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Inside Macintosh: PowerPC Numerics / Part 3 - Appendixes: Appendix E - MathLib Reference

Operations and Functions

Note
Throughout the tables that follow, in the Exceptions column, I = invalid; X = inexact; O = overflow; U = underflow; D = divide-by-zero.
Table E-6 Arithmetic operations
Compute Syntax Valid input range Exceptions
Sum x + y $-$ to + I X O U -
Difference x - y $-$ to + I X O U -
Product x * y $-$ to + I X O U -
Quotient x / y $-$ to + I X O U D
Square root sqrt(x) 0 to + I X - - -
Remainder remainder(x,y)
remquo(x,y,quo)
fmod(x,y) $-$ to + I - - - -

Table E-7 Conversions to integer type
Compute Syntax Valid input range Exceptions
Round in current direction rinttol(x)[75] $-2$ ³¹to2³¹+-1 I X - - -
Add 1/2 to magnitude and chop roundtol(x)[75] $-2$ ³¹to2³¹+-1 I X - - -

Table E-8 Conversions to integer in floating-point type
Compute Syntax Valid input range Exceptions
Round in current direction rint(x) $-$ to + - X - - -
nearbyint(x) $-$ to + - - - - -
Round upward ceil(x) $-$ to + - - - - -
Round downward floor(x) $-$ to + - - - - -
Add 1/2 to magnitude and chop round(x) $-$ to + - X - - -
Round toward zero trunc(x) $-$ to + - - - - -

Table E-9 Conversions between binary and decimal formats
Compute Syntax Valid input range Exceptions
Convert decimal struct to binary dec2num(&d) decimal struct - - - - -
Convert binary to decimal struct num2dec(&f,x,&d) $-$ to + - - - - -

Table E-10 Conversions between decimal formats
Compute Syntax Valid input range Exceptions
Convert decimal struct to string dec2str(&f,&d,s) decimal struct - - - - -
Convert decimal string to struct str2dec(s,&ix,&d,&vp) Numeric string - - - - -

Table E-11 Comparison operations
Compute Syntax Valid input range Exceptions
Positive difference or 0 fdim(x,y) $-$ to + - X O U -
Maximum of 2 numbers fmax(x,y) $-$ to + - - - - -
Minimum of 2 numbers fmin(x,y) $-$ to + - - - - -
Relationship of x, y relation(x,y) $-$ to + - - - - -

Table E-12 Sign manipulation functions
Compute Syntax Valid input range Exceptions
Copy the sign copysign(x,y) $-$ to + - - - - -
|x| fabs(x) $-$ to + - - - - -

Table E-13 Exponential functions
Compute Syntax Valid input range Exceptions
$e$ ^x exp(x) $-$ to + - X O U -
$2$ ^x exp2(x) $-$ to + - X O U -
$e$ ^x+-1 expm1(x) $-$ to + - X O U -
$x×2$ ⁿ ldexp(x,n) $-$ to + - X O U -
scalb(x,n) - X O U -
$x$ ^y pow(x,y) $-$ to + I X O U D

Table E-14 Logarithmic functions
Compute Syntax Valid input range Exceptions
Fraction and exponent fields of floating-point number frexp(x,&n) $-$ to + - - - - -
ln x log(x) 0 to + I X - - D
$log$ ₁₀x log10(x) 0 to + I X - - D
ln (x + 1) log1p(x) > -1 I X - - D
$log$ ₂x log2(x) 0 to + I X - - D
Exponent field of floating-point number logb(x) $-$ to + - - - - D
Split real number into fractional part and integer part modf(x,&y) $-$ to + - - - - -

Table E-15 Trigonometric functions
Compute Syntax Valid input range Exceptions
cos x cos(x) Any finite number I X - - -
sin x sin(x) Any finite number I X - U -
tan x tan(x) Any finite number I X - U -
arccos x acos(x) -1 to +1 I X - - -
arcsin x asin(x) -1 to +1 I X - U -
arctan x atan(x) $-$ to + - X - U -
arctan y/x atan2(x,y) $-$ to + - X - U -

Table E-16 Hyperbolic functions
Compute Syntax Valid input range Exceptions
cosh x cosh(x) $-$ to + - X O - -
sinh x sinh(x) $-$ to + - X O U -
tanh x tanh(x) $-$ to + - X - - -
arccosh x acosh(x) 1 to + I X - - -
arcsinh x asinh(x) $-$ to + - X - U -
arctanh x atanh(x) -1 to +1 I X - U -

Table E-17 Financial functions
Compute Syntax Valid input range Exceptions
Compound interest compound(r,p) 0 to + I X - - D
Annuity annuity(r,p) 0 to + I X - - D

Table E-18 Error and gamma functions
Compute Syntax Valid input range Exceptions
error erf(x) $-$ to + - X - U -
1 - error erfc(x) $-$ to + - X - U -
(x) gamma(x) 0 to + I X O - -
ln(|(x)|) lgamma(x) 0 to + I X O - -

Table E-19 Miscellaneous functions
Compute Syntax Valid input range Exceptions
Create NaN nan(tagp) character string - - - - -
Next representable number after x in direction of y nextafterd(x,y) $-$ to + - X O U -
Hypotenuse hypot(x,y) $-$ to + - X O U -
Random number generator randomx(&x) $1to2$ ³¹+-2 - - - - -

[75] Return type of long int.

