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Flocking/C/s/subrouts1
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Recent acquisitions » Acorn ADFS disks » adfs_ArchimedesWorld_15_03.adf » !AcornAns_AcornAns |
| Filename: | Flocking/C/s/subrouts1 |
| Read OK: | ✔ |
| File size: | 5E54 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
max16 * &7fffffff ;max positive number in 16 bit fixed point format (2^31-1)/65536
min16 * &80000000 ;min negative number -2^31 /65536
one * 65536
; rbbcinc
; a leaf APCS function
;
; C prototype:
; int rbbcinc(int r, int k)
;
; given limits 0 <= r < 2^k, return (r � 1) where � denotes a reversed bit ordering increment,
; subject to the stated limits.
; NB in this case, for the function f: n -> {for (k=c=0; c<n; c++, k=rbbcinc(k, l); return k;},
; we have f(f(n))=n.
; NB2 algo requires 2 <= k <= 32, but doesn't check for this - BEWARE!
; (for k=1 get no action taken, while for any other bad k get code executed at unintended address,
; hence unpredictable & likely system fatal).
;
EXPORT rbbcinc
rbnsta DCB "rbbcinc", 0
ALIGN
rbnend DCD &ff000000 + rbnend - rbnsta
rbbcinc
rbbc a1, a2, a3
MOVS pc, lr
; pow16
; a leaf APCS function
;
; C prototype:
; int pow16(int a, int b)
;
; returns 65536 * (a/65536)^(b/65536)
;
; is about 5 to 40 times faster than FPEmulator working with double floats
;
; nb if a<0 require b an integer
;
; nb2 unexpected return values:
; a=b=0 returns 1 actual value ill defined
; a<0, b non integer returns 0 actual value complex
; abs(bln(a)) > max16 unknown errors likely (to avoid, restrict b to �(2^11)one, roughly)
; a=0, b<0 returns max16 actual value +infinity
; a & b st result out of range unknown result
;
; nb precise nature of errors for other values not yet confirmed acceptable, though should be okay except
; perhaps in extreme cases (as of 22/11/95)
;
; Few subsequent notes on error:
;
; For result much bigger than one:
; since exp16 only yields 16 significant bits, pow16 gives no more than this, hence for result much bigger
; than one get increasing error, eg for a around 64one & b=1.03125one get errors st answer (around 73one)
; is only correct to top 15 or 16 bits (ie error upto around one/1024 to one/256)
;
; For 0<=a<=one, & b eg 2one, 3one, 13.125one etc get error typically no more than in low 1 or 2 bits
;
; For a large (say a>one) & b<0 get error typically in only lowest bit or no error
;
; **** Strongly recommend this fn is only used where accuracy not crucial or with limited range ****
; **** of arguments where you can confirm yourself accuracy in that range is adequate. ****
;
EXPORT pow16
pwnsta DCB "pow16", 0
ALIGN
pwnend DCD &ff000000 + pwnend - pwnsta
pow16
CMP a2, #0
MOVEQ a1, #&10000 ;if b=0 return one directly
MOVEQS pc, lr
CMP a2, #&10000
MOVEQS pc, lr ;handle trival case b=one directly, by returning a
CMP a1, #0
MOVGT ip, #0
BGT pow16_apos
BNE pow16_aneg
CMP a2, #0
MOV a1, #0 ;if a=0 and b>0 return 0
MOVLT a1, #max16+1 ;if a=0 and b<0 return max16
SUBLT a1, a1, #1
MOVS pc, lr
pow16_aneg
MOVS ip, a2, LSL #16
MOVNE a1, #0 ;if a<0 and b not an integer return 0
MOVNES pc, lr
AND ip, a2, #&10000 ;if a<0 then go on to evaluate (65536 * (-a/65536)^(b/65536))
RSB a1, a1, #0 ;with sign subsequently forced to + or - according to whether b/one
pow16_apos ;is even or odd ( eg (-2.5)^3 is just (-1)^3 * 2.5^3 )
STMFD sp!, {v1, v2, lr}
MOV v1, ip ;now evaluate (65536 * (a/65536)^(b/65536)), for a>0
MOV v2, a2 ;via exp16( ln16(a) * b / 65536 )
BL ln16 ;nb this uses property that exp(b.log(a)) = exp(log(a^b)) = a^b
mul16 a1, v2, a1, a2, a3, a4
BL exp16
CMP v1, #0
RSBNE a1, a1, #0 ;finally switch sign on answer if originally a<0 and b/one was odd
LDMFD sp!, {v1, v2, pc}^
; ln16
; a leaf APCS function
;
; C prototype:
; int ln16(int a)
;
; returns 65536 * ln (a/65536)
;
; is about 30 times faster than FPEmulator working with double floats
;
EXPORT ln16
lnnsta DCB "ln16", 0
ALIGN
lnnend DCD &ff000000 + lnnend - lnnsta
ln16
CMP a1, #0 ;if a<=0 return min16
MOVLE a1, #min16
MOVLES pc, lr ;else most significant bit is between b30 & b0
GBLA counter
counter SETA 30 ;find msb & store (msb_index - 15) in a4
WHILE counter > 1
TST a1, #1<<counter
MOVNE a4, #counter-15
BNE ln16_gotmsb
counter SETA counter-1
WEND
TST a1, #1<<1
MOVNE a4, #1-15
MOVEQ a4, #0-15
ln16_gotmsb ;if we set z = a1/(2^a4), will have ln(a/one) = ln(z/one * 2^a4)
CMP a4, #2 ; = ln(z/one) + a4*ln2
SUBGT a2, a4, #2 ;with z in range [0.5,1)
MOVGT a1, a1, LSR a2 ;so calc a1 = 4*( a1/(2^a4) ) - 3*one
RSBLE a2, a4, #2 ;which puts a1 in range �one suitable for approximation by poly
MOVLE a1, a1, LSL a2 ;leaving us to calculate a4*one*ln2 + one*ln((a1+3one)/4one)
SUB a1, a1, #&30000
ADD a2, a1, a1, LSL #2 ;start polynomial approximation calculation on a1
RSB a2, a2, a1, LSL #10
MOV a2, a2, ASR #16 ;for details of how this works see comments against similar code
SUB a2, a2, #&000e00 ;in exp16 function, directly below this function
SUB a2, a2, #&000034
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&003200
ADD a2, a2, #&000031
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&00e200
SUB a2, a2, #&0000f2
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&050000
ADD a2, a2, #&005500
ADD a2, a2, #&000065
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&040000
SUB a2, a2, #&009a00 ;end of polynomial approximation calculation
SUB a1, a2, #&000059 ;a1 now holds (2^20)*(approximated value)
ADD ip, a4, a4, LSL #1
ADD a2, ip, a4, LSL #3 ;now add in the a4*one*ln2 term using an explicit binary expansion
ADD a2, a4, a2, LSL #4 ;of approximately one*ln2
RSB a3, a4, a4, LSL #3
ADD a2, a3, a2, LSL #4 ;nb we actually add approx (2^20)*ln2, & then divide by 16
ADD a2, a4, a2, LSL #3 ;to reduce truncation error
ADD a1, a1, a2, LSL #5
ADD a1, a1, ip, ASR #1
MOV a1, a1, ASR #4
MOVS pc, lr
; exp16
; a leaf APCS function
;
; C prototype:
; int exp16(int a)
;
; returns 65536 * exp (a/65536)
;
; is about 45 times faster than FPEmulator working with double floats
;
EXPORT exp16
epnsta DCB "exp16", 0
ALIGN
epnend DCD &ff000000 + epnend - epnsta
exp16 ;this fn returns a value with only about 17 significant binary
;digits - eg for 'a' small or negative, get near maximal accuracy
;but for 'a' large (upto around 10one) where exp has value
CMP a1, #12*65536 ;~20000one can get error upto roughly 0.1one
MOVGT a1, #max16+1
SUBGT a1, a1, #1
MOVGTS pc, lr
CMP a1, #-12*65536
MOVLT a1, #0
MOVLTS pc, lr ;otherwise know |a| <= 12one
RSB a2, a1, a1, LSL #3 ;now set a = a/ln2 using explicit mul by 2_1.01110001010101000111
ADD a3, a1, a1, LSL #2 ;nb only need 1st 20 digits given range on a
ADD a3, a3, a3, LSL #4 ;nb2 this calc is approximate only, though will usually yield an
ADD a1, a2, a1, LSL #4 ;answer correct to the stored 16 binary places (else error one/65536)
ADD a1, a1, a3, ASR #10
ADD a1, a1, a2, ASR #16 ;thus exp(original a) = exp(new a * ln2) = 2^(new a), eval'd below:
ADD a1, a1, #8
MOV a1, a1, ASR #4 ;calc a = a/ln2 complete
MOV a4, a1, ASR #16 ;a4 now holds integer component of a
BIC a1, a1, a4, LSL #16 ;a1 now holds fractional component in range [0,1)*one
CMP a4, #15 ;do another check on a to ensure exp(a) is in range
MOVGE a1, #max16+1 ;& if not return maximal or minimal value as appropriate
SUBGE a1, a1, #1
MOVGES pc, lr
CMP a4, #-16
MOVLT a1, #0
MOVLTS pc, lr ;else need to return value (one * 2^(a4 + a1/one))
MOV a1, a1, LSL #1 ; = (one * 2^(a1/one) * 2^a4)
SUB a1, a1, #&10000 ;convert a1 to lie in [-1,-1), then apply poly approximation:
RSB a2, a1, a1, LSL #3
ADD a2, a1, a2, LSL #6
MOV a2, a2, ASR #15 ;a2 = 0.0008561*(2^20)*(a1/one)
ADD a2, a2, #&002800
ADD a2, a2, #&00007e ;a2 = 0.0008561*(2^20)*(a1/one) + 0.0098857*(2^20)
MOV ip, a1
mul16c a2, ip, a2, a3 ;a2 = 0.0008561*(2^20)*(a1/one)^2 + 0.0098857*(2^20)*(a1/one)
ADD a2, a2, #&015000
ADD a2, a2, #&000be0 ; etc
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&070000
ADD a2, a2, #&00d700
ADD a2, a2, #&00007e
MOV ip, a1
mul16c a2, ip, a2, a3 ;until we have
ADD a2, a2, #&160000 ;a2 = (2^20) ( 0.0008561(a1/one)^4 + 0.0098857(a1/one)^3 +
ADD a2, a2, #&00a000 ; 0.0849301(a1/one)^2 + 0.4901106(a1/one) +
ADD a2, a2, #&0000a7 ; 1.14142138 )
MOV a1, a2, ASR #4 ;now divide by 16 removing most truncation error from above calcs,
CMP a4, #0 ;leaving a2 = (2^16)*(approximated value)
RSBLT a4, a4, #0
MOVLT a1, a1, ASR a4 ;finally carry out the (a2 = a2 * 2^a4) step
MOVLTS pc, lr
MOVS a1, a1, LSL a4
MOVMI a1, #max16+1
SUBMI a1, a1, #1
MOVS pc, lr
; sig16
; a leaf APCS function
;
; C prototype:
; int sig16(int a)
;
; returns 65536 / ( 1 + exp (-a/65536) )
; the sigmoid function for neural net code
;
; is about 53 times faster than FPEmulator working with double floats
;
EXPORT sig16
sdnsta DCB "sig16", 0
ALIGN
sdnend DCD &ff000000 + sdnend - sdnsta
sig16 CMP a1, #12*65536
MOVGT a1, #one
MOVGTS pc, lr
CMP a1, #-12*65536
MOVLT a1, #0
MOVLTS pc, lr ;otherwise know |a| <= 12one
ANDS ip, a1, #1<<31 ;copy sign of a into b31 of ip
RSBMI a1, a1, #0 ;ensure a>=0
RSB a2, a1, a1, LSL #3 ;now set a = a/ln2 using explicit mul by 2_1.01110001010101000111
ADD a3, a1, a1, LSL #2 ;nb only need 1st 20 digits given range on a
ADD a3, a3, a3, LSL #4 ;nb2 this calc is approximate only, though will usually yield an
ADD a1, a2, a1, LSL #4 ;answer correct to the stored 16 binary places (else error one/65536)
ADD a1, a1, a3, ASR #10
ADD a1, a1, a2, ASR #16 ;thus exp(original a) = exp(new a * ln2) = 2^(new a), eval'd below:
ADD a1, a1, #8
MOV a1, a1, ASR #4 ;calc a = a/ln2 complete
MOV a4, a1, ASR #16 ;a4 now holds integer component of a
BIC a1, a1, a4, LSL #16 ;a1 now holds fractional component in range [0,1)*one
CMP a4, #15 ;do another check on a to ensure exp(a) is in range
BLT sig16_l1
MOV a1, #1 ;& if not, return near maximal or minimal value as appropriate
TST ip, #1<<31
RSBEQ a1, a1, #one
MOVS pc,lr
sig16_l1
ORR a4, a4, ip ;(temporarily store sign of original a in a4)
MOV a1, a1, LSL #1 ;else need value (one * 2^(a1/one) * 2^a4)
SUB a1, a1, #&10000 ;convert a1 to lie in [-1,-1), then apply poly approximation:
RSB a2, a1, a1, LSL #3
ADD a2, a1, a2, LSL #6
MOV a2, a2, ASR #15 ;a2 = 0.0008561*(2^20)*(a1/one)
ADD a2, a2, #&002800
ADD a2, a2, #&00007e ;a2 = 0.0008561*(2^20)*(a1/one) + 0.0098857*(2^20)
MOV ip, a1
mul16c a2, ip, a2, a3 ;a2 = 0.0008561*(2^20)*(a1/one)^2 + 0.0098857*(2^20)*(a1/one)
ADD a2, a2, #&015000
ADD a2, a2, #&000be0 ; etc
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&070000
ADD a2, a2, #&00d700
ADD a2, a2, #&00007e
MOV ip, a1
mul16c a2, ip, a2, a3 ;until we have
ADD a2, a2, #&160000 ;a2 = (2^20) ( 0.0008561(a1/one)^4 + 0.0098857(a1/one)^3 +
ADD a2, a2, #&00a000 ; 0.0849301(a1/one)^2 + 0.4901106(a1/one) +
ADD a2, a2, #&0000a7 ; 1.14142138 )
MOV a1, a2, ASR #4 ;now divide by 16 removing most truncation error from above calcs,
;leaving a2 = (2^16)*(approximated value)
BIC ip, a4, #1<<31 ;remove temp sign bit from a4
MOVS a2, a1, LSL ip ;finally carry out the (a2 = a2 * 2^a4) step
ADDCCS a2, a2, #one ;then add in one
MOVCS a1, a4, LSR #15 ;& if overflow, return maximal or minimal value as appropriate
EORCS a1, a1, #one
MOVCSS pc, lr
MOV a1, #0 ;result for operation a1 = 2^32 / a2
MOV a3, #1<<16 ;remainder reg
GBLA counter
counter SETA 16
WHILE counter > 0
ADD a1, a1, a1
ADD a3, a3, a3
CMP a3, a2
SUBHS a3, a3, a2
ORRHS a1, a1, #1
counter SETA counter-1
WEND ;reciprocal calculated
CMP a2, a3, LSL #1
ADDLS a1, a1, #1
TST a4, #1<<31 ;and finally, if original argument > 0
RSBEQ a1, a1, #one ;then flip value about y=1/2 line in graph of sig fn
MOVS pc, lr
; cos16
; a leaf APCS function
;
; C prototype:
; int cos16(int a)
;
; returns 65536 * cos ((a/65536)(pi/2))
;
; is about 44 times faster than FPEmulator working with double floats
;
EXPORT cos16
csnsta DCB "cos16", 0
ALIGN
csnend DCD &ff000000 + csnend - csnsta
cos16
EOR a4, a1, a1, LSL #1 ;since cos is periodic and cos((a/65536)(pi/2)) has period 4*one
TST a4, #&20000 ;eval is simpler than for ln or exp:
MOV a4, #0 ;we need only to truncate a to [0,4one) and then approx the function
MOVNE a4, #1 ;via a poly
TST a1, #&10000
MOV a1, a1, LSL #16 ;in fact further symmetries in cos over this range allow us to
MOV a1, a1, LSR #16 ;actually only approximate function over range [0,one)
RSBEQ a1, a1, #&10000 ;and reconstruct it over remainder of range [one,4one) from that part
MOV a1, a1, LSL #1 ;eg cos( (a/65536)(pi/2) ) for a in [2one, 3one)
SUB a1, a1, #&10000 ; = -cos( ((a-2one)/65536)(pi/2) )
RSB a2, a1, a1, LSL #3
ADD a2, a1, a2, LSL #8
MOV a2, a2, ASR #16
ADD a2, a2, #&002c00
ADD a2, a2, #&000086
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&00e900
SUB a2, a2, #&0000bd
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&030000
SUB a2, a2, #&007c00
SUB a2, a2, #&0000c6
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&080000
ADD a2, a2, #&00E200
ADD a2, a2, #&0000BD
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&0b0000
ADD a2, a2, #&005000
ADD a2, a2, #&000050
MOV a1, a2, ASR #4
TST a4, #1
RSBNE a1, a1, #0
MOVS pc, lr
; sin16
; a leaf APCS function
;
; C prototype:
; int sin16(int a)
;
; returns 65536 * sin ((a/65536)(pi/2))
;
; is about 44 times faster than FPEmulator working with double floats
;
EXPORT sin16
snnsta DCB "sin16", 0
ALIGN
snnend DCD &ff000000 + snnend - snnsta
sin16
TST a1, #&20000 ;eval of sin is almost identical to that of cos
MOV a4, #0
MOVNE a4, #1
TST a1, #&10000
MOV a1, a1, LSL #16
MOV a1, a1, LSR #16
RSBNE a1, a1, #&10000
MOV a1, a1, LSL #1
SUB a1, a1, #&10000
RSB a2, a1, a1, LSL #3
ADD a2, a1, a2, LSL #8
MOV a2, a2, ASR #16
ADD a2, a2, #&002c00
ADD a2, a2, #&000086
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&00e900
SUB a2, a2, #&0000bd
MOV ip, a1
mul16c a2, ip, a2, a3
SUB a2, a2, #&030000
SUB a2, a2, #&007c00
SUB a2, a2, #&0000c6
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&080000
ADD a2, a2, #&00E200
ADD a2, a2, #&0000BD
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&0b0000
ADD a2, a2, #&005000
ADD a2, a2, #&000050
MOV a1, a2, ASR #4
TST a4, #1
RSBNE a1, a1, #0
MOVS pc, lr
; acs16
; a leaf APCS function
;
; C prototype:
; int acs16(int a)
;
; returns 65536 * 2/pi * arccos (a/65536)
;
; for a out of range (ie abs a > 65536), reset a to �65536 as appropriate before eval
;
; is about 24 times faster than FPEmulator working with double floats
;
EXPORT acs16
acnsta DCB "acs16", 0
ALIGN
acnend DCD &ff000000 + acnend - acnsta
acs16
CMP a1, #65536
MOVGE a1, #0
MOVGES pc, lr
CMP a1, #-65536
MOVLE a1, #2*65536
MOVLES pc, lr
STMFD sp!, {lr} ;now have arg in range (-one,one)
CMP a1, #0
RSBMI a1, a1, #0
MOVMI a4, #1 ;b0 in a4 set iff final result r needs replacing by 2*one-r
MOVPL a4, #0 ;now have arg in range [0,one)
SUB a2, a1, #&b500
SUBS a2, a2, #&0005
BLT acs16_arglow ;if arg < one/sqrt2 go and apply poly else first transmute into here
ORR a4, a4, #2 ;b1 in a4 clear iff penultimate result r need be replaced by one-r
MUL a2, a1, a1
MOV a1, a2, LSR #16
RSB a1, a1, #65536
sqrt16 a1, a1, a2, a3, ip, lr ;arg transmuted (ie replaced by one-sqrt(arg^2))
acs16_arglow
ADD a3, a1, a1, ASL #2
ADD a2, a3, a1, ASL #4
ADD a2, a2, a3, ASL #5
ADD a2, a2, a3, ASR #8
ADD a2, a2, #32
MOV a1, a2, ASR #6 ;range transform applied (ie replaced by arg*2sqrt2-one)
SUB a1, a1, #&10000 ;so arg lies in range [-1,1]
ADD a2, a1, a1, LSL #2 ;now apply poly
ADD a2, a2, a2, LSL #5
MOV a2, a2, ASR #14
ADD a2, a2, #&000500
ADD a2, a2, #&0000ae
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&000800
ADD a2, a2, #&000088
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&002000
ADD a2, a2, #&00009a
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&004600
ADD a2, a2, #&00009a
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&030000
ADD a2, a2, #&00d900
ADD a2, a2, #&0000b4
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&030000
ADD a2, a2, #&00ae00
ADD a2, a2, #&000052
MOV a1, a2, ASR #4
TST a4, #2
RSBEQ a1, a1, #65536
TST a4, #1
RSBNE a1, a1, #2*65536
LDMFD sp!, {pc}^
; asn16
; a leaf APCS function
;
; C prototype:
; int asn16(int a)
;
; returns 65536 * 2/pi * arcsin (a/65536)
;
; for a out of range (ie abs a > 65536), reset a to �65536 as appropriate before eval
;
; is about 24 times faster than FPEmulator working with double floats
;
EXPORT asn16
asnsta DCB "asn16", 0
ALIGN
asnend DCD &ff000000 + asnend - asnsta
asn16
CMP a1, #65536
MOVGE a1, #65536
MOVGES pc, lr
ADDS a2, a1, #65536 ;equiv to CMP a1,#-65536
SUBLE a1, a1, a2 ;equiv to MOVLE a1,#-65536 (which wouldn't work due to bad constant)
MOVLES pc, lr
STMFD sp!, {lr} ;now have arg in range (-one,one)
CMP a1, #0
RSBMI a1, a1, #0
MOVMI a4, #1 ;b0 in a4 set iff final result needs negating
MOVPL a4, #0 ;now have arg in range [0,one)
SUB a2, a1, #&b500
SUBS a2, a2, #&0005
BLT asn16_arglow ;if arg < one/sqrt2 go and apply poly else first transmute into here
ORR a4, a4, #2 ;b1 in a4 set iff penultimate result r needs to be replaced by one-r
MUL a2, a1, a1
MOV a1, a2, LSR #16
RSB a1, a1, #65536
sqrt16 a1, a1, a2, a3, ip, lr ;arg transmuted (ie replaced by one-sqrt(arg^2))
asn16_arglow
ADD a3, a1, a1, ASL #2
ADD a2, a3, a1, ASL #4
ADD a2, a2, a3, ASL #5
ADD a2, a2, a3, ASR #8
ADD a2, a2, #32
MOV a1, a2, ASR #6 ;range transform applied (ie replaced by arg*2sqrt2-one)
SUB a1, a1, #&10000 ;so arg lies in range [-1,1]
ADD a2, a1, a1, LSL #2 ;now apply poly
ADD a2, a2, a2, LSL #5
MOV a2, a2, ASR #14
ADD a2, a2, #&000500
ADD a2, a2, #&0000ae
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&000800
ADD a2, a2, #&000088
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&002000
ADD a2, a2, #&00009a
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&004600
ADD a2, a2, #&00009a
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&030000
ADD a2, a2, #&00d900
ADD a2, a2, #&0000b4
MOV ip, a1
mul16c a2, ip, a2, a3
ADD a2, a2, #&030000
ADD a2, a2, #&00ae00
ADD a2, a2, #&000052
MOV a1, a2, ASR #4
TST a4, #2
RSBNE a1, a1, #65536
TST a4, #1
RSBNE a1, a1, #0
LDMFD sp!, {pc}^
; gauss16
; a leaf APCS function
;
; C prototype:
; int gauss16(void)
;
; returns 65536 * ( pseudo randon variable with approximate distribution N(0,1) )
; note, the approximate gaussian distribution is achieved via the sum of n pseudo U[0,65535]
; random variables & application of the central limit theorem
; here we use n=8, giving an actual range of �(sqrt24) (*65536).
