corporation
-- Author: V. Thorsteinsson
--
-- The MATH package offers common exponential, logarithmic,
-- trigonometric and hyperbolic functions used in mathematical
-- calculation.
--
-- Most routines are implemented in assembly language for maximum
-- speed and accuracy. An 8087/287/387 coprocessor is used if
-- present and emulated in software if not.
--
-- The routines raise the exception ARGUMENT_ERROR if their
-- arguments are out of bounds.
--
-- The trigonometric functions can accept an optional CYCLE parameter
-- that allows you to work in degrees or grads if you prefer them to
-- radians. In this case, say for example:
--
-- A := SIN (90.0, CYCLE => 360.0);
--
-- to calculate the sine of a 90 degree angle.
--
generic
type REAL is digits <>;
package MATH is
PI : constant := 3.1415_92653_58979_32384_62643_38327_95029;
EXP_1 : constant := 2.7182_81828_45904_52353_60287_47135_26625;
function SQRT (X : REAL) return REAL;
function LOG (X : REAL; BASE : REAL := EXP_1) return REAL;
function EXP (X : REAL; BASE : REAL := EXP_1) return REAL;
function SIN (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL;
function COS (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL;
function TAN (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL;
function COT (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL;
function ARCSIN (X : REAL) return REAL;
function ARCCOS (X : REAL) return REAL;
function ARCTAN (X : REAL; Y : REAL := 1.0) return REAL;
function ARCCOT (X : REAL; Y : REAL := 1.0) return REAL;
function SINH (X : REAL) return REAL;
function COSH (X : REAL) return REAL;
function TANH (X : REAL) return REAL;
function COTH (X : REAL) return REAL;
function ARCSINH (X : REAL) return REAL;
function ARCCOSH (X : REAL) return REAL;
function ARCTANH (X : REAL) return REAL;
function ARCCOTH (X : REAL) return REAL;
ARGUMENT_ERROR : exception;
end MATH;
package body MATH is
function "rem" (LEFT, RIGHT : REAL) return REAL is
RESULT : REAL;
STATUS : INTEGER;
begin
pragma NATIVE (
16#CD#, 16#39#, 16#44#, 16#08#, 16#CD#, 16#39#, 16#04#, 16#CD#,
16#35#, 16#E4#, 16#33#, 16#C9#, 16#CD#, 16#39#, 16#7D#, 16#08#,
16#CD#, 16#3D#, 16#8B#, 16#45#, 16#08#, 16#9E#, 16#73#, 16#05#,
16#CD#, 16#35#, 16#E0#, 16#F7#, 16#D1#, 16#CD#, 16#35#, 16#F8#,
16#CD#, 16#39#, 16#7D#, 16#08#, 16#CD#, 16#3D#, 16#8B#, 16#45#,
16#08#, 16#9E#, 16#7A#, 16#F1#, 16#CD#, 16#39#, 16#D9#, 16#23#,
16#C9#, 16#74#, 16#03#, 16#CD#, 16#35#, 16#E0#, 16#CD#, 16#39#,
16#1D#, 16#CD#, 16#3D#);
return RESULT;
end "rem";
function MYTAN (X : REAL) return REAL is
RESULT : REAL;
PIOVER4 : REAL := PI / 4.0;
PIOVER2 : REAL := PI / 2.0;
STATUS_WORD : INTEGER;
ENVIRONMENT : array (1..8) of INTEGER;
begin
pragma NATIVE (
16#CD#, 16#35#, 16#EB#, 16#CD#, 16#39#, 16#04#, 16#CD#, 16#35#,
16#E4#, 16#33#, 16#DB#, 16#8B#, 16#CB#, 16#CD#, 16#39#, 16#7D#,
16#18#, 16#CD#, 16#3D#, 16#8B#, 16#45#, 16#18#, 16#9E#, 16#73#,
16#05#, 16#CD#, 16#35#, 16#E0#, 16#F7#, 16#D1#, 16#CD#, 16#35#,
16#F8#, 16#CD#, 16#39#, 16#7D#, 16#18#, 16#CD#, 16#3D#, 16#8B#,
16#45#, 16#18#, 16#9E#, 16#7A#, 16#F1#, 16#CD#, 16#39#, 16#D9#,
16#CD#, 16#39#, 16#45#, 16#10#, 16#CD#, 16#35#, 16#C9#, 16#CD#,
16#34#, 16#D1#, 16#CD#, 16#39#, 16#7D#, 16#18#, 16#CD#, 16#3D#,
16#8B#, 16#45#, 16#18#, 16#9E#, 16#76#, 16#07#, 16#CD#, 16#34#,
