mirror of
https://github.com/Ed94/Odin.git
synced 2026-08-05 15:18:49 +00:00
Add log1p, erf, erfc, ilogb logb (implemented based of FreeBSD's)
This commit is contained in:
gingerBill
@@ -0,0 +1,198 @@
|
||||
package math
|
||||
|
||||
// The original C code, the long comment, and the constants
|
||||
// below are from FreeBSD's /usr/src/lib/msun/src/s_log1p.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.
|
||||
// ====================================================
|
||||
//
|
||||
//
|
||||
// double log1p(double x)
|
||||
//
|
||||
// Method :
|
||||
// 1. Argument Reduction: find k and f such that
|
||||
// 1+x = 2**k * (1+f),
|
||||
// where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
//
|
||||
// Note. If k=0, then f=x is exact. However, if k!=0, then f
|
||||
// may not be representable exactly. In that case, a correction
|
||||
// term is need. Let u=1+x rounded. Let c = (1+x)-u, then
|
||||
// log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
|
||||
// and add back the correction term c/u.
|
||||
// (Note: when x > 2**53, one can simply return log(x))
|
||||
//
|
||||
// 2. Approximation of log1p(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) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
|
||||
// (the values of Lp1 to Lp7 are listed in the program)
|
||||
// and
|
||||
// | 2 14 | -58.45
|
||||
// | Lp1*s +...+Lp7*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
|
||||
// log1p(f) = f - (hfsq - s*(hfsq+R)).
|
||||
//
|
||||
// 3. Finally, log1p(x) = k*ln2 + log1p(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:
|
||||
// log1p(x) is NaN with signal if x < -1 (including -INF) ;
|
||||
// log1p(+INF) is +INF; log1p(-1) is -INF with signal;
|
||||
// log1p(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.
|
||||
//
|
||||
// Note: Assuming log() return accurate answer, the following
|
||||
// algorithm can be used to compute log1p(x) to within a few ULP:
|
||||
//
|
||||
// u = 1+x;
|
||||
// if(u==1.0) return x ; else
|
||||
// return log(u)*(x/(u-1.0));
|
||||
//
|
||||
// See HP-15C Advanced Functions Handbook, p.193.
|
||||
|
||||
log1p :: proc {
|
||||
log1p_f16,
|
||||
log1p_f32,
|
||||
log1p_f64,
|
||||
log1p_f16le,
|
||||
log1p_f16be,
|
||||
log1p_f32le,
|
||||
log1p_f32be,
|
||||
log1p_f64le,
|
||||
log1p_f64be,
|
||||
}
|
||||
log1p_f16 :: proc "contextless" (x: f16) -> f16 { return f16(log1p_f64(f64(x))) }
|
||||
log1p_f32 :: proc "contextless" (x: f32) -> f32 { return f32(log1p_f64(f64(x))) }
|
||||
log1p_f16le :: proc "contextless" (x: f16le) -> f16le { return f16le(log1p_f64(f64(x))) }
|
||||
log1p_f16be :: proc "contextless" (x: f16be) -> f16be { return f16be(log1p_f64(f64(x))) }
|
||||
log1p_f32le :: proc "contextless" (x: f32le) -> f32le { return f32le(log1p_f64(f64(x))) }
|
||||
log1p_f32be :: proc "contextless" (x: f32be) -> f32be { return f32be(log1p_f64(f64(x))) }