;
; for general n, recall we need to return:
; (sum n U[0,65535] random variables) * 2sqrt(3n)*65536/(65535n) - sqrt(3n)*65536
;
EXPORT gauss16
gansta DCB "gauss16", 0
ALIGN
ganend DCD &ff000000 + ganend - gansta
gauss16
ADR a1, gaussseed1
LDMIA a1, {a2, a3}
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
MOV ip, a2, LSR #16
MOV a4, a2, LSL #16
ADD ip, ip, a4, LSR #16
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
ADD ip, ip, a2, LSR #16
MOV a4, a2, LSL #16
ADD ip, ip, a4, LSR #16
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
ADD ip, ip, a2, LSR #16
MOV a4, a2, LSL #16
ADD ip, ip, a4, LSR #16
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
ADD ip, ip, a2, LSR #16
MOV a4, a2, LSL #16
ADD ip, ip, a4, LSR #16 ;sum now in ip
STMIA a1, {a2, a3}
RSB a1, ip, ip, ASL #3
RSB a2, ip, ip, ASL #2
ADD a1, a2, a1, ASL #4
ADD a1, a1, ip, ASL #9
ADD a2, ip, ip, ASL #4
ADD a2, a2, ip, ASL #6
ADD a1, a1, a2, LSR #10
MOV a1, a1, LSR #9
SUB a1, a1, #&4E000
SUB a1, a1, #&00620
SUB a1, a1, #&00004
MOVS pc, lr
gaussseed1 DCD -1 ;bits b0-b31 of seed
DCD -1 ;bit b32 of seed (in lsb of word)
; sgauss16
; a leaf APCS function
;
; C prototype:
; void sgauss16(int seed)
;
; sets the seed for gauss16
;
EXPORT sgauss16
sgnsta DCB "sgauss16", 0
ALIGN
sgnend DCD &ff000000 + sgnend - sgnsta
sgauss16
ADR a2, gaussseed1
MOV a3, #1
STMIA a2, {a1, a3}
MOVS pc, lr
; rand16
; a leaf APCS function
;
; C prototype:
; int rand16(void)
;
; returns 65536 * ( pseudo randon variable with approximate distribution U(-1,1) )
;
EXPORT rand16
ransta DCB "rand16", 0
ALIGN
ranend DCD &ff000000 + ranend - ransta
rand16
ADR ip, randseed1
LDMIA ip, {a2, a3}
rand16_loop
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
MOV a1, a2, LSL #15
MOV a1, a1, ASR #15
CMP a1, #&ffff0000
BEQ rand16_loop
STMIA ip, {a2, a3}
MOVS pc, lr
; randu16
; a leaf APCS function
;
; C prototype:
; int randu16(void)
;
; returns 65536 * ( pseudo randon variable with approximate distribution U(0,1) )
;
EXPORT randu16
runsta DCB "randu16", 0
ALIGN
runend DCD &ff000000 + runend - runsta
randu16
ADR ip, randseed1
LDMIA ip, {a2, a3}
randu16_loop
MOVS a3, a3, LSR #1
MOVS a4, a2, RRX
ADC a3, a3, a3
EOR a4, a4, a2, LSL #12
EOR a2, a4, a4, LSR #20
MOVS a1, a2, LSR #16
BEQ randu16_loop
STMIA ip, {a2, a3}
MOVS pc, lr
randseed1 DCD -1 ;bits b0-b31 of seed
DCD -1 ;bit b32 of seed (in lsb of word)
; srand16
; a leaf APCS function
;
; C prototype:
; void srand16(int seed)
;
; sets the seed for rand16
;
EXPORT srand16
srnsta DCB "srand16", 0
ALIGN
srnend DCD &ff000000 + srnend - srnsta
srand16
ADR a2, randseed1
MOV a3, #1
STMIA a2, {a1, a3}
MOVS pc, lr
; div_frac16
; a leaf APCS function
;
; C prototype:
; int div_frac16(int number, int divisor)
;
; returns integer part of 65536*number/divisor
; assumes abs number < 65536 * abs divisor
; if this needs checking, must be done by caller
;
EXPORT div_frac16
dfnsta DCB "div_frac16", 0
ALIGN
dfnend DCD &ff000000 + dfnend - dfnsta
div_frac16
div16 a1, a2, a1, a3, a4
MOVS pc, lr
; mul_frac16
; a leaf APCS function
;
; C prototype:
; int mul_frac16(int x, int a)
;
; returns 32-bit signed integer x*a/65536
; assumes result fits into 32-bit signed representation
; note, no other restrictions on a - if can guarantee abs a < 65536, use mul_frac16c instead as is quicker
;
EXPORT mul_frac16
mfnsta DCB "mul_frac16", 0
ALIGN
mfnend DCD &ff000000 + mfnend - mfnsta
mul_frac16
mul16 a1, a2, a1, a3, a4, ip
MOVS pc, lr
; mul_frac16c
; a leaf APCS function
;
; C prototype:
; int mul_frac16c(int x, int a)
;
; returns 32-bit signed integer x*a/65536
; assumes abs a <=65536
; if it is possible that abs a > 65536, caller must check range & either not call fn or round down to 65536
;
EXPORT mul_frac16c
mfcnsta DCB "mul_frac16c", 0
ALIGN
mfcnend DCD &ff000000 + mfcnend - mfcnsta
mul_frac16c
mul16c a1, a2, a1, a3
MOVS pc, lr
; sqrt_frac16
; a leaf APCS function
;
; C prototype:
; int sqrt_frac16(unsigned int x)
;
; returns 32-bit integer sqrt(x<<16)
;
EXPORT sqrt_frac16
sqfnsta DCB "sqrt_frac16", 0
ALIGN
sqfnend DCD &ff000000 + sqfnend - sqfnsta
sqrt_frac16
sqrt16 a1, a1, a2, a3, a4, ip
MOVS pc, lr
END
00000000 0a 6d 61 78 31 36 09 2a 09 26 37 66 66 66 66 66 |.max16.*.&7fffff|
00000010 66 66 09 3b 6d 61 78 20 70 6f 73 69 74 69 76 65 |ff.;max positive|
00000020 20 6e 75 6d 62 65 72 20 69 6e 20 31 36 20 62 69 | number in 16 bi|
00000030 74 20 66 69 78 65 64 20 70 6f 69 6e 74 20 66 6f |t fixed point fo|
00000040 72 6d 61 74 20 28 32 5e 33 31 2d 31 29 2f 36 35 |rmat (2^31-1)/65|
00000050 35 33 36 0a 6d 69 6e 31 36 09 2a 09 26 38 30 30 |536.min16.*.&800|
00000060 30 30 30 30 30 09 3b 6d 69 6e 20 6e 65 67 61 74 |00000.;min negat|
00000070 69 76 65 20 6e 75 6d 62 65 72 09 09 09 09 20 20 |ive number.... |
00000080 2d 32 5e 33 31 20 20 20 2f 36 35 35 33 36 0a 6f |-2^31 /65536.o|
00000090 6e 65 09 2a 09 36 35 35 33 36 0a 0a 0a 0a 3b 20 |ne.*.65536....; |
000000a0 72 62 62 63 69 6e 63 0a 3b 20 61 20 6c 65 61 66 |rbbcinc.; a leaf|
000000b0 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e 0a 3b | APCS function.;|
000000c0 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 3a 0a |.; C prototype:.|
000000d0 3b 20 69 6e 74 20 72 62 62 63 69 6e 63 28 69 6e |; int rbbcinc(in|
000000e0 74 20 72 2c 20 69 6e 74 20 6b 29 0a 3b 0a 3b 20 |t r, int k).;.; |
000000f0 67 69 76 65 6e 20 6c 69 6d 69 74 73 20 30 20 3c |given limits 0 <|
00000100 3d 20 72 20 3c 20 32 5e 6b 2c 20 72 65 74 75 72 |= r < 2^k, retur|
00000110 6e 20 28 72 20 a4 20 31 29 20 77 68 65 72 65 20 |n (r . 1) where |
00000120 a4 20 64 65 6e 6f 74 65 73 20 61 20 72 65 76 65 |. denotes a reve|
00000130 72 73 65 64 20 62 69 74 20 6f 72 64 65 72 69 6e |rsed bit orderin|
00000140 67 20 69 6e 63 72 65 6d 65 6e 74 2c 0a 3b 20 73 |g increment,.; s|
00000150 75 62 6a 65 63 74 20 74 6f 20 74 68 65 20 73 74 |ubject to the st|
00000160 61 74 65 64 20 6c 69 6d 69 74 73 2e 0a 3b 20 4e |ated limits..; N|
00000170 42 20 69 6e 20 74 68 69 73 20 63 61 73 65 2c 20 |B in this case, |
00000180 66 6f 72 20 74 68 65 20 66 75 6e 63 74 69 6f 6e |for the function|
00000190 20 66 3a 20 6e 20 2d 3e 20 7b 66 6f 72 20 28 6b | f: n -> {for (k|
000001a0 3d 63 3d 30 3b 20 63 3c 6e 3b 20 63 2b 2b 2c 20 |=c=0; c<n; c++, |
000001b0 6b 3d 72 62 62 63 69 6e 63 28 6b 2c 20 6c 29 3b |k=rbbcinc(k, l);|
000001c0 20 72 65 74 75 72 6e 20 6b 3b 7d 2c 0a 3b 20 77 | return k;},.; w|
000001d0 65 20 68 61 76 65 20 66 28 66 28 6e 29 29 3d 6e |e have f(f(n))=n|
000001e0 2e 0a 3b 20 4e 42 32 20 61 6c 67 6f 20 72 65 71 |..; NB2 algo req|
000001f0 75 69 72 65 73 20 32 20 3c 3d 20 6b 20 3c 3d 20 |uires 2 <= k <= |
00000200 33 32 2c 20 62 75 74 20 64 6f 65 73 6e 27 74 20 |32, but doesn't |
00000210 63 68 65 63 6b 20 66 6f 72 20 74 68 69 73 20 2d |check for this -|
00000220 20 42 45 57 41 52 45 21 0a 3b 20 28 66 6f 72 20 | BEWARE!.; (for |
00000230 6b 3d 31 20 67 65 74 20 6e 6f 20 61 63 74 69 6f |k=1 get no actio|
00000240 6e 20 74 61 6b 65 6e 2c 20 77 68 69 6c 65 20 66 |n taken, while f|
00000250 6f 72 20 61 6e 79 20 6f 74 68 65 72 20 62 61 64 |or any other bad|
00000260 20 6b 20 67 65 74 20 63 6f 64 65 20 65 78 65 63 | k get code exec|
00000270 75 74 65 64 20 61 74 20 75 6e 69 6e 74 65 6e 64 |uted at unintend|
00000280 65 64 20 61 64 64 72 65 73 73 2c 0a 3b 20 20 68 |ed address,.; h|
00000290 65 6e 63 65 20 75 6e 70 72 65 64 69 63 74 61 62 |ence unpredictab|
000002a0 6c 65 20 26 20 6c 69 6b 65 6c 79 20 73 79 73 74 |le & likely syst|
000002b0 65 6d 20 66 61 74 61 6c 29 2e 0a 3b 0a 0a 20 20 |em fatal)..;.. |
000002c0 20 20 20 20 20 20 45 58 50 4f 52 54 20 20 72 62 | EXPORT rb|
000002d0 62 63 69 6e 63 0a 0a 72 62 6e 73 74 61 20 20 44 |bcinc..rbnsta D|
000002e0 43 42 20 20 20 20 20 22 72 62 62 63 69 6e 63 22 |CB "rbbcinc"|
000002f0 2c 20 30 0a 20 20 20 20 20 20 20 20 41 4c 49 47 |, 0. ALIG|
00000300 4e 0a 72 62 6e 65 6e 64 20 20 44 43 44 20 20 20 |N.rbnend DCD |
00000310 20 20 26 66 66 30 30 30 30 30 30 20 2b 20 72 62 | &ff000000 + rb|
00000320 6e 65 6e 64 20 2d 20 72 62 6e 73 74 61 0a 0a 72 |nend - rbnsta..r|
00000330 62 62 63 69 6e 63 0a 0a 20 20 20 20 20 20 20 20 |bbcinc.. |
00000340 72 62 62 63 20 20 20 20 61 31 2c 20 61 32 2c 20 |rbbc a1, a2, |
00000350 61 33 0a 20 20 20 20 20 20 20 20 4d 4f 56 53 20 |a3. MOVS |
00000360 20 20 20 70 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 70 | pc, lr....; p|
00000370 6f 77 31 36 0a 3b 20 61 20 6c 65 61 66 20 41 50 |ow16.; a leaf AP|
00000380 43 53 20 66 75 6e 63 74 69 6f 6e 0a 3b 0a 3b 20 |CS function.;.; |
00000390 43 20 70 72 6f 74 6f 74 79 70 65 3a 0a 3b 20 69 |C prototype:.; i|
000003a0 6e 74 20 70 6f 77 31 36 28 69 6e 74 20 61 2c 20 |nt pow16(int a, |
000003b0 69 6e 74 20 62 29 0a 3b 0a 3b 20 72 65 74 75 72 |int b).;.; retur|
000003c0 6e 73 20 36 35 35 33 36 20 2a 20 28 61 2f 36 35 |ns 65536 * (a/65|
000003d0 35 33 36 29 5e 28 62 2f 36 35 35 33 36 29 0a 3b |536)^(b/65536).;|
000003e0 0a 3b 20 69 73 20 61 62 6f 75 74 20 35 20 74 6f |.; is about 5 to|
000003f0 20 34 30 20 74 69 6d 65 73 20 66 61 73 74 65 72 | 40 times faster|
00000400 20 74 68 61 6e 20 46 50 45 6d 75 6c 61 74 6f 72 | than FPEmulator|
00000410 20 77 6f 72 6b 69 6e 67 20 77 69 74 68 20 64 6f | working with do|
00000420 75 62 6c 65 20 66 6c 6f 61 74 73 0a 3b 0a 3b 20 |uble floats.;.; |
00000430 6e 62 20 69 66 20 61 3c 30 20 72 65 71 75 69 72 |nb if a<0 requir|
00000440 65 20 62 20 61 6e 20 69 6e 74 65 67 65 72 0a 3b |e b an integer.;|
00000450 0a 3b 20 6e 62 32 20 75 6e 65 78 70 65 63 74 65 |.; nb2 unexpecte|
00000460 64 20 72 65 74 75 72 6e 20 76 61 6c 75 65 73 3a |d return values:|
00000470 0a 3b 20 61 3d 62 3d 30 09 09 09 09 72 65 74 75 |.; a=b=0....retu|
00000480 72 6e 73 20 31 09 61 63 74 75 61 6c 20 76 61 6c |rns 1.actual val|
00000490 75 65 20 69 6c 6c 20 64 65 66 69 6e 65 64 0a 3b |ue ill defined.;|
000004a0 20 61 3c 30 2c 20 62 20 6e 6f 6e 20 69 6e 74 65 | a<0, b non inte|
000004b0 67 65 72 09 09 72 65 74 75 72 6e 73 20 30 09 61 |ger..returns 0.a|
000004c0 63 74 75 61 6c 20 76 61 6c 75 65 20 63 6f 6d 70 |ctual value comp|
000004d0 6c 65 78 0a 3b 20 61 62 73 28 62 6c 6e 28 61 29 |lex.; abs(bln(a)|
000004e0 29 20 3e 20 6d 61 78 31 36 09 09 75 6e 6b 6e 6f |) > max16..unkno|
000004f0 77 6e 20 65 72 72 6f 72 73 20 6c 69 6b 65 6c 79 |wn errors likely|
00000500 20 28 74 6f 20 61 76 6f 69 64 2c 20 72 65 73 74 | (to avoid, rest|
00000510 72 69 63 74 20 62 20 74 6f 20 b1 28 32 5e 31 31 |rict b to .(2^11|
00000520 29 6f 6e 65 2c 20 72 6f 75 67 68 6c 79 29 0a 3b |)one, roughly).;|
00000530 20 61 3d 30 2c 20 62 3c 30 09 09 09 72 65 74 75 | a=0, b<0...retu|
00000540 72 6e 73 20 6d 61 78 31 36 09 61 63 74 75 61 6c |rns max16.actual|
00000550 20 76 61 6c 75 65 20 2b 69 6e 66 69 6e 69 74 79 | value +infinity|
00000560 0a 3b 20 61 20 26 20 62 20 73 74 20 72 65 73 75 |.; a & b st resu|
00000570 6c 74 20 6f 75 74 20 6f 66 20 72 61 6e 67 65 09 |lt out of range.|
00000580 75 6e 6b 6e 6f 77 6e 20 72 65 73 75 6c 74 0a 3b |unknown result.;|
00000590 0a 3b 20 6e 62 20 70 72 65 63 69 73 65 20 6e 61 |.; nb precise na|
000005a0 74 75 72 65 20 6f 66 20 65 72 72 6f 72 73 20 66 |ture of errors f|
000005b0 6f 72 20 6f 74 68 65 72 20 76 61 6c 75 65 73 20 |or other values |
000005c0 6e 6f 74 20 79 65 74 20 63 6f 6e 66 69 72 6d 65 |not yet confirme|
000005d0 64 20 61 63 63 65 70 74 61 62 6c 65 2c 20 74 68 |d acceptable, th|
000005e0 6f 75 67 68 20 73 68 6f 75 6c 64 20 62 65 20 6f |ough should be o|
000005f0 6b 61 79 20 65 78 63 65 70 74 0a 3b 20 70 65 72 |kay except.; per|
00000600 68 61 70 73 20 69 6e 20 65 78 74 72 65 6d 65 20 |haps in extreme |
00000610 63 61 73 65 73 20 28 61 73 20 6f 66 20 32 32 2f |cases (as of 22/|
00000620 31 31 2f 39 35 29 0a 3b 0a 3b 20 46 65 77 20 73 |11/95).;.; Few s|
00000630 75 62 73 65 71 75 65 6e 74 20 6e 6f 74 65 73 20 |ubsequent notes |
00000640 6f 6e 20 65 72 72 6f 72 3a 0a 3b 0a 3b 20 46 6f |on error:.;.; Fo|
00000650 72 20 72 65 73 75 6c 74 20 6d 75 63 68 20 62 69 |r result much bi|
00000660 67 67 65 72 20 74 68 61 6e 20 6f 6e 65 3a 0a 3b |gger than one:.;|
00000670 20 73 69 6e 63 65 20 65 78 70 31 36 20 6f 6e 6c | since exp16 onl|
00000680 79 20 79 69 65 6c 64 73 20 31 36 20 73 69 67 6e |y yields 16 sign|
00000690 69 66 69 63 61 6e 74 20 62 69 74 73 2c 20 70 6f |ificant bits, po|
000006a0 77 31 36 20 67 69 76 65 73 20 6e 6f 20 6d 6f 72 |w16 gives no mor|
000006b0 65 20 74 68 61 6e 20 74 68 69 73 2c 20 68 65 6e |e than this, hen|
000006c0 63 65 20 66 6f 72 20 72 65 73 75 6c 74 20 6d 75 |ce for result mu|
000006d0 63 68 20 62 69 67 67 65 72 0a 3b 20 74 68 61 6e |ch bigger.; than|
000006e0 20 6f 6e 65 20 67 65 74 20 69 6e 63 72 65 61 73 | one get increas|
000006f0 69 6e 67 20 65 72 72 6f 72 2c 20 65 67 20 66 6f |ing error, eg fo|
00000700 72 20 61 20 61 72 6f 75 6e 64 20 36 34 6f 6e 65 |r a around 64one|
00000710 20 26 20 62 3d 31 2e 30 33 31 32 35 6f 6e 65 20 | & b=1.03125one |
00000720 67 65 74 20 65 72 72 6f 72 73 20 73 74 20 61 6e |get errors st an|
00000730 73 77 65 72 20 28 61 72 6f 75 6e 64 20 37 33 6f |swer (around 73o|
00000740 6e 65 29 0a 3b 20 69 73 20 6f 6e 6c 79 20 63 6f |ne).; is only co|
00000750 72 72 65 63 74 20 74 6f 20 74 6f 70 20 31 35 20 |rrect to top 15 |
00000760 6f 72 20 31 36 20 62 69 74 73 20 28 69 65 20 65 |or 16 bits (ie e|
00000770 72 72 6f 72 20 75 70 74 6f 20 61 72 6f 75 6e 64 |rror upto around|
00000780 20 6f 6e 65 2f 31 30 32 34 20 74 6f 20 6f 6e 65 | one/1024 to one|
00000790 2f 32 35 36 29 0a 3b 0a 3b 20 46 6f 72 20 30 3c |/256).;.; For 0<|
000007a0 3d 61 3c 3d 6f 6e 65 2c 20 26 20 62 20 65 67 20 |=a<=one, & b eg |
000007b0 32 6f 6e 65 2c 20 33 6f 6e 65 2c 20 31 33 2e 31 |2one, 3one, 13.1|
000007c0 32 35 6f 6e 65 20 65 74 63 20 67 65 74 20 65 72 |25one etc get er|
000007d0 72 6f 72 20 74 79 70 69 63 61 6c 6c 79 20 6e 6f |ror typically no|
000007e0 20 6d 6f 72 65 20 74 68 61 6e 20 69 6e 20 6c 6f | more than in lo|
000007f0 77 20 31 20 6f 72 20 32 20 62 69 74 73 0a 3b 0a |w 1 or 2 bits.;.|
00000800 3b 20 46 6f 72 20 61 20 6c 61 72 67 65 20 28 73 |; For a large (s|
00000810 61 79 20 61 3e 6f 6e 65 29 20 26 20 62 3c 30 20 |ay a>one) & b<0 |
00000820 67 65 74 20 65 72 72 6f 72 20 74 79 70 69 63 61 |get error typica|
00000830 6c 6c 79 20 69 6e 20 6f 6e 6c 79 20 6c 6f 77 65 |lly in only lowe|
00000840 73 74 20 62 69 74 20 6f 72 20 6e 6f 20 65 72 72 |st bit or no err|
00000850 6f 72 0a 3b 0a 3b 20 20 20 2a 2a 2a 2a 20 20 53 |or.;.; **** S|
00000860 74 72 6f 6e 67 6c 79 20 72 65 63 6f 6d 6d 65 6e |trongly recommen|
00000870 64 20 74 68 69 73 20 66 6e 20 69 73 20 6f 6e 6c |d this fn is onl|
00000880 79 20 75 73 65 64 20 77 68 65 72 65 20 61 63 63 |y used where acc|
00000890 75 72 61 63 79 20 6e 6f 74 20 63 72 75 63 69 61 |uracy not crucia|
000008a0 6c 20 6f 72 20 77 69 74 68 20 6c 69 6d 69 74 65 |l or with limite|
000008b0 64 20 72 61 6e 67 65 20 2a 2a 2a 2a 0a 3b 20 20 |d range ****.; |
000008c0 20 2a 2a 2a 2a 20 20 6f 66 20 61 72 67 75 6d 65 | **** of argume|
000008d0 6e 74 73 20 77 68 65 72 65 20 79 6f 75 20 63 61 |nts where you ca|
000008e0 6e 20 63 6f 6e 66 69 72 6d 20 79 6f 75 72 73 65 |n confirm yourse|
000008f0 6c 66 20 61 63 63 75 72 61 63 79 20 69 6e 20 74 |lf accuracy in t|
00000900 68 61 74 20 72 61 6e 67 65 20 69 73 20 61 64 65 |hat range is ade|
00000910 71 75 61 74 65 2e 20 20 20 20 20 20 20 20 20 20 |quate. |
00000920 2a 2a 2a 2a 0a 3b 0a 0a 20 20 20 20 20 20 20 20 |****.;.. |
00000930 45 58 50 4f 52 54 20 20 70 6f 77 31 36 0a 0a 70 |EXPORT pow16..p|
00000940 77 6e 73 74 61 20 20 44 43 42 20 20 20 20 20 22 |wnsta DCB "|
00000950 70 6f 77 31 36 22 2c 20 30 0a 20 20 20 20 20 20 |pow16", 0. |
00000960 20 20 41 4c 49 47 4e 0a 70 77 6e 65 6e 64 20 20 | ALIGN.pwnend |
00000970 44 43 44 20 20 20 20 20 26 66 66 30 30 30 30 30 |DCD &ff00000|
00000980 30 20 2b 20 70 77 6e 65 6e 64 20 2d 20 70 77 6e |0 + pwnend - pwn|
00000990 73 74 61 0a 0a 70 6f 77 31 36 0a 0a 09 43 4d 50 |sta..pow16...CMP|
000009a0 09 61 32 2c 20 23 30 0a 09 4d 4f 56 45 51 09 61 |.a2, #0..MOVEQ.a|
000009b0 31 2c 20 23 26 31 30 30 30 30 09 09 3b 69 66 20 |1, #&10000..;if |
000009c0 62 3d 30 20 72 65 74 75 72 6e 20 6f 6e 65 20 64 |b=0 return one d|
000009d0 69 72 65 63 74 6c 79 0a 09 4d 4f 56 45 51 53 09 |irectly..MOVEQS.|
000009e0 70 63 2c 20 6c 72 0a 09 43 4d 50 09 61 32 2c 20 |pc, lr..CMP.a2, |
000009f0 23 26 31 30 30 30 30 0a 09 4d 4f 56 45 51 53 09 |#&10000..MOVEQS.|
00000a00 70 63 2c 20 6c 72 09 09 09 3b 68 61 6e 64 6c 65 |pc, lr...;handle|
00000a10 20 74 72 69 76 61 6c 20 63 61 73 65 20 62 3d 6f | trival case b=o|
00000a20 6e 65 20 64 69 72 65 63 74 6c 79 2c 20 62 79 20 |ne directly, by |
00000a30 72 65 74 75 72 6e 69 6e 67 20 61 0a 09 43 4d 50 |returning a..CMP|
00000a40 09 61 31 2c 20 23 30 0a 09 4d 4f 56 47 54 09 69 |.a1, #0..MOVGT.i|
00000a50 70 2c 20 23 30 0a 09 42 47 54 09 70 6f 77 31 36 |p, #0..BGT.pow16|
00000a60 5f 61 70 6f 73 0a 09 42 4e 45 09 70 6f 77 31 36 |_apos..BNE.pow16|
00000a70 5f 61 6e 65 67 0a 09 43 4d 50 09 61 32 2c 20 23 |_aneg..CMP.a2, #|
00000a80 30 0a 09 4d 4f 56 09 61 31 2c 20 23 30 09 09 09 |0..MOV.a1, #0...|
