sysinfo/fp68k.txt
  misc. 68881/882/040 FPU info

 IEEE floating point types
subnormal	Real, 0 mantissa integer bit.

denormal	Normal exp (not 0/subnormal/INF/NaN), but integer bit is 0.
		The Intel FPU does not handle this.

normal		Real, above exp floor, '1.' integer in mantissa;
		 1.0 is at 1/2 valid range, 3F8/3FF/3FFF8 (S/D/X).

INF		Infinite - at exp ceiling, all zeroes following.

NaN		Not-a-Number - at exp ceiling, signal(quiet) bit, non-zero man.

 Sizes, '1.' integer implied
single/S		32 bits: sign.1 exp.8 man.23; 24 total bits mantissa

double/D		64 bits: sign.1 exp.11 man.52; 53 total bits mantissa

 Sizes, integer-explicit
extended/X	80 bits: sign.1 exp.15 man.64; 64 total bits mantissa

long double	96 bits: two unused bytes after exp for 32-bit alignment

packed decimal	96 bits
 Format (17-digit mantissa)
  S = man sign
  E = exp sign
  C = control
  X = exp
  M = man
  SECC XXXX XXXX XXXX TTTT CCCC CCCC MMMM MMMM ...

 Glue Apple/IBM PowerPC (deprecated)
double double	128 bits: sum high+low
		 >105 total bits mantissa


 Various exceptions - most can be turned off
index	bit	name
14?	2	bad format
48	1	unordered condition
49	3	inexact error
50	4	divide by zero
51	5	underflow error
52	7	operand error
53	6	overflow error
54	0	signaling NAN
55	n/a	unimplemented data type

 FPSR conditional predication bitmask
	#4  IEEE non-aware
	#3  NaN (unordered)
	#2  Negative
	#1  Positive (no condition bits on)
	#0  Zero

 Rounding
  The 68881 has the same rounding and precision modes (S/D/X) as Intel.
  Unlike Intel, the 68881 makes use of three rounding bits for accuracy.
 These are: Guard, Round and Sticky.  The FPU rounds when storing (FPx).


 NaN load values
NOTE: FPSP in NetBSD does not set this (t_operr)
001		root - sign copied at first
002		add/subtract
004		divide
008		multiply
009		modulo (SANE)
033		sin/cos/tan (SANE)
034		acos/asin (math lib)
036		logarithm (SANE)
037		power (SANE)
038		compund/annuity (non-NCEG)
042		gamma (SANE)
255		std QNaN/initial (all ones positive)

 Add/Subtract NaN order
INF-INF		-NAN(002)
INF+-INF	NAN(002)

 Quirks
sqrt(-0)	Intel result: -0; same on 68881?


 Various SANE Functions (in interpreter)

::exp2(double_t n) {
	!isfinite(n) ? n >;
	n>=16384 ? INF >;
	n|0==>x; n-=x; n*n ==> s
	oddpoly(n,s,-1.523098106341779462e-5,
		.02665544475689997673,
		18.97838386125113054,
		1372.201370995018779) ==> n
	scalb(2*n/((s+213.2829591390430817)*s
		+3959.336226071100526-n)+1,x)
}

::log2(n) {
	!isfinite(n) ? n >;
	n<=0 ? n ? -nan(36):-INF >;
	nexp(n) ==> e; nfra(n) ==> n
	if (n<.7071067811865475355)	## .5~/2
		{n+=n; e-=1}
	n-=1 =0 ? e >;
	n/= n+2; n*n ==> s
	oddpoly(n,s,.002827064759880235567,
		.01818284789116497536,
		.1077109054851084084,
		1.247016105029232686,
		-6.419405568907133719,
		5.641063644979311328)
	 /((s-2.8764776622921654)*s
		+1.955043680438308967)+e
}

::log10(n) {
  log2(n)/3.3219280948873623478		## log2(10)
}

::tanh(n) {		##sinh(n)/cosh(n)

	!isfinite(n) ? n >;
	n<=4e-10 ? 0 >;		##2**-31
	n>16 ? 1 >;
	exp1(-n*2) ==> r
	copysign(r/(r+2),n)
}

## the rest are incomplete

::sin(n) {
	+n=NaN ? n >;
	+n=INF ? sNaN(n,33) >;
	frem(n,2*pi) ==> n
	>=pi ? -sin(n-pi) >;
	n>=pi/2 ? cos(n-(pi/2)) >;
	oddpoly(n,n*n,..)
}

## cos(n) is sin(pi/2+n)
::cos(n) {
	+n=NaN ? n >;
	+n=INF ? sNaN(n,33) >;
	+frem(n,2*pi) ==> n
	evenpoly(n,n*n,..)
}
::tan(n) {
	## !isfinite(n) ==> nan(33)
	sin(n)/cos(n)
}

::asin(n) {
	atan(n/sqrt(1-n*n))
}
::acos(n)
	atan(sqrt(1-n*n)/n)
}

::sinh(n) {
	exp(n)/2-exp(-n)/2
}
::cosh(n) {
	exp(n)/2+exp(-n)/2
}