feat: additional math libraries

stdlibs/math/frexp.gno

@@ -0,0 +1,43 @@
+// Copyright 2009 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
+
+import (
+	imath "internal/math"
+)
+
+// Frexp breaks f into a normalized fraction
+// and an integral power of two.
+// It returns frac and exp satisfying f == frac × 2**exp,
+// with the absolute value of frac in the interval [½, 1).
+//
+// Special cases are:
+//
+//	Frexp(±0) = ±0, 0
+//	Frexp(±Inf) = ±Inf, 0
+//	Frexp(NaN) = NaN, 0
+func Frexp(f float64) (frac float64, exp int) {
+	// if haveArchFrexp {
+	// 	return archFrexp(f)
+	// }
+	return frexp(f)
+}
+
+func frexp(f float64) (frac float64, exp int) {
+	// special cases
+	switch {
+	case f == 0:
+		return f, 0 // correctly return -0
+	case IsInf(f, 0) || IsNaN(f):
+		return f, 0
+	}
+	f, exp = normalize(f)
+	x := imath.Float64bits(f)
+	exp += int((x>>shift)&mask) - bias + 1
+	x &^= mask << shift
+	x |= (-1 + bias) << shift
+	frac = imath.Float64frombits(x)
+	return
+}

stdlibs/math/log.gno

@@ -0,0 +1,129 @@
+// Copyright 2009 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
+
+/*
+	Floating-point logarithm.
+*/
+
+// The original C code, the long comment, and the constants
+// below are from FreeBSD's /usr/src/lib/msun/src/e_log.c
+// and came with this notice. The go code is a simpler
+// 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_log(x)
+// Return the logarithm of x
+//
+// Method :
+//   1. Argument Reduction: find k and f such that
+//			x = 2**k * (1+f),
+//	   where  sqrt(2)/2 < 1+f < sqrt(2) .
+//
+//   2. Approximation of log(1+f).
+//	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+//		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+//	     	 = 2s + s*R
+//      We use a special Reme algorithm on [0,0.1716] to generate
+//	a polynomial of degree 14 to approximate R.  The maximum error
+//	of this polynomial approximation is bounded by 2**-58.45. In
+//	other words,
+//		        2      4      6      8      10      12      14
+//	    R(z) ~ L1*s +L2*s +L3*s +L4*s +L5*s  +L6*s  +L7*s
+//	(the values of L1 to L7 are listed in the program) and
+//	    |      2          14          |     -58.45
+//	    | L1*s +...+L7*s    -  R(z) | <= 2
+//	    |                             |
+//	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+//	In order to guarantee error in log below 1ulp, we compute log by
+//		log(1+f) = f - s*(f - R)		(if f is not too large)
+//		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
+//
+//	3. Finally,  log(x) = k*Ln2 + log(1+f).
+//			    = k*Ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*Ln2_lo)))
+//	   Here Ln2 is split into two floating point number:
+//			Ln2_hi + Ln2_lo,
+//	   where n*Ln2_hi is always exact for |n| < 2000.
+//
+// Special cases:
+//	log(x) is NaN with signal if x < 0 (including -INF) ;
+//	log(+INF) is +INF; log(0) is -INF with signal;
+//	log(NaN) is that NaN with no signal.
+//
+// Accuracy:
+//	according to an error analysis, the error is always less than
+//	1 ulp (unit in the last place).
+//
+// Constants:
+// The hexadecimal values are the intended ones for the following
+// constants. The decimal values may be used, provided that the
+// compiler will convert from decimal to binary accurately enough
+// to produce the hexadecimal values shown.
+
+// Log returns the natural logarithm of x.
+//
+// Special cases are:
+//
+//	Log(+Inf) = +Inf
+//	Log(0) = -Inf
+//	Log(x < 0) = NaN
+//	Log(NaN) = NaN
+func Log(x float64) float64 {
+	// if haveArchLog {
+	// 	return archLog(x)
+	// }
+	return log(x)
+}
+
+func log(x float64) float64 {
+	const (
+		Ln2Hi = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
+		Ln2Lo = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
+		L1    = 6.666666666666735130e-01   /* 3FE55555 55555593 */
+		L2    = 3.999999999940941908e-01   /* 3FD99999 9997FA04 */
+		L3    = 2.857142874366239149e-01   /* 3FD24924 94229359 */
+		L4    = 2.222219843214978396e-01   /* 3FCC71C5 1D8E78AF */
+		L5    = 1.818357216161805012e-01   /* 3FC74664 96CB03DE */
+		L6    = 1.531383769920937332e-01   /* 3FC39A09 D078C69F */
+		L7    = 1.479819860511658591e-01   /* 3FC2F112 DF3E5244 */
+	)
+
+	// special cases
+	switch {
+	case IsNaN(x) || IsInf(x, 1):
+		return x
+	case x < 0:
+		return NaN()
+	case x == 0:
+		return Inf(-1)
+	}
+
+	// reduce
+	f1, ki := Frexp(x)
+	if f1 < Sqrt2/2 {
+		f1 *= 2
+		ki--
+	}
+	f := f1 - 1
+	k := float64(ki)
+
+	// compute
+	s := f / (2 + f)
+	s2 := s * s
+	s4 := s2 * s2
+	t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
+	t2 := s4 * (L2 + s4*(L4+s4*L6))
+	R := t1 + t2
+	hfsq := 0.5 * f * f
+	return k*Ln2Hi - ((hfsq - (s*(hfsq+R) + k*Ln2Lo)) - f)
+}