00000a90 3b 69 66 20 61 3d 30 20 61 6e 64 20 62 3e 30 20 |;if a=0 and b>0 |
00000aa0 72 65 74 75 72 6e 20 30 0a 09 4d 4f 56 4c 54 09 |return 0..MOVLT.|
00000ab0 61 31 2c 20 23 6d 61 78 31 36 2b 31 09 09 3b 69 |a1, #max16+1..;i|
00000ac0 66 20 61 3d 30 20 61 6e 64 20 62 3c 30 20 72 65 |f a=0 and b<0 re|
00000ad0 74 75 72 6e 20 6d 61 78 31 36 0a 09 53 55 42 4c |turn max16..SUBL|
00000ae0 54 09 61 31 2c 20 61 31 2c 20 23 31 0a 09 4d 4f |T.a1, a1, #1..MO|
00000af0 56 53 09 70 63 2c 20 6c 72 0a 70 6f 77 31 36 5f |VS.pc, lr.pow16_|
00000b00 61 6e 65 67 0a 09 4d 4f 56 53 09 69 70 2c 20 61 |aneg..MOVS.ip, a|
00000b10 32 2c 20 4c 53 4c 20 23 31 36 0a 09 4d 4f 56 4e |2, LSL #16..MOVN|
00000b20 45 09 61 31 2c 20 23 30 09 09 09 3b 69 66 20 61 |E.a1, #0...;if a|
00000b30 3c 30 20 61 6e 64 20 62 20 6e 6f 74 20 61 6e 20 |<0 and b not an |
00000b40 69 6e 74 65 67 65 72 20 72 65 74 75 72 6e 20 30 |integer return 0|
00000b50 0a 09 4d 4f 56 4e 45 53 09 70 63 2c 20 6c 72 0a |..MOVNES.pc, lr.|
00000b60 09 41 4e 44 09 69 70 2c 20 61 32 2c 20 23 26 31 |.AND.ip, a2, #&1|
00000b70 30 30 30 30 09 09 3b 69 66 20 61 3c 30 20 74 68 |0000..;if a<0 th|
00000b80 65 6e 20 67 6f 20 6f 6e 20 74 6f 20 65 76 61 6c |en go on to eval|
00000b90 75 61 74 65 20 28 36 35 35 33 36 20 2a 20 28 2d |uate (65536 * (-|
00000ba0 61 2f 36 35 35 33 36 29 5e 28 62 2f 36 35 35 33 |a/65536)^(b/6553|
00000bb0 36 29 29 0a 09 52 53 42 09 61 31 2c 20 61 31 2c |6))..RSB.a1, a1,|
00000bc0 20 23 30 09 09 3b 77 69 74 68 20 73 69 67 6e 20 | #0..;with sign |
00000bd0 73 75 62 73 65 71 75 65 6e 74 6c 79 20 66 6f 72 |subsequently for|
00000be0 63 65 64 20 74 6f 20 2b 20 6f 72 20 2d 20 61 63 |ced to + or - ac|
00000bf0 63 6f 72 64 69 6e 67 20 74 6f 20 77 68 65 74 68 |cording to wheth|
00000c00 65 72 20 62 2f 6f 6e 65 0a 70 6f 77 31 36 5f 61 |er b/one.pow16_a|
00000c10 70 6f 73 09 09 09 09 3b 69 73 20 65 76 65 6e 20 |pos....;is even |
00000c20 6f 72 20 6f 64 64 20 28 20 65 67 20 28 2d 32 2e |or odd ( eg (-2.|
00000c30 35 29 5e 33 20 69 73 20 6a 75 73 74 20 28 2d 31 |5)^3 is just (-1|
00000c40 29 5e 33 20 2a 20 32 2e 35 5e 33 20 29 0a 09 53 |)^3 * 2.5^3 )..S|
00000c50 54 4d 46 44 09 73 70 21 2c 20 7b 76 31 2c 20 76 |TMFD.sp!, {v1, v|
00000c60 32 2c 20 6c 72 7d 0a 09 4d 4f 56 09 76 31 2c 20 |2, lr}..MOV.v1, |
00000c70 69 70 09 09 09 3b 6e 6f 77 20 65 76 61 6c 75 61 |ip...;now evalua|
00000c80 74 65 20 28 36 35 35 33 36 20 2a 20 28 61 2f 36 |te (65536 * (a/6|
00000c90 35 35 33 36 29 5e 28 62 2f 36 35 35 33 36 29 29 |5536)^(b/65536))|
00000ca0 2c 20 66 6f 72 20 61 3e 30 0a 09 4d 4f 56 09 76 |, for a>0..MOV.v|
00000cb0 32 2c 20 61 32 09 09 09 3b 76 69 61 20 65 78 70 |2, a2...;via exp|
00000cc0 31 36 28 20 6c 6e 31 36 28 61 29 20 2a 20 62 20 |16( ln16(a) * b |
00000cd0 2f 20 36 35 35 33 36 20 29 0a 09 42 4c 09 6c 6e |/ 65536 )..BL.ln|
00000ce0 31 36 09 09 09 3b 6e 62 20 74 68 69 73 20 75 73 |16...;nb this us|
00000cf0 65 73 20 70 72 6f 70 65 72 74 79 20 74 68 61 74 |es property that|
00000d00 20 65 78 70 28 62 2e 6c 6f 67 28 61 29 29 20 3d | exp(b.log(a)) =|
00000d10 20 65 78 70 28 6c 6f 67 28 61 5e 62 29 29 20 3d | exp(log(a^b)) =|
00000d20 20 61 5e 62 0a 20 20 20 20 20 20 20 20 6d 75 6c | a^b. mul|
00000d30 31 36 09 61 31 2c 20 76 32 2c 20 61 31 2c 20 61 |16.a1, v2, a1, a|
00000d40 32 2c 20 61 33 2c 20 61 34 0a 09 42 4c 09 65 78 |2, a3, a4..BL.ex|
00000d50 70 31 36 0a 09 43 4d 50 09 76 31 2c 20 23 30 0a |p16..CMP.v1, #0.|
00000d60 09 52 53 42 4e 45 09 61 31 2c 20 61 31 2c 20 23 |.RSBNE.a1, a1, #|
00000d70 30 09 09 3b 66 69 6e 61 6c 6c 79 20 73 77 69 74 |0..;finally swit|
00000d80 63 68 20 73 69 67 6e 20 6f 6e 20 61 6e 73 77 65 |ch sign on answe|
00000d90 72 20 69 66 20 6f 72 69 67 69 6e 61 6c 6c 79 20 |r if originally |
00000da0 61 3c 30 20 61 6e 64 20 62 2f 6f 6e 65 20 77 61 |a<0 and b/one wa|
00000db0 73 20 6f 64 64 0a 09 4c 44 4d 46 44 09 73 70 21 |s odd..LDMFD.sp!|
00000dc0 2c 20 7b 76 31 2c 20 76 32 2c 20 70 63 7d 5e 0a |, {v1, v2, pc}^.|
00000dd0 0a 0a 0a 3b 20 6c 6e 31 36 0a 3b 20 61 20 6c 65 |...; ln16.; a le|
00000de0 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e |af APCS function|
00000df0 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 |.;.; C prototype|
00000e00 3a 0a 3b 20 69 6e 74 20 6c 6e 31 36 28 69 6e 74 |:.; int ln16(int|
00000e10 20 61 29 0a 3b 0a 3b 20 72 65 74 75 72 6e 73 20 | a).;.; returns |
00000e20 36 35 35 33 36 20 2a 20 6c 6e 20 28 61 2f 36 35 |65536 * ln (a/65|
00000e30 35 33 36 29 0a 3b 0a 3b 20 69 73 20 61 62 6f 75 |536).;.; is abou|
00000e40 74 20 33 30 20 74 69 6d 65 73 20 66 61 73 74 65 |t 30 times faste|
00000e50 72 20 74 68 61 6e 20 46 50 45 6d 75 6c 61 74 6f |r than FPEmulato|
00000e60 72 20 77 6f 72 6b 69 6e 67 20 77 69 74 68 20 64 |r working with d|
00000e70 6f 75 62 6c 65 20 66 6c 6f 61 74 73 0a 3b 0a 0a |ouble floats.;..|
00000e80 20 20 20 20 20 20 20 20 45 58 50 4f 52 54 20 20 | EXPORT |
00000e90 6c 6e 31 36 0a 0a 6c 6e 6e 73 74 61 20 20 44 43 |ln16..lnnsta DC|
00000ea0 42 20 20 20 20 20 22 6c 6e 31 36 22 2c 20 30 0a |B "ln16", 0.|
00000eb0 20 20 20 20 20 20 20 20 41 4c 49 47 4e 0a 6c 6e | ALIGN.ln|
00000ec0 6e 65 6e 64 20 20 44 43 44 20 20 20 20 20 26 66 |nend DCD &f|
00000ed0 66 30 30 30 30 30 30 20 2b 20 6c 6e 6e 65 6e 64 |f000000 + lnnend|
00000ee0 20 2d 20 6c 6e 6e 73 74 61 0a 0a 6c 6e 31 36 0a | - lnnsta..ln16.|
00000ef0 0a 09 43 4d 50 09 61 31 2c 20 23 30 09 09 09 3b |..CMP.a1, #0...;|
00000f00 69 66 20 61 3c 3d 30 20 72 65 74 75 72 6e 20 6d |if a<=0 return m|
00000f10 69 6e 31 36 0a 09 4d 4f 56 4c 45 09 61 31 2c 20 |in16..MOVLE.a1, |
00000f20 23 6d 69 6e 31 36 0a 09 4d 4f 56 4c 45 53 09 70 |#min16..MOVLES.p|
00000f30 63 2c 20 6c 72 09 09 09 3b 65 6c 73 65 20 6d 6f |c, lr...;else mo|
00000f40 73 74 20 73 69 67 6e 69 66 69 63 61 6e 74 20 62 |st significant b|
00000f50 69 74 20 69 73 20 62 65 74 77 65 65 6e 20 62 33 |it is between b3|
00000f60 30 20 26 20 62 30 0a 09 47 42 4c 41 09 63 6f 75 |0 & b0..GBLA.cou|
00000f70 6e 74 65 72 0a 63 6f 75 6e 74 65 72 09 53 45 54 |nter.counter.SET|
00000f80 41 09 33 30 09 09 09 3b 66 69 6e 64 20 6d 73 62 |A.30...;find msb|
00000f90 20 26 20 73 74 6f 72 65 20 28 6d 73 62 5f 69 6e | & store (msb_in|
00000fa0 64 65 78 20 2d 20 31 35 29 20 69 6e 20 61 34 0a |dex - 15) in a4.|
00000fb0 09 57 48 49 4c 45 09 63 6f 75 6e 74 65 72 20 3e |.WHILE.counter >|
00000fc0 20 31 0a 09 54 53 54 09 61 31 2c 20 23 31 3c 3c | 1..TST.a1, #1<<|
00000fd0 63 6f 75 6e 74 65 72 0a 09 4d 4f 56 4e 45 09 61 |counter..MOVNE.a|
00000fe0 34 2c 20 23 63 6f 75 6e 74 65 72 2d 31 35 0a 09 |4, #counter-15..|
00000ff0 42 4e 45 09 6c 6e 31 36 5f 67 6f 74 6d 73 62 0a |BNE.ln16_gotmsb.|
00001000 63 6f 75 6e 74 65 72 09 53 45 54 41 09 63 6f 75 |counter.SETA.cou|
00001010 6e 74 65 72 2d 31 0a 09 57 45 4e 44 0a 09 54 53 |nter-1..WEND..TS|
00001020 54 09 61 31 2c 20 23 31 3c 3c 31 0a 09 4d 4f 56 |T.a1, #1<<1..MOV|
00001030 4e 45 09 61 34 2c 20 23 31 2d 31 35 0a 09 4d 4f |NE.a4, #1-15..MO|
00001040 56 45 51 09 61 34 2c 20 23 30 2d 31 35 0a 6c 6e |VEQ.a4, #0-15.ln|
00001050 31 36 5f 67 6f 74 6d 73 62 09 09 09 09 3b 69 66 |16_gotmsb....;if|
00001060 20 77 65 20 73 65 74 20 7a 20 3d 20 61 31 2f 28 | we set z = a1/(|
00001070 32 5e 61 34 29 2c 20 77 69 6c 6c 20 68 61 76 65 |2^a4), will have|
00001080 20 6c 6e 28 61 2f 6f 6e 65 29 20 3d 20 6c 6e 28 | ln(a/one) = ln(|
00001090 7a 2f 6f 6e 65 20 2a 20 32 5e 61 34 29 0a 09 43 |z/one * 2^a4)..C|
000010a0 4d 50 09 61 34 2c 20 23 32 09 09 09 3b 09 09 09 |MP.a4, #2...;...|
000010b0 09 09 20 20 20 20 20 20 3d 20 6c 6e 28 7a 2f 6f |.. = ln(z/o|
000010c0 6e 65 29 20 2b 20 61 34 2a 6c 6e 32 0a 09 53 55 |ne) + a4*ln2..SU|
000010d0 42 47 54 09 61 32 2c 20 61 34 2c 20 23 32 09 09 |BGT.a2, a4, #2..|
000010e0 3b 77 69 74 68 20 7a 20 69 6e 20 72 61 6e 67 65 |;with z in range|
000010f0 20 5b 30 2e 35 2c 31 29 0a 09 4d 4f 56 47 54 09 | [0.5,1)..MOVGT.|
00001100 61 31 2c 20 61 31 2c 20 4c 53 52 20 61 32 09 09 |a1, a1, LSR a2..|
00001110 3b 73 6f 20 63 61 6c 63 20 61 31 20 3d 20 34 2a |;so calc a1 = 4*|
00001120 28 20 61 31 2f 28 32 5e 61 34 29 20 29 20 2d 20 |( a1/(2^a4) ) - |
00001130 33 2a 6f 6e 65 0a 09 52 53 42 4c 45 09 61 32 2c |3*one..RSBLE.a2,|
00001140 20 61 34 2c 20 23 32 09 09 3b 77 68 69 63 68 20 | a4, #2..;which |
00001150 70 75 74 73 20 61 31 20 69 6e 20 72 61 6e 67 65 |puts a1 in range|
00001160 20 b1 6f 6e 65 20 73 75 69 74 61 62 6c 65 20 66 | .one suitable f|
00001170 6f 72 20 61 70 70 72 6f 78 69 6d 61 74 69 6f 6e |or approximation|
00001180 20 62 79 20 70 6f 6c 79 0a 09 4d 4f 56 4c 45 09 | by poly..MOVLE.|
00001190 61 31 2c 20 61 31 2c 20 4c 53 4c 20 61 32 09 09 |a1, a1, LSL a2..|
000011a0 3b 6c 65 61 76 69 6e 67 20 75 73 20 74 6f 20 63 |;leaving us to c|
000011b0 61 6c 63 75 6c 61 74 65 20 61 34 2a 6f 6e 65 2a |alculate a4*one*|
000011c0 6c 6e 32 20 2b 20 6f 6e 65 2a 6c 6e 28 28 61 31 |ln2 + one*ln((a1|
000011d0 2b 33 6f 6e 65 29 2f 34 6f 6e 65 29 0a 09 53 55 |+3one)/4one)..SU|
000011e0 42 09 61 31 2c 20 61 31 2c 20 23 26 33 30 30 30 |B.a1, a1, #&3000|
000011f0 30 0a 09 41 44 44 09 61 32 2c 20 61 31 2c 20 61 |0..ADD.a2, a1, a|
00001200 31 2c 20 4c 53 4c 20 23 32 09 3b 73 74 61 72 74 |1, LSL #2.;start|
00001210 20 70 6f 6c 79 6e 6f 6d 69 61 6c 20 61 70 70 72 | polynomial appr|
00001220 6f 78 69 6d 61 74 69 6f 6e 20 63 61 6c 63 75 6c |oximation calcul|
00001230 61 74 69 6f 6e 20 6f 6e 20 61 31 0a 09 52 53 42 |ation on a1..RSB|
00001240 09 61 32 2c 20 61 32 2c 20 61 31 2c 20 4c 53 4c |.a2, a2, a1, LSL|
00001250 20 23 31 30 0a 09 4d 4f 56 09 61 32 2c 20 61 32 | #10..MOV.a2, a2|
00001260 2c 20 41 53 52 20 23 31 36 09 09 3b 66 6f 72 20 |, ASR #16..;for |
00001270 64 65 74 61 69 6c 73 20 6f 66 20 68 6f 77 20 74 |details of how t|
00001280 68 69 73 20 77 6f 72 6b 73 20 73 65 65 20 63 6f |his works see co|
00001290 6d 6d 65 6e 74 73 20 61 67 61 69 6e 73 74 20 73 |mments against s|
000012a0 69 6d 69 6c 61 72 20 63 6f 64 65 0a 09 53 55 42 |imilar code..SUB|
000012b0 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 65 30 |.a2, a2, #&000e0|
000012c0 30 09 3b 69 6e 20 65 78 70 31 36 20 66 75 6e 63 |0.;in exp16 func|
000012d0 74 69 6f 6e 2c 20 64 69 72 65 63 74 6c 79 20 62 |tion, directly b|
000012e0 65 6c 6f 77 20 74 68 69 73 20 66 75 6e 63 74 69 |elow this functi|
000012f0 6f 6e 0a 09 53 55 42 09 61 32 2c 20 61 32 2c 20 |on..SUB.a2, a2, |
00001300 23 26 30 30 30 30 33 34 0a 20 20 20 20 20 20 20 |#&000034. |
00001310 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c | MOV.ip, a1..mul|
00001320 31 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 |16c.a2, ip, a2, |
00001330 61 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 |a3..ADD.a2, a2, |
00001340 23 26 30 30 33 32 30 30 0a 09 41 44 44 09 61 32 |#&003200..ADD.a2|
00001350 2c 20 61 32 2c 20 23 26 30 30 30 30 33 31 0a 20 |, a2, #&000031. |
00001360 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 | MOV.ip, a|
00001370 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 |1..mul16c.a2, ip|
00001380 2c 20 61 32 2c 20 61 33 0a 09 53 55 42 09 61 32 |, a2, a3..SUB.a2|
00001390 2c 20 61 32 2c 20 23 26 30 30 65 32 30 30 0a 09 |, a2, #&00e200..|
000013a0 53 55 42 09 61 32 2c 20 61 32 2c 20 23 26 30 30 |SUB.a2, a2, #&00|
000013b0 30 30 66 32 0a 20 20 20 20 20 20 20 20 4d 4f 56 |00f2. MOV|
000013c0 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 |.ip, a1..mul16c.|
000013d0 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a 09 |a2, ip, a2, a3..|
000013e0 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 35 |ADD.a2, a2, #&05|
000013f0 30 30 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 |0000..ADD.a2, a2|
00001400 2c 20 23 26 30 30 35 35 30 30 0a 09 41 44 44 09 |, #&005500..ADD.|
00001410 61 32 2c 20 61 32 2c 20 23 26 30 30 30 30 36 35 |a2, a2, #&000065|
00001420 0a 20 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c |. MOV.ip,|
00001430 20 61 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 | a1..mul16c.a2, |
00001440 69 70 2c 20 61 32 2c 20 61 33 0a 09 53 55 42 09 |ip, a2, a3..SUB.|
00001450 61 32 2c 20 61 32 2c 20 23 26 30 34 30 30 30 30 |a2, a2, #&040000|
00001460 0a 09 53 55 42 09 61 32 2c 20 61 32 2c 20 23 26 |..SUB.a2, a2, #&|
00001470 30 30 39 61 30 30 09 3b 65 6e 64 20 6f 66 20 70 |009a00.;end of p|
00001480 6f 6c 79 6e 6f 6d 69 61 6c 20 61 70 70 72 6f 78 |olynomial approx|
00001490 69 6d 61 74 69 6f 6e 20 63 61 6c 63 75 6c 61 74 |imation calculat|
000014a0 69 6f 6e 0a 09 53 55 42 09 61 31 2c 20 61 32 2c |ion..SUB.a1, a2,|
000014b0 20 23 26 30 30 30 30 35 39 09 3b 61 31 20 6e 6f | #&000059.;a1 no|
000014c0 77 20 68 6f 6c 64 73 20 28 32 5e 32 30 29 2a 28 |w holds (2^20)*(|
000014d0 61 70 70 72 6f 78 69 6d 61 74 65 64 20 76 61 6c |approximated val|
000014e0 75 65 29 0a 09 41 44 44 09 69 70 2c 20 61 34 2c |ue)..ADD.ip, a4,|
000014f0 20 61 34 2c 20 4c 53 4c 20 23 31 0a 09 41 44 44 | a4, LSL #1..ADD|
00001500 09 61 32 2c 20 69 70 2c 20 61 34 2c 20 4c 53 4c |.a2, ip, a4, LSL|
00001510 20 23 33 09 3b 6e 6f 77 20 61 64 64 20 69 6e 20 | #3.;now add in |
00001520 74 68 65 20 61 34 2a 6f 6e 65 2a 6c 6e 32 20 74 |the a4*one*ln2 t|
00001530 65 72 6d 20 75 73 69 6e 67 20 61 6e 20 65 78 70 |erm using an exp|
00001540 6c 69 63 69 74 20 62 69 6e 61 72 79 20 65 78 70 |licit binary exp|
00001550 61 6e 73 69 6f 6e 0a 09 41 44 44 09 61 32 2c 20 |ansion..ADD.a2, |
00001560 61 34 2c 20 61 32 2c 20 4c 53 4c 20 23 34 09 3b |a4, a2, LSL #4.;|
00001570 6f 66 20 61 70 70 72 6f 78 69 6d 61 74 65 6c 79 |of approximately|
00001580 20 6f 6e 65 2a 6c 6e 32 0a 09 52 53 42 09 61 33 | one*ln2..RSB.a3|
00001590 2c 20 61 34 2c 20 61 34 2c 20 4c 53 4c 20 23 33 |, a4, a4, LSL #3|
000015a0 0a 09 41 44 44 09 61 32 2c 20 61 33 2c 20 61 32 |..ADD.a2, a3, a2|
000015b0 2c 20 4c 53 4c 20 23 34 09 3b 6e 62 20 77 65 20 |, LSL #4.;nb we |
000015c0 61 63 74 75 61 6c 6c 79 20 61 64 64 20 61 70 70 |actually add app|
000015d0 72 6f 78 20 28 32 5e 32 30 29 2a 6c 6e 32 2c 20 |rox (2^20)*ln2, |
000015e0 26 20 74 68 65 6e 20 64 69 76 69 64 65 20 62 79 |& then divide by|
000015f0 20 31 36 0a 09 41 44 44 09 61 32 2c 20 61 34 2c | 16..ADD.a2, a4,|
00001600 20 61 32 2c 20 4c 53 4c 20 23 33 09 3b 74 6f 20 | a2, LSL #3.;to |
00001610 72 65 64 75 63 65 20 74 72 75 6e 63 61 74 69 6f |reduce truncatio|
00001620 6e 20 65 72 72 6f 72 0a 09 41 44 44 09 61 31 2c |n error..ADD.a1,|
00001630 20 61 31 2c 20 61 32 2c 20 4c 53 4c 20 23 35 0a | a1, a2, LSL #5.|
00001640 09 41 44 44 09 61 31 2c 20 61 31 2c 20 69 70 2c |.ADD.a1, a1, ip,|
00001650 20 41 53 52 20 23 31 0a 09 4d 4f 56 09 61 31 2c | ASR #1..MOV.a1,|
00001660 20 61 31 2c 20 41 53 52 20 23 34 0a 20 20 20 20 | a1, ASR #4. |
00001670 20 20 20 20 4d 4f 56 53 20 20 20 20 70 63 2c 20 | MOVS pc, |
00001680 6c 72 0a 0a 0a 0a 3b 20 65 78 70 31 36 0a 3b 20 |lr....; exp16.; |
00001690 61 20 6c 65 61 66 20 41 50 43 53 20 66 75 6e 63 |a leaf APCS func|
000016a0 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f |tion.;.; C proto|
000016b0 74 79 70 65 3a 0a 3b 20 69 6e 74 20 65 78 70 31 |type:.; int exp1|
000016c0 36 28 69 6e 74 20 61 29 0a 3b 0a 3b 20 72 65 74 |6(int a).;.; ret|
000016d0 75 72 6e 73 20 36 35 35 33 36 20 2a 20 65 78 70 |urns 65536 * exp|
000016e0 20 28 61 2f 36 35 35 33 36 29 0a 3b 0a 3b 20 69 | (a/65536).;.; i|
000016f0 73 20 61 62 6f 75 74 20 34 35 20 74 69 6d 65 73 |s about 45 times|
00001700 20 66 61 73 74 65 72 20 74 68 61 6e 20 46 50 45 | faster than FPE|
00001710 6d 75 6c 61 74 6f 72 20 77 6f 72 6b 69 6e 67 20 |mulator working |
00001720 77 69 74 68 20 64 6f 75 62 6c 65 20 66 6c 6f 61 |with double floa|
00001730 74 73 0a 3b 0a 0a 20 20 20 20 20 20 20 20 45 58 |ts.;.. EX|
00001740 50 4f 52 54 20 20 65 78 70 31 36 0a 0a 65 70 6e |PORT exp16..epn|
00001750 73 74 61 20 20 44 43 42 20 20 20 20 20 22 65 78 |sta DCB "ex|
00001760 70 31 36 22 2c 20 30 0a 20 20 20 20 20 20 20 20 |p16", 0. |
00001770 41 4c 49 47 4e 0a 65 70 6e 65 6e 64 20 20 44 43 |ALIGN.epnend DC|
00001780 44 20 20 20 20 20 26 66 66 30 30 30 30 30 30 20 |D &ff000000 |
00001790 2b 20 65 70 6e 65 6e 64 20 2d 20 65 70 6e 73 74 |+ epnend - epnst|
000017a0 61 0a 0a 65 78 70 31 36 09 09 09 09 09 3b 74 68 |a..exp16.....;th|
000017b0 69 73 20 66 6e 20 72 65 74 75 72 6e 73 20 61 20 |is fn returns a |
000017c0 76 61 6c 75 65 20 77 69 74 68 20 6f 6e 6c 79 20 |value with only |
000017d0 61 62 6f 75 74 20 31 37 20 73 69 67 6e 69 66 69 |about 17 signifi|
000017e0 63 61 6e 74 20 62 69 6e 61 72 79 0a 09 09 09 09 |cant binary.....|
000017f0 09 3b 64 69 67 69 74 73 20 2d 20 65 67 20 66 6f |.;digits - eg fo|
00001800 72 20 27 61 27 20 73 6d 61 6c 6c 20 6f 72 20 6e |r 'a' small or n|
00001810 65 67 61 74 69 76 65 2c 20 67 65 74 20 6e 65 61 |egative, get nea|
00001820 72 20 6d 61 78 69 6d 61 6c 20 61 63 63 75 72 61 |r maximal accura|
00001830 63 79 0a 09 09 09 09 09 3b 62 75 74 20 66 6f 72 |cy......;but for|
00001840 20 27 61 27 20 6c 61 72 67 65 20 28 75 70 74 6f | 'a' large (upto|
00001850 20 61 72 6f 75 6e 64 20 31 30 6f 6e 65 29 20 77 | around 10one) w|
00001860 68 65 72 65 20 65 78 70 20 68 61 73 20 76 61 6c |here exp has val|
00001870 75 65 0a 09 43 4d 50 09 61 31 2c 20 23 31 32 2a |ue..CMP.a1, #12*|
