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math: Implementation of the math module using more modern syntax
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The math module is one of the easiest modules to convert to the "new" syntax for
module specifications.

Functions there are lifted from `<math.h>` on Linux. Presumably, the functions
are generally available on all platforms. In the long run, it would be
interesting to write all of them in XL, but for now it's mostly a waste of time.

Signed-off-by: Christophe de Dinechin <christophe@dinechin.org>
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@c3d
c3d committed Jul 1, 2021
1 parent 1e2a64d commit 8a4e81e
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109 changes: 82 additions & 27 deletions native/lib/xl.math.xl
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// If not, see <https://www.gnu.org/licenses/>.
// *****************************************************************************

MATH is
// ----------------------------------------------------------------------------
// Implementation of the math module
// ----------------------------------------------------------------------------
with
X:real
Y:real
Z:real
N:natural
I:integer
Base:real

// Basic math functions
abs X:integer as integer is builtin IAbs
abs X:real as real is builtin FAbs
sqrt X:real as real is C sqrt
// Generic implementation of abs and sign
generic_abs T is (if T < 0 then -T else T)
generic_sign T is (if T < 0 then -1 else if T > 0 then 1 else 0)

sin X:real as real is C sin
cos X:real as real is C cos
tan X:real as real is C tan
asin X:real as real is C asin
acos X:real as real is C acos
atan X:real as real is C atan
atan Y:real, X:real as real is C atan2
abs I as integer is generic_abs I
sign I as integer is generic_sign I
abs X as real is generic_abs X
sign X as real is generic_sign X

sinh X:real as real is C sinh
cosh X:real as real is C cosh
tanh X:real as real is C tanh
asinh X:real as real is C asinh
acosh X:real as real is C acosh
atanh X:real as real is C atanh
// Nearest integer
ceil X as real is C "ceil"
floor X as real is C "floor"

exp X:real as real is C exp
expm1 X:real as real is C expm1
log X:real as real is C log
log10 X:real as real is C log10
log2 X:real as real is C log2
log1p X:real as real is C log1p
// C interface for base functions
sqrt X as real is C "sqrt"
exp X as real is C "exp"
exp2 X as real is C "exp2"
log X as real is C "log"
ln X as real is log X
log10 X as real is C "log10"
log2 X as real is C "log2"
logb X as integer is C "logb"
log(Base,X) as real is (log X / log Base)
hypot(X,Y) as real is C "hypot"
cbrt X as real is C "cbrt"
erf X as real is C "erf"
lgamma X as real is C "lgamma"
fma X,Y,Z as real is C "fma"

// Circular trigonometry
sin X as real is C "sin"
cos X as real is C "cos"
tan X as real is C "tan"
asin X as real is C "asin"
acos X as real is C "acos"
atan X as real is C "atan"
atan Y/X as real is C "atan2"

// Hyperbolic trigonometry
sinh X as real is C "sinh"
cosh X as real is C "cosh"
tanh X as real is C "tanh"
asinh X as real is C "asinh"
acosh X as real is C "acosh"
atanh X as real is C "atanh"

// Bessel functions
j0 X as real is C "j0"
j1 X as real is C "j1"
jn I, X as real is C "jn"
y0 X as real is C "y0"
y1 X as real is C "y1"
yn I, X as real is C "yn"

// Optimized forms
(exp X)-1.0 as real is C "expm1"
log (1.0+X) as real is C "log1p"
log (X+1.0) as real is C "log1p"
2.0^X as real is C "exp2"

// Constants
pi is 3.1415926535897932384626433
e is 2.7182818284590452353602875

// Optimized expressions
// constant (log2 [[e]]) is 1.442695040888963407359924681001892137

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@dumblob

dumblob Jul 2, 2021

Why is actually constant needed here? Shouldn't pattern matching itself be enough to "change" log2 [[e]] to 1.442695040888963...? Or is it because of ambiguity through precision?

