Fast non-754 floating point library for Freescale 56F800E series
We wanted to use floating point but there was no FPU. This is modelled after AD's fast floating point system, with 16-bit manissa and 16-bit exponent, though not exactly the same. It runs about three times faster than regular IEEE754 software floating point. Mostly written in assembly, so only runs on the 56F8000 series of processors. Includes basic trigonometric functions (in C), etc., along with conversion, compare, and arithmetric.
The below from a user manual for our code. It doesn't look so good in plain text. Pdf format available if anyone wants it.
6
3
An Overview of FFloat Numbers
3.1
Format for FFloat Numbers
FFloat numbers are 32-bit
3
binary numbers. They are represented by a mantissa (a fractional
value) multiplied by a base number raised to an exponent (an integral value).
The mantissa is a signed two’s complement
4
16-bit binary number, and is represented by the
rightmost 16 bits of the FFloat number. It has a range between -2
15
(-32768, 0x8000)
5
and 2
15
-1
(32767, 0x7FFF), but is interpreted as a fractional value between -1 (inclusive) and 1 (exclusive).
To get the real fractional value, divide the FFloat mantissa value by 2
15
.
The exponent is also a signed two’s complement 16-bit binary number, and is represented by the
leftmost 16 bits of the FFloat number. Though we have 16 bits to work with, we will only be
using the bottom 8 bits to represent the exponent value, which means that the range of the
exponent is between –2
7
(-128, 0xFF80) and 2
7
-1 (127, 0x007F). The top 8 bits of the exponent
are sign bits: all ones for negative values, and all zeros for nonnegative values.
To get the real floating-point numerical value, we take the real fractional value of the FFloat
mantissa and multiply it by 2 raised to the exponent of the FFloat number:
numerical value = (FFloat mantissa/2
15
)
2^(FFloat exponent).
Even though we are only using 8 bits to represent the exponent, we can represent numbers
between 2
-128
(2.93
10
-39
) and 2
127
(1.70
10
38
), which is more than sufficient for our
calculations.
For convenience, we will represent FFloat numbers in hexadecimal rather than in binary, so that
only 8 digits, instead of 32, are needed (a hexadecimal number can be represented by a 4-bit
binary number).
3.2
Handling Exceptional Values
For FFloat numbers, there are three types of values that must be handled in a special manner:
zero, overflow values, and underflow values.
Zero: We have decided to set zero equal to 0xFF800000. The mantissa is zero, and the exponent
is set to its most negative value (-2
7
). It was determined that if zero is defined this way, our
FFloat addition and subtraction functions could be written without special exception handling for
adding or subtracting zero, thereby saving processing time.
Overflow: Occurs if the magnitude of an FFloat number is larger than 0x007F7FFF (for positive
values) or 0x007F8000 (for negative values). To check for overflow, the exponent of the FFloat
number is compared to the value 0x007F (2
7
-1)
6
. If the FFloat number is determined to be too
3
A bit is a 1 or 0.
4
See Appendix A (Section 6) for a more in-depth discussion on two’s complement.
5
By convention, hexadecimal numbers are preceded by the characters 0x.
6
We used the built-in assembly instruction cmp.w, which compares two 16-bit words.
7
#ifndef ALREADY_READ_FFLOATV2A_H
#define ALREADY_READ_FFLOATV2A_H
/*******************************************************************************
FFloat Number Definitions
*******************************************************************************/
#define MINUSONEFF 0x00008000 //FFloat number -1
#define ZEROFF 0xFF800000 //FFloat number 0
#define ONEFF 0x00014000 //FFloat number 1
#define TWOFF 0x00024000 //FFloat number 2
#define THREEFF 0x00026000 //FFloat number 3
#define FOURFF 0x00034000 //FFloat number 4
#define FIVEFF 0x00035000 //FFloat number 5
#define SIXFF 0x00036000 //FFloat number 6
#define SEVENFF 0x00037000 //FFloat number 7
#define EIGHTFF 0x00044000 //FFloat number 8
#define NINEFF 0x00044800 //FFloat number 9
#define TENFF 0x00045000 //FFloat number 10
#define ELEVENFF 0x00045800 //FFloat number 11
#define TWELVEFF 0x00046000 //FFloat number 12
#define NOMINALBATVOLTAGE 0x00044800
/*******************************************************************************
FFloat Data Type Definition
*******************************************************************************/
typedef unsigned char bool;
typedef long unsigned int ffloat;
/*******************************************************************************