00001880 36 35 35 33 36 09 09 3b 7e 32 30 30 30 30 6f 6e |65536..;~20000on|
00001890 65 20 63 61 6e 20 67 65 74 20 65 72 72 6f 72 20 |e can get error |
000018a0 75 70 74 6f 20 72 6f 75 67 68 6c 79 20 30 2e 31 |upto roughly 0.1|
000018b0 6f 6e 65 0a 09 4d 4f 56 47 54 09 61 31 2c 20 23 |one..MOVGT.a1, #|
000018c0 6d 61 78 31 36 2b 31 0a 09 53 55 42 47 54 09 61 |max16+1..SUBGT.a|
000018d0 31 2c 20 61 31 2c 20 23 31 0a 09 4d 4f 56 47 54 |1, a1, #1..MOVGT|
000018e0 53 09 70 63 2c 20 6c 72 0a 09 43 4d 50 09 61 31 |S.pc, lr..CMP.a1|
000018f0 2c 20 23 2d 31 32 2a 36 35 35 33 36 0a 09 4d 4f |, #-12*65536..MO|
00001900 56 4c 54 09 61 31 2c 20 23 30 0a 09 4d 4f 56 4c |VLT.a1, #0..MOVL|
00001910 54 53 09 70 63 2c 20 6c 72 09 09 09 3b 6f 74 68 |TS.pc, lr...;oth|
00001920 65 72 77 69 73 65 20 6b 6e 6f 77 20 7c 61 7c 20 |erwise know |a| |
00001930 3c 3d 20 31 32 6f 6e 65 0a 09 52 53 42 09 61 32 |<= 12one..RSB.a2|
00001940 2c 20 61 31 2c 20 61 31 2c 20 4c 53 4c 20 23 33 |, a1, a1, LSL #3|
00001950 09 3b 6e 6f 77 20 73 65 74 20 61 20 3d 20 61 2f |.;now set a = a/|
00001960 6c 6e 32 20 75 73 69 6e 67 20 65 78 70 6c 69 63 |ln2 using explic|
00001970 69 74 20 6d 75 6c 20 62 79 20 32 5f 31 2e 30 31 |it mul by 2_1.01|
00001980 31 31 30 30 30 31 30 31 30 31 30 31 30 30 30 31 |1100010101010001|
00001990 31 31 0a 09 41 44 44 09 61 33 2c 20 61 31 2c 20 |11..ADD.a3, a1, |
000019a0 61 31 2c 20 4c 53 4c 20 23 32 09 3b 6e 62 20 6f |a1, LSL #2.;nb o|
000019b0 6e 6c 79 20 6e 65 65 64 20 31 73 74 20 32 30 20 |nly need 1st 20 |
000019c0 64 69 67 69 74 73 20 67 69 76 65 6e 20 72 61 6e |digits given ran|
000019d0 67 65 20 6f 6e 20 61 0a 09 41 44 44 09 61 33 2c |ge on a..ADD.a3,|
000019e0 20 61 33 2c 20 61 33 2c 20 4c 53 4c 20 23 34 09 | a3, a3, LSL #4.|
000019f0 3b 6e 62 32 20 74 68 69 73 20 63 61 6c 63 20 69 |;nb2 this calc i|
00001a00 73 20 61 70 70 72 6f 78 69 6d 61 74 65 20 6f 6e |s approximate on|
00001a10 6c 79 2c 20 74 68 6f 75 67 68 20 77 69 6c 6c 20 |ly, though will |
00001a20 75 73 75 61 6c 6c 79 20 79 69 65 6c 64 20 61 6e |usually yield an|
00001a30 0a 09 41 44 44 09 61 31 2c 20 61 32 2c 20 61 31 |..ADD.a1, a2, a1|
00001a40 2c 20 4c 53 4c 20 23 34 09 3b 61 6e 73 77 65 72 |, LSL #4.;answer|
00001a50 20 63 6f 72 72 65 63 74 20 74 6f 20 74 68 65 20 | correct to the |
00001a60 73 74 6f 72 65 64 20 31 36 20 62 69 6e 61 72 79 |stored 16 binary|
00001a70 20 70 6c 61 63 65 73 20 28 65 6c 73 65 20 65 72 | places (else er|
00001a80 72 6f 72 20 6f 6e 65 2f 36 35 35 33 36 29 0a 09 |ror one/65536)..|
00001a90 41 44 44 09 61 31 2c 20 61 31 2c 20 61 33 2c 20 |ADD.a1, a1, a3, |
00001aa0 41 53 52 20 23 31 30 0a 09 41 44 44 09 61 31 2c |ASR #10..ADD.a1,|
00001ab0 20 61 31 2c 20 61 32 2c 20 41 53 52 20 23 31 36 | a1, a2, ASR #16|
00001ac0 09 3b 74 68 75 73 20 65 78 70 28 6f 72 69 67 69 |.;thus exp(origi|
00001ad0 6e 61 6c 20 61 29 20 20 3d 20 65 78 70 28 6e 65 |nal a) = exp(ne|
00001ae0 77 20 61 20 2a 20 6c 6e 32 29 20 3d 20 32 5e 28 |w a * ln2) = 2^(|
00001af0 6e 65 77 20 61 29 2c 20 65 76 61 6c 27 64 20 62 |new a), eval'd b|
00001b00 65 6c 6f 77 3a 0a 09 41 44 44 09 61 31 2c 20 61 |elow:..ADD.a1, a|
00001b10 31 2c 20 23 38 0a 09 4d 4f 56 09 61 31 2c 20 61 |1, #8..MOV.a1, a|
00001b20 31 2c 20 41 53 52 20 23 34 09 09 3b 63 61 6c 63 |1, ASR #4..;calc|
00001b30 20 61 20 3d 20 61 2f 6c 6e 32 20 63 6f 6d 70 6c | a = a/ln2 compl|
00001b40 65 74 65 0a 09 4d 4f 56 09 61 34 2c 20 61 31 2c |ete..MOV.a4, a1,|
00001b50 20 41 53 52 20 23 31 36 09 09 3b 61 34 20 6e 6f | ASR #16..;a4 no|
00001b60 77 20 68 6f 6c 64 73 20 69 6e 74 65 67 65 72 20 |w holds integer |
00001b70 63 6f 6d 70 6f 6e 65 6e 74 20 6f 66 20 61 0a 09 |component of a..|
00001b80 42 49 43 09 61 31 2c 20 61 31 2c 20 61 34 2c 20 |BIC.a1, a1, a4, |
00001b90 4c 53 4c 20 23 31 36 09 3b 61 31 20 6e 6f 77 20 |LSL #16.;a1 now |
00001ba0 68 6f 6c 64 73 20 66 72 61 63 74 69 6f 6e 61 6c |holds fractional|
00001bb0 20 63 6f 6d 70 6f 6e 65 6e 74 20 69 6e 20 72 61 | component in ra|
00001bc0 6e 67 65 20 5b 30 2c 31 29 2a 6f 6e 65 0a 09 43 |nge [0,1)*one..C|
00001bd0 4d 50 09 61 34 2c 20 23 31 35 09 09 09 3b 64 6f |MP.a4, #15...;do|
00001be0 20 61 6e 6f 74 68 65 72 20 63 68 65 63 6b 20 6f | another check o|
00001bf0 6e 20 61 20 74 6f 20 65 6e 73 75 72 65 20 65 78 |n a to ensure ex|
00001c00 70 28 61 29 20 69 73 20 69 6e 20 72 61 6e 67 65 |p(a) is in range|
00001c10 0a 09 4d 4f 56 47 45 09 61 31 2c 20 23 6d 61 78 |..MOVGE.a1, #max|
00001c20 31 36 2b 31 09 09 3b 26 20 69 66 20 6e 6f 74 20 |16+1..;& if not |
00001c30 72 65 74 75 72 6e 20 6d 61 78 69 6d 61 6c 20 6f |return maximal o|
00001c40 72 20 6d 69 6e 69 6d 61 6c 20 76 61 6c 75 65 20 |r minimal value |
00001c50 61 73 20 61 70 70 72 6f 70 72 69 61 74 65 0a 09 |as appropriate..|
00001c60 53 55 42 47 45 09 61 31 2c 20 61 31 2c 20 23 31 |SUBGE.a1, a1, #1|
00001c70 0a 09 4d 4f 56 47 45 53 09 70 63 2c 20 6c 72 0a |..MOVGES.pc, lr.|
00001c80 09 43 4d 50 09 61 34 2c 20 23 2d 31 36 0a 09 4d |.CMP.a4, #-16..M|
00001c90 4f 56 4c 54 09 61 31 2c 20 23 30 0a 09 4d 4f 56 |OVLT.a1, #0..MOV|
00001ca0 4c 54 53 09 70 63 2c 20 6c 72 09 09 09 3b 65 6c |LTS.pc, lr...;el|
00001cb0 73 65 20 6e 65 65 64 20 74 6f 20 72 65 74 75 72 |se need to retur|
00001cc0 6e 20 76 61 6c 75 65 20 28 6f 6e 65 20 2a 20 32 |n value (one * 2|
00001cd0 5e 28 61 34 20 2b 20 61 31 2f 6f 6e 65 29 29 0a |^(a4 + a1/one)).|
00001ce0 09 4d 4f 56 09 61 31 2c 20 61 31 2c 20 4c 53 4c |.MOV.a1, a1, LSL|
00001cf0 20 23 31 09 09 3b 09 09 09 20 3d 20 28 6f 6e 65 | #1..;... = (one|
00001d00 20 2a 20 32 5e 28 61 31 2f 6f 6e 65 29 20 2a 20 | * 2^(a1/one) * |
00001d10 32 5e 61 34 29 0a 09 53 55 42 09 61 31 2c 20 61 |2^a4)..SUB.a1, a|
00001d20 31 2c 20 23 26 31 30 30 30 30 09 09 3b 63 6f 6e |1, #&10000..;con|
00001d30 76 65 72 74 20 61 31 20 74 6f 20 6c 69 65 20 69 |vert a1 to lie i|
00001d40 6e 20 5b 2d 31 2c 2d 31 29 2c 20 74 68 65 6e 20 |n [-1,-1), then |
00001d50 61 70 70 6c 79 20 70 6f 6c 79 20 61 70 70 72 6f |apply poly appro|
00001d60 78 69 6d 61 74 69 6f 6e 3a 0a 09 52 53 42 09 61 |ximation:..RSB.a|
00001d70 32 2c 20 61 31 2c 20 61 31 2c 20 4c 53 4c 20 23 |2, a1, a1, LSL #|
00001d80 33 0a 09 41 44 44 09 61 32 2c 20 61 31 2c 20 61 |3..ADD.a2, a1, a|
00001d90 32 2c 20 4c 53 4c 20 23 36 0a 09 4d 4f 56 09 61 |2, LSL #6..MOV.a|
00001da0 32 2c 20 61 32 2c 20 41 53 52 20 23 31 35 09 09 |2, a2, ASR #15..|
00001db0 3b 61 32 20 3d 20 30 2e 30 30 30 38 35 36 31 2a |;a2 = 0.0008561*|
00001dc0 28 32 5e 32 30 29 2a 28 61 31 2f 6f 6e 65 29 0a |(2^20)*(a1/one).|
00001dd0 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00001de0 30 32 38 30 30 0a 09 41 44 44 09 61 32 2c 20 61 |02800..ADD.a2, a|
00001df0 32 2c 20 23 26 30 30 30 30 37 65 09 3b 61 32 20 |2, #&00007e.;a2 |
00001e00 3d 20 30 2e 30 30 30 38 35 36 31 2a 28 32 5e 32 |= 0.0008561*(2^2|
00001e10 30 29 2a 28 61 31 2f 6f 6e 65 29 20 2b 20 30 2e |0)*(a1/one) + 0.|
00001e20 30 30 39 38 38 35 37 2a 28 32 5e 32 30 29 0a 20 |0098857*(2^20). |
00001e30 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 | MOV.ip, a|
00001e40 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 |1..mul16c.a2, ip|
00001e50 2c 20 61 32 2c 20 61 33 09 09 3b 61 32 20 3d 20 |, a2, a3..;a2 = |
00001e60 30 2e 30 30 30 38 35 36 31 2a 28 32 5e 32 30 29 |0.0008561*(2^20)|
00001e70 2a 28 61 31 2f 6f 6e 65 29 5e 32 20 2b 20 30 2e |*(a1/one)^2 + 0.|
00001e80 30 30 39 38 38 35 37 2a 28 32 5e 32 30 29 2a 28 |0098857*(2^20)*(|
00001e90 61 31 2f 6f 6e 65 29 0a 09 41 44 44 09 61 32 2c |a1/one)..ADD.a2,|
00001ea0 20 61 32 2c 20 23 26 30 31 35 30 30 30 0a 09 41 | a2, #&015000..A|
00001eb0 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 |DD.a2, a2, #&000|
00001ec0 62 65 30 09 3b 20 65 74 63 0a 20 20 20 20 20 20 |be0.; etc. |
00001ed0 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 | MOV.ip, a1..mu|
00001ee0 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c |l16c.a2, ip, a2,|
00001ef0 20 61 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c | a3..ADD.a2, a2,|
00001f00 20 23 26 30 37 30 30 30 30 0a 09 41 44 44 09 61 | #&070000..ADD.a|
00001f10 32 2c 20 61 32 2c 20 23 26 30 30 64 37 30 30 0a |2, a2, #&00d700.|
00001f20 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00001f30 30 30 30 37 65 0a 20 20 20 20 20 20 20 20 4d 4f |0007e. MO|
00001f40 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 |V.ip, a1..mul16c|
00001f50 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 09 |.a2, ip, a2, a3.|
00001f60 09 3b 75 6e 74 69 6c 20 77 65 20 68 61 76 65 0a |.;until we have.|
00001f70 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 31 |.ADD.a2, a2, #&1|
00001f80 36 30 30 30 30 09 3b 61 32 20 3d 20 28 32 5e 32 |60000.;a2 = (2^2|
00001f90 30 29 20 28 20 30 2e 30 30 30 38 35 36 31 28 61 |0) ( 0.0008561(a|
00001fa0 31 2f 6f 6e 65 29 5e 34 20 2b 20 30 2e 30 30 39 |1/one)^4 + 0.009|
00001fb0 38 38 35 37 28 61 31 2f 6f 6e 65 29 5e 33 20 2b |8857(a1/one)^3 +|
00001fc0 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 |..ADD.a2, a2, #&|
00001fd0 30 30 61 30 30 30 09 3b 09 20 20 20 20 20 20 20 |00a000.;. |
00001fe0 30 2e 30 38 34 39 33 30 31 28 61 31 2f 6f 6e 65 |0.0849301(a1/one|
00001ff0 29 5e 32 20 2b 20 30 2e 34 39 30 31 31 30 36 28 |)^2 + 0.4901106(|
00002000 61 31 2f 6f 6e 65 29 20 2b 0a 09 41 44 44 09 61 |a1/one) +..ADD.a|
00002010 32 2c 20 61 32 2c 20 23 26 30 30 30 30 61 37 09 |2, a2, #&0000a7.|
00002020 3b 09 20 20 20 20 20 20 20 31 2e 31 34 31 34 32 |;. 1.14142|
00002030 31 33 38 20 20 20 20 20 20 20 20 20 20 20 20 20 |138 |
00002040 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | |
00002050 20 20 20 20 20 20 29 0a 09 4d 4f 56 09 61 31 2c | )..MOV.a1,|
00002060 20 61 32 2c 20 41 53 52 20 23 34 09 09 3b 6e 6f | a2, ASR #4..;no|
00002070 77 20 64 69 76 69 64 65 20 62 79 20 31 36 20 72 |w divide by 16 r|
00002080 65 6d 6f 76 69 6e 67 20 6d 6f 73 74 20 74 72 75 |emoving most tru|
00002090 6e 63 61 74 69 6f 6e 20 65 72 72 6f 72 20 66 72 |ncation error fr|
000020a0 6f 6d 20 61 62 6f 76 65 20 63 61 6c 63 73 2c 0a |om above calcs,.|
000020b0 09 43 4d 50 09 61 34 2c 20 23 30 09 09 09 3b 6c |.CMP.a4, #0...;l|
000020c0 65 61 76 69 6e 67 20 61 32 20 3d 20 28 32 5e 31 |eaving a2 = (2^1|
000020d0 36 29 2a 28 61 70 70 72 6f 78 69 6d 61 74 65 64 |6)*(approximated|
000020e0 20 76 61 6c 75 65 29 0a 09 52 53 42 4c 54 09 61 | value)..RSBLT.a|
000020f0 34 2c 20 61 34 2c 20 23 30 0a 09 4d 4f 56 4c 54 |4, a4, #0..MOVLT|
00002100 09 61 31 2c 20 61 31 2c 20 41 53 52 20 61 34 09 |.a1, a1, ASR a4.|
00002110 09 3b 66 69 6e 61 6c 6c 79 20 63 61 72 72 79 20 |.;finally carry |
00002120 6f 75 74 20 74 68 65 20 28 61 32 20 3d 20 61 32 |out the (a2 = a2|
00002130 20 2a 20 32 5e 61 34 29 20 73 74 65 70 0a 09 4d | * 2^a4) step..M|
00002140 4f 56 4c 54 53 09 70 63 2c 20 6c 72 0a 09 4d 4f |OVLTS.pc, lr..MO|
00002150 56 53 09 61 31 2c 20 61 31 2c 20 4c 53 4c 20 61 |VS.a1, a1, LSL a|
00002160 34 0a 09 4d 4f 56 4d 49 09 61 31 2c 20 23 6d 61 |4..MOVMI.a1, #ma|
00002170 78 31 36 2b 31 0a 09 53 55 42 4d 49 09 61 31 2c |x16+1..SUBMI.a1,|
00002180 20 61 31 2c 20 23 31 0a 20 20 20 20 20 20 20 20 | a1, #1. |
00002190 4d 4f 56 53 20 20 20 20 70 63 2c 20 6c 72 0a 0a |MOVS pc, lr..|
000021a0 0a 0a 3b 20 73 69 67 31 36 0a 3b 20 61 20 6c 65 |..; sig16.; a le|
000021b0 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e |af APCS function|
000021c0 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 |.;.; C prototype|
000021d0 3a 0a 3b 20 69 6e 74 20 73 69 67 31 36 28 69 6e |:.; int sig16(in|
000021e0 74 20 61 29 0a 3b 0a 3b 20 72 65 74 75 72 6e 73 |t a).;.; returns|
000021f0 20 36 35 35 33 36 20 2f 20 28 20 31 20 2b 20 20 | 65536 / ( 1 + |
00002200 65 78 70 20 28 2d 61 2f 36 35 35 33 36 29 20 29 |exp (-a/65536) )|
00002210 0a 3b 20 74 68 65 20 73 69 67 6d 6f 69 64 20 66 |.; the sigmoid f|
00002220 75 6e 63 74 69 6f 6e 20 66 6f 72 20 6e 65 75 72 |unction for neur|
00002230 61 6c 20 6e 65 74 20 63 6f 64 65 0a 3b 0a 3b 20 |al net code.;.; |
00002240 69 73 20 61 62 6f 75 74 20 35 33 20 74 69 6d 65 |is about 53 time|
00002250 73 20 66 61 73 74 65 72 20 74 68 61 6e 20 46 50 |s faster than FP|
00002260 45 6d 75 6c 61 74 6f 72 20 77 6f 72 6b 69 6e 67 |Emulator working|
00002270 20 77 69 74 68 20 64 6f 75 62 6c 65 20 66 6c 6f | with double flo|
00002280 61 74 73 0a 3b 0a 0a 20 20 20 20 20 20 20 20 45 |ats.;.. E|
00002290 58 50 4f 52 54 20 20 73 69 67 31 36 0a 0a 73 64 |XPORT sig16..sd|
000022a0 6e 73 74 61 20 20 44 43 42 20 20 20 20 20 22 73 |nsta DCB "s|
000022b0 69 67 31 36 22 2c 20 30 0a 20 20 20 20 20 20 20 |ig16", 0. |
000022c0 20 41 4c 49 47 4e 0a 73 64 6e 65 6e 64 20 20 44 | ALIGN.sdnend D|
000022d0 43 44 20 20 20 20 20 26 66 66 30 30 30 30 30 30 |CD &ff000000|
000022e0 20 2b 20 73 64 6e 65 6e 64 20 2d 20 73 64 6e 73 | + sdnend - sdns|
000022f0 74 61 0a 0a 73 69 67 31 36 09 43 4d 50 09 61 31 |ta..sig16.CMP.a1|
00002300 2c 20 23 31 32 2a 36 35 35 33 36 0a 09 4d 4f 56 |, #12*65536..MOV|
00002310 47 54 09 61 31 2c 20 23 6f 6e 65 0a 09 4d 4f 56 |GT.a1, #one..MOV|
00002320 47 54 53 09 70 63 2c 20 6c 72 0a 09 43 4d 50 09 |GTS.pc, lr..CMP.|
00002330 61 31 2c 20 23 2d 31 32 2a 36 35 35 33 36 0a 09 |a1, #-12*65536..|
00002340 4d 4f 56 4c 54 09 61 31 2c 20 23 30 0a 09 4d 4f |MOVLT.a1, #0..MO|
00002350 56 4c 54 53 09 70 63 2c 20 6c 72 09 09 09 3b 6f |VLTS.pc, lr...;o|
00002360 74 68 65 72 77 69 73 65 20 6b 6e 6f 77 20 7c 61 |therwise know |a|
00002370 7c 20 3c 3d 20 31 32 6f 6e 65 0a 09 41 4e 44 53 || <= 12one..ANDS|
00002380 09 69 70 2c 20 61 31 2c 20 23 31 3c 3c 33 31 09 |.ip, a1, #1<<31.|
00002390 09 3b 63 6f 70 79 20 73 69 67 6e 20 6f 66 20 61 |.;copy sign of a|
000023a0 20 69 6e 74 6f 20 62 33 31 20 6f 66 20 69 70 0a | into b31 of ip.|
000023b0 09 52 53 42 4d 49 09 61 31 2c 20 61 31 2c 20 23 |.RSBMI.a1, a1, #|
000023c0 30 09 09 3b 65 6e 73 75 72 65 20 61 3e 3d 30 0a |0..;ensure a>=0.|
000023d0 09 52 53 42 09 61 32 2c 20 61 31 2c 20 61 31 2c |.RSB.a2, a1, a1,|
000023e0 20 4c 53 4c 20 23 33 09 3b 6e 6f 77 20 73 65 74 | LSL #3.;now set|
000023f0 20 61 20 3d 20 61 2f 6c 6e 32 20 75 73 69 6e 67 | a = a/ln2 using|
00002400 20 65 78 70 6c 69 63 69 74 20 6d 75 6c 20 62 79 | explicit mul by|
00002410 20 32 5f 31 2e 30 31 31 31 30 30 30 31 30 31 30 | 2_1.01110001010|
00002420 31 30 31 30 30 30 31 31 31 0a 09 41 44 44 09 61 |101000111..ADD.a|
00002430 33 2c 20 61 31 2c 20 61 31 2c 20 4c 53 4c 20 23 |3, a1, a1, LSL #|
00002440 32 09 3b 6e 62 20 6f 6e 6c 79 20 6e 65 65 64 20 |2.;nb only need |
00002450 31 73 74 20 32 30 20 64 69 67 69 74 73 20 67 69 |1st 20 digits gi|
00002460 76 65 6e 20 72 61 6e 67 65 20 6f 6e 20 61 0a 09 |ven range on a..|
00002470 41 44 44 09 61 33 2c 20 61 33 2c 20 61 33 2c 20 |ADD.a3, a3, a3, |
00002480 4c 53 4c 20 23 34 09 3b 6e 62 32 20 74 68 69 73 |LSL #4.;nb2 this|
00002490 20 63 61 6c 63 20 69 73 20 61 70 70 72 6f 78 69 | calc is approxi|
000024a0 6d 61 74 65 20 6f 6e 6c 79 2c 20 74 68 6f 75 67 |mate only, thoug|
000024b0 68 20 77 69 6c 6c 20 75 73 75 61 6c 6c 79 20 79 |h will usually y|
000024c0 69 65 6c 64 20 61 6e 0a 09 41 44 44 09 61 31 2c |ield an..ADD.a1,|
000024d0 20 61 32 2c 20 61 31 2c 20 4c 53 4c 20 23 34 09 | a2, a1, LSL #4.|
000024e0 3b 61 6e 73 77 65 72 20 63 6f 72 72 65 63 74 20 |;answer correct |
000024f0 74 6f 20 74 68 65 20 73 74 6f 72 65 64 20 31 36 |to the stored 16|
00002500 20 62 69 6e 61 72 79 20 70 6c 61 63 65 73 20 28 | binary places (|
00002510 65 6c 73 65 20 65 72 72 6f 72 20 6f 6e 65 2f 36 |else error one/6|
00002520 35 35 33 36 29 0a 09 41 44 44 09 61 31 2c 20 61 |5536)..ADD.a1, a|
00002530 31 2c 20 61 33 2c 20 41 53 52 20 23 31 30 0a 09 |1, a3, ASR #10..|
00002540 41 44 44 09 61 31 2c 20 61 31 2c 20 61 32 2c 20 |ADD.a1, a1, a2, |
00002550 41 53 52 20 23 31 36 09 3b 74 68 75 73 20 65 78 |ASR #16.;thus ex|
00002560 70 28 6f 72 69 67 69 6e 61 6c 20 61 29 20 20 3d |p(original a) =|
00002570 20 65 78 70 28 6e 65 77 20 61 20 2a 20 6c 6e 32 | exp(new a * ln2|
00002580 29 20 3d 20 32 5e 28 6e 65 77 20 61 29 2c 20 65 |) = 2^(new a), e|
00002590 76 61 6c 27 64 20 62 65 6c 6f 77 3a 0a 09 41 44 |val'd below:..AD|
000025a0 44 09 61 31 2c 20 61 31 2c 20 23 38 0a 09 4d 4f |D.a1, a1, #8..MO|
000025b0 56 09 61 31 2c 20 61 31 2c 20 41 53 52 20 23 34 |V.a1, a1, ASR #4|
000025c0 09 09 3b 63 61 6c 63 20 61 20 3d 20 61 2f 6c 6e |..;calc a = a/ln|
000025d0 32 20 63 6f 6d 70 6c 65 74 65 0a 09 4d 4f 56 09 |2 complete..MOV.|
000025e0 61 34 2c 20 61 31 2c 20 41 53 52 20 23 31 36 09 |a4, a1, ASR #16.|
000025f0 09 3b 61 34 20 6e 6f 77 20 68 6f 6c 64 73 20 69 |.;a4 now holds i|
00002600 6e 74 65 67 65 72 20 63 6f 6d 70 6f 6e 65 6e 74 |nteger component|
00002610 20 6f 66 20 61 0a 09 42 49 43 09 61 31 2c 20 61 | of a..BIC.a1, a|
00002620 31 2c 20 61 34 2c 20 4c 53 4c 20 23 31 36 09 3b |1, a4, LSL #16.;|
00002630 61 31 20 6e 6f 77 20 68 6f 6c 64 73 20 66 72 61 |a1 now holds fra|
00002640 63 74 69 6f 6e 61 6c 20 63 6f 6d 70 6f 6e 65 6e |ctional componen|
00002650 74 20 69 6e 20 72 61 6e 67 65 20 5b 30 2c 31 29 |t in range [0,1)|
00002660 2a 6f 6e 65 0a 09 43 4d 50 09 61 34 2c 20 23 31 |*one..CMP.a4, #1|
00002670 35 09 09 09 3b 64 6f 20 61 6e 6f 74 68 65 72 20 |5...;do another |