|
||||
log1p_f64le :: proc "contextless" (x: f64le) -> f64le { return f64le(log1p_f64(f64(x))) }
|
||||
log1p_f64be :: proc "contextless" (x: f64be) -> f64be { return f64be(log1p_f64(f64(x))) }
|
||||
|
||||
log1p_f64 :: proc "contextless" (x: f64) -> f64 {
|
||||
SQRT2_M1 :: 0h3fda827999fcef34 // Sqrt(2)-1
|
||||
SQRT2_HALF_M1 :: 0hbfd2bec333018866 // Sqrt(2)/2-1
|
||||
SMALL :: 0h3e20000000000000 // 2**-29
|
||||
TINY :: 1.0 / (1 << 54) // 2**-54
|
||||
TWO53 :: 1 << 53 // 2**53
|
||||
LN2HI :: 0h3fe62e42fee00000
|
||||
LN2LO :: 0h3dea39ef35793c76
|
||||
LP1 :: 0h3FE5555555555593
|
||||
LP2 :: 0h3FD999999997FA04
|
||||
LP3 :: 0h3FD2492494229359
|
||||
LP4 :: 0h3FCC71C51D8E78AF
|
||||
LP5 :: 0h3FC7466496CB03DE
|
||||
LP6 :: 0h3FC39A09D078C69F
|
||||
LP7 :: 0h3FC2F112DF3E5244
|
||||
|
||||
switch {
|
||||
case x < -1 || is_nan(x):
|
||||
return nan_f64()
|
||||
case x == -1:
|
||||
return inf_f64(-1)
|
||||
case is_inf(x, 1):
|
||||
return inf_f64(+1)
|
||||
}
|
||||
absx := abs(x)
|
||||
|
||||
f: f64
|
||||
iu: u64
|
||||
k := 1
|
||||
if absx < SQRT2_M1 { // |x| < Sqrt(2)-1
|
||||
if absx < SMALL { // |x| < 2**-29
|
||||
if absx < TINY { // |x| < 2**-54
|
||||
return x
|
||||
}
|
||||
return x - x*x*0.5
|
||||
}
|
||||
if x > SQRT2_HALF_M1 { // Sqrt(2)/2-1 < x
|
||||
// (Sqrt(2)/2-1) < x < (Sqrt(2)-1)
|
||||
k = 0
|
||||
f = x
|
||||
iu = 1
|
||||
}
|
||||
}
|
||||
c: f64
|
||||
if k != 0 {
|
||||
u: f64
|
||||
if absx < TWO53 { // 1<<53
|
||||
u = 1.0 + x
|
||||
iu = transmute(u64)u
|
||||
k = int((iu >> 52) - 1023)
|
||||
// correction term
|
||||
if k > 0 {
|
||||
c = 1.0 - (u - x)
|
||||
} else {
|
||||
c = x - (u - 1.0)
|
||||
}
|
||||
c /= u
|
||||
} else {
|
||||
u = x
|
||||
iu = transmute(u64)u
|
||||
k = int((iu >> 52) - 1023)
|
||||
c = 0
|
||||
}
|
||||
iu &= 0x000fffffffffffff
|
||||
if iu < 0x0006a09e667f3bcd { // mantissa of Sqrt(2)
|
||||
u = transmute(f64)(iu | 0x3ff0000000000000) // normalize u
|
||||
} else {
|
||||
k += 1
|
||||
u = transmute(f64)(iu | 0x3fe0000000000000) // normalize u/2
|
||||
iu = (0x0010000000000000 - iu) >> 2
|
||||
}
|
||||
f = u - 1.0 // Sqrt(2)/2 < u < Sqrt(2)
|
||||
}
|
||||
hfsq := 0.5 * f * f
|
||||
s, R, z: f64
|
||||
if iu == 0 { // |f| < 2**-20
|
||||
if f == 0 {
|
||||
if k == 0 {
|
||||
return 0
|
||||
}
|
||||
c += f64(k) * LN2LO
|
||||
return f64(k)*LN2HI + c
|
||||
}
|
||||
R = hfsq * (1.0 - 0.66666666666666666*f) // avoid division
|
||||
if k == 0 {
|
||||
return f - R
|
||||
}
|
||||
return f64(k)*LN2HI - ((R - (f64(k)*LN2LO + c)) - f)
|
||||
}
|
||||
s = f / (2.0 + f)
|
||||
z = s * s
|
||||
R = z * (LP1 + z*(LP2+z*(LP3+z*(LP4+z*(LP5+z*(LP6+z*LP7))))))
|
||||
if k == 0 {
|
||||
return f - (hfsq - s*(hfsq+R))
|
||||
}
|
||||
return f64(k)*LN2HI - ((hfsq - (s*(hfsq+R) + (f64(k)*LN2LO + c))) - f)
|
||||
}
|
||||
Reference in New Issue
Block a user