FFloat FUNCTION PROTOTYPES
*******************************************************************************/
asm ffloat FFabs(register ffloat ffnum);
asm ffloat FFneg(register ffloat ffnum);
asm ffloat S16int2FFloat(register short int inum);
asm ffloat S32int2FFloat(register long int inum);
asm ffloat U32int2FFloat(register long unsigned int unum);
asm ffloat FFadd(register ffloat ffnum1,register ffloat ffnum2);
asm ffloat FFdiv(register ffloat ffnum1,register ffloat ffnum2);
asm short int FFloatTrunc2S16int(register ffloat ffnum);
asm short int FFloatRnd2S16int(register ffloat ffnum);
asm ffloat FFmult(register ffloat ffnum1,register ffloat ffnum2);
asm ffloat FFsub(register ffloat ffnum1,register ffloat ffnum2);
asm ffloat IEEE2FFloat(register float fnum);
float FFloat2IEEE(ffloat ffnum);
asm bool FFgt(register ffloat ffnum1, register ffloat ffnum2);
asm bool FFlt(register ffloat ffnum1, register ffloat ffnum2);
asm bool FFgte(register ffloat a, register ffloat b);
asm bool FFlte(register ffloat a, register ffloat b);
asm bool FFgtz(register ffloat ffnum);
asm bool FFltz(register ffloat ffnum);
asm bool FFeqz(register ffloat ffnum);
ffloat FFatan(ffloat xin);
ffloat FFsin(ffloat xin);
ffloat FFcos(ffloat xin);
#endif
**********************************************************
Function code begins below
**********************************************************
#include "FFloatV2A.h"
ffloat FFatan(ffloat xin)
{
int k,klo,khi;
ffloat xdiff0, xdiff1;
ffloat x=xin;
static ffloat xlo = 0x0005b000;
static ffloat xhi = 0x00055000;
static ffloat ya[151] = {0x00019eaa, 0x00019eb5, 0x00019ec0, 0x00019ecc, 0x00019ed8, 0x00019ee4, 0x00019ef1, 0x00019efe, 0x00019f0c, 0x00019f19, 0x00019f28, 0x00019f36, 0x00019f46, 0x00019f55, 0x00019f66, 0x00019f76, 0x00019f88, 0x00019f99, 0x00019fac, 0x00019fbf, 0x00019fd3, 0x00019fe8, 0x00019ffd, 0x0001a013, 0x0001a02a, 0x0001a042, 0x0001a05b, 0x0001a075, 0x0001a090, 0x0001a0ac, 0x0001a0ca, 0x0001a0e9, 0x0001a109, 0x0001a12b, 0x0001a14e, 0x0001a173, 0x0001a19a, 0x0001a1c3, 0x0001a1ee, 0x0001a21c, 0x0001a24c, 0x0001a27f, 0x0001a2b5, 0x0001a2ef, 0x0001a32c, 0x0001a36d, 0x0001a3b3, 0x0001a3fd, 0x0001a44d, 0x0001a4a2, 0x0001a4ff, 0x0001a563, 0x0001a5d0, 0x0001a646, 0x0001a6c7, 0x0001a754, 0x0001a7f0, 0x0001a89d, 0x0001a95d, 0x0001aa33, 0x0001ab25, 0x0001ac37, 0x0001ad71, 0x0001aeda, 0x0001b07f, 0x0001b26e, 0x0001b4bc, 0x0001b785, 0x0001baf1, 0x0001bf38, 0x0000894e, 0x00009757, 0x0000a9a2, 0xffff8292, 0xffffbd49, 0xff800000, 0xffff42b6, 0xffff7d6d, 0x0000565d, 0x000068a8, 0x000076b1, 0x000140c7, 0x0001450e, 0x0001487a, 0x00014b43, 0x00014d91, 0x00014f80, 0x00015125, 0x0001528e, 0x000153c8, 0x000154da, 0x000155cc, 0x000156a2, 0x00015762, 0x0001580f, 0x000158ab, 0x00015938, 0x000159b9, 0x00015a2f, 0x00015a9c, 0x00015b00, 0x00015b5d, 0x00015bb2, 0x00015c02, 0x00015c4c, 0x00015c92, 0x00015cd3, 0x00015d10, 0x00015d4a, 0x00015d80, 0x00015db3, 0x00015de3, 0x00015e11, 0x00015e3c, 0x00015e65, 0x00015e8c, 0x00015eb1, 0x00015ed4, 0x00015ef6, 0x00015f16, 0x00015f35, 0x00015f53, 0x00015f6f, 0x00015f8a, 0x00015fa4, 0x00015fbd, 0x00015fd5, 0x00015fec, 0x00016002, 0x00016017, 0x0001602c, 0x00016040, 0x00016053, 0x00016066, 0x00016077, 0x00016089, 0x00016099, 0x000160aa, 0x000160b9, 0x000160c9, 0x000160d7, 0x000160e6, 0x000160f3, 0x00016101, 0x0001610e, 0x0001611b, 0x00016127, 0x00016133, 0x0001613f, 0x0001614a, 0x00016155};
static ffloat y2a[151] = {0xff800000, 0xfff443e4, 0xfff446b6, 0xfff449b0, 0xfff44cd5, 0xfff45029, 0xfff453af, 0xfff4576a, 0xfff45b5f, 0xfff45f92, 0xfff46408, 0xfff468c6, 0xfff46dd1, 0xfff47331, 0xfff478ec, 0xfff47f0a, 0xfff542c9, 0xfff54648, 0xfff54a06, 0xfff54e0a, 0xfff55259, 0xfff556fa, 0xfff55bf6, 0xfff56156, 0xfff56722, 0xfff56d66, 0xfff5742f, 0xfff57b8a, 0xfff641c3, 0xfff6461c, 0xfff64ad8, 0xfff65004, 0xfff655ac, 0xfff65be0, 0xfff662b0, 0xfff66a30, 0xfff67278, 0xfff67ba1, 0xfff742e5, 0xfff7488b, 0xfff74ed9, 0xfff755e6, 0xfff75dd0, 0xfff766ba, 0xfff770cc, 0xfff77c39, 0xfff8449e, 0xfff84c0f, 0xfff8549c, 0xfff85e7b, 0xfff869ef, 0xfff8774e, 0xfff9437f, 0xfff94cc5, 0xfff957cc, 0xfff96504, 0xfff974fc, 0xfffa4439, 0xfffa5032, 0xfffa5f16, 0xfffa71cd, 0xfffb44d0, 0xfffb542e, 0xfffb684a, 0xfffc4182, 0xfffc538f, 0xfffc6c5c, 0xfffd4779, 0xfffd5fe2, 0xfffe4133, 0xfffe5918, 0xfffe77b6, 0xffff4b62, 0xffff503a, 0xfffe707d, 0xff800000, 0xfffe8f82, 0xffffafc5, 0xffffb49d, 0xfffe8849, 0xfffea6e7, 0xfffebecc, 0xfffda01d, 0xfffdb886, 0xfffc93a3, 0xfffcac70, 0xfffcbe7d, 0xfffb97b5, 0xfffbabd1, 0xfffbbb2f, 0xfffa8e32, 0xfffaa0e9, 0xfffaafcd, 0xfffabbc6, 0xfff98b03, 0xfff99afb, 0xfff9a833, 0xfff9b33a, 0xfff9bc80, 0xfff888b1, 0xfff89610, 0xfff8a184, 0xfff8ab63, 0xfff8b3f0, 0xfff8bb61, 0xfff783c6, 0xfff78f33, 0xfff79945, 0xfff7a22f, 0xfff7aa19, 0xfff7b126, 0xfff7b774, 0xfff7bd1a, 0xfff6845e, 0xfff68d87, 0xfff695cf, 0xfff69d4f, 0xfff6a41f, 0xfff6aa53, 0xfff6affb, 0xfff6b527, 0xfff6b9e3, 0xfff6be3c, 0xfff58475, 0xfff58bd0, 0xfff59299, 0xfff598dd, 0xfff59ea9, 0xfff5a409, 0xfff5a905, 0xfff5ada6, 0xfff5b1f5, 0xfff5b5f9, 0xfff5b9b7, 0xfff5bd36, 0xfff480f5, 0xfff48713, 0xfff48cce, 0xfff4922e, 0xfff49739, 0xfff49bf7, 0xfff4a06d, 0xfff4a4a0, 0xfff4a895, 0xfff4ac50, 0xfff4afd6, 0xfff4b32a, 0xfff4b64f, 0xfff4b949, 0xfff4bc1b, 0xfff4bc1b};