00002680 63 68 65 63 6b 20 6f 6e 20 61 20 74 6f 20 65 6e |check on a to en|
00002690 73 75 72 65 20 65 78 70 28 61 29 20 69 73 20 69 |sure exp(a) is i|
000026a0 6e 20 72 61 6e 67 65 0a 09 42 4c 54 09 73 69 67 |n range..BLT.sig|
000026b0 31 36 5f 6c 31 0a 09 4d 4f 56 09 61 31 2c 20 23 |16_l1..MOV.a1, #|
000026c0 31 09 09 09 3b 26 20 69 66 20 6e 6f 74 2c 20 72 |1...;& if not, r|
000026d0 65 74 75 72 6e 20 6e 65 61 72 20 6d 61 78 69 6d |eturn near maxim|
000026e0 61 6c 20 6f 72 20 6d 69 6e 69 6d 61 6c 20 76 61 |al or minimal va|
000026f0 6c 75 65 20 61 73 20 61 70 70 72 6f 70 72 69 61 |lue as appropria|
00002700 74 65 0a 09 54 53 54 09 69 70 2c 20 23 31 3c 3c |te..TST.ip, #1<<|
00002710 33 31 0a 09 52 53 42 45 51 09 61 31 2c 20 61 31 |31..RSBEQ.a1, a1|
00002720 2c 20 23 6f 6e 65 0a 09 4d 4f 56 53 09 70 63 2c |, #one..MOVS.pc,|
00002730 6c 72 0a 73 69 67 31 36 5f 6c 31 0a 09 4f 52 52 |lr.sig16_l1..ORR|
00002740 09 61 34 2c 20 61 34 2c 20 69 70 09 09 3b 28 74 |.a4, a4, ip..;(t|
00002750 65 6d 70 6f 72 61 72 69 6c 79 20 73 74 6f 72 65 |emporarily store|
00002760 20 73 69 67 6e 20 6f 66 20 6f 72 69 67 69 6e 61 | sign of origina|
00002770 6c 20 61 20 69 6e 20 61 34 29 0a 09 4d 4f 56 09 |l a in a4)..MOV.|
00002780 61 31 2c 20 61 31 2c 20 4c 53 4c 20 23 31 09 09 |a1, a1, LSL #1..|
00002790 3b 65 6c 73 65 20 6e 65 65 64 20 20 76 61 6c 75 |;else need valu|
000027a0 65 20 28 6f 6e 65 20 2a 20 32 5e 28 61 31 2f 6f |e (one * 2^(a1/o|
000027b0 6e 65 29 20 2a 20 32 5e 61 34 29 0a 09 53 55 42 |ne) * 2^a4)..SUB|
000027c0 09 61 31 2c 20 61 31 2c 20 23 26 31 30 30 30 30 |.a1, a1, #&10000|
000027d0 09 09 3b 63 6f 6e 76 65 72 74 20 61 31 20 74 6f |..;convert a1 to|
000027e0 20 6c 69 65 20 69 6e 20 5b 2d 31 2c 2d 31 29 2c | lie in [-1,-1),|
000027f0 20 74 68 65 6e 20 61 70 70 6c 79 20 70 6f 6c 79 | then apply poly|
00002800 20 61 70 70 72 6f 78 69 6d 61 74 69 6f 6e 3a 0a | approximation:.|
00002810 09 52 53 42 09 61 32 2c 20 61 31 2c 20 61 31 2c |.RSB.a2, a1, a1,|
00002820 20 4c 53 4c 20 23 33 0a 09 41 44 44 09 61 32 2c | LSL #3..ADD.a2,|
00002830 20 61 31 2c 20 61 32 2c 20 4c 53 4c 20 23 36 0a | a1, a2, LSL #6.|
00002840 09 4d 4f 56 09 61 32 2c 20 61 32 2c 20 41 53 52 |.MOV.a2, a2, ASR|
00002850 20 23 31 35 09 09 3b 61 32 20 3d 20 30 2e 30 30 | #15..;a2 = 0.00|
00002860 30 38 35 36 31 2a 28 32 5e 32 30 29 2a 28 61 31 |08561*(2^20)*(a1|
00002870 2f 6f 6e 65 29 0a 09 41 44 44 09 61 32 2c 20 61 |/one)..ADD.a2, a|
00002880 32 2c 20 23 26 30 30 32 38 30 30 0a 09 41 44 44 |2, #&002800..ADD|
00002890 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 30 37 |.a2, a2, #&00007|
000028a0 65 09 3b 61 32 20 3d 20 30 2e 30 30 30 38 35 36 |e.;a2 = 0.000856|
000028b0 31 2a 28 32 5e 32 30 29 2a 28 61 31 2f 6f 6e 65 |1*(2^20)*(a1/one|
000028c0 29 20 2b 20 30 2e 30 30 39 38 38 35 37 2a 28 32 |) + 0.0098857*(2|
000028d0 5e 32 30 29 0a 20 20 20 20 20 20 20 20 4d 4f 56 |^20). MOV|
000028e0 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 |.ip, a1..mul16c.|
000028f0 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 09 09 |a2, ip, a2, a3..|
00002900 3b 61 32 20 3d 20 30 2e 30 30 30 38 35 36 31 2a |;a2 = 0.0008561*|
00002910 28 32 5e 32 30 29 2a 28 61 31 2f 6f 6e 65 29 5e |(2^20)*(a1/one)^|
00002920 32 20 2b 20 30 2e 30 30 39 38 38 35 37 2a 28 32 |2 + 0.0098857*(2|
00002930 5e 32 30 29 2a 28 61 31 2f 6f 6e 65 29 0a 09 41 |^20)*(a1/one)..A|
00002940 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 31 35 |DD.a2, a2, #&015|
00002950 30 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |000..ADD.a2, a2,|
00002960 20 23 26 30 30 30 62 65 30 09 3b 20 65 74 63 0a | #&000be0.; etc.|
00002970 20 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 | MOV.ip, |
00002980 61 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 |a1..mul16c.a2, i|
00002990 70 2c 20 61 32 2c 20 61 33 0a 09 41 44 44 09 61 |p, a2, a3..ADD.a|
000029a0 32 2c 20 61 32 2c 20 23 26 30 37 30 30 30 30 0a |2, a2, #&070000.|
000029b0 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
000029c0 30 64 37 30 30 0a 09 41 44 44 09 61 32 2c 20 61 |0d700..ADD.a2, a|
000029d0 32 2c 20 23 26 30 30 30 30 37 65 0a 20 20 20 20 |2, #&00007e. |
000029e0 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 | MOV.ip, a1..|
000029f0 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 61 |mul16c.a2, ip, a|
00002a00 32 2c 20 61 33 09 09 3b 75 6e 74 69 6c 20 77 65 |2, a3..;until we|
00002a10 20 68 61 76 65 0a 09 41 44 44 09 61 32 2c 20 61 | have..ADD.a2, a|
00002a20 32 2c 20 23 26 31 36 30 30 30 30 09 3b 61 32 20 |2, #&160000.;a2 |
00002a30 3d 20 28 32 5e 32 30 29 20 28 20 30 2e 30 30 30 |= (2^20) ( 0.000|
00002a40 38 35 36 31 28 61 31 2f 6f 6e 65 29 5e 34 20 2b |8561(a1/one)^4 +|
00002a50 20 30 2e 30 30 39 38 38 35 37 28 61 31 2f 6f 6e | 0.0098857(a1/on|
00002a60 65 29 5e 33 20 2b 0a 09 41 44 44 09 61 32 2c 20 |e)^3 +..ADD.a2, |
00002a70 61 32 2c 20 23 26 30 30 61 30 30 30 09 3b 09 20 |a2, #&00a000.;. |
00002a80 20 20 20 20 20 20 30 2e 30 38 34 39 33 30 31 28 | 0.0849301(|
00002a90 61 31 2f 6f 6e 65 29 5e 32 20 2b 20 30 2e 34 39 |a1/one)^2 + 0.49|
00002aa0 30 31 31 30 36 28 61 31 2f 6f 6e 65 29 20 2b 0a |01106(a1/one) +.|
00002ab0 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00002ac0 30 30 30 61 37 09 3b 09 20 20 20 20 20 20 20 31 |000a7.;. 1|
00002ad0 2e 31 34 31 34 32 31 33 38 20 20 20 20 20 20 20 |.14142138 |
00002ae0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | |
00002af0 20 20 20 20 20 20 20 20 20 20 20 20 29 0a 09 4d | )..M|
00002b00 4f 56 09 61 31 2c 20 61 32 2c 20 41 53 52 20 23 |OV.a1, a2, ASR #|
00002b10 34 09 09 3b 6e 6f 77 20 64 69 76 69 64 65 20 62 |4..;now divide b|
00002b20 79 20 31 36 20 72 65 6d 6f 76 69 6e 67 20 6d 6f |y 16 removing mo|
00002b30 73 74 20 74 72 75 6e 63 61 74 69 6f 6e 20 65 72 |st truncation er|
00002b40 72 6f 72 20 66 72 6f 6d 20 61 62 6f 76 65 20 63 |ror from above c|
00002b50 61 6c 63 73 2c 0a 09 09 09 09 09 3b 6c 65 61 76 |alcs,......;leav|
00002b60 69 6e 67 20 61 32 20 3d 20 28 32 5e 31 36 29 2a |ing a2 = (2^16)*|
00002b70 28 61 70 70 72 6f 78 69 6d 61 74 65 64 20 76 61 |(approximated va|
00002b80 6c 75 65 29 0a 09 42 49 43 09 69 70 2c 20 61 34 |lue)..BIC.ip, a4|
00002b90 2c 20 23 31 3c 3c 33 31 09 09 3b 72 65 6d 6f 76 |, #1<<31..;remov|
00002ba0 65 20 74 65 6d 70 20 73 69 67 6e 20 62 69 74 20 |e temp sign bit |
00002bb0 66 72 6f 6d 20 61 34 0a 09 4d 4f 56 53 09 61 32 |from a4..MOVS.a2|
00002bc0 2c 20 61 31 2c 20 4c 53 4c 20 69 70 09 09 3b 66 |, a1, LSL ip..;f|
00002bd0 69 6e 61 6c 6c 79 20 63 61 72 72 79 20 6f 75 74 |inally carry out|
00002be0 20 74 68 65 20 28 61 32 20 3d 20 61 32 20 2a 20 | the (a2 = a2 * |
00002bf0 32 5e 61 34 29 20 73 74 65 70 0a 09 41 44 44 43 |2^a4) step..ADDC|
00002c00 43 53 09 61 32 2c 20 61 32 2c 20 23 6f 6e 65 09 |CS.a2, a2, #one.|
00002c10 09 3b 74 68 65 6e 20 61 64 64 20 69 6e 20 6f 6e |.;then add in on|
00002c20 65 0a 09 4d 4f 56 43 53 09 61 31 2c 20 61 34 2c |e..MOVCS.a1, a4,|
00002c30 20 4c 53 52 20 23 31 35 09 09 3b 26 20 69 66 20 | LSR #15..;& if |
00002c40 6f 76 65 72 66 6c 6f 77 2c 20 72 65 74 75 72 6e |overflow, return|
00002c50 20 6d 61 78 69 6d 61 6c 20 6f 72 20 6d 69 6e 69 | maximal or mini|
00002c60 6d 61 6c 20 76 61 6c 75 65 20 61 73 20 61 70 70 |mal value as app|
00002c70 72 6f 70 72 69 61 74 65 0a 09 45 4f 52 43 53 09 |ropriate..EORCS.|
00002c80 61 31 2c 20 61 31 2c 20 23 6f 6e 65 0a 09 4d 4f |a1, a1, #one..MO|
00002c90 56 43 53 53 09 70 63 2c 20 6c 72 0a 09 4d 4f 56 |VCSS.pc, lr..MOV|
00002ca0 09 61 31 2c 20 23 30 09 09 09 3b 72 65 73 75 6c |.a1, #0...;resul|
00002cb0 74 20 66 6f 72 20 6f 70 65 72 61 74 69 6f 6e 20 |t for operation |
00002cc0 61 31 20 3d 20 32 5e 33 32 20 2f 20 61 32 0a 09 |a1 = 2^32 / a2..|
00002cd0 4d 4f 56 09 61 33 2c 20 23 31 3c 3c 31 36 09 09 |MOV.a3, #1<<16..|
00002ce0 3b 72 65 6d 61 69 6e 64 65 72 20 72 65 67 0a 09 |;remainder reg..|
00002cf0 47 42 4c 41 09 63 6f 75 6e 74 65 72 0a 63 6f 75 |GBLA.counter.cou|
00002d00 6e 74 65 72 09 53 45 54 41 09 31 36 0a 09 57 48 |nter.SETA.16..WH|
00002d10 49 4c 45 09 63 6f 75 6e 74 65 72 20 3e 20 30 0a |ILE.counter > 0.|
00002d20 09 41 44 44 09 61 31 2c 20 61 31 2c 20 61 31 0a |.ADD.a1, a1, a1.|
00002d30 09 41 44 44 09 61 33 2c 20 61 33 2c 20 61 33 0a |.ADD.a3, a3, a3.|
00002d40 09 43 4d 50 09 61 33 2c 20 61 32 0a 09 53 55 42 |.CMP.a3, a2..SUB|
00002d50 48 53 09 61 33 2c 20 61 33 2c 20 61 32 0a 09 4f |HS.a3, a3, a2..O|
00002d60 52 52 48 53 09 61 31 2c 20 61 31 2c 20 23 31 0a |RRHS.a1, a1, #1.|
00002d70 63 6f 75 6e 74 65 72 20 53 45 54 41 09 63 6f 75 |counter SETA.cou|
00002d80 6e 74 65 72 2d 31 0a 09 57 45 4e 44 09 09 09 09 |nter-1..WEND....|
00002d90 3b 72 65 63 69 70 72 6f 63 61 6c 20 63 61 6c 63 |;reciprocal calc|
00002da0 75 6c 61 74 65 64 0a 09 43 4d 50 09 61 32 2c 20 |ulated..CMP.a2, |
00002db0 61 33 2c 20 4c 53 4c 20 23 31 0a 09 41 44 44 4c |a3, LSL #1..ADDL|
00002dc0 53 09 61 31 2c 20 61 31 2c 20 23 31 0a 09 54 53 |S.a1, a1, #1..TS|
00002dd0 54 09 61 34 2c 20 23 31 3c 3c 33 31 09 09 3b 61 |T.a4, #1<<31..;a|
00002de0 6e 64 20 66 69 6e 61 6c 6c 79 2c 20 69 66 20 6f |nd finally, if o|
00002df0 72 69 67 69 6e 61 6c 20 61 72 67 75 6d 65 6e 74 |riginal argument|
00002e00 20 3e 20 30 0a 09 52 53 42 45 51 09 61 31 2c 20 | > 0..RSBEQ.a1, |
00002e10 61 31 2c 20 23 6f 6e 65 09 09 3b 74 68 65 6e 20 |a1, #one..;then |
00002e20 66 6c 69 70 20 76 61 6c 75 65 20 61 62 6f 75 74 |flip value about|
00002e30 20 79 3d 31 2f 32 20 6c 69 6e 65 20 69 6e 20 67 | y=1/2 line in g|
00002e40 72 61 70 68 20 6f 66 20 73 69 67 20 66 6e 0a 20 |raph of sig fn. |
00002e50 20 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 70 | MOVS p|
00002e60 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 63 6f 73 31 36 |c, lr....; cos16|
00002e70 0a 3b 20 61 20 6c 65 61 66 20 41 50 43 53 20 66 |.; a leaf APCS f|
00002e80 75 6e 63 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 |unction.;.; C pr|
00002e90 6f 74 6f 74 79 70 65 3a 0a 3b 20 69 6e 74 20 63 |ototype:.; int c|
00002ea0 6f 73 31 36 28 69 6e 74 20 61 29 0a 3b 0a 3b 20 |os16(int a).;.; |
00002eb0 72 65 74 75 72 6e 73 20 36 35 35 33 36 20 2a 20 |returns 65536 * |
00002ec0 63 6f 73 20 28 28 61 2f 36 35 35 33 36 29 28 70 |cos ((a/65536)(p|
00002ed0 69 2f 32 29 29 0a 3b 0a 3b 20 69 73 20 61 62 6f |i/2)).;.; is abo|
00002ee0 75 74 20 34 34 20 74 69 6d 65 73 20 66 61 73 74 |ut 44 times fast|
00002ef0 65 72 20 74 68 61 6e 20 46 50 45 6d 75 6c 61 74 |er than FPEmulat|
00002f00 6f 72 20 77 6f 72 6b 69 6e 67 20 77 69 74 68 20 |or working with |
00002f10 64 6f 75 62 6c 65 20 66 6c 6f 61 74 73 0a 3b 0a |double floats.;.|
00002f20 0a 20 20 20 20 20 20 20 20 45 58 50 4f 52 54 20 |. EXPORT |
00002f30 20 63 6f 73 31 36 0a 0a 63 73 6e 73 74 61 20 20 | cos16..csnsta |
00002f40 44 43 42 20 20 20 20 20 22 63 6f 73 31 36 22 2c |DCB "cos16",|
00002f50 20 30 0a 20 20 20 20 20 20 20 20 41 4c 49 47 4e | 0. ALIGN|
00002f60 0a 63 73 6e 65 6e 64 20 20 44 43 44 20 20 20 20 |.csnend DCD |
00002f70 20 26 66 66 30 30 30 30 30 30 20 2b 20 63 73 6e | &ff000000 + csn|
00002f80 65 6e 64 20 2d 20 63 73 6e 73 74 61 0a 0a 63 6f |end - csnsta..co|
00002f90 73 31 36 0a 0a 09 45 4f 52 09 61 34 2c 20 61 31 |s16...EOR.a4, a1|
00002fa0 2c 20 61 31 2c 20 4c 53 4c 20 23 31 09 3b 73 69 |, a1, LSL #1.;si|
00002fb0 6e 63 65 20 63 6f 73 20 69 73 20 70 65 72 69 6f |nce cos is perio|
00002fc0 64 69 63 20 61 6e 64 20 63 6f 73 28 28 61 2f 36 |dic and cos((a/6|
00002fd0 35 35 33 36 29 28 70 69 2f 32 29 29 20 68 61 73 |5536)(pi/2)) has|
00002fe0 20 70 65 72 69 6f 64 20 34 2a 6f 6e 65 0a 09 54 | period 4*one..T|
00002ff0 53 54 09 61 34 2c 20 23 26 32 30 30 30 30 09 09 |ST.a4, #&20000..|
00003000 3b 65 76 61 6c 20 69 73 20 73 69 6d 70 6c 65 72 |;eval is simpler|
00003010 20 74 68 61 6e 20 66 6f 72 20 6c 6e 20 6f 72 20 | than for ln or |
00003020 65 78 70 3a 0a 09 4d 4f 56 09 61 34 2c 20 23 30 |exp:..MOV.a4, #0|
00003030 09 09 09 3b 77 65 20 6e 65 65 64 20 6f 6e 6c 79 |...;we need only|
00003040 20 74 6f 20 74 72 75 6e 63 61 74 65 20 61 20 74 | to truncate a t|
00003050 6f 20 5b 30 2c 34 6f 6e 65 29 20 61 6e 64 20 74 |o [0,4one) and t|
00003060 68 65 6e 20 61 70 70 72 6f 78 20 74 68 65 20 66 |hen approx the f|
00003070 75 6e 63 74 69 6f 6e 0a 09 4d 4f 56 4e 45 09 61 |unction..MOVNE.a|
00003080 34 2c 20 23 31 09 09 09 3b 76 69 61 20 61 20 70 |4, #1...;via a p|
00003090 6f 6c 79 0a 09 54 53 54 09 61 31 2c 20 23 26 31 |oly..TST.a1, #&1|
000030a0 30 30 30 30 0a 09 4d 4f 56 09 61 31 2c 20 61 31 |0000..MOV.a1, a1|
000030b0 2c 20 4c 53 4c 20 23 31 36 09 09 3b 69 6e 20 66 |, LSL #16..;in f|
000030c0 61 63 74 20 66 75 72 74 68 65 72 20 73 79 6d 6d |act further symm|
000030d0 65 74 72 69 65 73 20 69 6e 20 63 6f 73 20 6f 76 |etries in cos ov|
000030e0 65 72 20 74 68 69 73 20 72 61 6e 67 65 20 61 6c |er this range al|
000030f0 6c 6f 77 20 75 73 20 74 6f 0a 09 4d 4f 56 09 61 |low us to..MOV.a|
00003100 31 2c 20 61 31 2c 20 4c 53 52 20 23 31 36 09 09 |1, a1, LSR #16..|
00003110 3b 61 63 74 75 61 6c 6c 79 20 6f 6e 6c 79 20 61 |;actually only a|
00003120 70 70 72 6f 78 69 6d 61 74 65 20 66 75 6e 63 74 |pproximate funct|
00003130 69 6f 6e 20 6f 76 65 72 20 72 61 6e 67 65 20 5b |ion over range [|
00003140 30 2c 6f 6e 65 29 0a 09 52 53 42 45 51 09 61 31 |0,one)..RSBEQ.a1|
00003150 2c 20 61 31 2c 20 23 26 31 30 30 30 30 09 09 3b |, a1, #&10000..;|
00003160 61 6e 64 20 72 65 63 6f 6e 73 74 72 75 63 74 20 |and reconstruct |
00003170 69 74 20 6f 76 65 72 20 72 65 6d 61 69 6e 64 65 |it over remainde|
00003180 72 20 6f 66 20 72 61 6e 67 65 20 5b 6f 6e 65 2c |r of range [one,|
00003190 34 6f 6e 65 29 20 66 72 6f 6d 20 74 68 61 74 20 |4one) from that |
000031a0 70 61 72 74 0a 09 4d 4f 56 09 61 31 2c 20 61 31 |part..MOV.a1, a1|
000031b0 2c 20 4c 53 4c 20 23 31 09 09 3b 65 67 20 20 63 |, LSL #1..;eg c|
000031c0 6f 73 28 20 28 61 2f 36 35 35 33 36 29 28 70 69 |os( (a/65536)(pi|
000031d0 2f 32 29 20 29 20 66 6f 72 20 61 20 69 6e 20 5b |/2) ) for a in [|
000031e0 32 6f 6e 65 2c 20 33 6f 6e 65 29 0a 09 53 55 42 |2one, 3one)..SUB|
000031f0 09 61 31 2c 20 61 31 2c 20 23 26 31 30 30 30 30 |.a1, a1, #&10000|
00003200 09 09 3b 20 3d 20 2d 63 6f 73 28 20 28 28 61 2d |..; = -cos( ((a-|
00003210 32 6f 6e 65 29 2f 36 35 35 33 36 29 28 70 69 2f |2one)/65536)(pi/|
00003220 32 29 20 29 0a 09 52 53 42 09 61 32 2c 20 61 31 |2) )..RSB.a2, a1|
00003230 2c 20 61 31 2c 20 4c 53 4c 20 23 33 0a 09 41 44 |, a1, LSL #3..AD|
00003240 44 09 61 32 2c 20 61 31 2c 20 61 32 2c 20 4c 53 |D.a2, a1, a2, LS|
00003250 4c 20 23 38 0a 09 4d 4f 56 09 61 32 2c 20 61 32 |L #8..MOV.a2, a2|
00003260 2c 20 41 53 52 20 23 31 36 0a 09 41 44 44 09 61 |, ASR #16..ADD.a|
00003270 32 2c 20 61 32 2c 20 23 26 30 30 32 63 30 30 0a |2, a2, #&002c00.|
00003280 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00003290 30 30 30 38 36 0a 20 20 20 20 20 20 20 20 4d 4f |00086. MO|
000032a0 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 |V.ip, a1..mul16c|
000032b0 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a |.a2, ip, a2, a3.|
000032c0 09 53 55 42 09 61 32 2c 20 61 32 2c 20 23 26 30 |.SUB.a2, a2, #&0|
000032d0 30 65 39 30 30 0a 09 53 55 42 09 61 32 2c 20 61 |0e900..SUB.a2, a|
000032e0 32 2c 20 23 26 30 30 30 30 62 64 0a 20 20 20 20 |2, #&0000bd. |
000032f0 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 | MOV.ip, a1..|
00003300 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 61 |mul16c.a2, ip, a|
00003310 32 2c 20 61 33 0a 09 53 55 42 09 61 32 2c 20 61 |2, a3..SUB.a2, a|
00003320 32 2c 20 23 26 30 33 30 30 30 30 0a 09 53 55 42 |2, #&030000..SUB|
00003330 09 61 32 2c 20 61 32 2c 20 23 26 30 30 37 63 30 |.a2, a2, #&007c0|
00003340 30 0a 09 53 55 42 09 61 32 2c 20 61 32 2c 20 23 |0..SUB.a2, a2, #|
00003350 26 30 30 30 30 63 36 0a 20 20 20 20 20 20 20 20 |&0000c6. |
00003360 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 |MOV.ip, a1..mul1|
00003370 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 |6c.a2, ip, a2, a|
00003380 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 |3..ADD.a2, a2, #|
00003390 26 30 38 30 30 30 30 0a 09 41 44 44 09 61 32 2c |&080000..ADD.a2,|
000033a0 20 61 32 2c 20 23 26 30 30 45 32 30 30 0a 09 41 | a2, #&00E200..A|
000033b0 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 |DD.a2, a2, #&000|
000033c0 30 42 44 0a 20 20 20 20 20 20 20 20 4d 4f 56 09 |0BD. MOV.|
000033d0 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 61 |ip, a1..mul16c.a|
000033e0 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a 09 41 |2, ip, a2, a3..A|
000033f0 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 62 30 |DD.a2, a2, #&0b0|
00003400 30 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |000..ADD.a2, a2,|
00003410 20 23 26 30 30 35 30 30 30 0a 09 41 44 44 09 61 | #&005000..ADD.a|
00003420 32 2c 20 61 32 2c 20 23 26 30 30 30 30 35 30 0a |2, a2, #&000050.|
00003430 09 4d 4f 56 09 61 31 2c 20 61 32 2c 20 41 53 52 |.MOV.a1, a2, ASR|
00003440 20 23 34 0a 09 54 53 54 09 61 34 2c 20 23 31 0a | #4..TST.a4, #1.|
00003450 09 52 53 42 4e 45 09 61 31 2c 20 61 31 2c 20 23 |.RSBNE.a1, a1, #|
