ti/real.h

#include <ti/real.h>

Surprisingly, the TI-84 Plus CE is actually sold to students as a calculator and not a gaming console. TI actually even implemented an entire highly-accurate floating-point package!

TI’s floating-point routines use binary-coded decimal, in which each hexadecimal nibble represents one decimal digit. Each real_t has 14 digits (7 bytes) in the significand, an 8-bit exponent which the OS limits to +/- 99, and a sign byte. They provide precision similar to a standard double on a PC, albeit with a smaller exponent range. Using real_t is much slower than float because of the vastly greater precision. (Remember that the C SDK implements double as float, which is allowed by the C standard.)

The SDK calls them real_t because float is already taken. The OS floating-point routines also support complex numbers quite well and transparently, but SDK support is not implemented.

A C++ wrapper is available as <ti/real> but no documentation has been written. Please see the examples in the standalone folder and consult the header itself.

API Documentation

API Documentation 

TI’s decimal floating-point library.

Authors

Matt “MateoConLechuga” Waltz

Jacob “jacobly” Young

Defines

os_OP1: OP1 Variable.

os_OP2: OP2 Variable.

os_OP3: OP3 Variable.

os_OP4: OP4 Variable.

os_OP5: OP5 Variable.

os_OP6: OP6 Variable.

os_OP7: OP7 Variable.

os_StatVars

Contains data used by the statistics package.

If you use this area, mark it invalid:

#include <ti/vars.h>
// . . .
os_DelRes();

Type: uint8_t[531]

Typedefs

typedef struct real_t real_t: Structure of real variable type.

typedef struct cplx_t cplx_t: Structure of complex variable type.

Functions

real_t os_RealCopy(const real_t *src)

Copies a real_t type.

Parameters: src – [in] Pointer to original real_t
Returns: Copied real_t

real_t os_RealAcosRad(const real_t *arg): Takes the arccosine of a real_t, giving the answer in radians.

Note

Ensure -1 <= *arg <= 1, or program will crash.

real_t os_RealAsinRad(const real_t *arg): Takes the arcsine of a real_t, giving the answer in radians.

Note

Ensure -1 <= *arg <= 1, or program will crash.

real_t os_RealAtanRad(const real_t *arg): Takes the arctangent of a real_t, giving the answers in radians.

real_t os_RealCosRad(const real_t *arg): Takes the cosine of a real_t given in radians.

real_t os_RealRadToDeg(const real_t *arg): Converts a real_t from radians to degrees.

real_t os_RealExp(const real_t *arg): Evaluates the exponential function (e^x, where e=2.717..) of a real_t.

real_t os_RealFloor(const real_t *arg): Takes the floor of a real_t.

real_t os_RealFrac(const real_t *arg): Extracts the fractional part of a real_t.

real_t os_RealRoundInt(const real_t *arg): Rounds a real_t to the nearest integer.

real_t os_RealLog(const real_t *arg): Takes the natural logarithm of a real_t.

Note

To take log base 10, divide this value by ln(10)

real_t os_RealNeg(const real_t *arg): Negates a real_t.

real_t os_RealDegToRad(const real_t *arg): Converts a real_t from degrees to radians.

real_t os_RealInv(const real_t *arg): Takes the reciprocal of a real_t.

real_t os_RealSinRad(const real_t *arg): Takes the sine of a real_t given in radians.

real_t os_RealSqrt(const real_t *arg): Takes the square root of a real_t.

real_t os_RealTanRad(const real_t *arg): Takes the tangent of a real_t given in radians.

real_t os_RealInt(const real_t *arg): Extracts the integer part of a real_t.

cplx_t os_CplxSquare(const cplx_t *arg): Calculates the square of a cplx_t.

real_t os_RealAdd(const real_t *arg1, const real_t *arg2): Adds two real_t values.

real_t os_RealDiv(const real_t *arg1, const real_t *arg2): Divides two real_t values.

real_t os_RealGcd(const real_t *arg1, const real_t *arg2): Calculates the Greatest Common Divisor of two real_t values.

real_t os_RealLcm(const real_t *arg1, const real_t *arg2): Calculates the Least Common Multiple of two real_t values.

real_t os_RealMax(const real_t *arg1, const real_t *arg2): Returns the larger of two real_t values.

real_t os_RealMin(const real_t *arg1, const real_t *arg2): Returns the smaller of two real_t values.

real_t os_RealMul(const real_t *arg1, const real_t *arg2): Multiplies two real_t values.

real_t os_RealNcr(const real_t *total, const real_t *num): Calculates the value of nCr (binomial coefficient) for two real_t values.

real_t os_RealNpr(const real_t *total, const real_t *num): Calculates the value of nPr (permutation number) for two real_t values.

real_t os_RealPow(const real_t *base, const real_t *exp): Raises one real_t value to the power of another.

real_t os_RealRandInt(const real_t *min, const real_t *max): Returns a random real_t between min and max.

real_t os_RealMod(const real_t *arg1, const real_t *arg2): Calculates the remainder (modulo) of two real_t values.

real_t os_RealSub(const real_t *arg1, const real_t *arg2): Subtracts two real_t values.

real_t os_RealRound(const real_t *arg, char digits)

Rounds a real_t.

Note

digits must be in the range 0 - 9

Parameters

arg – [in] Real variable.
digits – [in] Number of digits to round to.

int os_RealCompare(const real_t *arg1, const real_t *arg2)

Compares two real_t.

Note

os_RealCompare(arg1, arg2) op 0 computes arg1 op arg2 for any comparison operator op.

Parameters

arg1 – [in] Real variable 1.
arg2 – [in] Real variable 2.

Returns

-1, 0, or 1 if arg1 is less than, equal to, or greater than arg2.

int24_t os_RealToInt24(const real_t *arg)

Converts a real_t to an integer.

Note

Saturates on overflow

Parameters: arg – [in] Real variable.

real_t os_Int24ToReal(int24_t arg)

Converts an integer to a real_t.

Note

Saturates on overflow

Parameters: arg – Integer value.

float os_RealToFloat(const real_t *arg)

Converts a real_t to a float.

Note

Saturates on overflow

Parameters: arg – Real variable.

real_t os_FloatToReal(float arg)

Converts a float to a real_t.

Note

Saturates on overflow

Parameters: arg – [in] Float value.

int os_RealToStr(char *result, const real_t *arg, int8_t maxLength, uint8_t mode, int8_t digits)

This converts a ti-float to a ti-ascii string.

Parameters

result – [in] Zero terminated string copied to this address
arg – [in] Real to convert
maxLength – [in]
<=0: use default max length (14)

>0: max length of result, minimum of 6
mode – [in]
0: Use current mode for everything (digits ignored)

1: Normal mode

2: Sci mode

3: Eng mode
>4: Use current Normal/Sci/Eng mode (digits still used)
digits – [in]
-1: Float mode

0-9: Fix # mode

Returns

Length of result

real_t os_StrToReal(const char *string, char **end)

This converts a ti-ascii string to a ti-float.

String format regexp: / *[-\032+]?[0-9]*(.[0-9]*)?([eE\033][-\032+]?[0-9]*)?/

Parameters

string – [in] TI-ascii string to convert
end – [in] If non-null, pointer to end of parsed number is stored here

Returns

resulting TI-float; on exponent overflow this is +-9.9999999999999e99

struct real_t

#include <real.h>

Structure of real variable type.

Public Members

int8_t sign

int8_t exp

uint8_t mant[7]

struct cplx_t

#include <real.h>

Structure of complex variable type.

Public Members

real_t real

real_t imag

ti/real.h

API Documentation

API Documentation 