static int numpoints = 151;
static ffloat h = 0xffff4444;
static ffloat hinv = 0x00027800;
klo = FFloatTrunc2S16int(FFmult(FFsub(x,xlo),hinv));
khi=klo+1;
if(FFlt(x,xlo)){
return(ya[0]);
}else if(FFgt(x,xhi)){
return(ya[numpoints-1]);
}
xdiff0 = FFsub(x, FFadd(xlo, FFmult(h,S16int2FFloat(klo))));
xdiff1 = FFsub(xdiff0, h);
return ( FFadd(ya[klo], FFadd(FFmult(FFmult(FFsub(ya[khi],ya[klo]), hinv), xdiff0), FFmult(FFmult(y2a[khi], xdiff0), xdiff1))) );
}
ffloat FFcos(ffloat xin)
{
int k,klo,khi;
ffloat xdiff0, xdiff1;
ffloat x=xin;
static ffloat xlo = 0x00029b78;
static ffloat xhi = 0x00026487;
static ffloat ya[31] = {0x00008000, 0x000082cc, 0x00008b10, 0x00009872, 0x0000aa59, 0xffff8000, 0xffffb0e4, 0xfffd94f6, 0xfffd6b09, 0xffff4f1b, 0x00004000, 0x000055a6, 0x0000678d, 0x000074ef, 0x00007d33, 0x00014000, 0x00007d33, 0x000074ef, 0x0000678d, 0x000055a6, 0x00004000, 0xffff4f1b, 0xfffd6b09, 0xfffd94f6, 0xffffb0e4, 0xffff8000, 0x0000aa59, 0x00009872, 0x00008b10, 0x000082cc, 0x00008000};
static ffloat y2a[31] = {0xff800000, 0xffff7cbe, 0xffff7481, 0xffff672d, 0xffff5556, 0xfffe7f88, 0xfffe4ed1, 0xfffc6aa5, 0xfffc955a, 0xfffeb12e, 0xfffe8077, 0xffffaaa9, 0xffff98d2, 0xffff8b7e, 0xffff8341, 0xffff8077, 0xffff8341, 0xffff8b7e, 0xffff98d2, 0xffffaaa9, 0xfffe8077, 0xfffeb12e, 0xfffc955a, 0xfffc6aa5, 0xfffe4ed1, 0xfffe7f88, 0xffff5556, 0xffff672d, 0xffff7481, 0xffff7cbe, 0xffff7cbe};
static int numpoints = 31;
static ffloat h = 0xfffe6b3b;
static ffloat hinv = 0x00034c64;
static ffloat pi2=0x00036487;
static ffloat pi2inv=0xfffe517c;
if(FFlt(xin,xlo)){
x=FFadd(
xin,
FFmult(
S16int2FFloat(
FFloatTrunc2S16int(
FFmult(
FFsub(xhi,xin),
pi2inv
)
)
),
pi2
)
);
}else if(FFgt(xin,xhi)){
x=FFsub(
xin,
FFmult(
S16int2FFloat(
FFloatTrunc2S16int(
FFmult(
FFsub(xin,xlo),
pi2inv
)
)
),
pi2
)
);
}
klo = FFloatTrunc2S16int(FFmult(FFsub(x,xlo),hinv));
khi=klo+1;
xdiff0 = FFsub(x, FFadd(xlo, FFmult(h,S16int2FFloat(klo))));
xdiff1 = FFsub(xdiff0, h);
return ( FFadd(ya[klo], FFadd(FFmult(FFmult(FFsub(ya[khi],ya[klo]), hinv), xdiff0), FFmult(FFmult(y2a[khi], xdiff0), xdiff1))) );
}
//Return the negative of ffnum
asm ffloat FFneg(register ffloat ffnum)
{
move.w A1,Y0 //store ffnum exp in Y0
move.w A0,A //A holds mantissa of ffnum
neg A //full 36-bit negate
asr A //shift right to prevent overflow of clb
jeq Zero //Don't normalize if zero
//ffnum != 0
clb A,X0 //Count sign bits
asll.l X0,A //Normalize
sub X0,Y0 //Adjust exponent
inc.w Y0 //Return to normal scale
clb Y0,X0 //check number of sign bits in exponent
cmp.w #8,X0 //If less than 8 (exp > 8 bits),
jlt Exp_Err //jump to exponent exception handler
Continue:
rtsd //delayed return from subroutine
move.w A1,A0 //Move mantissa of sum to lower word of ffnum1 (return value)
move.w Y0,A1 //Move exponent to upper word of ffnum1 (return value)
sxt.l A //Sign-extend A to 36 bits
//end of main neg function
Zero:
rtsd //Delayed return from subroutine - will execute next three words
move.w #$FF80,A //Set exp of sum to minimum
clr.w A0 //Set mantissa of sum to 0
//end of zero handler
Exp_Err:
cmp.w #$007F,Y0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop //Delay slot filler
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three cycles
move.w #$8000,A0 //Most negative mantissa
nop //Delay slot filler
//end
Underflow:
cmp.w #$FF80,Y0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
}
//Return the absolute value of ffnum
asm ffloat FFabs(register ffloat ffnum)
{
move.w A1,Y0 //store ffnum exp in Y0
move.w A0,A //A holds mantissa of ffnum
abs A //full-width absolute value
asr A //shift right to prevent overflow of clb
jeq Zero //Don't normalize if zero
//ffnum != 0
clb A,X0 //Count sign bits
asll.l X0,A //Normalize
sub X0,Y0 //Adjust exponent
inc.w Y0 //Return to normal scale
clb Y0,X0 //check number of sign bits in exponent
cmp.w #8,X0 //If less than 8 (exp > 8 bits),
jlt Exp_Err //jump to exponent exception handler
Continue:
rtsd //delayed return from subroutine
