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><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="FUNCTIONS-MATH"
>9.3. Mathematical Functions and Operators</A
></H1
><P
> Mathematical operators are provided for many
<SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> types. For types without
common mathematical conventions for all possible permutations
(e.g., date/time types) we
describe the actual behavior in subsequent sections.
</P
><P
> <A
HREF="functions-math.html#FUNCTIONS-MATH-OP-TABLE"
>Table 9-2</A
> shows the available mathematical operators.
</P
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-MATH-OP-TABLE"
></A
><P
><B
>Table 9-2. Mathematical Operators</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><THEAD
><TR
><TH
>Operator</TH
><TH
>Description</TH
><TH
>Example</TH
><TH
>Result</TH
></TR
></THEAD
><TBODY
><TR
><TD
> <TT
CLASS="LITERAL"
>+</TT
> </TD
><TD
>addition</TD
><TD
><TT
CLASS="LITERAL"
>2 + 3</TT
></TD
><TD
><TT
CLASS="LITERAL"
>5</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>-</TT
> </TD
><TD
>subtraction</TD
><TD
><TT
CLASS="LITERAL"
>2 - 3</TT
></TD
><TD
><TT
CLASS="LITERAL"
>-1</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>*</TT
> </TD
><TD
>multiplication</TD
><TD
><TT
CLASS="LITERAL"
>2 * 3</TT
></TD
><TD
><TT
CLASS="LITERAL"
>6</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>/</TT
> </TD
><TD
>division (integer division truncates results)</TD
><TD
><TT
CLASS="LITERAL"
>4 / 2</TT
></TD
><TD
><TT
CLASS="LITERAL"
>2</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>%</TT
> </TD
><TD
>modulo (remainder)</TD
><TD
><TT
CLASS="LITERAL"
>5 % 4</TT
></TD
><TD
><TT
CLASS="LITERAL"
>1</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>^</TT
> </TD
><TD
>exponentiation</TD
><TD
><TT
CLASS="LITERAL"
>2.0 ^ 3.0</TT
></TD
><TD
><TT
CLASS="LITERAL"
>8</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>|/</TT
> </TD
><TD
>square root</TD
><TD
><TT
CLASS="LITERAL"
>|/ 25.0</TT
></TD
><TD
><TT
CLASS="LITERAL"
>5</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>||/</TT
> </TD
><TD
>cube root</TD
><TD
><TT
CLASS="LITERAL"
>||/ 27.0</TT
></TD
><TD
><TT
CLASS="LITERAL"
>3</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>!</TT
> </TD
><TD
>factorial</TD
><TD
><TT
CLASS="LITERAL"
>5 !</TT
></TD
><TD
><TT
CLASS="LITERAL"
>120</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>!!</TT
> </TD
><TD
>factorial (prefix operator)</TD
><TD
><TT
CLASS="LITERAL"
>!! 5</TT
></TD
><TD
><TT
CLASS="LITERAL"
>120</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>@</TT
> </TD
><TD
>absolute value</TD
><TD
><TT
CLASS="LITERAL"
>@ -5.0</TT
></TD
><TD
><TT
CLASS="LITERAL"
>5</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&</TT
> </TD
><TD
>bitwise AND</TD
><TD
><TT
CLASS="LITERAL"
>91 & 15</TT
></TD
><TD
><TT
CLASS="LITERAL"
>11</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>|</TT
> </TD
><TD
>bitwise OR</TD
><TD
><TT
CLASS="LITERAL"
>32 | 3</TT
></TD
><TD
><TT
CLASS="LITERAL"
>35</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>#</TT
> </TD
><TD
>bitwise XOR</TD
><TD
><TT
CLASS="LITERAL"
>17 # 5</TT
></TD
><TD
><TT
CLASS="LITERAL"
>20</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>~</TT
> </TD
><TD
>bitwise NOT</TD
><TD
><TT
CLASS="LITERAL"
>~1</TT
></TD
><TD
><TT
CLASS="LITERAL"
>-2</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
><<</TT
> </TD
><TD
>bitwise shift left</TD
><TD
><TT
CLASS="LITERAL"
>1 << 4</TT
></TD
><TD
><TT
CLASS="LITERAL"
>16</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>>></TT
> </TD
><TD
>bitwise shift right</TD
><TD
><TT
CLASS="LITERAL"
>8 >> 2</TT
></TD
><TD
><TT
CLASS="LITERAL"
>2</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><P
> The bitwise operators are also available for the bit
string types <TT
CLASS="TYPE"
>bit</TT
> and <TT
CLASS="TYPE"
>bit varying</TT
>, as
shown in <A
HREF="functions-math.html#FUNCTIONS-MATH-BIT-TABLE"
>Table 9-3</A
>.