**Table E-6 Arithmetic operations**
Compute	Syntax	Valid input range	Exceptions
Sum	x + y	$-$ to +	I X O U -
Difference	x - y	$-$ to +	I X O U -
Product	x * y	$-$ to +	I X O U -
Quotient	x / y	$-$ to +	I X O U D
Square root	sqrt(x)	0 to +	I X - - -
Remainder	remainder(x,y) remquo(x,y,quo) fmod(x,y)	$-$ to +	I - - - -

**Table E-7 Conversions to integer type**
Compute	Syntax	Valid input range	Exceptions
Round in current direction	rinttol(x)[75]	$-2$ ³¹to2³¹+-1	I X - - -
Add 1/2 to magnitude and chop	roundtol(x)[75]	$-2$ ³¹to2³¹+-1	I X - - -

**Table E-8 Conversions to integer in floating-point type**
Compute	Syntax	Valid input range	Exceptions
Round in current direction	rint(x)	$-$ to +	- X - - -
	nearbyint(x)	$-$ to +	- - - - -
Round upward	ceil(x)	$-$ to +	- - - - -
Round downward	floor(x)	$-$ to +	- - - - -
Add 1/2 to magnitude and chop	round(x)	$-$ to +	- X - - -
Round toward zero	trunc(x)	$-$ to +	- - - - -

**Table E-9 Conversions between binary and decimal formats**
Compute	Syntax	Valid input range	Exceptions
Convert `decimal` struct to binary	dec2num(&d)	`decimal` struct	- - - - -
Convert binary to `decimal` struct	num2dec(&f,x,&d)	$-$ to +	- - - - -

**Table E-10 Conversions between decimal formats**
Compute	Syntax	Valid input range	Exceptions
Convert `decimal` struct to string	dec2str(&f,&d,s)	`decimal` struct	- - - - -
Convert decimal string to struct	str2dec(s,&ix,&d,&vp)	Numeric string	- - - - -

Table E-11 Comparison operations
Compute	Syntax	Valid input range	Exceptions
Positive difference or 0	fdim(x,y)	$-$ to +	- X O U -
Maximum of 2 numbers	fmax(x,y)	$-$ to +	- - - - -
Minimum of 2 numbers	fmin(x,y)	$-$ to +	- - - - -
Relationship of x, y	relation(x,y)	$-$ to +	- - - - -

Table E-12 Sign manipulation functions
Compute	Syntax	Valid input range	Exceptions
Copy the sign	copysign(x,y)	$-$ to +	- - - - -
\|x\|	fabs(x)	$-$ to +	- - - - -

Table E-13 Exponential functions
Compute	Syntax	Valid input range	Exceptions
$e$ ^x	exp(x)	$-$ to +	- X O U -
$2$ ^x	exp2(x)	$-$ to +	- X O U -
$e$ ^x+-1	expm1(x)	$-$ to +	- X O U -
$x×2$ ⁿ	ldexp(x,n)	$-$ to +	- X O U -
	scalb(x,n)		- X O U -
$x$ ^y	pow(x,y)	$-$ to +	I X O U D

Table E-14 Logarithmic functions
Compute	Syntax	Valid input range	Exceptions
Fraction and exponent fields of floating-point number	frexp(x,&n)	$-$ to +	- - - - -
ln x	log(x)	0 to +	I X - - D
$log$ ₁₀x	log10(x)	0 to +	I X - - D
ln (x + 1)	log1p(x)	> -1	I X - - D
$log$ ₂x	`log2(x)`	0 to +	I X - - D
Exponent field of floating-point number	`logb(x)`	$-$ to +	- - - - D
Split real number into fractional part and integer part	`modf(x,&y)`	$-$ to +	- - - - -

Table E-15 Trigonometric functions
Compute	Syntax	Valid input range	Exceptions
cos x	cos(x)	Any finite number	I X - - -
sin x	sin(x)	Any finite number	I X - U -
tan x	tan(x)	Any finite number	I X - U -
arccos x	acos(x)	-1 to +1	I X - - -
arcsin x	asin(x)	-1 to +1	I X - U -
arctan x	atan(x)	$-$ to +	- X - U -
arctan y/x	atan2(x,y)	$-$ to +	- X - U -

Table E-16 Hyperbolic functions
Compute	Syntax	Valid input range	Exceptions
cosh x	cosh(x)	$-$ to +	- X O - -
sinh x	sinh(x)	$-$ to +	- X O U -
tanh x	tanh(x)	$-$ to +	- X - - -
arccosh x	acosh(x)	1 to +	I X - - -
arcsinh x	asinh(x)	$-$ to +	- X - U -
arctanh x	atanh(x)	-1 to +1	I X - U -

Table E-17 Financial functions
Compute	Syntax	Valid input range	Exceptions
Compound interest	compound(r,p)	0 to +	I X - - D
Annuity	annuity(r,p)	0 to +	I X - - D

Table E-18 Error and gamma functions
Compute	Syntax	Valid input range	Exceptions
error	erf(x)	$-$ to +	- X - U -
1 - error	erfc(x)	$-$ to +	- X - U -
(x)	gamma(x)	0 to +	I X O - -
ln(\|(x)\|)	lgamma(x)	0 to +	I X O - -

Table E-19 Miscellaneous functions
Compute	Syntax	Valid input range	Exceptions
Create NaN	nan(tagp)	character string	- - - - -
Next representable number after x in direction of y	nextafterd(x,y)	$-$ to +	- X O U -
Hypotenuse	hypot(x,y)	$-$ to +	- X O U -
Random number generator	randomx(&x)	$1to2$ ³¹+-2	- - - - -

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