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Add polylog function #4046

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036bfb5
Add RR versions of some flint special functions
d-torrance Dec 6, 2025
1732cc5
Add polylog function
d-torrance Dec 1, 2025
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48 changes: 35 additions & 13 deletions M2/Macaulay2/d/actors3.d
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Expand Up @@ -891,8 +891,7 @@ regularizedGamma(e:Expr):Expr := (
when a.0
is s:RRcell do (
when a.1
is x:RRcell do toExpr(
midpointRR(regularizedGamma(toRRi(s.v), toRRi(x.v)))) -- # typical value: regularizedGamma, RR, RR, RR
is x:RRcell do toExpr(regularizedGamma(s.v, x.v)) -- # typical value: regularizedGamma, RR, RR, RR
is x:RRicell do toExpr(regularizedGamma(toRRi(s.v), x.v)) -- # typical value: regularizedGamma, RR, RRi, RRi
is x:CCcell do toExpr(regularizedGamma(toCC(s.v), x.v)) -- # typical value: regularizedGamma, RR, CC, CC
else WrongArgRRorCC(2))
Expand Down Expand Up @@ -956,7 +955,7 @@ erfc(e:Expr):Expr := (
setupfun("erfc",erfc).Protected=false;
inverseErf(e:Expr):Expr := (
when e
is x:RRcell do toExpr(midpointRR(inverseErf(toRRi(x.v)))) -- # typical value: inverseErf, RR, RR
is x:RRcell do toExpr(inverseErf(x.v)) -- # typical value: inverseErf, RR, RR
is x:RRicell do toExpr(inverseErf(x.v)) -- # typical value: inverseErf, RRi, RRi
else WrongArgRRorRRi());
setupfun("inverseErf",inverseErf).Protected=false;
Expand All @@ -976,15 +975,13 @@ BesselJ(e:Expr):Expr := (
else WrongArgRRorCC(2))
else (
when s.1
is x:RRcell do toExpr(
midpointRR(BesselJ(toRRi(n.v), toRRi(x.v))))
is x:RRcell do toExpr(BesselJ(toRR(n.v), x.v))
is x:RRicell do toExpr(BesselJ(toRRi(n.v,precision(x.v)),x.v))
is x:CCcell do toExpr(BesselJ(toCC(n.v), x.v ))
else WrongArgRRorCC(2)))
is n:RRcell do (
when s.1
is x:RRcell do toExpr(
midpointRR(BesselJ(toRRi(n.v), toRRi(x.v))))
is x:RRcell do toExpr(BesselJ(n.v, x.v))
is x:RRicell do toExpr(BesselJ(toRRi(n.v), x.v))
is x:CCcell do toExpr(BesselJ(toCC(n.v), x.v ))
else WrongArgRRorCC(2))
Expand Down Expand Up @@ -1017,15 +1014,13 @@ BesselY(e:Expr):Expr := (
else WrongArgRRorCC(2))
else (
when s.1
is x:RRcell do toExpr(
midpointRR(BesselY(toRRi(n.v), toRRi(x.v))))
is x:RRcell do toExpr(BesselY(toRR(n.v), x.v))
is x:RRicell do toExpr(BesselY(toRRi(n.v,precision(x.v)),x.v))
is x:CCcell do toExpr(BesselY(toCC(n.v), x.v ))
else WrongArgRRorCC(2)))
is n:RRcell do (
when s.1
is x:RRcell do toExpr(
midpointRR(BesselY(toRRi(n.v), toRRi(x.v))))
is x:RRcell do toExpr(BesselY(n.v, x.v))
is x:RRicell do toExpr(BesselY(toRRi(n.v), x.v))
is x:CCcell do toExpr(BesselY(toCC(n.v), x.v ))
else WrongArgRRorCC(2))
Expand Down Expand Up @@ -1102,8 +1097,7 @@ regularizedBeta(xx:Expr,yy:Expr,zz:Expr):Expr := (
when yy
is y:RRcell do (
when zz
is z:RRcell do toExpr(
midpointRR(regularizedBeta(toRRi(x.v), toRRi(y.v), toRRi(z.v)))) -- # typical value: regularizedBeta, RR, RR, RR, RR
is z:RRcell do toExpr(regularizedBeta(x.v, y.v, z.v)) -- # typical value: regularizedBeta, RR, RR, RR, RR
is z:RRicell do toExpr(regularizedBeta(toRRi(x.v), toRRi(y.v), z.v)) -- # typical value: regularizedBeta, RR, RR, RRi, RRi
is z:CCcell do toExpr(regularizedBeta(toCC(x.v), toCC(y.v), z.v)) -- # typical value: regularizedBeta, RR, RR, CC, CC
else WrongArgRRorCC(3))
Expand Down Expand Up @@ -1151,6 +1145,34 @@ regularizedBeta(e:Expr):Expr := (
else WrongNumArgs(3));
setupfun("regularizedBeta",regularizedBeta).Protected=false;