Bit string operands of <TT
CLASS="LITERAL"
>&</TT
>, <TT
CLASS="LITERAL"
>|</TT
>,
and <TT
CLASS="LITERAL"
>#</TT
> must be of equal length. When bit
shifting, the original length of the string is preserved, as shown
in the table.
</P
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-MATH-BIT-TABLE"
></A
><P
><B
>Table 9-3. Bit String Bitwise Operators</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><THEAD
><TR
><TH
>Example</TH
><TH
>Result</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
>B'10001' & B'01101'</TT
></TD
><TD
><TT
CLASS="LITERAL"
>00001</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>B'10001' | B'01101'</TT
></TD
><TD
><TT
CLASS="LITERAL"
>11101</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>B'10001' # B'01101'</TT
></TD
><TD
><TT
CLASS="LITERAL"
>11110</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>~ B'10001'</TT
></TD
><TD
><TT
CLASS="LITERAL"
>01110</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>B'10001' << 3</TT
></TD
><TD
><TT
CLASS="LITERAL"
>01000</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
>B'10001' >> 2</TT
></TD
><TD
><TT
CLASS="LITERAL"
>00100</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><P
> <A
HREF="functions-math.html#FUNCTIONS-MATH-FUNC-TABLE"
>Table 9-4</A
> shows the available
mathematical functions. In the table, <TT
CLASS="LITERAL"
>dp</TT
>
indicates <TT
CLASS="TYPE"
>double precision</TT
>. Many of these functions
are provided in multiple forms with different argument types.
Except where noted, any given form of a function returns the same
data type as its argument.
The functions working with <TT
CLASS="TYPE"
>double precision</TT
> data are mostly
implemented on top of the host system's C library; accuracy and behavior in
boundary cases may therefore vary depending on the host system.
</P
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-MATH-FUNC-TABLE"
></A
><P
><B
>Table 9-4. Mathematical Functions</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><COL><THEAD
><TR
><TH
>Function</TH
><TH
>Return Type</TH
><TH
>Description</TH
><TH
>Example</TH
><TH
>Result</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>abs</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>(same as <VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TD
><TD
>absolute value</TD
><TD
><TT
CLASS="LITERAL"
>abs(-17.4)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>17.4</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>cbrt</CODE
>(<TT
CLASS="TYPE"
>dp</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
>cube root</TD
><TD
><TT
CLASS="LITERAL"
>cbrt(27.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>3</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>ceil</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>smallest integer not less than argument</TD
><TD
><TT
CLASS="LITERAL"
>ceil(-42.8)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>-42</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>degrees</CODE
>(<TT
CLASS="TYPE"
>dp</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
>radians to degrees</TD
><TD
><TT
CLASS="LITERAL"
>degrees(0.5)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>28.6478897565412</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>exp</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>exponential</TD
><TD
><TT
CLASS="LITERAL"
>exp(1.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>2.71828182845905</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>floor</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>largest integer not greater than argument</TD
><TD
><TT
CLASS="LITERAL"
>floor(-42.8)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>-43</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>ln</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>natural logarithm</TD
><TD
><TT
CLASS="LITERAL"
>ln(2.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>0.693147180559945</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>log</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>base 10 logarithm</TD
><TD
><TT
CLASS="LITERAL"
>log(100.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>2</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>log</CODE
>(<VAR
CLASS="PARAMETER"
>b</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>,
<VAR
CLASS="PARAMETER"
>x</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>numeric</TT
></TD
><TD
>logarithm to base <VAR
CLASS="PARAMETER"
>b</VAR
></TD
><TD
><TT
CLASS="LITERAL"
>log(2.0, 64.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>6.0000000000</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>mod</CODE
>(<VAR
CLASS="PARAMETER"
>y</VAR
>,
<VAR
CLASS="PARAMETER"
>x</VAR
>)</TT
></TD
><TD
>(same as argument types)</TD
><TD
>remainder of <VAR
CLASS="PARAMETER"
>y</VAR
>/<VAR
CLASS="PARAMETER"
>x</VAR
></TD
><TD
><TT
CLASS="LITERAL"
>mod(9,4)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>1</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>pi</CODE
>()</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
><SPAN
CLASS="QUOTE"
>"π"</SPAN
> constant</TD
><TD
><TT
CLASS="LITERAL"
>pi()</TT
></TD
><TD
><TT
CLASS="LITERAL"
>3.14159265358979</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>pow</CODE
>(<VAR