00003460 30 0a 20 20 20 20 20 20 20 20 4d 4f 56 53 20 20 |0. MOVS |
00003470 20 20 70 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 73 69 | pc, lr....; si|
00003480 6e 31 36 0a 3b 20 61 20 6c 65 61 66 20 41 50 43 |n16.; a leaf APC|
00003490 53 20 66 75 6e 63 74 69 6f 6e 0a 3b 0a 3b 20 43 |S function.;.; C|
000034a0 20 70 72 6f 74 6f 74 79 70 65 3a 0a 3b 20 69 6e | prototype:.; in|
000034b0 74 20 73 69 6e 31 36 28 69 6e 74 20 61 29 0a 3b |t sin16(int a).;|
000034c0 0a 3b 20 72 65 74 75 72 6e 73 20 36 35 35 33 36 |.; returns 65536|
000034d0 20 2a 20 73 69 6e 20 28 28 61 2f 36 35 35 33 36 | * sin ((a/65536|
000034e0 29 28 70 69 2f 32 29 29 0a 3b 0a 3b 20 69 73 20 |)(pi/2)).;.; is |
000034f0 61 62 6f 75 74 20 34 34 20 74 69 6d 65 73 20 66 |about 44 times f|
00003500 61 73 74 65 72 20 74 68 61 6e 20 46 50 45 6d 75 |aster than FPEmu|
00003510 6c 61 74 6f 72 20 77 6f 72 6b 69 6e 67 20 77 69 |lator working wi|
00003520 74 68 20 64 6f 75 62 6c 65 20 66 6c 6f 61 74 73 |th double floats|
00003530 0a 3b 0a 0a 20 20 20 20 20 20 20 20 45 58 50 4f |.;.. EXPO|
00003540 52 54 20 20 73 69 6e 31 36 0a 0a 73 6e 6e 73 74 |RT sin16..snnst|
00003550 61 20 20 44 43 42 20 20 20 20 20 22 73 69 6e 31 |a DCB "sin1|
00003560 36 22 2c 20 30 0a 20 20 20 20 20 20 20 20 41 4c |6", 0. AL|
00003570 49 47 4e 0a 73 6e 6e 65 6e 64 20 20 44 43 44 20 |IGN.snnend DCD |
00003580 20 20 20 20 26 66 66 30 30 30 30 30 30 20 2b 20 | &ff000000 + |
00003590 73 6e 6e 65 6e 64 20 2d 20 73 6e 6e 73 74 61 0a |snnend - snnsta.|
000035a0 0a 73 69 6e 31 36 0a 0a 09 54 53 54 09 61 31 2c |.sin16...TST.a1,|
000035b0 20 23 26 32 30 30 30 30 09 09 3b 65 76 61 6c 20 | #&20000..;eval |
000035c0 6f 66 20 73 69 6e 20 69 73 20 61 6c 6d 6f 73 74 |of sin is almost|
000035d0 20 69 64 65 6e 74 69 63 61 6c 20 74 6f 20 74 68 | identical to th|
000035e0 61 74 20 6f 66 20 63 6f 73 0a 09 4d 4f 56 09 61 |at of cos..MOV.a|
000035f0 34 2c 20 23 30 0a 09 4d 4f 56 4e 45 09 61 34 2c |4, #0..MOVNE.a4,|
00003600 20 23 31 0a 09 54 53 54 09 61 31 2c 20 23 26 31 | #1..TST.a1, #&1|
00003610 30 30 30 30 0a 09 4d 4f 56 09 61 31 2c 20 61 31 |0000..MOV.a1, a1|
00003620 2c 20 4c 53 4c 20 23 31 36 0a 09 4d 4f 56 09 61 |, LSL #16..MOV.a|
00003630 31 2c 20 61 31 2c 20 4c 53 52 20 23 31 36 0a 09 |1, a1, LSR #16..|
00003640 52 53 42 4e 45 09 61 31 2c 20 61 31 2c 20 23 26 |RSBNE.a1, a1, #&|
00003650 31 30 30 30 30 0a 09 4d 4f 56 09 61 31 2c 20 61 |10000..MOV.a1, a|
00003660 31 2c 20 4c 53 4c 20 23 31 0a 09 53 55 42 09 61 |1, LSL #1..SUB.a|
00003670 31 2c 20 61 31 2c 20 23 26 31 30 30 30 30 0a 09 |1, a1, #&10000..|
00003680 52 53 42 09 61 32 2c 20 61 31 2c 20 61 31 2c 20 |RSB.a2, a1, a1, |
00003690 4c 53 4c 20 23 33 0a 09 41 44 44 09 61 32 2c 20 |LSL #3..ADD.a2, |
000036a0 61 31 2c 20 61 32 2c 20 4c 53 4c 20 23 38 0a 09 |a1, a2, LSL #8..|
000036b0 4d 4f 56 09 61 32 2c 20 61 32 2c 20 41 53 52 20 |MOV.a2, a2, ASR |
000036c0 23 31 36 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |#16..ADD.a2, a2,|
000036d0 20 23 26 30 30 32 63 30 30 0a 09 41 44 44 09 61 | #&002c00..ADD.a|
000036e0 32 2c 20 61 32 2c 20 23 26 30 30 30 30 38 36 0a |2, a2, #&000086.|
000036f0 20 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 | MOV.ip, |
00003700 61 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 |a1..mul16c.a2, i|
00003710 70 2c 20 61 32 2c 20 61 33 0a 09 53 55 42 09 61 |p, a2, a3..SUB.a|
00003720 32 2c 20 61 32 2c 20 23 26 30 30 65 39 30 30 0a |2, a2, #&00e900.|
00003730 09 53 55 42 09 61 32 2c 20 61 32 2c 20 23 26 30 |.SUB.a2, a2, #&0|
00003740 30 30 30 62 64 0a 20 20 20 20 20 20 20 20 4d 4f |000bd. MO|
00003750 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 |V.ip, a1..mul16c|
00003760 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a |.a2, ip, a2, a3.|
00003770 09 53 55 42 09 61 32 2c 20 61 32 2c 20 23 26 30 |.SUB.a2, a2, #&0|
00003780 33 30 30 30 30 0a 09 53 55 42 09 61 32 2c 20 61 |30000..SUB.a2, a|
00003790 32 2c 20 23 26 30 30 37 63 30 30 0a 09 53 55 42 |2, #&007c00..SUB|
000037a0 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 30 63 |.a2, a2, #&0000c|
000037b0 36 0a 20 20 20 20 20 20 20 20 4d 4f 56 09 69 70 |6. MOV.ip|
000037c0 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c |, a1..mul16c.a2,|
000037d0 20 69 70 2c 20 61 32 2c 20 61 33 0a 09 41 44 44 | ip, a2, a3..ADD|
000037e0 09 61 32 2c 20 61 32 2c 20 23 26 30 38 30 30 30 |.a2, a2, #&08000|
000037f0 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 |0..ADD.a2, a2, #|
00003800 26 30 30 45 32 30 30 0a 09 41 44 44 09 61 32 2c |&00E200..ADD.a2,|
00003810 20 61 32 2c 20 23 26 30 30 30 30 42 44 0a 20 20 | a2, #&0000BD. |
00003820 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 | MOV.ip, a1|
00003830 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 2c |..mul16c.a2, ip,|
00003840 20 61 32 2c 20 61 33 0a 09 41 44 44 09 61 32 2c | a2, a3..ADD.a2,|
00003850 20 61 32 2c 20 23 26 30 62 30 30 30 30 0a 09 41 | a2, #&0b0000..A|
00003860 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 35 |DD.a2, a2, #&005|
00003870 30 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |000..ADD.a2, a2,|
00003880 20 23 26 30 30 30 30 35 30 0a 09 4d 4f 56 09 61 | #&000050..MOV.a|
00003890 31 2c 20 61 32 2c 20 41 53 52 20 23 34 0a 09 54 |1, a2, ASR #4..T|
000038a0 53 54 09 61 34 2c 20 23 31 0a 09 52 53 42 4e 45 |ST.a4, #1..RSBNE|
000038b0 09 61 31 2c 20 61 31 2c 20 23 30 0a 20 20 20 20 |.a1, a1, #0. |
000038c0 20 20 20 20 4d 4f 56 53 20 20 20 20 70 63 2c 20 | MOVS pc, |
000038d0 6c 72 0a 0a 0a 0a 3b 20 61 63 73 31 36 0a 3b 20 |lr....; acs16.; |
000038e0 61 20 6c 65 61 66 20 41 50 43 53 20 66 75 6e 63 |a leaf APCS func|
000038f0 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f |tion.;.; C proto|
00003900 74 79 70 65 3a 0a 3b 20 69 6e 74 20 61 63 73 31 |type:.; int acs1|
00003910 36 28 69 6e 74 20 61 29 0a 3b 0a 3b 20 72 65 74 |6(int a).;.; ret|
00003920 75 72 6e 73 20 36 35 35 33 36 20 2a 20 32 2f 70 |urns 65536 * 2/p|
00003930 69 20 2a 20 61 72 63 63 6f 73 20 28 61 2f 36 35 |i * arccos (a/65|
00003940 35 33 36 29 0a 3b 0a 3b 20 66 6f 72 20 61 20 6f |536).;.; for a o|
00003950 75 74 20 6f 66 20 72 61 6e 67 65 20 28 69 65 20 |ut of range (ie |
00003960 61 62 73 20 61 20 3e 20 36 35 35 33 36 29 2c 20 |abs a > 65536), |
00003970 72 65 73 65 74 20 61 20 74 6f 20 b1 36 35 35 33 |reset a to .6553|
00003980 36 20 61 73 20 61 70 70 72 6f 70 72 69 61 74 65 |6 as appropriate|
00003990 20 62 65 66 6f 72 65 20 65 76 61 6c 0a 3b 0a 3b | before eval.;.;|
000039a0 20 69 73 20 61 62 6f 75 74 20 32 34 20 74 69 6d | is about 24 tim|
000039b0 65 73 20 66 61 73 74 65 72 20 74 68 61 6e 20 46 |es faster than F|
000039c0 50 45 6d 75 6c 61 74 6f 72 20 77 6f 72 6b 69 6e |PEmulator workin|
000039d0 67 20 77 69 74 68 20 64 6f 75 62 6c 65 20 66 6c |g with double fl|
000039e0 6f 61 74 73 0a 3b 0a 0a 20 20 20 20 20 20 20 20 |oats.;.. |
000039f0 45 58 50 4f 52 54 20 20 61 63 73 31 36 0a 0a 61 |EXPORT acs16..a|
00003a00 63 6e 73 74 61 20 20 44 43 42 20 20 20 20 20 22 |cnsta DCB "|
00003a10 61 63 73 31 36 22 2c 20 30 0a 20 20 20 20 20 20 |acs16", 0. |
00003a20 20 20 41 4c 49 47 4e 0a 61 63 6e 65 6e 64 20 20 | ALIGN.acnend |
00003a30 44 43 44 20 20 20 20 20 26 66 66 30 30 30 30 30 |DCD &ff00000|
00003a40 30 20 2b 20 61 63 6e 65 6e 64 20 2d 20 61 63 6e |0 + acnend - acn|
00003a50 73 74 61 0a 0a 61 63 73 31 36 0a 0a 09 43 4d 50 |sta..acs16...CMP|
00003a60 09 61 31 2c 20 23 36 35 35 33 36 0a 09 4d 4f 56 |.a1, #65536..MOV|
00003a70 47 45 09 61 31 2c 20 23 30 0a 09 4d 4f 56 47 45 |GE.a1, #0..MOVGE|
00003a80 53 09 70 63 2c 20 6c 72 0a 09 43 4d 50 09 61 31 |S.pc, lr..CMP.a1|
00003a90 2c 20 23 2d 36 35 35 33 36 0a 09 4d 4f 56 4c 45 |, #-65536..MOVLE|
00003aa0 09 61 31 2c 20 23 32 2a 36 35 35 33 36 0a 09 4d |.a1, #2*65536..M|
00003ab0 4f 56 4c 45 53 09 70 63 2c 20 6c 72 0a 09 53 54 |OVLES.pc, lr..ST|
00003ac0 4d 46 44 09 73 70 21 2c 20 7b 6c 72 7d 09 09 3b |MFD.sp!, {lr}..;|
00003ad0 6e 6f 77 20 68 61 76 65 20 61 72 67 20 69 6e 20 |now have arg in |
00003ae0 72 61 6e 67 65 20 28 2d 6f 6e 65 2c 6f 6e 65 29 |range (-one,one)|
00003af0 0a 09 43 4d 50 09 61 31 2c 20 23 30 0a 09 52 53 |..CMP.a1, #0..RS|
00003b00 42 4d 49 09 61 31 2c 20 61 31 2c 20 23 30 0a 09 |BMI.a1, a1, #0..|
00003b10 4d 4f 56 4d 49 09 61 34 2c 20 23 31 09 09 09 3b |MOVMI.a4, #1...;|
00003b20 62 30 20 69 6e 20 61 34 20 73 65 74 20 69 66 66 |b0 in a4 set iff|
00003b30 20 66 69 6e 61 6c 20 72 65 73 75 6c 74 20 72 20 | final result r |
00003b40 6e 65 65 64 73 20 72 65 70 6c 61 63 69 6e 67 20 |needs replacing |
00003b50 62 79 20 32 2a 6f 6e 65 2d 72 0a 09 4d 4f 56 50 |by 2*one-r..MOVP|
00003b60 4c 09 61 34 2c 20 23 30 09 09 09 3b 6e 6f 77 20 |L.a4, #0...;now |
00003b70 68 61 76 65 20 61 72 67 20 69 6e 20 72 61 6e 67 |have arg in rang|
00003b80 65 20 5b 30 2c 6f 6e 65 29 0a 09 53 55 42 09 61 |e [0,one)..SUB.a|
00003b90 32 2c 20 61 31 2c 20 23 26 62 35 30 30 0a 09 53 |2, a1, #&b500..S|
00003ba0 55 42 53 09 61 32 2c 20 61 32 2c 20 23 26 30 30 |UBS.a2, a2, #&00|
00003bb0 30 35 0a 09 42 4c 54 09 61 63 73 31 36 5f 61 72 |05..BLT.acs16_ar|
00003bc0 67 6c 6f 77 09 09 3b 69 66 20 61 72 67 20 3c 20 |glow..;if arg < |
00003bd0 6f 6e 65 2f 73 71 72 74 32 20 67 6f 20 61 6e 64 |one/sqrt2 go and|
00003be0 20 61 70 70 6c 79 20 70 6f 6c 79 20 65 6c 73 65 | apply poly else|
00003bf0 20 66 69 72 73 74 20 74 72 61 6e 73 6d 75 74 65 | first transmute|
00003c00 20 69 6e 74 6f 20 68 65 72 65 0a 09 4f 52 52 09 | into here..ORR.|
00003c10 61 34 2c 20 61 34 2c 20 23 32 09 09 3b 62 31 20 |a4, a4, #2..;b1 |
00003c20 69 6e 20 61 34 20 63 6c 65 61 72 20 69 66 66 20 |in a4 clear iff |
00003c30 70 65 6e 75 6c 74 69 6d 61 74 65 20 72 65 73 75 |penultimate resu|
00003c40 6c 74 20 72 20 6e 65 65 64 20 62 65 20 72 65 70 |lt r need be rep|
00003c50 6c 61 63 65 64 20 62 79 20 6f 6e 65 2d 72 0a 09 |laced by one-r..|
00003c60 4d 55 4c 09 61 32 2c 20 61 31 2c 20 61 31 0a 09 |MUL.a2, a1, a1..|
00003c70 4d 4f 56 09 61 31 2c 20 61 32 2c 20 4c 53 52 20 |MOV.a1, a2, LSR |
00003c80 23 31 36 0a 09 52 53 42 09 61 31 2c 20 61 31 2c |#16..RSB.a1, a1,|
00003c90 20 23 36 35 35 33 36 0a 09 73 71 72 74 31 36 09 | #65536..sqrt16.|
00003ca0 61 31 2c 20 61 31 2c 20 61 32 2c 20 61 33 2c 20 |a1, a1, a2, a3, |
00003cb0 69 70 2c 20 6c 72 09 3b 61 72 67 20 74 72 61 6e |ip, lr.;arg tran|
00003cc0 73 6d 75 74 65 64 20 28 69 65 20 72 65 70 6c 61 |smuted (ie repla|
00003cd0 63 65 64 20 62 79 20 6f 6e 65 2d 73 71 72 74 28 |ced by one-sqrt(|
00003ce0 61 72 67 5e 32 29 29 0a 61 63 73 31 36 5f 61 72 |arg^2)).acs16_ar|
00003cf0 67 6c 6f 77 0a 09 41 44 44 09 61 33 2c 20 61 31 |glow..ADD.a3, a1|
00003d00 2c 20 61 31 2c 20 41 53 4c 20 23 32 0a 09 41 44 |, a1, ASL #2..AD|
00003d10 44 09 61 32 2c 20 61 33 2c 20 61 31 2c 20 41 53 |D.a2, a3, a1, AS|
00003d20 4c 20 23 34 0a 09 41 44 44 09 61 32 2c 20 61 32 |L #4..ADD.a2, a2|
00003d30 2c 20 61 33 2c 20 41 53 4c 20 23 35 0a 09 41 44 |, a3, ASL #5..AD|
00003d40 44 09 61 32 2c 20 61 32 2c 20 61 33 2c 20 41 53 |D.a2, a2, a3, AS|
00003d50 52 09 23 38 0a 09 41 44 44 09 61 32 2c 20 61 32 |R.#8..ADD.a2, a2|
00003d60 2c 20 23 33 32 0a 09 4d 4f 56 09 61 31 2c 20 61 |, #32..MOV.a1, a|
00003d70 32 2c 20 41 53 52 20 23 36 09 09 3b 72 61 6e 67 |2, ASR #6..;rang|
00003d80 65 20 74 72 61 6e 73 66 6f 72 6d 20 61 70 70 6c |e transform appl|
00003d90 69 65 64 20 28 69 65 20 72 65 70 6c 61 63 65 64 |ied (ie replaced|
00003da0 20 62 79 20 61 72 67 2a 32 73 71 72 74 32 2d 6f | by arg*2sqrt2-o|
00003db0 6e 65 29 0a 09 53 55 42 09 61 31 2c 20 61 31 2c |ne)..SUB.a1, a1,|
00003dc0 20 23 26 31 30 30 30 30 09 09 3b 73 6f 20 61 72 | #&10000..;so ar|
00003dd0 67 20 6c 69 65 73 20 69 6e 20 72 61 6e 67 65 20 |g lies in range |
00003de0 5b 2d 31 2c 31 5d 0a 09 41 44 44 09 61 32 2c 20 |[-1,1]..ADD.a2, |
00003df0 61 31 2c 20 61 31 2c 20 4c 53 4c 20 23 32 09 3b |a1, a1, LSL #2.;|
00003e00 6e 6f 77 20 61 70 70 6c 79 20 70 6f 6c 79 0a 09 |now apply poly..|
00003e10 41 44 44 09 61 32 2c 20 61 32 2c 20 61 32 2c 20 |ADD.a2, a2, a2, |
00003e20 4c 53 4c 20 23 35 0a 09 4d 4f 56 09 61 32 2c 20 |LSL #5..MOV.a2, |
00003e30 61 32 2c 20 41 53 52 20 23 31 34 0a 09 41 44 44 |a2, ASR #14..ADD|
00003e40 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 35 30 |.a2, a2, #&00050|
00003e50 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 |0..ADD.a2, a2, #|
00003e60 26 30 30 30 30 61 65 0a 20 20 20 20 20 20 20 20 |&0000ae. |
00003e70 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 |MOV.ip, a1..mul1|
00003e80 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 |6c.a2, ip, a2, a|
00003e90 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 |3..ADD.a2, a2, #|
00003ea0 26 30 30 30 38 30 30 0a 09 41 44 44 09 61 32 2c |&000800..ADD.a2,|
00003eb0 20 61 32 2c 20 23 26 30 30 30 30 38 38 0a 20 20 | a2, #&000088. |
00003ec0 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 | MOV.ip, a1|
00003ed0 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 2c |..mul16c.a2, ip,|
00003ee0 20 61 32 2c 20 61 33 0a 09 41 44 44 09 61 32 2c | a2, a3..ADD.a2,|
00003ef0 20 61 32 2c 20 23 26 30 30 32 30 30 30 0a 09 41 | a2, #&002000..A|
00003f00 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 |DD.a2, a2, #&000|
00003f10 30 39 61 0a 20 20 20 20 20 20 20 20 4d 4f 56 09 |09a. MOV.|
00003f20 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 61 |ip, a1..mul16c.a|
00003f30 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a 09 41 |2, ip, a2, a3..A|
00003f40 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 34 |DD.a2, a2, #&004|
00003f50 36 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |600..ADD.a2, a2,|
00003f60 20 23 26 30 30 30 30 39 61 0a 20 20 20 20 20 20 | #&00009a. |
00003f70 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 | MOV.ip, a1..mu|
00003f80 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c |l16c.a2, ip, a2,|
00003f90 20 61 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c | a3..ADD.a2, a2,|
00003fa0 20 23 26 30 33 30 30 30 30 0a 09 41 44 44 09 61 | #&030000..ADD.a|
00003fb0 32 2c 20 61 32 2c 20 23 26 30 30 64 39 30 30 0a |2, a2, #&00d900.|
00003fc0 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00003fd0 30 30 30 62 34 0a 20 20 20 20 20 20 20 20 4d 4f |000b4. MO|
00003fe0 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 |V.ip, a1..mul16c|
00003ff0 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a |.a2, ip, a2, a3.|
00004000 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 |.ADD.a2, a2, #&0|
00004010 33 30 30 30 30 0a 09 41 44 44 09 61 32 2c 20 61 |30000..ADD.a2, a|
00004020 32 2c 20 23 26 30 30 61 65 30 30 0a 09 41 44 44 |2, #&00ae00..ADD|
00004030 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 30 35 |.a2, a2, #&00005|
00004040 32 0a 09 4d 4f 56 09 61 31 2c 20 61 32 2c 20 41 |2..MOV.a1, a2, A|
00004050 53 52 20 23 34 0a 09 54 53 54 09 61 34 2c 20 23 |SR #4..TST.a4, #|
00004060 32 0a 09 52 53 42 45 51 09 61 31 2c 20 61 31 2c |2..RSBEQ.a1, a1,|
00004070 20 23 36 35 35 33 36 0a 09 54 53 54 09 61 34 2c | #65536..TST.a4,|
00004080 20 23 31 0a 09 52 53 42 4e 45 09 61 31 2c 20 61 | #1..RSBNE.a1, a|
00004090 31 2c 20 23 32 2a 36 35 35 33 36 0a 09 4c 44 4d |1, #2*65536..LDM|
000040a0 46 44 09 73 70 21 2c 20 7b 70 63 7d 5e 0a 0a 0a |FD.sp!, {pc}^...|
000040b0 0a 3b 20 61 73 6e 31 36 0a 3b 20 61 20 6c 65 61 |.; asn16.; a lea|
000040c0 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e 0a |f APCS function.|
000040d0 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 3a |;.; C prototype:|
000040e0 0a 3b 20 69 6e 74 20 61 73 6e 31 36 28 69 6e 74 |.; int asn16(int|
000040f0 20 61 29 0a 3b 0a 3b 20 72 65 74 75 72 6e 73 20 | a).;.; returns |
00004100 36 35 35 33 36 20 2a 20 32 2f 70 69 20 2a 20 61 |65536 * 2/pi * a|
00004110 72 63 73 69 6e 20 28 61 2f 36 35 35 33 36 29 0a |rcsin (a/65536).|
00004120 3b 0a 3b 20 66 6f 72 20 61 20 6f 75 74 20 6f 66 |;.; for a out of|
00004130 20 72 61 6e 67 65 20 28 69 65 20 61 62 73 20 61 | range (ie abs a|
00004140 20 3e 20 36 35 35 33 36 29 2c 20 72 65 73 65 74 | > 65536), reset|
00004150 20 61 20 74 6f 20 b1 36 35 35 33 36 20 61 73 20 | a to .65536 as |
00004160 61 70 70 72 6f 70 72 69 61 74 65 20 62 65 66 6f |appropriate befo|
00004170 72 65 20 65 76 61 6c 0a 3b 0a 3b 20 69 73 20 61 |re eval.;.; is a|
00004180 62 6f 75 74 20 32 34 20 74 69 6d 65 73 20 66 61 |bout 24 times fa|
00004190 73 74 65 72 20 74 68 61 6e 20 46 50 45 6d 75 6c |ster than FPEmul|
000041a0 61 74 6f 72 20 77 6f 72 6b 69 6e 67 20 77 69 74 |ator working wit|
000041b0 68 20 64 6f 75 62 6c 65 20 66 6c 6f 61 74 73 0a |h double floats.|
000041c0 3b 0a 0a 20 20 20 20 20 20 20 20 45 58 50 4f 52 |;.. EXPOR|
000041d0 54 20 20 61 73 6e 31 36 0a 0a 61 73 6e 73 74 61 |T asn16..asnsta|
000041e0 20 20 44 43 42 20 20 20 20 20 22 61 73 6e 31 36 | DCB "asn16|
000041f0 22 2c 20 30 0a 20 20 20 20 20 20 20 20 41 4c 49 |", 0. ALI|
00004200 47 4e 0a 61 73 6e 65 6e 64 20 20 44 43 44 20 20 |GN.asnend DCD |
00004210 20 20 20 26 66 66 30 30 30 30 30 30 20 2b 20 61 | &ff000000 + a|
00004220 73 6e 65 6e 64 20 2d 20 61 73 6e 73 74 61 0a 0a |snend - asnsta..|
