COMPARISONS 
x>y x>0 x≤y x≤0
Executes the next step if the condition is true.
Otherwise the next step is ignored. 

FLAGS 
F? n
Executes the next step if flag n is set. n = 0..9.
Otherwise the next step is ignored. 
To enter the command F? 7:
• In RUN mode enter the number 7.
• In PRGM mode select the F? n function.
• The function will appear as F? 7. 
SF n
Sets flag n 
To set flag 4:
• In RUN mode enter the number 4.
• In PRGM mode select the SF n function.
• The function will appear as SF 4.
Set flags appear as highlighted register numbers in Register View.
Note that F3 is automatically set when entering a number. 
CF n
Clears flag n 
To clear flag 1:
• In RUN mode enter the number 1.
• In PRGM mode select the CF n function.
• The function will appear as CF 1. 
CFLAGS
Clears all flags F0…F9.

f REG or setting the power switch to OFF also clears all flags.
Note that flags F2 and F3 are automatically cleared on testing (F? 2, F? 3).

SYSTEM 
BEEP
Notification sound 
Recommended to signal that the program requires the user's attention. 
DONE
Completion sound 
Recommended to signal that a result is available. 
OHNO
Error sound 
Recommended to signal an error or failure situation. 
SEC
Returns in x the number of seconds since midnight. 

ERROR 1
Halts program execution and displays Error 

ERROR 2
Same as Error 1 with error sound


REGISTERS 
STi
Store x indirectly in the register defined by the integer part of R.9.

Since R.9 is used as register address, looping through a range of registers is possible via the ISG and DSE commands.
The accepted range is 0..20 (where 20 = LASTx register.) 
RCi
Recall indirectly to x the value in the register defined by the integer part of R.9.

Since R.9 is used as register address, looping through a range of registers is possible via the ISG and DSE commands.
The accepted range is 0..20 (where 20 = LASTx register.) 
x≷i
Exchange x indirectly with the value in the register defined by the integer part of R.9. 
The accepted range is 0..20 (where 20 = LASTx register.) 
x≷nn
Exchange x with the value in register nn. 
nn = 0..20 (where 20 = LASTx register.) 
P≷S
Swap primary registers R0..R9 with secondary registers R.0..R.9.


REGS
Shows the Register View.

Note that you can run/stop or singlestep a program in Register View.
(Tap the ? to see how.) 
HYPERBOLICS 
SINH COSH TANH
Calculates the hyperbolic sine, cosine, or tangent.

sinh 3.2 = 12.25, cosh 3.2 = 12.29, tanh 3.2 = 1.00 
SINH^{1} COSH^{1} TANH^{1}
Calculates the inverse hyperbolic sine, cosine, or tangent.

sinh^{1} 51.777 = 4.64, cosh^{1} 51.777 = 4.64 (x≥1), tanh^{1} 0.777 = 1.04 (1<x<1) 
STATISTICS 
L.R.
Linear regression. Computes yintercept and slope for the linear function approximated by x and y values accumulated using ∑+.
The value of the yintercept is placed in the Xregister; the value of the slope is placed in the Yregister.

sinh 3.2 = 12.25, cosh 3.2 = 12.29, tanh 3.2 = 1.00 
ŷ
Linear estimate. Computes estimated value of y for a given value of x.

sinh^{1} 51.777 = 4.64, cosh^{1} 51.777 = 4.64 (x≥1), tanh^{1} 0.777 = 1.04 (1<x<1) 
x̂
Linear estimate. Computes estimated value of x for a given value of y.

Exchanges R0..R3 with RS0..RS3.

x̅,y̅
Computes means (averages) of x and y values accumulated using ∑+.

Exchanges R4..R9 with RS4..RS9.

x̅w,s
Computes weighted mean and standard deviation of x values with frequency y accumulated using ∑+. 

r
Correlation coefficient. Computes "goodness of fit" between the x and y values accumulated using ∑+ and
the linear function which they approximate.


sx,sy
Computes standard deviations of x and y values accumulated using ∑+.