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@c3d

c3d Jul 2, 2021

Author Owner

This is not really needed. It’s an implementation hint, suggesting to use a constant rather than, say, a function. See https://xlr.sourceforge.io/#implementations-hints
// constant (log10 [[e]]) is 0.434294481903251827651128918916605082
// constant (log 2.0) is 0.693147180559945309417232121458176568
// constant (pi/2.0) is 1.570796326794896619231321691639751442
// constant (pi/4.0) is 0.785398163397448309615660845819875721
// constant (pi*0.5) is constant(pi/2.0)
// constant (pi*0.25) is constant(pi/4.0)
// constant (1.0/[[pi]]) is 0.318309886183790671537767526745028724
// constant (2.0/[[pi]]) is 0.636619772367581343075535053490057448
// constant (2.0/sqrt [[pi]]) is 1.128379167095512573896158903121545172
// constant (sqrt 2.0) is 1.414213562373095048801688724209698079
// constant (1.0/sqrt 2.0) is 0.707106781186547524400844362104849039
// constant (sqrt 2.0/2.0) is 0.707106781186547524400844362104849039
141 changes: 88 additions & 53 deletions native/lib/xl.math.xs
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Expand Up @@ -34,64 +34,99 @@
// If not, see <https://www.gnu.org/licenses/>.
// *****************************************************************************

module ARBITRARY_PRECISION
with
X:real
Y:real
Z:real
N:natural
I:integer
Base:real

module COMPLEX
module QUATERNION
module VECTOR
module MATRIX
module STATISTICS
// Functions on integer values
abs I as integer
sign I as integer

// Functions on real values
abs X as real
sign X as real
ceil X as real
floor X as real
sqrt X as real
exp X as real
exp2 X as real
log X as real
ln X as real
log10 X as real
log2 X as real
logb X as integer
log(Base,X) as real
hypot(X,Y) as real
hypothenuse(X,Y)as real is hypot(X,Y)
cbrt X as real
CubeRoot X as real is cbrt X
erf X as real
ErrorFunction X as real is erf X
lgamma X as real
LogGamma X as real is lgamma X
fma X,Y,Z as real
X*Y+Z as real is fma X,Y,Z
Z+X*Y as real is fma X,Y,Z

// Using the `MATH` module by default uses `real` functions and constants
use REAL
use MATH[real].FUNCTIONS
use MATH[real].CONSTANTS
// Circular trigonometry
sin X as real
cos X as real
tan X as real
asin X as real
acos X as real
atan X as real
atan Y/X as real

// Hyperbolic trigonometry
sinh X as real
cosh X as real
tanh X as real
asinh X as real
acosh X as real
atanh X as real

module MATH[type number] with
// ----------------------------------------------------------------------------
// Interface of the math module for a given number type
// ----------------------------------------------------------------------------
// Bessel functions
j0 X as real
j1 X as real
jn I, X as real
J 0, X as real is j0 X
J 1, X as real is j1 X
J I, X as real is jn I,X
y0 X as real
y1 X as real
yn I, X as real
Y 0, X as real is y0 X
Y 1, X as real is y1 X
Y I, X as real is yn I, X

module FUNCTIONS with
// ------------------------------------------------------------------------
// Interface for basic math functions
// ------------------------------------------------------------------------
// Optimized forms
(exp X) - 1.0 as real
log (1.0+X) as real
log (X+1.0) as real
2.0^X as real

Abs X:number as number
Sign X:number as integer
Sqrt X:number as number
// Constants
pi
e

Sin X:number as number
Cos X:number as number
Tan X:number as number
ArcSin X:number as number
ArcCos X:number as number
ArcTan X:number as number
ArcTan Y:number, X:number as number

SinH X:number as number
CosH X:number as number
TanH X:number as number
ArcSinH X:number as number
ArcCosH X:number as number
ArcTanH X:number as number