stdlibs/math/log10.gno

@@ -0,0 +1,37 @@
+// Copyright 2009 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
+
+// Log10 returns the decimal logarithm of x.
+// The special cases are the same as for Log.
+func Log10(x float64) float64 {
+	// if haveArchLog10 {
+	// 	return archLog10(x)
+	// }
+	return log10(x)
+}
+
+func log10(x float64) float64 {
+	return Log(x) * (1 / Ln10)
+}
+
+// Log2 returns the binary logarithm of x.
+// The special cases are the same as for Log.
+func Log2(x float64) float64 {
+	// if haveArchLog2 {
+	// 	return archLog2(x)
+	// }
+	return log2(x)
+}
+
+func log2(x float64) float64 {
+	frac, exp := Frexp(x)
+	// Make sure exact powers of two give an exact answer.
+	// Don't depend on Log(0.5)*(1/Ln2)+exp being exactly exp-1.
+	if frac == 0.5 {
+		return float64(exp - 1)
+	}
+	return Log(frac)*(1/Ln2) + float64(exp)
+}

stdlibs/math/pow.gno

@@ -0,0 +1,161 @@
+// Copyright 2009 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
+
+import (
+	imath "internal/math"
+)
+
+func isOddInt(x float64) bool {
+	xi, xf := Modf(x)
+	return xf == 0 && int64(xi)&1 == 1
+}
+
+// Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
+// updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
+
+// Pow returns x**y, the base-x exponential of y.
+//
+// Special cases are (in order):
+//
+//	Pow(x, ±0) = 1 for any x
+//	Pow(1, y) = 1 for any y
+//	Pow(x, 1) = x for any x
+//	Pow(NaN, y) = NaN
+//	Pow(x, NaN) = NaN
+//	Pow(±0, y) = ±Inf for y an odd integer < 0
+//	Pow(±0, -Inf) = +Inf
+//	Pow(±0, +Inf) = +0
+//	Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
+//	Pow(±0, y) = ±0 for y an odd integer > 0
+//	Pow(±0, y) = +0 for finite y > 0 and not an odd integer
+//	Pow(-1, ±Inf) = 1
+//	Pow(x, +Inf) = +Inf for |x| > 1
+//	Pow(x, -Inf) = +0 for |x| > 1
+//	Pow(x, +Inf) = +0 for |x| < 1
+//	Pow(x, -Inf) = +Inf for |x| < 1
+//	Pow(+Inf, y) = +Inf for y > 0
+//	Pow(+Inf, y) = +0 for y < 0
+//	Pow(-Inf, y) = Pow(-0, -y)
+//	Pow(x, y) = NaN for finite x < 0 and finite non-integer y
+func Pow(x, y float64) float64 {
+	// if haveArchPow {
+	// 	return archPow(x, y)
+	// }
+	return pow(x, y)
+}
+
+func pow(x, y float64) float64 {
+	switch {
+	case y == 0 || x == 1:
+		return 1
+	case y == 1:
+		return x
+	case IsNaN(x) || IsNaN(y):
+		return NaN()
+	case x == 0:
+		switch {
+		case y < 0:
+			if isOddInt(y) {
+				return Copysign(Inf(1), x)
+			}
+			return Inf(1)
+		case y > 0:
+			if isOddInt(y) {
+				return x
+			}
+			return 0
+		}
+	case IsInf(y, 0):
+		switch {
+		case x == -1:
+			return 1
+		case (Abs(x) < 1) == IsInf(y, 1):
+			return 0
+		default:
+			return Inf(1)
+		}
+	case IsInf(x, 0):
+		if IsInf(x, -1) {
+			return Pow(1/x, -y) // Pow(-0, -y)
+		}
+		switch {
+		case y < 0:
+			return 0
+		case y > 0:
+			return Inf(1)
+		}
+	case y == 0.5:
+		return Sqrt(x)
+	case y == -0.5:
+		return 1 / Sqrt(x)
+	}
+
+	yi, yf := Modf(Abs(y))
+	if yf != 0 && x < 0 {
+		return NaN()
+	}
+	if yi >= 1<<63 {
+		// yi is a large even int that will lead to overflow (or underflow to 0)
+		// for all x except -1 (x == 1 was handled earlier)
+		switch {
+		case x == -1:
+			return 1
+		case (Abs(x) < 1) == (y > 0):
+			return 0
+		default:
+			return Inf(1)
+		}
+	}
+
+	// ans = a1 * 2**ae (= 1 for now).
+	a1 := 1.0
+	ae := 0
+
+	// ans *= x**yf
+	if yf != 0 {
+		if yf > 0.5 {
+			yf--
+			yi++
+		}
+		a1 = Exp(yf * Log(x))
+	}
+
+	// ans *= x**yi
+	// by multiplying in successive squarings
+	// of x according to bits of yi.
+	// accumulate powers of two into exp.
+	x1, xe := Frexp(x)
+	for i := int64(yi); i != 0; i >>= 1 {
+		if xe < -1<<12 || 1<<12 < xe {
+			// catch xe before it overflows the left shift below
+			// Since i !=0 it has at least one bit still set, so ae will accumulate xe
+			// on at least one more iteration, ae += xe is a lower bound on ae
+			// the lower bound on ae exceeds the size of a float64 exp
+			// so the final call to Ldexp will produce under/overflow (0/Inf)
+			ae += xe
+			break
+		}
+		if i&1 == 1 {
+			a1 *= x1
+			ae += xe
+		}
+		x1 *= x1
+		xe <<= 1
+		if x1 < .5 {
+			x1 += x1
+			xe--
+		}
+	}
+
+	// ans = a1*2**ae
+	// if y < 0 { ans = 1 / ans }
+	// but in the opposite order
+	if y < 0 {
+		a1 = 1 / a1
+		ae = -ae
+	}
+	return Ldexp(a1, ae)
+}