Q
Computes area under the standard normal distribution curve to the left of x.


Q^{1}
Computes x, given the area under the standard normal distribution curve to the left of x.


SWAP∑
Swap statistical values with locations used on RPN32, and vice versa.

RPN32 
RPN25 
Statistics 
R.0 
R3 
n 
R.1 
R7 
∑x 
R.2 
R6 
∑x² 
R.3 
R4 
∑y 
R.4 
R8 
∑y² 
R.5 
R5 
∑xy 

P(y,x)
Permutations of y objects taken x at a time.

P(7,5) = 2520
P(y,x) = y!/(yx)!
For very large but close values of x and y, the function LN(x!) may prove useful. 
C(y,x)
Combinations of y objects taken x at a time (binomial coefficient.).

C(7,5) = 21
C(y,x) = y!/(x!(yx)!) 
MISCELLANEOUS 
∆%
Percent difference between x and base y. 

%∑
Percent that x is of ∑x (R7). 

%MARKUP
Percentage to add to cost price to make a gross profit of x%. 
To make a profit of 30%, what is the percentage of markup?
Answer: 42.86% 
∛x
Cube root of x.

x = any positive or negative real number 
TIME
24hr time (hours, minutes, secs, 1/1000 secs)

To measure program execution time in secs.ms:
TIME CHS STO.8 {execute program} TIME RCL.8 H.MS+ EEX 4 ×

H.MS+
Adds hours, minutes, seconds, or degrees, minutes, seconds in Yregister to those in displayed Xregister.


PSE LEN
Extended pause length.
Sets pause length used by the PAUSE instruction to any value 0 < x ≤ 86,400 seconds. The value x = 0 restores the standard pause length defined in Settings.
Seconds remaining are shown in the status display.
If x < 0, the last 10 seconds are counted down with sound. 
An extended pause in progress does not fade the PAUSE message.
The pause may be ended by pressing any key.
If ending the pause in a running program, the program stops.
Exceptions: number keys, decimal point, CHS, EEX. This allows inputting a number while pausing.
If the number input is followed by ENTER, a paused program will resume running. 
LOGy
Logarithm of x to base y.

log_{7} 5 = 0.8271 
LN(x!)
Logarithm of x!, where 0 < x < 4.4673257•10^{97}.

To divide 439 ! by 433 ! :
439 LN(x!) 433 LN(x!)  e^{x} = 6.1965•10^{15}

RAN#
Returns a random number 0 ≤ x < 1.


FILL RAN#
Fills registers R0..R.8 with random numbers r in the range x <
r < +x. If x = 0, then x = 1. 
x = 40:
Registers will be filled with random numbers from 39.9999.. to +39.9999.. 
GCD
(Highest Common Factor). Finds the largest positive integer which divides both positive integers x and y. 
GCD(51,119) = 17 
LCM
(Least Common Multiple).
Finds the smallest positive integer that both positivie integers x and y can divide. 
LCM(51,119) = 357 
QUAD/CUBE
Solves quadratic and cubic equations

Quadratic equation: ax² + bx + c = 0. Arguments: 0 in T, a in Z, b in Y, c in X
Returns: x,y = x₁,x₂ or u,v (if conjugate complex solution, u ± iv), z = discriminant
Cubic equation: ax³ + bx² + cx + d = 0. Arguments: a in T, b in Z, c in Y, d in X
Returns: x,y,z = x₁,x₂,x₃ or x₁,u,v (if type = 1)
t = type of roots (1: one real, two complex; 2: three real, at least two equal; 3: three real and distinct) 
LIN EQ2
Solves system of linear equations in two unknowns:
ax + by = c
dx + ey = f

Input values:
a b c = R4 R5 R6
d e f = R1 R2 R3
Example:
7.32x  9.08y = 3.14
12.39x + 7y = 0.05
Solutions:
x = 0.14, y = 0.24, Det = z = 163.74