00004230 61 73 6e 31 36 0a 0a 09 43 4d 50 09 61 31 2c 20 |asn16...CMP.a1, |
00004240 23 36 35 35 33 36 0a 09 4d 4f 56 47 45 09 61 31 |#65536..MOVGE.a1|
00004250 2c 20 23 36 35 35 33 36 0a 09 4d 4f 56 47 45 53 |, #65536..MOVGES|
00004260 09 70 63 2c 20 6c 72 0a 09 41 44 44 53 09 61 32 |.pc, lr..ADDS.a2|
00004270 2c 20 61 31 2c 20 23 36 35 35 33 36 09 09 3b 65 |, a1, #65536..;e|
00004280 71 75 69 76 20 74 6f 20 43 4d 50 20 61 31 2c 23 |quiv to CMP a1,#|
00004290 2d 36 35 35 33 36 0a 09 53 55 42 4c 45 09 61 31 |-65536..SUBLE.a1|
000042a0 2c 20 61 31 2c 20 61 32 09 09 3b 65 71 75 69 76 |, a1, a2..;equiv|
000042b0 20 74 6f 20 4d 4f 56 4c 45 20 61 31 2c 23 2d 36 | to MOVLE a1,#-6|
000042c0 35 35 33 36 20 28 77 68 69 63 68 20 77 6f 75 6c |5536 (which woul|
000042d0 64 6e 27 74 20 77 6f 72 6b 20 64 75 65 20 74 6f |dn't work due to|
000042e0 20 62 61 64 20 63 6f 6e 73 74 61 6e 74 29 0a 09 | bad constant)..|
000042f0 4d 4f 56 4c 45 53 09 70 63 2c 20 6c 72 0a 09 53 |MOVLES.pc, lr..S|
00004300 54 4d 46 44 09 73 70 21 2c 20 7b 6c 72 7d 09 09 |TMFD.sp!, {lr}..|
00004310 3b 6e 6f 77 20 68 61 76 65 20 61 72 67 20 69 6e |;now have arg in|
00004320 20 72 61 6e 67 65 20 28 2d 6f 6e 65 2c 6f 6e 65 | range (-one,one|
00004330 29 0a 09 43 4d 50 09 61 31 2c 20 23 30 0a 09 52 |)..CMP.a1, #0..R|
00004340 53 42 4d 49 09 61 31 2c 20 61 31 2c 20 23 30 0a |SBMI.a1, a1, #0.|
00004350 09 4d 4f 56 4d 49 09 61 34 2c 20 23 31 09 09 09 |.MOVMI.a4, #1...|
00004360 3b 62 30 20 69 6e 20 61 34 20 73 65 74 20 69 66 |;b0 in a4 set if|
00004370 66 20 66 69 6e 61 6c 20 72 65 73 75 6c 74 20 6e |f final result n|
00004380 65 65 64 73 20 6e 65 67 61 74 69 6e 67 0a 09 4d |eeds negating..M|
00004390 4f 56 50 4c 09 61 34 2c 20 23 30 09 09 09 3b 6e |OVPL.a4, #0...;n|
000043a0 6f 77 20 68 61 76 65 20 61 72 67 20 69 6e 20 72 |ow have arg in r|
000043b0 61 6e 67 65 20 5b 30 2c 6f 6e 65 29 0a 09 53 55 |ange [0,one)..SU|
000043c0 42 09 61 32 2c 20 61 31 2c 20 23 26 62 35 30 30 |B.a2, a1, #&b500|
000043d0 0a 09 53 55 42 53 09 61 32 2c 20 61 32 2c 20 23 |..SUBS.a2, a2, #|
000043e0 26 30 30 30 35 0a 09 42 4c 54 09 61 73 6e 31 36 |&0005..BLT.asn16|
000043f0 5f 61 72 67 6c 6f 77 09 09 3b 69 66 20 61 72 67 |_arglow..;if arg|
00004400 20 3c 20 6f 6e 65 2f 73 71 72 74 32 20 67 6f 20 | < one/sqrt2 go |
00004410 61 6e 64 20 61 70 70 6c 79 20 70 6f 6c 79 20 65 |and apply poly e|
00004420 6c 73 65 20 66 69 72 73 74 20 74 72 61 6e 73 6d |lse first transm|
00004430 75 74 65 20 69 6e 74 6f 20 68 65 72 65 0a 09 4f |ute into here..O|
00004440 52 52 09 61 34 2c 20 61 34 2c 20 23 32 09 09 3b |RR.a4, a4, #2..;|
00004450 62 31 20 69 6e 20 61 34 20 73 65 74 20 69 66 66 |b1 in a4 set iff|
00004460 20 70 65 6e 75 6c 74 69 6d 61 74 65 20 72 65 73 | penultimate res|
00004470 75 6c 74 20 72 20 6e 65 65 64 73 20 74 6f 20 62 |ult r needs to b|
00004480 65 20 72 65 70 6c 61 63 65 64 20 62 79 20 6f 6e |e replaced by on|
00004490 65 2d 72 0a 09 4d 55 4c 09 61 32 2c 20 61 31 2c |e-r..MUL.a2, a1,|
000044a0 20 61 31 0a 09 4d 4f 56 09 61 31 2c 20 61 32 2c | a1..MOV.a1, a2,|
000044b0 20 4c 53 52 20 23 31 36 0a 09 52 53 42 09 61 31 | LSR #16..RSB.a1|
000044c0 2c 20 61 31 2c 20 23 36 35 35 33 36 0a 09 73 71 |, a1, #65536..sq|
000044d0 72 74 31 36 09 61 31 2c 20 61 31 2c 20 61 32 2c |rt16.a1, a1, a2,|
000044e0 20 61 33 2c 20 69 70 2c 20 6c 72 09 3b 61 72 67 | a3, ip, lr.;arg|
000044f0 20 74 72 61 6e 73 6d 75 74 65 64 20 28 69 65 20 | transmuted (ie |
00004500 72 65 70 6c 61 63 65 64 20 62 79 20 6f 6e 65 2d |replaced by one-|
00004510 73 71 72 74 28 61 72 67 5e 32 29 29 0a 61 73 6e |sqrt(arg^2)).asn|
00004520 31 36 5f 61 72 67 6c 6f 77 0a 09 41 44 44 09 61 |16_arglow..ADD.a|
00004530 33 2c 20 61 31 2c 20 61 31 2c 20 41 53 4c 20 23 |3, a1, a1, ASL #|
00004540 32 0a 09 41 44 44 09 61 32 2c 20 61 33 2c 20 61 |2..ADD.a2, a3, a|
00004550 31 2c 20 41 53 4c 20 23 34 0a 09 41 44 44 09 61 |1, ASL #4..ADD.a|
00004560 32 2c 20 61 32 2c 20 61 33 2c 20 41 53 4c 20 23 |2, a2, a3, ASL #|
00004570 35 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 61 |5..ADD.a2, a2, a|
00004580 33 2c 20 41 53 52 09 23 38 0a 09 41 44 44 09 61 |3, ASR.#8..ADD.a|
00004590 32 2c 20 61 32 2c 20 23 33 32 0a 09 4d 4f 56 09 |2, a2, #32..MOV.|
000045a0 61 31 2c 20 61 32 2c 20 41 53 52 20 23 36 09 09 |a1, a2, ASR #6..|
000045b0 3b 72 61 6e 67 65 20 74 72 61 6e 73 66 6f 72 6d |;range transform|
000045c0 20 61 70 70 6c 69 65 64 20 28 69 65 20 72 65 70 | applied (ie rep|
000045d0 6c 61 63 65 64 20 62 79 20 61 72 67 2a 32 73 71 |laced by arg*2sq|
000045e0 72 74 32 2d 6f 6e 65 29 0a 09 53 55 42 09 61 31 |rt2-one)..SUB.a1|
000045f0 2c 20 61 31 2c 20 23 26 31 30 30 30 30 09 09 3b |, a1, #&10000..;|
00004600 73 6f 20 61 72 67 20 6c 69 65 73 20 69 6e 20 72 |so arg lies in r|
00004610 61 6e 67 65 20 5b 2d 31 2c 31 5d 0a 09 41 44 44 |ange [-1,1]..ADD|
00004620 09 61 32 2c 20 61 31 2c 20 61 31 2c 20 4c 53 4c |.a2, a1, a1, LSL|
00004630 20 23 32 09 3b 6e 6f 77 20 61 70 70 6c 79 20 70 | #2.;now apply p|
00004640 6f 6c 79 0a 09 41 44 44 09 61 32 2c 20 61 32 2c |oly..ADD.a2, a2,|
00004650 20 61 32 2c 20 4c 53 4c 20 23 35 0a 09 4d 4f 56 | a2, LSL #5..MOV|
00004660 09 61 32 2c 20 61 32 2c 20 41 53 52 20 23 31 34 |.a2, a2, ASR #14|
00004670 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 |..ADD.a2, a2, #&|
00004680 30 30 30 35 30 30 0a 09 41 44 44 09 61 32 2c 20 |000500..ADD.a2, |
00004690 61 32 2c 20 23 26 30 30 30 30 61 65 0a 20 20 20 |a2, #&0000ae. |
000046a0 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a | MOV.ip, a1.|
000046b0 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 |.mul16c.a2, ip, |
000046c0 61 32 2c 20 61 33 0a 09 41 44 44 09 61 32 2c 20 |a2, a3..ADD.a2, |
000046d0 61 32 2c 20 23 26 30 30 30 38 30 30 0a 09 41 44 |a2, #&000800..AD|
000046e0 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 30 30 |D.a2, a2, #&0000|
000046f0 38 38 0a 20 20 20 20 20 20 20 20 4d 4f 56 09 69 |88. MOV.i|
00004700 70 2c 20 61 31 0a 09 6d 75 6c 31 36 63 09 61 32 |p, a1..mul16c.a2|
00004710 2c 20 69 70 2c 20 61 32 2c 20 61 33 0a 09 41 44 |, ip, a2, a3..AD|
00004720 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 32 30 |D.a2, a2, #&0020|
00004730 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 |00..ADD.a2, a2, |
00004740 23 26 30 30 30 30 39 61 0a 20 20 20 20 20 20 20 |#&00009a. |
00004750 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d 75 6c | MOV.ip, a1..mul|
00004760 31 36 63 09 61 32 2c 20 69 70 2c 20 61 32 2c 20 |16c.a2, ip, a2, |
00004770 61 33 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 |a3..ADD.a2, a2, |
00004780 23 26 30 30 34 36 30 30 0a 09 41 44 44 09 61 32 |#&004600..ADD.a2|
00004790 2c 20 61 32 2c 20 23 26 30 30 30 30 39 61 0a 20 |, a2, #&00009a. |
000047a0 20 20 20 20 20 20 20 4d 4f 56 09 69 70 2c 20 61 | MOV.ip, a|
000047b0 31 0a 09 6d 75 6c 31 36 63 09 61 32 2c 20 69 70 |1..mul16c.a2, ip|
000047c0 2c 20 61 32 2c 20 61 33 0a 09 41 44 44 09 61 32 |, a2, a3..ADD.a2|
000047d0 2c 20 61 32 2c 20 23 26 30 33 30 30 30 30 0a 09 |, a2, #&030000..|
000047e0 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 30 30 |ADD.a2, a2, #&00|
000047f0 64 39 30 30 0a 09 41 44 44 09 61 32 2c 20 61 32 |d900..ADD.a2, a2|
00004800 2c 20 23 26 30 30 30 30 62 34 0a 20 20 20 20 20 |, #&0000b4. |
00004810 20 20 20 4d 4f 56 09 69 70 2c 20 61 31 0a 09 6d | MOV.ip, a1..m|
00004820 75 6c 31 36 63 09 61 32 2c 20 69 70 2c 20 61 32 |ul16c.a2, ip, a2|
00004830 2c 20 61 33 0a 09 41 44 44 09 61 32 2c 20 61 32 |, a3..ADD.a2, a2|
00004840 2c 20 23 26 30 33 30 30 30 30 0a 09 41 44 44 09 |, #&030000..ADD.|
00004850 61 32 2c 20 61 32 2c 20 23 26 30 30 61 65 30 30 |a2, a2, #&00ae00|
00004860 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 23 26 |..ADD.a2, a2, #&|
00004870 30 30 30 30 35 32 0a 09 4d 4f 56 09 61 31 2c 20 |000052..MOV.a1, |
00004880 61 32 2c 20 41 53 52 20 23 34 0a 09 54 53 54 09 |a2, ASR #4..TST.|
00004890 61 34 2c 20 23 32 0a 09 52 53 42 4e 45 09 61 31 |a4, #2..RSBNE.a1|
000048a0 2c 20 61 31 2c 20 23 36 35 35 33 36 0a 09 54 53 |, a1, #65536..TS|
000048b0 54 09 61 34 2c 20 23 31 0a 09 52 53 42 4e 45 09 |T.a4, #1..RSBNE.|
000048c0 61 31 2c 20 61 31 2c 20 23 30 0a 09 4c 44 4d 46 |a1, a1, #0..LDMF|
000048d0 44 09 73 70 21 2c 20 7b 70 63 7d 5e 0a 0a 0a 0a |D.sp!, {pc}^....|
000048e0 3b 20 67 61 75 73 73 31 36 0a 3b 20 61 20 6c 65 |; gauss16.; a le|
000048f0 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e |af APCS function|
00004900 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 |.;.; C prototype|
00004910 3a 0a 3b 20 69 6e 74 20 67 61 75 73 73 31 36 28 |:.; int gauss16(|
00004920 76 6f 69 64 29 0a 3b 0a 3b 20 72 65 74 75 72 6e |void).;.; return|
00004930 73 20 36 35 35 33 36 20 2a 20 28 20 70 73 65 75 |s 65536 * ( pseu|
00004940 64 6f 20 72 61 6e 64 6f 6e 20 76 61 72 69 61 62 |do randon variab|
00004950 6c 65 20 77 69 74 68 20 61 70 70 72 6f 78 69 6d |le with approxim|
00004960 61 74 65 20 64 69 73 74 72 69 62 75 74 69 6f 6e |ate distribution|
00004970 20 4e 28 30 2c 31 29 20 29 0a 3b 20 6e 6f 74 65 | N(0,1) ).; note|
00004980 2c 20 74 68 65 20 61 70 70 72 6f 78 69 6d 61 74 |, the approximat|
00004990 65 20 67 61 75 73 73 69 61 6e 20 64 69 73 74 72 |e gaussian distr|
000049a0 69 62 75 74 69 6f 6e 20 69 73 20 61 63 68 69 65 |ibution is achie|
000049b0 76 65 64 20 76 69 61 20 74 68 65 20 73 75 6d 20 |ved via the sum |
000049c0 6f 66 20 6e 20 70 73 65 75 64 6f 20 55 5b 30 2c |of n pseudo U[0,|
000049d0 36 35 35 33 35 5d 0a 3b 20 20 20 20 20 20 20 72 |65535].; r|
000049e0 61 6e 64 6f 6d 20 76 61 72 69 61 62 6c 65 73 20 |andom variables |
000049f0 26 20 61 70 70 6c 69 63 61 74 69 6f 6e 20 6f 66 |& application of|
00004a00 20 74 68 65 20 63 65 6e 74 72 61 6c 20 6c 69 6d | the central lim|
00004a10 69 74 20 74 68 65 6f 72 65 6d 0a 3b 20 20 20 20 |it theorem.; |
00004a20 20 20 20 68 65 72 65 20 77 65 20 75 73 65 20 6e | here we use n|
00004a30 3d 38 2c 20 67 69 76 69 6e 67 20 61 6e 20 61 63 |=8, giving an ac|
00004a40 74 75 61 6c 20 72 61 6e 67 65 20 6f 66 20 b1 28 |tual range of .(|
00004a50 73 71 72 74 32 34 29 20 28 2a 36 35 35 33 36 29 |sqrt24) (*65536)|
00004a60 2e 0a 3b 0a 3b 20 20 20 20 20 20 20 66 6f 72 20 |..;.; for |
00004a70 67 65 6e 65 72 61 6c 20 6e 2c 20 72 65 63 61 6c |general n, recal|
00004a80 6c 20 77 65 20 6e 65 65 64 20 74 6f 20 72 65 74 |l we need to ret|
00004a90 75 72 6e 3a 0a 3b 20 20 20 20 20 20 20 28 73 75 |urn:.; (su|
00004aa0 6d 20 6e 20 55 5b 30 2c 36 35 35 33 35 5d 20 72 |m n U[0,65535] r|
00004ab0 61 6e 64 6f 6d 20 76 61 72 69 61 62 6c 65 73 29 |andom variables)|
00004ac0 20 2a 20 32 73 71 72 74 28 33 6e 29 2a 36 35 35 | * 2sqrt(3n)*655|
00004ad0 33 36 2f 28 36 35 35 33 35 6e 29 20 20 2d 20 20 |36/(65535n) - |
00004ae0 73 71 72 74 28 33 6e 29 2a 36 35 35 33 36 0a 3b |sqrt(3n)*65536.;|
00004af0 0a 0a 09 45 58 50 4f 52 54 09 67 61 75 73 73 31 |...EXPORT.gauss1|
00004b00 36 0a 0a 67 61 6e 73 74 61 20 20 44 43 42 20 20 |6..gansta DCB |
00004b10 20 20 20 22 67 61 75 73 73 31 36 22 2c 20 30 0a | "gauss16", 0.|
00004b20 20 20 20 20 20 20 20 20 41 4c 49 47 4e 0a 67 61 | ALIGN.ga|
00004b30 6e 65 6e 64 20 20 44 43 44 20 20 20 20 20 26 66 |nend DCD &f|
00004b40 66 30 30 30 30 30 30 20 2b 20 67 61 6e 65 6e 64 |f000000 + ganend|
00004b50 20 2d 20 67 61 6e 73 74 61 0a 0a 67 61 75 73 73 | - gansta..gauss|
00004b60 31 36 0a 0a 09 41 44 52 09 61 31 2c 20 67 61 75 |16...ADR.a1, gau|
00004b70 73 73 73 65 65 64 31 0a 09 4c 44 4d 49 41 09 61 |ssseed1..LDMIA.a|
00004b80 31 2c 20 7b 61 32 2c 20 61 33 7d 0a 0a 09 4d 4f |1, {a2, a3}...MO|
00004b90 56 53 20 20 20 20 61 33 2c 20 61 33 2c 20 4c 53 |VS a3, a3, LS|
00004ba0 52 20 23 31 0a 20 20 20 20 20 20 20 20 4d 4f 56 |R #1. MOV|
00004bb0 53 20 20 20 20 61 34 2c 20 61 32 2c 20 52 52 58 |S a4, a2, RRX|
00004bc0 0a 20 20 20 20 20 20 20 20 41 44 43 20 20 20 20 |. ADC |
00004bd0 20 61 33 2c 20 61 33 2c 20 61 33 0a 20 20 20 20 | a3, a3, a3. |
00004be0 20 20 20 20 45 4f 52 20 20 20 20 20 61 34 2c 20 | EOR a4, |
00004bf0 61 34 2c 20 61 32 2c 20 4c 53 4c 20 23 31 32 0a |a4, a2, LSL #12.|
00004c00 20 20 20 20 20 20 20 20 45 4f 52 20 20 20 20 20 | EOR |
00004c10 61 32 2c 20 61 34 2c 20 61 34 2c 20 4c 53 52 20 |a2, a4, a4, LSR |
00004c20 23 32 30 0a 09 4d 4f 56 09 69 70 2c 20 61 32 2c |#20..MOV.ip, a2,|
00004c30 20 4c 53 52 20 23 31 36 0a 09 4d 4f 56 09 61 34 | LSR #16..MOV.a4|
00004c40 2c 20 61 32 2c 20 4c 53 4c 20 23 31 36 0a 09 41 |, a2, LSL #16..A|
00004c50 44 44 09 69 70 2c 20 69 70 2c 20 61 34 2c 20 4c |DD.ip, ip, a4, L|
00004c60 53 52 20 23 31 36 0a 0a 09 4d 4f 56 53 20 20 20 |SR #16...MOVS |
00004c70 20 61 33 2c 20 61 33 2c 20 4c 53 52 20 23 31 0a | a3, a3, LSR #1.|
00004c80 20 20 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 | MOVS |
00004c90 61 34 2c 20 61 32 2c 20 52 52 58 0a 20 20 20 20 |a4, a2, RRX. |
00004ca0 20 20 20 20 41 44 43 20 20 20 20 20 61 33 2c 20 | ADC a3, |
00004cb0 61 33 2c 20 61 33 0a 20 20 20 20 20 20 20 20 45 |a3, a3. E|
00004cc0 4f 52 20 20 20 20 20 61 34 2c 20 61 34 2c 20 61 |OR a4, a4, a|
00004cd0 32 2c 20 4c 53 4c 20 23 31 32 0a 20 20 20 20 20 |2, LSL #12. |
00004ce0 20 20 20 45 4f 52 20 20 20 20 20 61 32 2c 20 61 | EOR a2, a|
00004cf0 34 2c 20 61 34 2c 20 4c 53 52 20 23 32 30 0a 09 |4, a4, LSR #20..|
00004d00 41 44 44 09 69 70 2c 20 69 70 2c 20 61 32 2c 20 |ADD.ip, ip, a2, |
00004d10 4c 53 52 20 23 31 36 0a 09 4d 4f 56 09 61 34 2c |LSR #16..MOV.a4,|
00004d20 20 61 32 2c 20 4c 53 4c 20 23 31 36 0a 09 41 44 | a2, LSL #16..AD|
00004d30 44 09 69 70 2c 20 69 70 2c 20 61 34 2c 20 4c 53 |D.ip, ip, a4, LS|
00004d40 52 20 23 31 36 0a 0a 09 4d 4f 56 53 20 20 20 20 |R #16...MOVS |
00004d50 61 33 2c 20 61 33 2c 20 4c 53 52 20 23 31 0a 20 |a3, a3, LSR #1. |
00004d60 20 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 61 | MOVS a|
00004d70 34 2c 20 61 32 2c 20 52 52 58 0a 20 20 20 20 20 |4, a2, RRX. |
00004d80 20 20 20 41 44 43 20 20 20 20 20 61 33 2c 20 61 | ADC a3, a|
00004d90 33 2c 20 61 33 0a 20 20 20 20 20 20 20 20 45 4f |3, a3. EO|
00004da0 52 20 20 20 20 20 61 34 2c 20 61 34 2c 20 61 32 |R a4, a4, a2|
00004db0 2c 20 4c 53 4c 20 23 31 32 0a 20 20 20 20 20 20 |, LSL #12. |
00004dc0 20 20 45 4f 52 20 20 20 20 20 61 32 2c 20 61 34 | EOR a2, a4|
00004dd0 2c 20 61 34 2c 20 4c 53 52 20 23 32 30 0a 09 41 |, a4, LSR #20..A|
00004de0 44 44 09 69 70 2c 20 69 70 2c 20 61 32 2c 20 4c |DD.ip, ip, a2, L|
00004df0 53 52 20 23 31 36 0a 09 4d 4f 56 09 61 34 2c 20 |SR #16..MOV.a4, |
00004e00 61 32 2c 20 4c 53 4c 20 23 31 36 0a 09 41 44 44 |a2, LSL #16..ADD|
00004e10 09 69 70 2c 20 69 70 2c 20 61 34 2c 20 4c 53 52 |.ip, ip, a4, LSR|
00004e20 20 23 31 36 0a 0a 09 4d 4f 56 53 20 20 20 20 61 | #16...MOVS a|
00004e30 33 2c 20 61 33 2c 20 4c 53 52 20 23 31 0a 20 20 |3, a3, LSR #1. |
00004e40 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 61 34 | MOVS a4|
00004e50 2c 20 61 32 2c 20 52 52 58 0a 20 20 20 20 20 20 |, a2, RRX. |
00004e60 20 20 41 44 43 20 20 20 20 20 61 33 2c 20 61 33 | ADC a3, a3|
00004e70 2c 20 61 33 0a 20 20 20 20 20 20 20 20 45 4f 52 |, a3. EOR|
00004e80 20 20 20 20 20 61 34 2c 20 61 34 2c 20 61 32 2c | a4, a4, a2,|
00004e90 20 4c 53 4c 20 23 31 32 0a 20 20 20 20 20 20 20 | LSL #12. |
00004ea0 20 45 4f 52 20 20 20 20 20 61 32 2c 20 61 34 2c | EOR a2, a4,|
00004eb0 20 61 34 2c 20 4c 53 52 20 23 32 30 0a 09 41 44 | a4, LSR #20..AD|
00004ec0 44 09 69 70 2c 20 69 70 2c 20 61 32 2c 20 4c 53 |D.ip, ip, a2, LS|
00004ed0 52 20 23 31 36 0a 09 4d 4f 56 09 61 34 2c 20 61 |R #16..MOV.a4, a|
00004ee0 32 2c 20 4c 53 4c 20 23 31 36 0a 09 41 44 44 09 |2, LSL #16..ADD.|
00004ef0 69 70 2c 20 69 70 2c 20 61 34 2c 20 4c 53 52 20 |ip, ip, a4, LSR |
00004f00 23 31 36 09 3b 73 75 6d 20 6e 6f 77 20 69 6e 20 |#16.;sum now in |
00004f10 69 70 0a 0a 09 53 54 4d 49 41 09 61 31 2c 20 7b |ip...STMIA.a1, {|
00004f20 61 32 2c 20 61 33 7d 0a 0a 09 52 53 42 09 61 31 |a2, a3}...RSB.a1|
00004f30 2c 20 69 70 2c 20 69 70 2c 20 41 53 4c 20 23 33 |, ip, ip, ASL #3|
00004f40 0a 09 52 53 42 09 61 32 2c 20 69 70 2c 20 69 70 |..RSB.a2, ip, ip|
00004f50 2c 20 41 53 4c 20 23 32 0a 09 41 44 44 09 61 31 |, ASL #2..ADD.a1|
00004f60 2c 20 61 32 2c 20 61 31 2c 20 41 53 4c 20 23 34 |, a2, a1, ASL #4|
00004f70 0a 09 41 44 44 09 61 31 2c 20 61 31 2c 20 69 70 |..ADD.a1, a1, ip|
00004f80 2c 20 41 53 4c 20 23 39 0a 09 41 44 44 09 61 32 |, ASL #9..ADD.a2|
00004f90 2c 20 69 70 2c 20 69 70 2c 20 41 53 4c 20 23 34 |, ip, ip, ASL #4|
00004fa0 0a 09 41 44 44 09 61 32 2c 20 61 32 2c 20 69 70 |..ADD.a2, a2, ip|
00004fb0 2c 20 41 53 4c 20 23 36 0a 09 41 44 44 09 61 31 |, ASL #6..ADD.a1|
00004fc0 2c 20 61 31 2c 20 61 32 2c 20 4c 53 52 20 23 31 |, a1, a2, LSR #1|
00004fd0 30 0a 09 4d 4f 56 09 61 31 2c 20 61 31 2c 20 4c |0..MOV.a1, a1, L|
00004fe0 53 52 20 23 39 0a 09 53 55 42 09 61 31 2c 20 61 |SR #9..SUB.a1, a|
00004ff0 31 2c 20 23 26 34 45 30 30 30 0a 09 53 55 42 09 |1, #&4E000..SUB.|
00005000 61 31 2c 20 61 31 2c 20 23 26 30 30 36 32 30 0a |a1, a1, #&00620.|
00005010 09 53 55 42 09 61 31 2c 20 61 31 2c 20 23 26 30 |.SUB.a1, a1, #&0|
00005020 30 30 30 34 0a 0a 20 20 20 20 20 20 20 20 4d 4f |0004.. MO|
00005030 56 53 20 20 20 20 70 63 2c 20 6c 72 0a 0a 67 61 |VS pc, lr..ga|