Exp X:number as number
Exp X:number - 1 as number
Log X:number as number
Log10 X:number as number
Log2 X:number as number
Log2i X:number as integer
Log (1 + X:number) as number


module CONSTANTS is
// ------------------------------------------------------------------------
// Interface for math constants
// ------------------------------------------------------------------------
ZERO is number 0
ONE is number 1
TWO is number 2
PI is number 3.1415926535897932384626433
// Optimized expressions
// constant (log2 [[e]])
// constant (log10 [[e]])
// constant (log 2.0)
// constant (pi/2.0)
// constant (pi/4.0)
// constant (pi*0.5)
// constant (pi*0.25)
// constant (1.0/[[pi]])
// constant (2.0/[[pi]])
// constant (2.0/sqrt [[pi]])
// constant (1.0/[[pi]])
// constant (2.0/[[pi]])
// constant (2.0/sqrt [[pi]])
// constant (sqrt 2.0)
// constant (1.0/sqrt 2.0)
// constant (sqrt 2.0/2.0)
19 changes: 2 additions & 17 deletions src/builtins.xl
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Expand Up @@ -150,23 +150,8 @@ Source:text from First:natural as text is text_range(Source, First, not 0)
parse Source:text is C "xl_parse_text"

// Basic math functions
abs X is if X < 0 then -X else X
pi is 3.1415926535897932384626433
sin X:real as real is C "sin"
cos X:real as real is C "cos"
tan X:real as real is C "tan"
asin X:real as real is C "asin"
acos X:real as real is C "acos"
atan X:real as real is C "atan"
exp X:real as real is C "exp"
exp2 X:real as real is C "exp2"
expm1 X:real as real is C "expm1"
log X:real as real is C "log"
log2 X:real as real is C "log2"
log10 X:real as real is C "log10"
log1p X:real as real is C "log1p"
sqrt X:real as real is C "sqrt"
atan Y:real / X:real as real is C "atan2"
abs X is if X < 0 then -X else X
sign X is if X < 0 then -1 else if X > 0 then 1 else 0

// If-then-else statement
if [[true]] then True else False is True
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59 changes: 50 additions & 9 deletions src/posix.cpp
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Expand Up @@ -71,21 +71,62 @@ double fn(double x, double y) \
NATIVE(fn); \
}

MATH(sin);
MATH(cos);
MATH(tan);
MATH(asin);
MATH(acos);
MATH(atan);
#define MATH2I(fn) \
namespace \
{ \
double fn(int x, double y) \
{ \
return ::fn(x, y); \
} \
NATIVE(fn); \
}

#define MATH3(fn) \
namespace \
{ \
double fn(double x, double y, double z) \
{ \
return ::fn(x, y, z); \
} \
NATIVE(fn); \
}

MATH(ceil);
MATH(floor);
MATH(sqrt);
MATH(exp);
MATH(expm1);
MATH(exp2);
MATH(expm1);
MATH(log);
MATH(log2);
MATH(log10);
MATH(log1p);
MATH(sqrt);
MATH2(atan2);
MATH(logb);
MATH2(hypot);
MATH(cbrt);
MATH(erf);
MATH(lgamma);
MATH3(fma);
MATH2(pow);

MATH(sin);
MATH(cos);
MATH(tan);
MATH(asin);
MATH(acos);
MATH(atan);
MATH2(atan2);
MATH(sinh);
MATH(cosh);
MATH(tanh);
MATH(asinh);
MATH(acosh);
MATH(atanh);
MATH(j0);
MATH(j1);
MATH2I(jn);
MATH(y0);
MATH(y1);
MATH2I(yn);

XL_END
2 changes: 2 additions & 0 deletions tests/01.Evaluation/04-write-types.xl
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// along with XL, in a file named COPYING.
// If not, see <https://www.gnu.org/licenses/>.
// *****************************************************************************
import XL.MATH

print "Hello"
print 'C'
print 12
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2 changes: 1 addition & 1 deletion tests/01.Evaluation/bug3327.ref
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@@ -1 +1 @@
23.1407
8.53973
4 changes: 3 additions & 1 deletion tests/01.Evaluation/bug3327.xl
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Expand Up @@ -31,4 +31,6 @@
// along with XL, in a file named COPYING.
// If not, see <https://www.gnu.org/licenses/>.
// *****************************************************************************
exp(1) * pi
import XL.MATH

pi * exp(1)
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