LIN EQ3
Solves system of linear equations in three unknowns:
a_{11}x+a_{12}y+a_{13}z = b_{1}
a_{21}x+a_{22}y+a_{23}z = b_{2}
a_{31}x+a_{32}y+a_{33}z = b_{3}

Input values:
a_{11} a_{12} a_{13} = R7 R8 R9
a_{21} a_{22} a_{23} = R4 R5 R6
a_{31} a_{32} a_{33} = R1 R2 R3
b_{1} b_{2} b_{3} = R.1 R.2 R.3
Example:
3.14x + 10.02y  7z = 1
0.25x + 30.3y  9.1z = 2
3.5x + 27.4y + 8z = 3
Solutions:
x = 0.29, y = 0.11, z = 0.14, Det = t = 1052.86

UTILITIES 
DECR
Decrements x by 1 
Useful in tests like "IF condition = true THEN decrement x" since only one step is required 
INCR
Increments x by 1 
Useful in tests like "IF condition = true THEN increment x" since only one step is required 
MIN
Compares x and y and puts the smaller value into X, the larger into Y 

MAX
Compares x and y and puts the larger value into X, the smaller into Y 

ODD
Returns 1 if INT(x) is odd, 0 otherwise


DIV
Returns in X the integer value of y/x. The sign is the same as x. 

MOD
Returns in X the remainder of y/x, in
Y the remainder of y/x 

RATIO
Converts x to a close rational y/x, with numerator and denominator limited to y (1E6 if y = 0 or noninteger).

y = 1000, x = π: RATIO = 355/113
y = 1E5, x = e: RATIO = 49171/18089 
EXP/MANT
Returns in X the mantissa, in Y the exponent of x.


CHG MAG
Changes the magnitude of y by x: if y is positive, then x is added, otherwise subtracted from y. 
y = 5, x = 3: CHG MAG = 8 y = 5, x = 3: CHG MAG = 8 
CHOP
Returns 0 if the absolute value of x is less than 5E10. Useful for eliminating floatingpoint representation errors. 

STACK OPERATIONS 
R↑
Rolls stack up 

DELy
Removes y and lowers the part of the stack above X 

FETCHz
Brings z to X, keeping the other operands in the same order. 

xy≷zt
Swap x,y with z,t. 

x≷t
Swaps x and t (reverse contents of Y, Z, T) 

y≷z
Swaps y and z 

z≷t
Swaps z and t 

x≷t
Swap x and t 

x≷z
Swaps x and z (reverse contents of X, Y, Z) 

REV STK
Reverses stack order 

PUSH STK
Saves entire stack on a 4level "stack of stacks" 

POP STK
Copies the latest PUSHed stack to the regular stack and drops the "stack of stacks". 
The oldest entry is copied down to level 3 (like T to Z on the regular stack.)
If the "stack of stack" is empty, POP STK clears the regular stack.
CLEAR REG removes all pushed stacks. 
COMPLEX NUMBERS 
c_+
Complex add z+it to x+iy 

c_
Complex subtract x+iy from z+it 

c_×
Complex multiply x+iy by z+it 

c_÷
Complex divide z+it by x+iy 

c_ENTER
Copy x+iy to z+it 

c_CHS
Complex change sign of x+iy 

c_x≷y
Exchange x+iy with z+it 

c_R↓
Complex roll down 

c_STO n
Complex store x+iy in Rn (n = 0..9) 
To enter the command c_STO 2:
• In RUN mode enter the number 2.
• In PRGM mode select the c_STO n function.
• The function will appear as c_STO 2. 
c_RCL n
Complex recall x+iy from Rn (n = 0..9) 
To enter the command c_RCL 5:
• In RUN mode enter the number 5.
• In PRGM mode select the c_RCL n function.
• The function will appear as c_RCL 5. 
c_LASTx
Complex retrieve x+iy from LastX 

c_ABS
Complex absolute value of x+iy 
3+4i = 5.00 
c_RND
Complex round to display x+iy 