move.w A,A0 //Move mantissa of sum to lower word of ffnum1 (return value)
move.w Y0,A1 //Move exponent to upper word of ffnum1 (return value)
sxt.l A //Sign-extend A to 36 bits
//end of main abs function
Zero:
rtsd //Delayed return from subroutine - will execute next three words
move.w #$FF80,A //Set exp of sum to minimum
clr.w A0 //Set mantissa of sum to 0
//end of zero handler
Exp_Err:
cmp.w #$007F,Y0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop //Delay slot filler
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three cycles
move.w #$8000,A0 //Most negative mantissa
nop //Delay slot filler
//end
Underflow:
cmp.w #$FF80,Y0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
}
//convert an int16 to an ffloat value
asm ffloat S16int2FFloat(register short int inum)
{
tst.w Y0
jeq Zero
//inum != 0
clb Y0,X0
asll.l X0,Y0 //normalize inum
neg X0 //set exponent
rtsd
add.w #15,X0
move.w X0,A //exponent
move.w Y0,A0 //mantissa
//FFloat zero = 0xFF800000
Zero:
rtsd
move.w #$FF80,A
clr.w A0
}
asm ffloat FFadd(register ffloat ffnum1,register ffloat ffnum2)
{
move.w A0,X0 //Store ffnum1 mantissa temporarily in X0
move.w B0,Y0 //Store ffnum2 mantissa temporarily in Y0
move.w A1,Y1 //Put ffnum1 exponent (exp1) in Y1
sub B,Y1 //Y1 = exp1 - exp2
//Setup: Larger ffnum exponent goes in Y0; mantissa to be shifted goes in B1;
//mantissa to stay the same goes in A1; abs exp difference goes in Y1
tlt B,A //Move ffnum2 (mantissa and exp) to A (not shifted) if Y1 neg
tlt X0,B //Move ffnum1 mantissa to B1 for shifting if Y1 neg
tge Y0,B //Move ffnum2 mantissa to B1 for shifting if Y1 not negative
abs Y1 //positive shift values
cmp.w #15,Y1 //More than 15-bit shift (ASRAC only works to 15 bits)?
jgt Neglect //If yes, an input ffnum will go to zero if shifted
move.w A1,Y0 //Move larger exp to Y0 for shifting
move.w A0,A //Move mantissa A0 to A1 for adding
asrac B1,Y1,A //Extend B1 to 36 bits, shift right by Y1, and add to A
asr A //Shift right to prevent overflow of CLB (next)
clb A,X0 //Count sign bits
asll.l X0,A //Normalize
tst.w A1 //Check if relevant part of result is zero
jeq Zero //Result is zero
sub X0,Y0 //Adjust exponent of exp1
inc.w Y0 //Return to normal scale
clb Y0,X0 //check number of sign bits in exponent
cmp.w #8,X0 //If less than 8 (exp > 8 bits),
jlt Exp_Err //jump to exponent exception handler
Continue:
rnd A //round to 16 bits in A1
rtsd //delayed return from subroutine
move.w A,A0 //Move mantissa of sum to lower word of ffnum1 (return value)
move.w Y0,A1 //Move exponent to upper word of ffnum1 (return value)
sxt.l A //Sign-extend A to 36 bits
//end of main add function
Zero:
rtsd //Delayed return from subroutine - will execute next three words
move.w #$FF80,A //Set exp of sum to minimum
clr.w A0 //Set mantissa of sum to 0
//end of zero handler
Exp_Err:
cmp.w #$007F,Y0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop //Delay slot filler
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three cycles
move.w #$8000,A0 //Most negative mantissa
nop //Delay slot filler
//end
Underflow:
cmp.w #$FF80,Y0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
Neglect:
rts //The input with the larger exp becomes the output
}
asm ffloat FFdiv(register ffloat ffnum1, register ffloat ffnum2)
{
move.w A1,X0 //Move exponent of ffnum1 to X0
move.w B1,Y0 //Move exponent of ffnum2 to Y0
move.w A0,Y1 //Move mantissa of ffnum1 to Y1 for sign check
move.w A0,A //Move mantissa of ffnum1 to A1
move.w B0,B //Move mantissa of ffnum2 to B1
eor.w B,Y1 //Calculate sign of final result
//(sign bit of result will be 1=negative if inputs signs differ)
abs A
abs B
jeq DivZero //ffnum2 cannot be zero
L1:
cmp A,B //Check result of B - A
bgt L2 //Ready to divide
brad L1 //Recheck (delayed branch)
asr A //Reduce ffnum1 mantissa by factor of 2
inc.w X0 //Increase ffnum1 exponent by one
//end
L2:
//Division of Positive Fractional Data (A1:A0 / B1)
BFCLR #$0001,SR //Clear carry bit: required for 1st DIV instruction
//REP #16
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
DIV B1,A //Form positive quotient in A0
move.w A0,A //Move A0 to A1
tst.w Y1 //Check sign needed for final result
BGE L3 //Branch if final sign is non-neg
NEG A //Negate mantissa if result is neg
L3:
clb A,Y1 //Count sign bits
asll.l Y1,A //Normalize
tst A //Check if relevant part of result is zero
jeq Zero //Result is zero
sub Y0,X0 //Adjust exponent of exp1
sub Y1,X0
clb X0,Y0 //check size of exponent word
cmp.w #8,Y0
jlt Exp_Err
Continue:
RTSD
MOVE.W A,A0
MOVE.W X0,A1
sxt.l A //Sign-extend A to 36 bits
//END
DivZero:
//Call error handler here
MOVE.W #$007F,A //Needs work here
