Implement `ln` based off FreeBSD's /usr/src/lib/msun/src/e_log.c

1 files changed, 117 insertions, 7 deletions

diff --git a/core/math/math_basic.odin b/core/math/math_basic.odin
index fe7b07d98..27c9bb366 100644
--- a/core/math/math_basic.odin
+++ b/core/math/math_basic.odin
@@ -33,13 +33,6 @@ foreign _ {
 	@(link_name="llvm.fmuladd.f64")
 	fmuladd_f64 :: proc(a, b, c: f64) -> f64 ---
 
-	@(link_name="llvm.log.f16")
-	ln_f16 :: proc(x: f16) -> f16 ---
-	@(link_name="llvm.log.f32")
-	ln_f32 :: proc(x: f32) -> f32 ---
-	@(link_name="llvm.log.f64")
-	ln_f64 :: proc(x: f64) -> f64 ---
-
 	@(link_name="llvm.exp.f16")
 	exp_f16 :: proc(x: f16) -> f16 ---
 	@(link_name="llvm.exp.f32")
@@ -57,3 +50,120 @@ sqrt_f32 :: proc "contextless" (x: f32) -> f32 {
 sqrt_f64 :: proc "contextless" (x: f64) -> f64 {
 	return intrinsics.sqrt(x)
 }
+
+
+
+ln_f64 :: proc "contextless" (x: f64) -> f64 {
+	// 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.
+	//
+	// ====================================================
+	// 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.
+	
+	LN2_HI :: 0h3fe62e42_fee00000 // 6.93147180369123816490e-01
+	LN2_LO :: 0h3dea39ef_35793c76 // 1.90821492927058770002e-10
+	L1     :: 0h3fe55555_55555593 // 6.666666666666735130e-01
+	L2     :: 0h3fd99999_9997fa04 // 3.999999999940941908e-01
+	L3     :: 0h3fd24924_94229359 // 2.857142874366239149e-01
+	L4     :: 0h3fcc71c5_1d8e78af // 2.222219843214978396e-01
+	L5     :: 0h3fc74664_96cb03de // 1.818357216161805012e-01
+	L6     :: 0h3fc39a09_d078c69f // 1.531383769920937332e-01
+	L7     :: 0h3fc2f112_df3e5244 // 1.479819860511658591e-01
+	
+	switch {
+	case is_nan(x) || is_inf(x, 1):
+		return x
+	case x < 0:
+		return nan_f64()
+	case x == 0:
+		return inf_f64(-1)
+	}
+
+	// reduce
+	f1, ki := frexp(x)
+	if f1 < SQRT_TWO/2 {
+		f1 *= 2
+		ki -= 1
+	}
+	f := f1 - 1
+	k := f64(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*LN2_LO)) - f)
+}
+
+ln_f16 :: proc "contextless" (x: f16) -> f16 { return #force_inline f16(ln_f64(f64(x))) }
+ln_f32 :: proc "contextless" (x: f32) -> f32 { return #force_inline f32(ln_f64(f64(x))) }
+ln_f16le :: proc "contextless" (x: f16le) -> f16le { return #force_inline f16le(ln_f64(f64(x))) }
+ln_f16be :: proc "contextless" (x: f16be) -> f16be { return #force_inline f16be(ln_f64(f64(x))) }
+ln_f32le :: proc "contextless" (x: f32le) -> f32le { return #force_inline f32le(ln_f64(f64(x))) }
+ln_f32be :: proc "contextless" (x: f32be) -> f32be { return #force_inline f32be(ln_f64(f64(x))) }
+ln_f64le :: proc "contextless" (x: f64le) -> f64le { return #force_inline f64le(ln_f64(f64(x))) }
+ln_f64be :: proc "contextless" (x: f64be) -> f64be { return #force_inline f64be(ln_f64(f64(x))) }
+ln :: proc{
+	ln_f16, ln_f16le, ln_f16be,
+	ln_f32, ln_f32le, ln_f32be,
+	ln_f64, ln_f64le, ln_f64be,
+}
\ No newline at end of file