c_LN
Complex ln(x+iy) 
ln(i) = 1.57i 
c_e^{x}
Complex e^{x+iy} 
e^{1.57i} = 1.00i 
c_LOG
Complex log(x+iy) 
log(i) = 0.6822i = π/(2·ln(10)i 
c_10^{x}
Complex 10^{x+iy} 
10^{1.57i} = 0.89 0.46i 
c_LOGz
Complex log(x+iy) to complex base (z+it) 
log_{(1+i)}(1.49+4.13i) = 2.001.00i 
c_y^{x}
Complex (z+it)^{x+iy} (where z+it ≠ 0) 
(1+i)^{2  i} = 1.49+4.13i 
c_1/x^{}
Complex reciprocal of (x+iy) 
1/(2+3i) = 0.150.23i 
c_√x
Complex square root of (x+iy) 
√(7+6i) = ±(2.85+1.05i) 
c_x^{2}
Complex square of (x+iy) 
√(72i) = 45.0028.00i 
c_x!
Complex factorial of (x+iy) = Γ(x+1 + iy) 
(72i)! = 2368.80+3064.87i
Note: (72i)! = Γ(7+12i) = Γ(82i) 
c_SIN, c_COS, c_TAN
Complex sine, cosine, tangent of (x+iy). All angles in radians. 
sin(2+3i) = 9.154.17i cos(2+3i) = 4.199.11i tan(2+3i) = 0.004+1.003i 
c_SIN^{1}, c_COS^{1}, c_TAN^{1}
Complex arc sine, arc cosine, arc tangent of (x+iy) 
sin^{1}(5+8i) = 0.562.94i
cos^{1}(5+8i) = 1.012.94i tan^{1}(5+8i) = 1.51+0.09i 
c_SINH, c_COSH, c_TANH
Complex hyperbolic sine, cosine, tangent of (x+iy) 
sinh(32i) =4.179.15i
cosh(1+2i) = 0.64+1.07i
tanh(1+2i) = 1.170.24i 
c_SINH^{1}, c_COSH^{1}, c_TANH^{1}
Complex inverse hyperbolic sine, cosine, tangent of (x+iy) 
sinh^{1}(85i) = 2.940.56i
cosh^{1}(5+8i) = 2.94+1.01i
tanh^{1}(85i) = 0.091.51i 
CONVERSIONS 
→RAD →DEG
Converts decimal degrees to radians, and vice versa 

→in →mm
Converts millimeters to inches, and vice versa 

→ft.in →cm
Converts centimeters to feet and inches, and vice versa. Use 2 digits to indicate inches after the decimal point. 
164 cm = 5.0457 = 5'4.57"
5'5" = 5.05' = 165.10 cm 
→ft →m
Converts meters to feet, and vice versa 

→ac →m^{2}
Converts square meters to acres, and vice versa 

→°F →°C
Converts degrees Celsius to degrees Fahrenheit, and vice versa 
0°C = 32°F, 100°C = 212°F, 37°C = 98.6°F
460°F = 273.33°C, 40°F = 40°C 
→oz →g
Converts grams to ounces, and vice versa 

→lbm →kg
Converts kilograms to pounds (mass), and vice versa 

→gal →ltr
Converts liters to gallons, and vice versa 
20 ltr = 5.28 gal
61.55 gal = 232.99 ltr 
→cup →dl
Converts deciliters to cups (US), and vice versa 
2 dl = 0.85 cups
1.5 cups = 3.55 dl 
→tbs →g (H_{2}O)
Converts grams (water) to tablespoons, and vice versa 
15 g = 1.01 tbs
6 tbs = 88.72 g 
→bbl →liter
Converts liters to barrels (US, oil), and vice versa 
500 ltr = 3.14 bbl
1 bbl = 158.99 ltr 
gas US gas UK
Express miles per gallon as liters per 100 km, and vice versa. Select US or UK units. 
8.4 ltr per 100 km ⇄ 28.00 mpg (US), 28 ltr per 100 km ⇄ 8.4 mpg (US)
8.4 ltr per 100 km ⇄ 33.63 mpg (UK), 33.63 ltr per 100 km ⇄ 8.4 mpg (UK) 