CLASS="PARAMETER"
>a</VAR
> <TT
CLASS="TYPE"
>dp</TT
>,
<VAR
CLASS="PARAMETER"
>b</VAR
> <TT
CLASS="TYPE"
>dp</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
><VAR
CLASS="PARAMETER"
>a</VAR
> raised to the power of <VAR
CLASS="PARAMETER"
>b</VAR
></TD
><TD
><TT
CLASS="LITERAL"
>pow(9.0, 3.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>729</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>pow</CODE
>(<VAR
CLASS="PARAMETER"
>a</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>,
<VAR
CLASS="PARAMETER"
>b</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>numeric</TT
></TD
><TD
><VAR
CLASS="PARAMETER"
>a</VAR
> raised to the power of <VAR
CLASS="PARAMETER"
>b</VAR
></TD
><TD
><TT
CLASS="LITERAL"
>pow(9.0, 3.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>729</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>radians</CODE
>(<TT
CLASS="TYPE"
>dp</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
>degrees to radians</TD
><TD
><TT
CLASS="LITERAL"
>radians(45.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>0.785398163397448</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>random</CODE
>()</TT
></TD
><TD
><TT
CLASS="TYPE"
>dp</TT
></TD
><TD
>random value between 0.0 and 1.0</TD
><TD
><TT
CLASS="LITERAL"
>random()</TT
></TD
><TD
> </TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>round</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>round to nearest integer</TD
><TD
><TT
CLASS="LITERAL"
>round(42.4)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>42</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>round</CODE
>(<VAR
CLASS="PARAMETER"
>v</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>, <VAR
CLASS="PARAMETER"
>s</VAR
> <TT
CLASS="TYPE"
>integer</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>numeric</TT
></TD
><TD
>round to <VAR
CLASS="PARAMETER"
>s</VAR
> decimal places</TD
><TD
><TT
CLASS="LITERAL"
>round(42.4382, 2)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>42.44</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>setseed</CODE
>(<TT
CLASS="TYPE"
>dp</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>int32</TT
></TD
><TD
>set seed for subsequent <TT
CLASS="LITERAL"
>random()</TT
> calls</TD
><TD
><TT
CLASS="LITERAL"
>setseed(0.54823)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>1177314959</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>sign</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>sign of the argument (-1, 0, +1)</TD
><TD
><TT
CLASS="LITERAL"
>sign(-8.4)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>-1</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>sqrt</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>square root</TD
><TD
><TT
CLASS="LITERAL"
>sqrt(2.0)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>1.4142135623731</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>trunc</CODE
>(<TT
CLASS="TYPE"
>dp</TT
> or <TT
CLASS="TYPE"
>numeric</TT
>)</TT
></TD
><TD
>(same as input)</TD
><TD
>truncate toward zero</TD
><TD
><TT
CLASS="LITERAL"
>trunc(42.8)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>42</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>trunc</CODE
>(<VAR
CLASS="PARAMETER"
>v</VAR
> <TT
CLASS="TYPE"
>numeric</TT
>, <VAR
CLASS="PARAMETER"
>s</VAR
> <TT
CLASS="TYPE"
>integer</TT
>)</TT
></TD
><TD
><TT
CLASS="TYPE"
>numeric</TT
></TD
><TD
>truncate to <VAR
CLASS="PARAMETER"
>s</VAR
> decimal places</TD
><TD
><TT
CLASS="LITERAL"
>trunc(42.4382, 2)</TT
></TD
><TD
><TT
CLASS="LITERAL"
>42.43</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><P
> Finally, <A
HREF="functions-math.html#FUNCTIONS-MATH-TRIG-TABLE"
>Table 9-5</A
> shows the
available trigonometric functions. All trigonometric functions
take arguments and return values of type <TT
CLASS="TYPE"
>double
precision</TT
>.
</P
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-MATH-TRIG-TABLE"
></A
><P
><B
>Table 9-5. Trigonometric Functions</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><THEAD
><TR
><TH
>Function</TH
><TH
>Description</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>acos</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>inverse cosine</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>asin</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>inverse sine</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>atan</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>inverse tangent</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>atan2</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>,
<VAR
CLASS="REPLACEABLE"
>y</VAR
>)</TT
></TD
><TD
>inverse tangent of
<TT
CLASS="LITERAL"
><VAR
CLASS="REPLACEABLE"
>x</VAR
>/<VAR
CLASS="REPLACEABLE"
>y</VAR
></TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>cos</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>cosine</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>cot</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>cotangent</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>sin</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>sine</TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>tan</CODE
>(<VAR
CLASS="REPLACEABLE"
>x</VAR
>)</TT
></TD
><TD
>tangent</TD
></TR
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