00005040 75 73 73 73 65 65 64 31 09 44 43 44 09 2d 31 09 |ussseed1.DCD.-1.|
00005050 09 3b 62 69 74 73 20 62 30 2d 62 33 31 20 6f 66 |.;bits b0-b31 of|
00005060 20 73 65 65 64 0a 09 09 44 43 44 09 2d 31 09 09 | seed...DCD.-1..|
00005070 3b 62 69 74 20 20 62 33 32 20 6f 66 20 73 65 65 |;bit b32 of see|
00005080 64 20 28 69 6e 20 6c 73 62 20 6f 66 20 77 6f 72 |d (in lsb of wor|
00005090 64 29 0a 0a 3b 20 73 67 61 75 73 73 31 36 0a 3b |d)..; sgauss16.;|
000050a0 20 61 20 6c 65 61 66 20 41 50 43 53 20 66 75 6e | a leaf APCS fun|
000050b0 63 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 |ction.;.; C prot|
000050c0 6f 74 79 70 65 3a 0a 3b 20 76 6f 69 64 20 73 67 |otype:.; void sg|
000050d0 61 75 73 73 31 36 28 69 6e 74 20 73 65 65 64 29 |auss16(int seed)|
000050e0 0a 3b 0a 3b 20 73 65 74 73 20 74 68 65 20 73 65 |.;.; sets the se|
000050f0 65 64 20 66 6f 72 20 67 61 75 73 73 31 36 0a 3b |ed for gauss16.;|
00005100 0a 0a 09 45 58 50 4f 52 54 09 73 67 61 75 73 73 |...EXPORT.sgauss|
00005110 31 36 0a 0a 73 67 6e 73 74 61 20 20 44 43 42 20 |16..sgnsta DCB |
00005120 20 20 20 20 22 73 67 61 75 73 73 31 36 22 2c 20 | "sgauss16", |
00005130 30 0a 20 20 20 20 20 20 20 20 41 4c 49 47 4e 0a |0. ALIGN.|
00005140 73 67 6e 65 6e 64 20 20 44 43 44 20 20 20 20 20 |sgnend DCD |
00005150 26 66 66 30 30 30 30 30 30 20 2b 20 73 67 6e 65 |&ff000000 + sgne|
00005160 6e 64 20 2d 20 73 67 6e 73 74 61 0a 0a 73 67 61 |nd - sgnsta..sga|
00005170 75 73 73 31 36 0a 0a 09 41 44 52 09 61 32 2c 20 |uss16...ADR.a2, |
00005180 67 61 75 73 73 73 65 65 64 31 0a 09 4d 4f 56 09 |gaussseed1..MOV.|
00005190 61 33 2c 20 23 31 0a 09 53 54 4d 49 41 09 61 32 |a3, #1..STMIA.a2|
000051a0 2c 20 7b 61 31 2c 20 61 33 7d 0a 20 20 20 20 20 |, {a1, a3}. |
000051b0 20 20 20 4d 4f 56 53 20 20 20 20 70 63 2c 20 6c | MOVS pc, l|
000051c0 72 0a 0a 0a 0a 3b 20 72 61 6e 64 31 36 0a 3b 20 |r....; rand16.; |
000051d0 61 20 6c 65 61 66 20 41 50 43 53 20 66 75 6e 63 |a leaf APCS func|
000051e0 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f |tion.;.; C proto|
000051f0 74 79 70 65 3a 0a 3b 20 69 6e 74 20 72 61 6e 64 |type:.; int rand|
00005200 31 36 28 76 6f 69 64 29 0a 3b 0a 3b 20 72 65 74 |16(void).;.; ret|
00005210 75 72 6e 73 20 36 35 35 33 36 20 2a 20 28 20 70 |urns 65536 * ( p|
00005220 73 65 75 64 6f 20 72 61 6e 64 6f 6e 20 76 61 72 |seudo randon var|
00005230 69 61 62 6c 65 20 77 69 74 68 20 61 70 70 72 6f |iable with appro|
00005240 78 69 6d 61 74 65 20 64 69 73 74 72 69 62 75 74 |ximate distribut|
00005250 69 6f 6e 20 55 28 2d 31 2c 31 29 20 29 0a 3b 0a |ion U(-1,1) ).;.|
00005260 0a 09 45 58 50 4f 52 54 09 72 61 6e 64 31 36 0a |..EXPORT.rand16.|
00005270 0a 72 61 6e 73 74 61 20 20 44 43 42 20 20 20 20 |.ransta DCB |
00005280 20 22 72 61 6e 64 31 36 22 2c 20 30 0a 20 20 20 | "rand16", 0. |
00005290 20 20 20 20 20 41 4c 49 47 4e 0a 72 61 6e 65 6e | ALIGN.ranen|
000052a0 64 20 20 44 43 44 20 20 20 20 20 26 66 66 30 30 |d DCD &ff00|
000052b0 30 30 30 30 20 2b 20 72 61 6e 65 6e 64 20 2d 20 |0000 + ranend - |
000052c0 72 61 6e 73 74 61 0a 0a 72 61 6e 64 31 36 0a 0a |ransta..rand16..|
000052d0 09 41 44 52 09 69 70 2c 20 72 61 6e 64 73 65 65 |.ADR.ip, randsee|
000052e0 64 31 0a 09 4c 44 4d 49 41 09 69 70 2c 20 7b 61 |d1..LDMIA.ip, {a|
000052f0 32 2c 20 61 33 7d 0a 72 61 6e 64 31 36 5f 6c 6f |2, a3}.rand16_lo|
00005300 6f 70 0a 09 4d 4f 56 53 09 61 33 2c 20 61 33 2c |op..MOVS.a3, a3,|
00005310 20 4c 53 52 20 23 31 0a 20 20 20 20 20 20 20 20 | LSR #1. |
00005320 4d 4f 56 53 09 61 34 2c 20 61 32 2c 20 52 52 58 |MOVS.a4, a2, RRX|
00005330 0a 20 20 20 20 20 20 20 20 41 44 43 09 61 33 2c |. ADC.a3,|
00005340 20 61 33 2c 20 61 33 0a 20 20 20 20 20 20 20 20 | a3, a3. |
00005350 45 4f 52 09 61 34 2c 20 61 34 2c 20 61 32 2c 20 |EOR.a4, a4, a2, |
00005360 4c 53 4c 20 23 31 32 0a 20 20 20 20 20 20 20 20 |LSL #12. |
00005370 45 4f 52 09 61 32 2c 20 61 34 2c 20 61 34 2c 20 |EOR.a2, a4, a4, |
00005380 4c 53 52 20 23 32 30 0a 09 4d 4f 56 09 61 31 2c |LSR #20..MOV.a1,|
00005390 20 61 32 2c 20 4c 53 4c 20 23 31 35 0a 09 4d 4f | a2, LSL #15..MO|
000053a0 56 09 61 31 2c 20 61 31 2c 20 41 53 52 20 23 31 |V.a1, a1, ASR #1|
000053b0 35 0a 09 43 4d 50 09 61 31 2c 20 23 26 66 66 66 |5..CMP.a1, #&fff|
000053c0 66 30 30 30 30 0a 09 42 45 51 09 72 61 6e 64 31 |f0000..BEQ.rand1|
000053d0 36 5f 6c 6f 6f 70 0a 09 53 54 4d 49 41 09 69 70 |6_loop..STMIA.ip|
000053e0 2c 20 7b 61 32 2c 20 61 33 7d 0a 20 20 20 20 20 |, {a2, a3}. |
000053f0 20 20 20 4d 4f 56 53 09 70 63 2c 20 6c 72 0a 0a | MOVS.pc, lr..|
00005400 0a 0a 3b 20 72 61 6e 64 75 31 36 0a 3b 20 61 20 |..; randu16.; a |
00005410 6c 65 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 |leaf APCS functi|
00005420 6f 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 |on.;.; C prototy|
00005430 70 65 3a 0a 3b 20 69 6e 74 20 72 61 6e 64 75 31 |pe:.; int randu1|
00005440 36 28 76 6f 69 64 29 0a 3b 0a 3b 20 72 65 74 75 |6(void).;.; retu|
00005450 72 6e 73 20 36 35 35 33 36 20 2a 20 28 20 70 73 |rns 65536 * ( ps|
00005460 65 75 64 6f 20 72 61 6e 64 6f 6e 20 76 61 72 69 |eudo randon vari|
00005470 61 62 6c 65 20 77 69 74 68 20 61 70 70 72 6f 78 |able with approx|
00005480 69 6d 61 74 65 20 64 69 73 74 72 69 62 75 74 69 |imate distributi|
00005490 6f 6e 20 55 28 30 2c 31 29 20 29 0a 3b 0a 0a 09 |on U(0,1) ).;...|
000054a0 45 58 50 4f 52 54 09 72 61 6e 64 75 31 36 0a 0a |EXPORT.randu16..|
000054b0 72 75 6e 73 74 61 20 20 44 43 42 20 20 20 20 20 |runsta DCB |
000054c0 22 72 61 6e 64 75 31 36 22 2c 20 30 0a 20 20 20 |"randu16", 0. |
000054d0 20 20 20 20 20 41 4c 49 47 4e 0a 72 75 6e 65 6e | ALIGN.runen|
000054e0 64 20 20 44 43 44 20 20 20 20 20 26 66 66 30 30 |d DCD &ff00|
000054f0 30 30 30 30 20 2b 20 72 75 6e 65 6e 64 20 2d 20 |0000 + runend - |
00005500 72 75 6e 73 74 61 0a 0a 72 61 6e 64 75 31 36 0a |runsta..randu16.|
00005510 0a 09 41 44 52 09 69 70 2c 20 72 61 6e 64 73 65 |..ADR.ip, randse|
00005520 65 64 31 0a 09 4c 44 4d 49 41 09 69 70 2c 20 7b |ed1..LDMIA.ip, {|
00005530 61 32 2c 20 61 33 7d 0a 72 61 6e 64 75 31 36 5f |a2, a3}.randu16_|
00005540 6c 6f 6f 70 0a 09 4d 4f 56 53 09 61 33 2c 20 61 |loop..MOVS.a3, a|
00005550 33 2c 20 4c 53 52 20 23 31 0a 20 20 20 20 20 20 |3, LSR #1. |
00005560 20 20 4d 4f 56 53 09 61 34 2c 20 61 32 2c 20 52 | MOVS.a4, a2, R|
00005570 52 58 0a 20 20 20 20 20 20 20 20 41 44 43 09 61 |RX. ADC.a|
00005580 33 2c 20 61 33 2c 20 61 33 0a 20 20 20 20 20 20 |3, a3, a3. |
00005590 20 20 45 4f 52 09 61 34 2c 20 61 34 2c 20 61 32 | EOR.a4, a4, a2|
000055a0 2c 20 4c 53 4c 20 23 31 32 0a 20 20 20 20 20 20 |, LSL #12. |
000055b0 20 20 45 4f 52 09 61 32 2c 20 61 34 2c 20 61 34 | EOR.a2, a4, a4|
000055c0 2c 20 4c 53 52 20 23 32 30 0a 09 4d 4f 56 53 09 |, LSR #20..MOVS.|
000055d0 61 31 2c 20 61 32 2c 20 4c 53 52 20 23 31 36 0a |a1, a2, LSR #16.|
000055e0 09 42 45 51 09 72 61 6e 64 75 31 36 5f 6c 6f 6f |.BEQ.randu16_loo|
000055f0 70 0a 09 53 54 4d 49 41 09 69 70 2c 20 7b 61 32 |p..STMIA.ip, {a2|
00005600 2c 20 61 33 7d 0a 20 20 20 20 20 20 20 20 4d 4f |, a3}. MO|
00005610 56 53 09 70 63 2c 20 6c 72 0a 0a 72 61 6e 64 73 |VS.pc, lr..rands|
00005620 65 65 64 31 09 44 43 44 09 2d 31 09 09 3b 62 69 |eed1.DCD.-1..;bi|
00005630 74 73 20 62 30 2d 62 33 31 20 6f 66 20 73 65 65 |ts b0-b31 of see|
00005640 64 0a 09 09 44 43 44 09 2d 31 09 09 3b 62 69 74 |d...DCD.-1..;bit|
00005650 20 20 62 33 32 20 6f 66 20 73 65 65 64 20 28 69 | b32 of seed (i|
00005660 6e 20 6c 73 62 20 6f 66 20 77 6f 72 64 29 0a 0a |n lsb of word)..|
00005670 3b 20 73 72 61 6e 64 31 36 0a 3b 20 61 20 6c 65 |; srand16.; a le|
00005680 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f 6e |af APCS function|
00005690 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 |.;.; C prototype|
000056a0 3a 0a 3b 20 76 6f 69 64 20 73 72 61 6e 64 31 36 |:.; void srand16|
000056b0 28 69 6e 74 20 73 65 65 64 29 0a 3b 0a 3b 20 73 |(int seed).;.; s|
000056c0 65 74 73 20 74 68 65 20 73 65 65 64 20 66 6f 72 |ets the seed for|
000056d0 20 72 61 6e 64 31 36 0a 3b 0a 0a 09 45 58 50 4f | rand16.;...EXPO|
000056e0 52 54 09 73 72 61 6e 64 31 36 0a 0a 73 72 6e 73 |RT.srand16..srns|
000056f0 74 61 20 20 44 43 42 20 20 20 20 20 22 73 72 61 |ta DCB "sra|
00005700 6e 64 31 36 22 2c 20 30 0a 20 20 20 20 20 20 20 |nd16", 0. |
00005710 20 41 4c 49 47 4e 0a 73 72 6e 65 6e 64 20 20 44 | ALIGN.srnend D|
00005720 43 44 20 20 20 20 20 26 66 66 30 30 30 30 30 30 |CD &ff000000|
00005730 20 2b 20 73 72 6e 65 6e 64 20 2d 20 73 72 6e 73 | + srnend - srns|
00005740 74 61 0a 0a 73 72 61 6e 64 31 36 0a 0a 09 41 44 |ta..srand16...AD|
00005750 52 09 61 32 2c 20 72 61 6e 64 73 65 65 64 31 0a |R.a2, randseed1.|
00005760 09 4d 4f 56 09 61 33 2c 20 23 31 0a 09 53 54 4d |.MOV.a3, #1..STM|
00005770 49 41 09 61 32 2c 20 7b 61 31 2c 20 61 33 7d 0a |IA.a2, {a1, a3}.|
00005780 20 20 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 | MOVS |
00005790 70 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 64 69 76 5f |pc, lr....; div_|
000057a0 66 72 61 63 31 36 0a 3b 20 61 20 6c 65 61 66 20 |frac16.; a leaf |
000057b0 41 50 43 53 20 66 75 6e 63 74 69 6f 6e 0a 3b 0a |APCS function.;.|
000057c0 3b 20 43 20 70 72 6f 74 6f 74 79 70 65 3a 0a 3b |; C prototype:.;|
000057d0 20 69 6e 74 20 64 69 76 5f 66 72 61 63 31 36 28 | int div_frac16(|
000057e0 69 6e 74 20 6e 75 6d 62 65 72 2c 20 69 6e 74 20 |int number, int |
000057f0 64 69 76 69 73 6f 72 29 0a 3b 0a 3b 20 72 65 74 |divisor).;.; ret|
00005800 75 72 6e 73 20 69 6e 74 65 67 65 72 20 70 61 72 |urns integer par|
00005810 74 20 6f 66 20 36 35 35 33 36 2a 6e 75 6d 62 65 |t of 65536*numbe|
00005820 72 2f 64 69 76 69 73 6f 72 0a 3b 20 61 73 73 75 |r/divisor.; assu|
00005830 6d 65 73 20 61 62 73 20 6e 75 6d 62 65 72 20 3c |mes abs number <|
00005840 20 36 35 35 33 36 20 2a 20 61 62 73 20 64 69 76 | 65536 * abs div|
00005850 69 73 6f 72 0a 3b 20 69 66 20 74 68 69 73 20 6e |isor.; if this n|
00005860 65 65 64 73 20 63 68 65 63 6b 69 6e 67 2c 20 6d |eeds checking, m|
00005870 75 73 74 20 62 65 20 64 6f 6e 65 20 62 79 20 63 |ust be done by c|
00005880 61 6c 6c 65 72 0a 3b 0a 0a 20 20 20 20 20 20 20 |aller.;.. |
00005890 20 45 58 50 4f 52 54 20 20 64 69 76 5f 66 72 61 | EXPORT div_fra|
000058a0 63 31 36 0a 0a 64 66 6e 73 74 61 20 20 44 43 42 |c16..dfnsta DCB|
000058b0 20 20 20 20 20 22 64 69 76 5f 66 72 61 63 31 36 | "div_frac16|
000058c0 22 2c 20 30 0a 20 20 20 20 20 20 20 20 41 4c 49 |", 0. ALI|
000058d0 47 4e 0a 64 66 6e 65 6e 64 20 20 44 43 44 20 20 |GN.dfnend DCD |
000058e0 20 20 20 26 66 66 30 30 30 30 30 30 20 2b 20 64 | &ff000000 + d|
000058f0 66 6e 65 6e 64 20 2d 20 64 66 6e 73 74 61 0a 0a |fnend - dfnsta..|
00005900 64 69 76 5f 66 72 61 63 31 36 0a 0a 20 20 20 20 |div_frac16.. |
00005910 20 20 20 20 64 69 76 31 36 20 20 20 61 31 2c 20 | div16 a1, |
00005920 61 32 2c 20 61 31 2c 20 61 33 2c 20 61 34 0a 20 |a2, a1, a3, a4. |
00005930 20 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 70 | MOVS p|
00005940 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 6d 75 6c 5f 66 |c, lr....; mul_f|
00005950 72 61 63 31 36 0a 3b 20 61 20 6c 65 61 66 20 41 |rac16.; a leaf A|
00005960 50 43 53 20 66 75 6e 63 74 69 6f 6e 0a 3b 0a 3b |PCS function.;.;|
00005970 20 43 20 70 72 6f 74 6f 74 79 70 65 3a 0a 3b 20 | C prototype:.; |
00005980 69 6e 74 20 6d 75 6c 5f 66 72 61 63 31 36 28 69 |int mul_frac16(i|
00005990 6e 74 20 78 2c 20 69 6e 74 20 61 29 0a 3b 0a 3b |nt x, int a).;.;|
000059a0 20 72 65 74 75 72 6e 73 20 33 32 2d 62 69 74 20 | returns 32-bit |
000059b0 73 69 67 6e 65 64 20 69 6e 74 65 67 65 72 20 78 |signed integer x|
000059c0 2a 61 2f 36 35 35 33 36 0a 3b 20 61 73 73 75 6d |*a/65536.; assum|
000059d0 65 73 20 72 65 73 75 6c 74 20 66 69 74 73 20 69 |es result fits i|
000059e0 6e 74 6f 20 33 32 2d 62 69 74 20 73 69 67 6e 65 |nto 32-bit signe|
000059f0 64 20 72 65 70 72 65 73 65 6e 74 61 74 69 6f 6e |d representation|
00005a00 0a 3b 20 6e 6f 74 65 2c 20 6e 6f 20 6f 74 68 65 |.; note, no othe|
00005a10 72 20 72 65 73 74 72 69 63 74 69 6f 6e 73 20 6f |r restrictions o|
00005a20 6e 20 61 20 2d 20 69 66 20 63 61 6e 20 67 75 61 |n a - if can gua|
00005a30 72 61 6e 74 65 65 20 61 62 73 20 61 20 3c 20 36 |rantee abs a < 6|
00005a40 35 35 33 36 2c 20 75 73 65 20 6d 75 6c 5f 66 72 |5536, use mul_fr|
00005a50 61 63 31 36 63 20 69 6e 73 74 65 61 64 20 61 73 |ac16c instead as|
00005a60 20 69 73 20 71 75 69 63 6b 65 72 0a 3b 0a 0a 20 | is quicker.;.. |
00005a70 20 20 20 20 20 20 20 45 58 50 4f 52 54 20 20 6d | EXPORT m|
00005a80 75 6c 5f 66 72 61 63 31 36 0a 0a 6d 66 6e 73 74 |ul_frac16..mfnst|
00005a90 61 20 20 44 43 42 20 20 20 20 20 22 6d 75 6c 5f |a DCB "mul_|
00005aa0 66 72 61 63 31 36 22 2c 20 30 0a 20 20 20 20 20 |frac16", 0. |
00005ab0 20 20 20 41 4c 49 47 4e 0a 6d 66 6e 65 6e 64 20 | ALIGN.mfnend |
00005ac0 20 44 43 44 20 20 20 20 20 26 66 66 30 30 30 30 | DCD &ff0000|
00005ad0 30 30 20 2b 20 6d 66 6e 65 6e 64 20 2d 20 6d 66 |00 + mfnend - mf|
00005ae0 6e 73 74 61 0a 0a 6d 75 6c 5f 66 72 61 63 31 36 |nsta..mul_frac16|
00005af0 0a 0a 20 20 20 20 20 20 20 20 6d 75 6c 31 36 20 |.. mul16 |
00005b00 20 20 61 31 2c 20 61 32 2c 20 61 31 2c 20 61 33 | a1, a2, a1, a3|
00005b10 2c 20 61 34 2c 20 69 70 0a 20 20 20 20 20 20 20 |, a4, ip. |
00005b20 20 4d 4f 56 53 20 20 20 20 70 63 2c 20 6c 72 0a | MOVS pc, lr.|
00005b30 0a 0a 0a 3b 20 6d 75 6c 5f 66 72 61 63 31 36 63 |...; mul_frac16c|
00005b40 0a 3b 20 61 20 6c 65 61 66 20 41 50 43 53 20 66 |.; a leaf APCS f|
00005b50 75 6e 63 74 69 6f 6e 0a 3b 0a 3b 20 43 20 70 72 |unction.;.; C pr|
00005b60 6f 74 6f 74 79 70 65 3a 0a 3b 20 69 6e 74 20 6d |ototype:.; int m|
00005b70 75 6c 5f 66 72 61 63 31 36 63 28 69 6e 74 20 78 |ul_frac16c(int x|
00005b80 2c 20 69 6e 74 20 61 29 0a 3b 0a 3b 20 72 65 74 |, int a).;.; ret|
00005b90 75 72 6e 73 20 33 32 2d 62 69 74 20 73 69 67 6e |urns 32-bit sign|
00005ba0 65 64 20 69 6e 74 65 67 65 72 20 78 2a 61 2f 36 |ed integer x*a/6|
00005bb0 35 35 33 36 0a 3b 20 61 73 73 75 6d 65 73 20 61 |5536.; assumes a|
00005bc0 62 73 20 61 20 3c 3d 36 35 35 33 36 0a 3b 20 69 |bs a <=65536.; i|
00005bd0 66 20 69 74 20 69 73 20 70 6f 73 73 69 62 6c 65 |f it is possible|
00005be0 20 74 68 61 74 20 61 62 73 20 61 20 3e 20 36 35 | that abs a > 65|
00005bf0 35 33 36 2c 20 63 61 6c 6c 65 72 20 6d 75 73 74 |536, caller must|
00005c00 20 63 68 65 63 6b 20 72 61 6e 67 65 20 26 20 65 | check range & e|
00005c10 69 74 68 65 72 20 6e 6f 74 20 63 61 6c 6c 20 66 |ither not call f|
00005c20 6e 20 6f 72 20 72 6f 75 6e 64 20 64 6f 77 6e 20 |n or round down |
00005c30 74 6f 20 36 35 35 33 36 0a 3b 0a 0a 20 20 20 20 |to 65536.;.. |
00005c40 20 20 20 20 45 58 50 4f 52 54 20 20 6d 75 6c 5f | EXPORT mul_|
00005c50 66 72 61 63 31 36 63 0a 0a 6d 66 63 6e 73 74 61 |frac16c..mfcnsta|
00005c60 20 44 43 42 20 20 20 20 20 22 6d 75 6c 5f 66 72 | DCB "mul_fr|
00005c70 61 63 31 36 63 22 2c 20 30 0a 20 20 20 20 20 20 |ac16c", 0. |
00005c80 20 20 41 4c 49 47 4e 0a 6d 66 63 6e 65 6e 64 20 | ALIGN.mfcnend |
00005c90 44 43 44 20 20 20 20 20 26 66 66 30 30 30 30 30 |DCD &ff00000|
00005ca0 30 20 2b 20 6d 66 63 6e 65 6e 64 20 2d 20 6d 66 |0 + mfcnend - mf|
00005cb0 63 6e 73 74 61 0a 0a 6d 75 6c 5f 66 72 61 63 31 |cnsta..mul_frac1|
00005cc0 36 63 0a 0a 20 20 20 20 20 20 20 20 6d 75 6c 31 |6c.. mul1|
00005cd0 36 63 20 20 61 31 2c 20 61 32 2c 20 61 31 2c 20 |6c a1, a2, a1, |
00005ce0 61 33 0a 20 20 20 20 20 20 20 20 4d 4f 56 53 20 |a3. MOVS |
00005cf0 20 20 20 70 63 2c 20 6c 72 0a 0a 0a 0a 3b 20 73 | pc, lr....; s|
00005d00 71 72 74 5f 66 72 61 63 31 36 0a 3b 20 61 20 6c |qrt_frac16.; a l|
00005d10 65 61 66 20 41 50 43 53 20 66 75 6e 63 74 69 6f |eaf APCS functio|
00005d20 6e 0a 3b 0a 3b 20 43 20 70 72 6f 74 6f 74 79 70 |n.;.; C prototyp|
00005d30 65 3a 0a 3b 20 69 6e 74 20 73 71 72 74 5f 66 72 |e:.; int sqrt_fr|
00005d40 61 63 31 36 28 75 6e 73 69 67 6e 65 64 20 69 6e |ac16(unsigned in|
00005d50 74 20 78 29 0a 3b 0a 3b 20 72 65 74 75 72 6e 73 |t x).;.; returns|
00005d60 20 33 32 2d 62 69 74 20 69 6e 74 65 67 65 72 20 | 32-bit integer |
00005d70 73 71 72 74 28 78 3c 3c 31 36 29 0a 3b 0a 0a 20 |sqrt(x<<16).;.. |
00005d80 20 20 20 20 20 20 20 45 58 50 4f 52 54 20 20 73 | EXPORT s|
00005d90 71 72 74 5f 66 72 61 63 31 36 0a 0a 73 71 66 6e |qrt_frac16..sqfn|
00005da0 73 74 61 20 44 43 42 20 20 20 20 20 22 73 71 72 |sta DCB "sqr|
00005db0 74 5f 66 72 61 63 31 36 22 2c 20 30 0a 20 20 20 |t_frac16", 0. |
00005dc0 20 20 20 20 20 41 4c 49 47 4e 0a 73 71 66 6e 65 | ALIGN.sqfne|
00005dd0 6e 64 20 44 43 44 20 20 20 20 20 26 66 66 30 30 |nd DCD &ff00|
00005de0 30 30 30 30 20 2b 20 73 71 66 6e 65 6e 64 20 2d |0000 + sqfnend -|
00005df0 20 73 71 66 6e 73 74 61 0a 0a 73 71 72 74 5f 66 | sqfnsta..sqrt_f|
00005e00 72 61 63 31 36 0a 0a 20 20 20 20 20 20 20 20 73 |rac16.. s|
00005e10 71 72 74 31 36 20 20 61 31 2c 20 61 31 2c 20 61 |qrt16 a1, a1, a|
00005e20 32 2c 20 61 33 2c 20 61 34 2c 20 69 70 0a 20 20 |2, a3, a4, ip. |
00005e30 20 20 20 20 20 20 4d 4f 56 53 20 20 20 20 70 63 | MOVS pc|
00005e40 2c 20 6c 72 0a 0a 0a 0a 20 20 20 20 20 20 20 20 |, lr.... |
00005e50 45 4e 44 0a |END.|
00005e54 
.