16#E1#, 16#F7#, 16#D3#, 16#F7#, 16#D1#, 16#CD#, 16#39#, 16#45#,
16#08#, 16#CD#, 16#34#, 16#D9#, 16#CD#, 16#39#, 16#7D#, 16#18#,
16#CD#, 16#3D#, 16#8B#, 16#45#, 16#18#, 16#9E#, 16#73#, 16#05#,
16#CD#, 16#34#, 16#E9#, 16#F7#, 16#D3#, 16#CD#, 16#39#, 16#D9#,
16#CD#, 16#35#, 16#F2#, 16#23#, 16#C9#, 16#74#, 16#03#, 16#CD#,
16#35#, 16#E0#, 16#23#, 16#DB#, 16#74#, 16#05#, 16#CD#, 16#3A#,
16#F1#, 16#EB#, 16#03#, 16#CD#, 16#3A#, 16#F9#, 16#CD#, 16#39#,
16#1D#, 16#CD#, 16#3D#);
return RESULT;
end MYTAN;
function MYCOT (X : REAL) return REAL is
-- Cotangent with no checking
begin
return 1.0 / MYTAN (X);
end MYCOT;
function SQRT (X : REAL) return REAL is
RESULT : REAL;
begin
if X < 0.0 then
raise ARGUMENT_ERROR;
end if;
pragma NATIVE (
16#CD#, 16#39#, 16#04#, 16#CD#, 16#35#, 16#FA#, 16#CD#, 16#39#,
16#1D#, 16#CD#, 16#3D#);
return RESULT;
end SQRT;
function LN (X : REAL) return REAL is
RESULT : REAL;
begin
pragma NATIVE (
16#CD#, 16#35#, 16#ED#, 16#CD#, 16#39#, 16#04#, 16#CD#, 16#35#,
16#F1#, 16#CD#, 16#39#, 16#1D#, 16#CD#, 16#3D#);
return RESULT;
end LN;
function LOG (X : REAL; BASE : REAL := EXP_1) return REAL is
begin
if X <= 0.0 or BASE <= 0.0 or BASE = 1.0 then
raise ARGUMENT_ERROR;
end if;
if BASE = EXP_1 then
return LN (X);
else
return LN (X) / LN (BASE);
end if;
end LOG;
function EXPONENTIAL (X : REAL) return REAL is
RESULT : REAL;
STATUS : INTEGER;
begin
pragma NATIVE (
16#CD#, 16#39#, 16#04#, 16#CD#, 16#35#, 16#EA#, 16#CD#, 16#3A#,
16#C9#, 16#CD#, 16#35#, 16#C0#, 16#CD#, 16#35#, 16#FC#, 16#CD#,
16#35#, 16#C0#, 16#CD#, 16#34#, 16#EA#, 16#CD#, 16#35#, 16#E4#,
16#CD#, 16#39#, 16#7D#, 16#08#, 16#CD#, 16#3D#, 16#8B#, 16#45#,
16#08#, 16#9E#, 16#CD#, 16#35#, 16#E1#, 16#CD#, 16#35#, 16#F0#,
16#CD#, 16#35#, 16#E8#, 16#CD#, 16#3A#, 16#C1#, 16#73#, 16#06#,
16#CD#, 16#35#, 16#E8#, 16#CD#, 16#3A#, 16#F1#, 16#CD#, 16#35#,
16#FD#, 16#CD#, 16#39#, 16#1D#, 16#CD#, 16#39#, 16#D8#, 16#CD#,
16#39#, 16#D8#);
return RESULT;
end EXPONENTIAL;
function EXP (X : REAL; BASE : REAL := EXP_1) return REAL is
begin
if BASE <= 0.0 then
raise ARGUMENT_ERROR;
end if;
if BASE = EXP_1 then
return EXPONENTIAL (X);
else
return EXPONENTIAL (X * LN (BASE));
end if;
end EXP;
function SIN (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL is
CT : REAL;
TX : REAL;
begin
if CYCLE = 0.0 then
raise ARGUMENT_ERROR;
end if;
TX := (X / CYCLE) * 2.0 * PI;
TX := TX rem (2.0 * PI); -- Floating-point remainder
if (TX = 0.0) or (TX = PI) then -- Avoid division by zero
return 0.0;
else
CT := MYCOT (TX / 2.0); -- Argument has already been checked
return (2.0 * CT) / (1.0 + CT * CT);
end if;
end SIN;
function COS (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL is
CT : REAL;
TX : REAL;
begin
if CYCLE = 0.0 then
raise ARGUMENT_ERROR;
end if;
TX := (X / CYCLE) * 2.0 * PI;
TX := TX rem (2.0 * PI);
if (TX = 0.0) or (TX = PI) then -- Avoid division by zero
return 1.0;
else
CT := MYCOT (TX / 2.0); -- Argument has already been checked
return - (1.0 - CT * CT) / (1.0 + CT * CT);
end if;
end COS;
function TAN (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL is
TX : REAL;
begin
if CYCLE = 0.0 then
raise ARGUMENT_ERROR;
end if;
TX := (X / CYCLE) * 2.0 * PI;
TX := TX rem (2.0 * PI);
return MYTAN (TX);
end TAN;
function COT (X : REAL; CYCLE : REAL := 2.0 * PI) return REAL is
begin
return 1.0 / TAN (X, CYCLE);
end COT;