RTSD
MOVE.W #$7FFF,A0
NOP
//END
Zero:
RTSD
MOVE.W #$FF80,A
CLR.W A0
//END
Exp_Err:
cmp.w #$007F,X0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$8000,A0 //Most negative mantissa
nop //filler for third delay slot
//end
Underflow:
cmp.w #$FF80,X0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
}
asm short int FFloatRnd2S16int(register ffloat ffnum)
{
move.w A1,Y0
move.w A0,A
//Scale so that exponent = 15; converts mantissa to integer scale
//Check if resulting mantissa is in range -32768 to 32767 (16 bit signed int)
sub.w #15,Y0
jgt Over //Number is outside range -32768 to 32767
cmp.w #-17,Y0
jlt Zero //Number is small and rounds to zero
rtsd
asll.l Y0,A //Scale to exponent = 15 (one word, two cycles)
rnd A //Convergent rounding (round down boundary case if even)
move.w A1,Y0
//end
Zero:
rtsd
clr.w Y0 //Result is zero
nop
nop
//end
Over:
tst A
blt Neg //branch to Neg: if number is below -32768
rtsd
move.w #$7FFF,Y0 //Set to most positive 16-bit value
nop //Filler for third delay slot
//end
Neg:
rtsd
move.w #$8000,Y0 //Set to most negative 16-bit value
nop //Filler for third delay slot
//end
}
asm short int FFloatTrunc2S16int(register ffloat ffnum)
{
move.w A1,Y0
move.w A0,A
//Scale so that exponent = 15; converts mantissa to integer scale
//Check if resulting mantissa is in range -32768 to 32767 (16 bit signed int)
sub.w #15,Y0
jgt Over //Number is outside range -32768 to 32767
cmp.w #-17,Y0
jlt Zero //Number is small and rounds to zero
rtsd
asll.l Y0,A //Scale to exponent = 15 (one word, two cycles)
move.w A1,Y0
nop //Filler for third delay slot
//end
Zero:
rtsd
clr.w Y0 //Result is zero
nop
nop
//end
Over:
tst A
blt Neg //branch to Neg: if number is below -32768
rtsd
move.w #$7FFF,Y0 //Set to most positive 16-bit value
nop //Filler for third delay slot
//end
Neg:
rtsd
move.w #$8000,Y0 //Set to most negative 16-bit value
nop //Filler for third delay slot
//end
}
//convert an unsigned int32 to an ffloat value
asm ffloat U32int2FFloat(register long unsigned int unum)
{
tst.l A
jeq Zero //unum = 0
jlt LongUnsigned //If 2^31 <= unum <= 2^32-1, unum will
//be a negative number
//unum <= 2^31 - 1
clb A,X0
asll.l X0,A //normalize unum
neg X0 //set exponent
add.w #31,X0
rtsd
move.w A1,A0 //mantissa
move.w X0,A1 //exponent
sxt.l A //sign-extend A to 36 bits
//FFloat zero = 0xFF800000
Zero:
rtsd
move.w #$FF80,A
clr.w A0
//If unum is between 2^31 and 2^32-1
LongUnsigned:
lsr.w A //divide mantissa by 2
move.w A1,A0 //move mantissa to its right place
//divide the mantissa by two and increase the exponent by 1
//this will correct the sign of A while keeping the absolute
//value of a the same
rtsd
move.w #32,A1 //exponent will always be 32 for this case
sxt.l A //sign-extend A to 36 bits
}
//convert an int32 to an ffloat value
asm ffloat S32int2FFloat(register long int inum)
{
//inum = 0
tst.l A
jeq Zero
//inum != 0
clb A,X0
asll.l X0,A //normalize inum
neg X0 //set exponent
add.w #31,X0
rtsd
move.w A1,A0 //mantissa
move.w X0,A1 //exponent
sxt.l A //sign-extend A to 36 bits
//FFloat zero = 0xFF800000
Zero:
rtsd
move.w #$FF80,A
clr.w A0
}
//typedef long unsigned int ffloat;
asm ffloat FFmult(register ffloat ffnum1, register ffloat ffnum2)
{
move.w B1,Y1 //This is to save exp2, use B for mult, and prepare for exp add
move.w A0,X0 //Can't multiply A0,B0 directly
move.w B0,Y0
mpyr X0,Y0,B //Multiply with round; result unlikely to differ from mpy, since truncated later
asr B //Shift right, so CLB can give correct count
clb B,X0 //Count sign bits for normalization
asll.l X0,B //Normalize
tst.w B1 //Check if relevant part of result is zero
jeq Zero //Go to zero handler
add A,Y1 //add A1 to Y1
sub X0,Y1 //Update exponent after normalization
inc.w Y1 //Return to normal scale
clb Y1,Y0 //count sign bits in exponent word
cmp.w #8,Y0 //If <8 (exp > 8 bits),
jlt Exp_Err //jump to exponent exception handler
Continue:
rtsd //return with 3-cyle delay
move.w Y1,A //Put exp in return register
rnd B //Round to 16 bits in B1
move.w B1,A0 //Move mantissa to A0
//end of mult routine
Zero:
rtsd //return with 3-cyle delay
move.w #$FF80,A //Set exp of sum to minimum
clr.w A0 //Set mantissa of sum to 0
//end of zero handler
Exp_Err:
cmp.w #$007F,Y1 //Check for overflow
jle Underflow //If not overflow, go to underflow check
tst.w B1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$7FFF,A0 //Max out mantissa
rtsd //Delayed return - will execute next three words
nop //Filler for third delay slot
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return - will execute next three words
move.w #$8000,A0 //Most negative mantissa
nop //Filler for third delay slot