polylog(e:Expr):Expr := (
when e
is a:Sequence do (
if length(a) == 2 then (
when a.0
is x:RRcell do (
when a.1
is y:RRcell do ( -- # typical value: polylog, RR, RR, RR
if y.v < 1 then toExpr(polylog(x.v, y.v))
else toExpr(polylog(toCC(x.v), toCC(y.v))))
is y:RRicell do toExpr(polylog(toRRi(x.v), y.v)) -- # typical value: polylog, RR, RRi, RRi
is y:CCcell do toExpr(polylog(toCC(x.v), y.v)) -- # typical value: polylog, RR, CC, CC
else WrongArgRRorCC(2))
is x:RRicell do (
when a.1
is y:RRcell do toExpr(polylog(x.v, toRRi(y.v))) -- # typical value: polylog, RRi, RR, RRi
is y:RRicell do toExpr(polylog(x.v, y.v)) -- # typical value: polylog, RRi, RRi, RRi
else WrongArgRRorCC(2))
is x:CCcell do (
when a.1
is y:RRcell do toExpr(polylog(x.v, toCC(y.v))) -- # typical value: polylog, CC, RR, CC
is y:CCcell do toExpr(polylog(x.v, y.v)) -- # typical value: polylog, CC, CC, CC
else WrongArgRRorCC(2))
else WrongArgRRorCC(1))
else WrongNumArgs(2))
else WrongNumArgs(2));
setupfun("polylog", polylog).Protected=false;

cosh(e:Expr):Expr := (
when e
is x:CCcell do toExpr(cosh(x.v)) -- # typical value: cosh, CC, CC
Expand Down
86 changes: 86 additions & 0 deletions M2/Macaulay2/d/ballarith.d
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Expand Up @@ -52,6 +52,11 @@ toRR(x:RRball, prec:ulong):RR := (
Ccode(int, "arf_get_mpfr(", y, ", arb_midref(", x, "), MPFR_RNDN)");
moveToRRandclear(y));

moveToRRandclear(x:RRball, prec:ulong):RR := (
r := toRR(x, prec);
clear(x);
r);

toRRi(x:RRball, prec:ulong):RRi := (
y := newRRimutable(prec);
Ccode(void, "arb_get_interval_mpfr((mpfr_ptr)&", y,
Expand Down Expand Up @@ -89,6 +94,17 @@ export Gamma(z:RRi,w:RRi):RRi := (
clear(y);
moveToRRiandclear(r, prec));

export regularizedGamma(z:RR,w:RR):RR := (
prec := min(precision(z), precision(w));
x := toRRball(z);
y := toRRball(w);
r := newRRball();
Ccode(void, "arb_hypgeom_gamma_upper(", r, ", ", x, ", ", y, ", 1, ",
prec, ")");
clear(x);
clear(y);
moveToRRandclear(r, prec));

export regularizedGamma(z:RRi,w:RRi):RRi := (
prec := min(precision(z), precision(w));
x := toRRball(z);
Expand Down Expand Up @@ -135,13 +151,30 @@ export erfc(x:RRi):RRi := (
clear(y);
moveToRRiandclear(r, precision(x)));

export inverseErf(x:RR):RR := (
y := toRRball(x);
r := newRRball();
Ccode(void, "arb_hypgeom_erfinv(", r, ", ", y, ", ", precision(x), ")");
clear(y);
moveToRRandclear(r, precision(x)));

export inverseErf(x:RRi):RRi := (
y := toRRball(x);
r := newRRball();
Ccode(void, "arb_hypgeom_erfinv(", r, ", ", y, ", ", precision(x), ")");
clear(y);
moveToRRiandclear(r, precision(x)));

export BesselJ(z:RR,w:RR):RR := (
prec := min(precision(z), precision(w));
x := toRRball(z);
y := toRRball(w);
r := newRRball();
Ccode(void, "arb_hypgeom_bessel_j(", r, ", ", x, ", ", y, ", ", prec, ")");
clear(x);
clear(y);
moveToRRandclear(r, prec));

export BesselJ(z:RRi,w:RRi):RRi := (
prec := min(precision(z), precision(w));
x := toRRball(z);
Expand All @@ -152,6 +185,16 @@ export BesselJ(z:RRi,w:RRi):RRi := (
clear(y);
moveToRRiandclear(r, prec));

export BesselY(z:RR,w:RR):RR := (
prec := min(precision(z), precision(w));
x := toRRball(z);
y := toRRball(w);
r := newRRball();
Ccode(void, "arb_hypgeom_bessel_y(", r, ", ", x, ", ", y, ", ", prec, ")");
clear(x);
clear(y);
moveToRRandclear(r, prec));