function ARCSIN (X : REAL) return REAL is
begin
if abs X > 1.0 then
raise ARGUMENT_ERROR;
end if;
return ARCTAN (X / SQRT ((1.0 - X) * (1.0 + X)));
end ARCSIN;
function ARCCOS (X : REAL) return REAL is
begin
if abs X > 1.0 then
raise ARGUMENT_ERROR;
end if;
return 2.0 * ARCTAN (SQRT ((1.0 - X) / (1.0 + X)));
end ARCCOS;
function ARCTAN (X : REAL; Y : REAL := 1.0) return REAL is
PIOVER2 : constant REAL := PI / 2.0;
function ATAN (X, Y : in REAL) return REAL is
RESULT : REAL;
begin
pragma NATIVE (
16#CD#, 16#39#, 16#04#, 16#CD#, 16#39#, 16#44#, 16#08#, 16#CD#,
16#35#, 16#F3#, 16#CD#, 16#39#, 16#1D#, 16#CD#, 16#3D#);
return RESULT;
end ATAN;
begin
if X = 0.0 and Y = 0.0 then
raise ARGUMENT_ERROR;
end if;
if X / Y < 0.0 then
return - ARCTAN (-X, Y);
elsif X > Y then
return PIOVER2 - ATAN (Y, X);
else
return ATAN (X, Y);
end if;
end ARCTAN;
function ARCCOT (X : REAL; Y : REAL := 1.0) return REAL is
begin
return ARCTAN (Y, X);
end ARCCOT;
function SINH (X : REAL) return REAL is
EABSX : constant REAL := EXP (abs X);
RESULT : REAL;
begin
RESULT := 0.5 * (EABSX - 1.0 + (EABSX - 1.0) / EABSX);
if X >= 0.0 then
return RESULT;
else
return - RESULT;
end if;
end SINH;
function COSH (X : REAL) return REAL is
EABSX : constant REAL := EXP (abs X);
begin
return 0.5 * (EABSX + 1.0 / EABSX);
end COSH;
function TANH (X : REAL) return REAL is
E2ABSX : constant REAL := EXP (2.0 * abs X);
RESULT : REAL;
begin
RESULT := (E2ABSX - 1.0) / (E2ABSX + 1.0);
if X >= 0.0 then
return RESULT;
else
return - RESULT;
end if;
end TANH;
function COTH (X : REAL) return REAL is
begin
return 1.0 / TANH (X);
end COTH;
function ARCSINH (X : REAL) return REAL is
ABSX : constant REAL := abs X;
function ASINH (X : REAL) return REAL is
SIGNX : constant INTEGER := INTEGER (X / ABSX);
Z : constant REAL :=
ABSX + ABSX / (1.0 / ABSX + SQRT (1.0 + (1.0 / ABSX / ABSX)));
RESULT : REAL;
begin
pragma NATIVE (
16#CD#, 16#3B#, 16#05#, 16#CD#, 16#35#, 16#ED#, 16#CD#, 16#3A#,
16#C9#, 16#CD#, 16#39#, 16#45#, 16#02#, 16#CD#, 16#35#, 16#E8#,
16#CD#, 16#3A#, 16#C1#, 16#CD#, 16#35#, 16#F1#, 16#CD#, 16#39#,
16#5D#, 16#0A#, 16#CD#, 16#3D#);
return RESULT;
end ASINH;
begin
return ASINH (X);
end ARCSINH;
function ARCCOSH (X : REAL) return REAL is
function ACOSH (X : REAL) return REAL is
Z : constant REAL := X + SQRT ((X - 1.0) * (X + 1.0));
RESULT : REAL;
begin
pragma NATIVE (
16#CD#, 16#35#, 16#ED#, 16#CD#, 16#39#, 16#05#, 16#CD#, 16#35#,
16#F1#, 16#CD#, 16#39#, 16#5D#, 16#08#, 16#CD#, 16#3D#);
return RESULT;
end ACOSH;
begin
if X < 1.0 then
raise ARGUMENT_ERROR;
end if;
return ACOSH (X);
end ARCCOSH;
function ARCTANH (X : REAL) return REAL is
ABSX : constant REAL := abs X;
function ATANH (X : REAL) return REAL is
SIGNX : constant INTEGER := INTEGER (X / ABSX);
Z : constant REAL := 2.0 * ABSX / (1.0 - ABSX);
RESULT : REAL;
begin
pragma NATIVE (
16#CD#, 16#3B#, 16#05#, 16#CD#, 16#35#, 16#ED#, 16#CD#, 16#3A#,
16#C9#, 16#CD#, 16#39#, 16#45#, 16#02#, 16#CD#, 16#35#, 16#E8#,
16#CD#, 16#3A#, 16#C1#, 16#CD#, 16#35#, 16#F1#, 16#CD#, 16#39#,
16#5D#, 16#0A#, 16#CD#, 16#3D#);
return RESULT / 2.0;
end ATANH;
begin
if abs X >= 1.0 then
raise ARGUMENT_ERROR;
end if;
return ATANH (X);
end ARCTANH;
function ARCCOTH (X : REAL) return REAL is
begin
return ARCTANH (1.0 / X);
end ARCCOTH;
end MATH;

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