//end
Underflow:
cmp.w #$FF80,Y1 //Check for underflow
jge Continue //Not an error - continue normal code
tst.w B1 //Positive or negative overflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return - will execute next three words
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //Filler for third delay slot
//end of Exp_Err
}
asm ffloat FFsub(register ffloat ffnum1,register ffloat ffnum2)
{
move.w A0,X0 //Store ffnum1 mantissa temporarily in X0
move.w B1,Y1 //Store ffnum2 mantissa temporarily in Y1
move.w B0,B //Prepare to negate B
asr B //Prevent overflow
inc.w Y1 //Adjust exponent
neg B //Negate
clb B,Y0 //Count leading bits
asll.l Y0,B //rescale
sub Y0,Y1 //adjust exponent
move.w B1,Y0
move.w Y1,B
move.w Y0,B0
move.w A1,Y1 //Put ffnum1 exponent (exp1) in Y1
sub B,Y1 //Y1 = exp1 - exp2
//Setup: Larger ffnum exponent goes in Y0; mantissa to be shifted goes in B1;
//mantissa to stay the same goes in A1; abs exp difference goes in Y1
tlt B,A //Move ffnum2 (mantissa and exp) to A (not shifted) if Y1 neg
tlt X0,B //Move ffnum1 mantissa to B1 for shifting if Y1 neg
tge Y0,B //Move ffnum2 mantissa to B1 for shifting if Y1 not negative
abs Y1 //positive shift values
cmp.w #15,Y1 //More than 15-bit shift (ASRAC only works to 15 bits)?
jgt Neglect //If yes, an input ffnum will go to zero if shifted
move.w A1,Y0 //Move larger exp to Y0 for shifting
move.w A0,A //Move mantissa A0 to A1 for adding
asrac B1,Y1,A //Extend B1 to 36 bits, shift right by Y1, and add to A
asr A //Shift right to prevent overflow of CLB (next)
clb A,X0 //Count sign bits
asll.l X0,A //Normalize
tst.w A1 //Check if relevant part of result is zero
jeq Zero //Result is zero
sub X0,Y0 //Adjust exponent of exp1
inc.w Y0 //Return to normal scale
clb Y0,X0 //check size of exponent word
cmp.w #8,X0
jlt Exp_Err
Continue:
rnd A //Round to 16 bits
rtsd //delayed return from subroutine
move.w A,A0 //Move mantissa of sum to lower word of ffnum1 (return value)
move.w Y0,A1 //Move exponent to upper word of ffnum1 (return value)
sxt.l A //Sign-extend A to 36 bits
//end of main add function
Zero:
rtsd //Delayed return from subroutine - will execute next three inst.
move.w #$FF80,A //Set exp of sum to minimum
clr.w A0 //Set mantissa of sum to 0
//end of zero handler
Exp_Err:
cmp.w #$007F,Y0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop //filler for third delay slot
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$8000,A0 //Most negative mantissa
nop //filler for third delay slot
//end
Underflow:
cmp.w #$FF80,Y0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU //If negative, go to negative handler
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three inst.
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three inst.
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
Neglect:
rts //The input with the larger exp becomes the output
}
asm ffloat IEEE2FFloat(register float fnum)
{
bftstl #$7F80,A1
jcs Zero //For IEEE, zero is indicated by zero exp.
move.w A1,Y0
bfclr #$FF00,A1
sxt.l A //Sign-extend A to 36 bits
bfset #$0080,A1
brclr #$8000,Y0,L1 //Branch if sign bit is positive
neg A //Negate mantissa if sign bit is negative
L1:
clb A,X0 //Normalize mantissa
asll.l X0,A
bfclr #$807F,Y0
lsrr.w #7,Y0
sub.w #119,Y0
sub X0,Y0 //FFloat exponent is ready
clb Y0,X0 //Check for overflow/underflow
cmp.w #8,X0
jlt Exp_Err
Continue:
rnd A
rtsd
move.w A,A0
move.w Y0,A1
sxt.l A //Sign-extend A to 36 bits
//end
Zero:
RTSD
MOVE.W #$FF80,A
CLR.W A0
//END
Exp_Err:
cmp.w #$007F,Y0
jle Underflow //If not overflow, go to underflow check
tst.w A1 //Positive or negative overflow?
jlt NegO //If negative, go to negative handler
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$7FFF,A0 //Max out mantissa
nop //filler for third delay slot
//end
NegO:
move.w #$007F,A //Max out exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$8000,A0 //Most negative mantissa
nop //filler for third delay slot
//end
Underflow:
cmp.w #$FF80,Y0 //Check for underflow
jge Continue //Not an error
tst.w A1 //Positive or negative underflow?
jlt NegU
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$4000,A0 //Minimum normalized positive mantissa
nop //Filler for third delay slot
//end
NegU:
move.w #$FF80,A //Minimum exponent
rtsd //Delayed return from subroutine - will execute next three words
move.w #$BFFF,A0 //Minimum (abs) normalized negative mantissa
nop //filler for third delay slot
//end of E_Err
}
//A not very good C function. Ok for testing other functions in simulation.
//Converts an FFloat number to an IEEE 754-compatible single precision floating point number.
