Fractional approximation program for the HP 32sII

for the HP 32sII Frac - Fractional approximation

Input

REG x : input

Resources to be used

VAR i   : index
VAR A~T : work memory (simple continued fraction)
VAR X   : input value
VAR Y   : accumulator
VAR Z   : work memory
FLAG0   : terminate approximation
LBL B   : local label
LBL C   : subroutine
LBL D   : local label
LBL E   : local label
LBL F   : entry point

Output

LASTx : input value
REG t : input value
REG z : error
REG y : numerator
REG x : denominator

Program list (Rev.1.08 Nov. 5 2009)




Fractional approximation using
simple continued fraction
recompose and
calculate error



F01 LBL F   CK=A4E5 016.5
F02 CF 0
F03 ABS
F04 STO X
F05 STO Y
F06 102
F07 100
F08 ÷
F09 STO i
F10 CLχ
F11 χ<>y
B01 LBL B   CK=4498 022.5
B02 IP
B03 STO (i)
B04 χ≠0?
B05 XEQ C
B06 RCL Y
B07 RCL-(i)
B08 χ=0?
B09 SF 0
B10 FS? 0
B11 GTO E
B12 1/χ
B13 STO Y
B14 ISG i
B15 GTO B
E01 LBL E   CK=9F32 013.5
E02 CF 0
E03 R↓
E04 RCL X
E05 ABS
E06 CLχ
E07 LASTχ
E08 R↓
E09 RTN



C01 LBL C   CK=83CE 010.5
C02 RCL i
C03 IP
C04 &chi<>  i
C05 STO Z
C06 0
C07 1
D01 LBL D   CK=645E 053.0
D02 ENTER
D03 ENTER
D04 RCL (i)
D05 ×
D06 R↑
D07 +
D08 DSE i
D09 GTO D
D10 ABS
D11 χ<>y
D12 ENTER
D13 ENTER
D14 LASTχ
D15 ÷
D16 RCL× X
D17 1
D18 -
D19 χ<> Z
D20 STO i
D21 CLχ
D22 2.E~12
D23 RCL Z
D24 ABS
D25 χ<y?
D26 SF 0
D27 R↑
D28 R↑
D29 PSE
D30 RTN

Examples

Operation: π XEQ F

Fractional approximations

Order 0 1 2 3 4 5 6 7 8

y 3 22 333 355 103,993 104,348 208,341 312,689 833,719

x 1 7 106 113 33,102 33,215 66,317 99,532 265,381

Coefficients

A B C D E F G H I

3 7 15 1 292 1 1 1 2

Note: Simple continued fraction expression of π, to 12 digits accuracy.

Order	0	1	2	3	4	5	6	7	8
y	3	22	333	355	103,993	104,348	208,341	312,689	833,719
x	1	7	106	113	33,102	33,215	66,317	99,532	265,381