export BesselY(z:RRi,w:RRi):RRi := (
prec := min(precision(z), precision(w));
x := toRRball(z);
Expand All @@ -174,6 +217,19 @@ export Beta(z:RRi,w:RRi):RRi := (
clear(y);
moveToRRiandclear(r, prec));

export regularizedBeta(u:RR,v:RR,w:RR):RR := (
prec := min(min(precision(u), precision(v)), precision(w));
x := toRRball(u);
y := toRRball(v);
z := toRRball(w);
r := newRRball();
Ccode(void, "arb_hypgeom_beta_lower(", r, ", ", y, ", ", z, ", ", x,
", 1, ", prec, ")");
clear(x);
clear(y);
clear(z);
moveToRRandclear(r, prec));

export regularizedBeta(u:RRi,v:RRi,w:RRi):RRi := (
prec := min(min(precision(u), precision(v)), precision(w));
x := toRRball(u);
Expand All @@ -187,6 +243,26 @@ export regularizedBeta(u:RRi,v:RRi,w:RRi):RRi := (
clear(z);
moveToRRiandclear(r, prec));

export polylog(z:RR, w:RR):RR := (
prec := min(precision(z), precision(w));
x := toRRball(z);
y := toRRball(w);
r := newRRball();
Ccode(void, "arb_polylog(", r, ", ", x, ", ", y, ", ", prec, ")");
clear(x);
clear(y);
moveToRRandclear(r, prec));

export polylog(z:RRi, w:RRi):RRi := (
prec := min(precision(z), precision(w));
x := toRRball(z);
y := toRRball(w);
r := newRRball();
Ccode(void, "arb_polylog(", r, ", ", x, ", ", y, ", ", prec, ")");
clear(x);
clear(y);
moveToRRiandclear(r, prec));

------------
-- CCBall --
------------
Expand Down Expand Up @@ -333,3 +409,13 @@ export regularizedBeta(u:CC,v:CC,w:CC):CC := (
clear(y);
clear(z);
moveToCCandclear(r, prec));

export polylog(z:CC, w:CC):CC := (
prec := min(precision(z), precision(w));
x := toCCball(z);
y := toCCball(w);
r := newCCball();
Ccode(void, "acb_polylog(", r, ", ", x, ", ", y, ", ", prec, ")");
clear(x);
clear(y);
moveToCCandclear(r, prec));
1 change: 1 addition & 0 deletions M2/Macaulay2/m2/exports.m2
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Expand Up @@ -1009,6 +1009,7 @@ export {
"poincare",
"poincareN",
"polarize",
"polylog",
"position",
"positions",
"power",
Expand Down
2 changes: 1 addition & 1 deletion M2/Macaulay2/m2/typicalvalues.m2
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Expand Up @@ -130,7 +130,7 @@ then generateTypicalValues(currentFileDirectory | "../d/")

-----------------------------------------------------------------------------
-- numerical functions that will be wrapped
redefs := hashTable apply({acos, agm, asin, atan, atan2, Beta, cos, cosh, cot, coth, csc, csch, Digamma, eint, erf, erfc, exp, expm1, Gamma, inverseErf, inverseRegularizedBeta, inverseRegularizedGamma, log, log1p, regularizedBeta, regularizedGamma, sec, sech, sin, sinh, sqrt, tan, tanh, zeta},
redefs := hashTable apply({acos, agm, asin, atan, atan2, Beta, cos, cosh, cot, coth, csc, csch, Digamma, eint, erf, erfc, exp, expm1, Gamma, inverseErf, inverseRegularizedBeta, inverseRegularizedGamma, log, log1p, polylog, regularizedBeta, regularizedGamma, sec, sech, sin, sinh, sqrt, tan, tanh, zeta},
f -> f => method());
variants := new MutableHashTable;

Expand Down
4 changes: 4 additions & 0 deletions M2/Macaulay2/tests/normal/numbers.m2
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Expand Up @@ -1013,6 +1013,10 @@ assert small abs(BesselY(1, ii) + 0.565159103992484 - 0.383186043874565*ii)
assert (abs(BesselY(ii, 1) + 0.476556612479964 + 1.50506915911039*ii) < 1e-14)
assert small abs(BesselY(ii, ii) + 0.665181892391867 - 0.395137431337008*ii)

assert small(polylog(1, 1/2) - log 2)
assert small(polylog(2, 1/2) - 1/12*pi^2 + 1/2*(log 2)^2)
assert(polylog(3, 1) == zeta 3)

assert Equation(truncate 1, 1)
assert Equation(truncate 1.9, 1)
assert Equation(truncate(-1.9), -1)
Expand Down
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