//typedef long unsigned int ffloat;
float FFloat2IEEE(ffloat ffnum)
{
float fout = 0;
long int iexp = 0;
long unsigned int tempout = 0, sign = 0, mantissa = 0, exp = 0;
void *VoidPointer;
float *FloatPointer;
long unsigned int *LintPointer;
if (ffnum&0xFFFF) //ffnum is not zero
{
mantissa = ffnum & 0x0000FFFF;
exp = ffnum&0xFFFF0000;
iexp = (long int)exp;
iexp += 0x007F0000; //Bias exponent positive by 127
if (iexp < 0x00010000) //Limit exponent size to allowed IEEE range
{
iexp = 0x00010000;
}
else if (iexp > 0x00FE0000)
{
iexp = 0x00FE0000;
}
if (mantissa&0x00008000) //ffnum is negative
{
sign = 0x80000000;
mantissa ^= 0x0000FFFF; //Negate
mantissa++;
}
while (!(mantissa&0x8000)) //normalize
{
mantissa <<= 1;
iexp -= 0x00010000;
}
if (iexp < 0x00010000) //Limit exponent size to allowed IEEE range
{
iexp = 0x00010000;
}
else if (iexp > 0x00FE0000)
{
iexp = 0x00FE0000;
}
exp = (long unsigned int)iexp;
exp <<= 7; //Shift exponent to correct position
mantissa <<= 8; //Shift to correct IEEE position
mantissa &= 0x007FFFFF; //Clear leading one
tempout = sign | exp | mantissa;
}
else exp = 0x00000000; //zero
VoidPointer = &(tempout); //obtain pointer to unsigned long int tempout
FloatPointer = VoidPointer; //convert to float
fout = *FloatPointer;
return(fout);
}
//return true if ffnum1>ffnum2, false otherwise
asm bool FFgt(register ffloat ffnum1, register ffloat ffnum2)
{
//First compare signs of numbers
tst.w A0
blt CheckSignANeg
//a is nonnegative
tst.w B0
//Both numbers are nonnegative - nonnegative exponents case
bge CasePNumExp
//If b is negative, a>b
rtsd
move.w #1,Y0
nop
nop
//a is negative
CheckSignANeg:
tst.w B0
//Both numbers are negative - negative exponents case
blt CaseNNumExp
//If b is nonnegative, a<b
rtsd
move.w #0,Y0
nop
nop
//If a and b are positive, go here
//larger exponent = larger #
CasePNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
blt aGTb //if(expB<expA) then a>b
bgt aNotGTb //if(expB>expA) then !(a>b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
blt aGTb //if(mantissaB<mantissaA) then a>b
rtsd
move.w #0,Y0
nop
nop
//If a and b are negative, go here
//larger exponent = smaller #
CaseNNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
bgt aGTb //if(expB>expA) then a>b
blt aNotGTb //if(expB<expA) then !(a>b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
blt aGTb //if(mantissaB<mantissaA) then a>b
rtsd
move.w #0,Y0
nop
nop
//if a>b, go here
aGTb:
rtsd
move.w #1,Y0
nop
nop
//if a<=b, go here
aNotGTb:
rtsd
move.w #0,Y0
nop
nop
}
//return true if ffnum>0, false otherwise
asm bool FFgtz(register ffloat ffnum)
{
//Test ffnum mantissa
tst.w A0
bgt Positive
//ffnum <= 0
rtsd //delayed return
clr.w Y0 //return value 0
nop //first filler instruction
nop //second filler instruction
//end
Positive:
//ffnum > 0
rtsd //delayed return
move.w #1,Y0 //return value 1
nop //first filler instruction
nop //second filler instruction
//end
}
//return true if ffnum<0, false otherwise
asm bool FFltz(register ffloat ffnum)
{
//Test ffnum mantissa
tst.w A0
blt Negative
//ffnum >= 0
rtsd //delayed return
clr.w Y0 //return value 0
nop //first filler instruction
nop //second filler instruction
//end
Negative:
//ffnum < 0
rtsd //delayed return
move.w #1,Y0 //return value 1
nop //first filler instruction
nop //second filler instruction
//end
}
//return true if ffnum=0, false otherwise
asm bool FFeqz(register ffloat ffnum)
{
//Test ffnum mantissa
tst.w A0
beq Zero
//ffnum != 0
rtsd //delayed return
clr.w Y0 //return value 0
nop //first filler instruction
nop //second filler instruction
//end
Zero:
//ffnum < 0
rtsd //delayed return
move.w #1,Y0 //return value 1
nop //first filler instruction
nop //second filler instruction
//end
}
//return true if ffnum1<ffnum2, false otherwise
asm bool FFlt(register ffloat ffnum1, register ffloat ffnum2)
{
//First compare signs of numbers
tst.w A0
blt CheckSignANeg
//a is nonnegative
tst.w B0
//Both numbers are nonnegative - nonnegative exponents case
bge CasePNumExp
//If b is negative, !(a<b)
rtsd
move.w #0,Y0
nop
nop
//a is negative
CheckSignANeg:
tst.w B0
//Both numbers are negative - negative exponents case
blt CaseNNumExp
//If b is nonnegative, a<b
rtsd
move.w #1,Y0
nop
nop
//If a and b are positive, go here
//larger exponent = larger #
CasePNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
bgt aLTb //if(expB>expA) then a<b
blt aNotLTb //if(expB<expA) then !(a<b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
bgt aLTb //if(mantissaB>mantissaA) then a<b
rtsd
move.w #0,Y0
nop
nop
//If a and b are negative, go here
