From d911eafd31a52f552ac475f62e39a9b2e6bbe661 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Sat, 26 Nov 2022 14:17:27 -0500 Subject: [PATCH] =?UTF-8?q?Inverses=20for=20=E2=80=A2math.Fact=20and=20?= =?UTF-8?q?=E2=80=A2math.LogFact?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- src/builtins/arithm.c | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/src/builtins/arithm.c b/src/builtins/arithm.c index 581a902f..41069110 100644 --- a/src/builtins/arithm.c +++ b/src/builtins/arithm.c @@ -90,6 +90,18 @@ GC1f(root, sqrt(xv), "√: Getting square root of non-number") f64 fact(f64 x) { return tgamma(x+1); } f64 logfact(f64 x) { return lgamma(x+1); } +NOINLINE f64 logfact_inv(f64 y) { + if (!(y >= -0.12)) thrM("⁼: required factorial result too small"); + if (y == INFINITY) return y; + f64 x = 4; + PLAINLOOP for (usz i = 0; i < 20; i++) { + f64 x0 = x; + x += (y - logfact(x)) / log(0.52 + x); + if (x == x0) break; + } + return x; +} +f64 fact_inv(f64 y) { return logfact_inv(log(y)); } #define P1(N) { if(isArr(x)) { SLOW1("arithm " #N, x); return arith_recm(N##_c1, x); } } B pow_c1(B t, B x) { if (isF64(x)) return m_f64( exp(x.f)); P1( pow); thrM("⋆: Getting exp of non-number"); } @@ -102,7 +114,7 @@ static NOINLINE B arith_recm_slow(f64 (*fn)(f64), BB2B rec, B x, char* s) { } #define MATH(n,N) B n##_c1(B t, B x) { return arith_recm_slow(n, n##_c1, x, #N); } MATH(cbrt,Cbrt) MATH(log2,Log2) MATH(log10,Log10) MATH(log1p,Log1p) MATH(expm1,Expm1) -MATH(fact,Fact) MATH(logfact,LogFact) MATH(erf,Erf) MATH(erfc,ErfC) +MATH(fact,Fact) MATH(logfact,LogFact) MATH(logfact_inv,LogFact⁼) MATH(fact_inv,Fact⁼) MATH(erf,Erf) MATH(erfc,ErfC) #define TRIG(n,N) MATH(n,N) MATH(a##n,A##n) MATH(n##h,N##h) MATH(a##n##h,A##n##h) TRIG(sin,Sin) TRIG(cos,Cos) TRIG(tan,Tan) #undef TRIG @@ -142,5 +154,7 @@ void arith_init() { INVERSE_PAIR(cosh, acosh) INVERSE_PAIR(tanh, atanh) INVERSE_PAIR(expm1, log1p) + c(BFn,bi_fact)->im = fact_inv_c1; + c(BFn,bi_logfact)->im = logfact_inv_c1; #undef INVERSE_PAIR }