feat(stdlibs): add math and math/bits (gnolang#1153)

Co-authored-by: Antonio Navarro Perez <[email protected]>

docs/reference/go-gno-compatibility.md

@@ -194,9 +194,9 @@ Legend:
 | log/slog                                    | `tbd`    |
 | log/syslog                                  | `nondet` |
 | maps                                        | `gnics`  |
-| math                                        | `part`   |
+| math                                        | `full`   |
 | math/big                                    | `tbd`    |
-| math/bits                                   | `todo`   |
+| math/bits                                   | `full`   |
 | math/cmplx                                  | `tbd`    |
 | math/rand                                   | `todo`   |
 | mime                                        | `tbd`    |

gnovm/stdlibs/math/abs.gno

@@ -4,16 +4,12 @@
 
 package math
 
-import (
-	imath "internal/math" // XXX
-)
-
 // Abs returns the absolute value of x.
 //
 // Special cases are:
 //
 //	Abs(±Inf) = +Inf
 //	Abs(NaN) = NaN
 func Abs(x float64) float64 {
-	return imath.Float64frombits(imath.Float64bits(x) &^ (1 << 63))
+	return Float64frombits(Float64bits(x) &^ (1 << 63))
 }

gnovm/stdlibs/math/acosh.gno

@@ -0,0 +1,62 @@
+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+// The original C code, the long comment, and the constants
+// below are from FreeBSD's /usr/src/lib/msun/src/e_acosh.c
+// and came with this notice. The go code is a simplified
+// version of the original C.
+//
+// ====================================================
+// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+//
+// Developed at SunPro, a Sun Microsystems, Inc. business.
+// Permission to use, copy, modify, and distribute this
+// software is freely granted, provided that this notice
+// is preserved.
+// ====================================================
+//
+//
+// __ieee754_acosh(x)
+// Method :
+//	Based on
+//	        acosh(x) = log [ x + sqrt(x*x-1) ]
+//	we have
+//	        acosh(x) := log(x)+ln2,	if x is large; else
+//	        acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+//	        acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+//
+// Special cases:
+//	acosh(x) is NaN with signal if x<1.
+//	acosh(NaN) is NaN without signal.
+//
+
+// Acosh returns the inverse hyperbolic cosine of x.
+//
+// Special cases are:
+//
+//	Acosh(+Inf) = +Inf
+//	Acosh(x) = NaN if x < 1
+//	Acosh(NaN) = NaN
+func Acosh(x float64) float64 {
+	return acosh(x)
+}
+
+func acosh(x float64) float64 {
+	const Large = 1 << 28 // 2**28
+	// first case is special case
+	switch {
+	case x < 1 || IsNaN(x):
+		return NaN()
+	case x == 1:
+		return 0
+	case x >= Large:
+		return Log(x) + Ln2 // x > 2**28
+	case x > 2:
+		return Log(2*x - 1/(x+Sqrt(x*x-1))) // 2**28 > x > 2
+	}
+	t := x - 1
+	return Log1p(t + Sqrt(2*t+t*t)) // 2 >= x > 1
+}