//larger exponent = smaller #
CaseNNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
blt aLTb //if(expB<expA) then a<b
bgt aNotLTb //if(expB>expA) then !(a<b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
bgt aLTb //if(mantissaB>mantissaA) then a<b
rtsd
move.w #0,Y0
nop
nop
//if a<b, go here
aLTb:
rtsd
move.w #1,Y0
nop
nop
//if a>=b, go here
aNotLTb:
rtsd
move.w #0,Y0
nop
nop
}
//return true if a>=b, false otherwise
asm bool FFgte(register ffloat a, register ffloat b)
{
//First compare signs of numbers
tst.w A0
blt CheckSignANeg
//a is nonnegative
tst.w B0
//Both numbers are nonnegative - nonnegative exponents case
bge CasePNumExp
//If b is negative, a>=b
rtsd
move.w #1,Y0
nop
nop
//a is negative
CheckSignANeg:
tst.w B0
//Both numbers are negative - negative exponents case
blt CaseNNumExp
//If b is nonnegative, a<b
rtsd
move.w #0,Y0
nop
nop
//If a and b are positive, go here
//larger exponent = larger #
CasePNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
blt aGTEb //if(expB<expA) then a>=b
bgt aNotGTEb //if(expB>expA) then !(a>=b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
ble aGTEb //if(mantissaB<=mantissaA) then a>=b
rtsd
move.w #0,Y0
nop
nop
//If a and b are negative, go here
//larger exponent = smaller #
CaseNNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
bgt aGTEb //if(expB>expA) then a>b
blt aNotGTEb //if(expB<expA) then !(a>b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
ble aGTEb //if(mantissaB<=mantissaA) then a>=b
rtsd
move.w #0,Y0
nop
nop
//if a>=b, go here
aGTEb:
rtsd
move.w #1,Y0
nop
nop
//if a<b, go here
aNotGTEb:
rtsd
move.w #0,Y0
nop
nop
}
//return true if a<=b, false otherwise
asm bool FFlte(register ffloat a, register ffloat b)
{
//First compare signs of numbers
tst.w A0
blt CheckSignANeg
//a is nonnegative
tst.w B0
//Both numbers are nonnegative - nonnegative exponents case
bge CasePNumExp
//If b is negative, !(a<=b)
rtsd
move.w #0,Y0
nop
nop
//a is negative
CheckSignANeg:
tst.w B0
//Both numbers are negative - negative exponents case
blt CaseNNumExp
//If b is nonnegative, a<b
rtsd
move.w #1,Y0
nop
nop
//If a and b are positive, go here
//larger exponent = larger #
CasePNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
bgt aLTEb //if(expB>expA) then a<=b
blt aNotLTEb //if(expB>expA) then !(a<=b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
bge aLTEb //if(mantissaB>=mantissaA) then a>=b
rtsd
move.w #0,Y0
nop
nop
//If a and b are negative, go here
//larger exponent = smaller #
CaseNNumExp:
//move exponent data to X0 and Y0 registers for comparison
move.w A1,X0
move.w B1,Y0
cmp.w X0,Y0
blt aLTEb //if(expB<expA) then a<=b
bgt aNotLTEb //if(expB>expA) then !(a<=b)
//If exponents are equal, check mantissas
move.w A0,X0
move.w B0,Y0
cmp.w X0,Y0
bge aLTEb //if(mantissaB>=mantissaA) then a>=b
rtsd
move.w #0,Y0
nop
nop
//if a<=b, go here
aLTEb:
rtsd
move.w #1,Y0
nop
nop
//if a>b, go here
aNotLTEb:
rtsd
move.w #0,Y0
nop
nop
}
ffloat FFsin(ffloat xin)
{
int k,klo,khi;
ffloat xdiff0, xdiff1;
ffloat x=xin;
static ffloat xlo = 0x00029b78;
static ffloat xhi = 0x00026487;
static ffloat ya[31] = {0xffccb968, 0xfffe958c, 0xffff97e0, 0x0000b4c3, 0x0000a0e0, 0x00009126, 0x00008643, 0x000080b3, 0x000080b3, 0x00008643, 0x00009126, 0x0000a0e0, 0x0000b4c3, 0xffff97e0, 0xfffe958c, 0xff800000, 0xfffe6a73, 0xffff681f, 0x00004b3c, 0x00005f1f, 0x00006ed9, 0x000079bc, 0x00007f4c, 0x00007f4c, 0x000079bc, 0x00006ed9, 0x00005f1f, 0x00004b3c, 0xffff681f, 0xfffe6a73, 0xffcc4698};
static ffloat y2a[31] = {0xff800000, 0xfffd6a0f, 0xfffe67be, 0xffff4af6, 0xffff5ec6, 0xffff6e72, 0xffff794a, 0xffff7ed5, 0xffff7ed5, 0xffff794a, 0xffff6e72, 0xffff5ec6, 0xffff4af6, 0xfffe67be, 0xfffd6a0f, 0xff800000, 0xfffd95f0, 0xfffe9841, 0xffffb509, 0xffffa139, 0xffff918d, 0xffff86b5, 0xffff812a, 0xffff812a, 0xffff86b5, 0xffff918d, 0xffffa139, 0xffffb509, 0xfffe9841, 0xfffd95f0, 0xfffd95f0};
static int numpoints = 31;
static ffloat h = 0xfffe6b3b;
static ffloat hinv = 0x00034c64;
static ffloat pi2=0x00036487;
static ffloat pi2inv=0xfffe517c;
if(FFlt(xin,xlo)){
x=FFadd(
xin,
FFmult(
S16int2FFloat(
FFloatTrunc2S16int(
FFmult(
FFsub(xhi,xin),
pi2inv
)
)
),
pi2
)
);
}else if(FFgt(xin,xhi)){
x=FFsub(
xin,
FFmult(
S16int2FFloat(
FFloatTrunc2S16int(
FFmult(
FFsub(xin,xlo),
pi2inv
)
)
),
pi2
)
);
}
klo = FFloatTrunc2S16int(FFmult(FFsub(x,xlo),hinv));
khi=klo+1;
xdiff0 = FFsub(x, FFadd(xlo, FFmult(h,S16int2FFloat(klo))));
xdiff1 = FFsub(xdiff0, h);
return ( FFadd(ya[klo], FFadd(FFmult(FFmult(FFsub(ya[khi],ya[klo]), hinv), xdiff0), FFmult(FFmult(y2a[khi], xdiff0), xdiff1))) );
}
