Differences

This shows you the differences between two versions of the page.

--- manual:chapter3:reals [2019/11/04 16:06]
jojo1973 More reformatting
+++ manual:chapter3:reals [2019/11/06 15:21] (current)
jojo1973 Added Special symbols
@@ Line 109: / Line 109: @@
 | ''[[manual:chapter6:binary:cmd_bmul|BMUL]]'' | Multiply | ''#1A4h #7h [[manual:chapter6:binary:cmd_bmul|BMUL]]'' |
 | ''[[manual:chapter6:binary:cmd_bdiv|BDIV]]'' | Divide | ''12 5 [[manual:chapter6:binary:cmd_bdiv|BDIV]]'' |
-| ''[[manual:chapter6:binary:cmd_bneg|BNEG]]'' | Negate (two's complement) | ''#11001b [[manual:chapter6:binary:cmd_bneg|BNEG]]'' |
+| ''[[manual:chapter6:binary:cmd_bneg|BNEG]]'' | Negate (Two's Complement) | ''#11001b [[manual:chapter6:binary:cmd_bneg|BNEG]]'' |
 | ''[[manual:chapter6:binary:cmd_band|BAND]]'' | Bitwise AND | ''#1101010b #1100010b [[manual:chapter6:binary:cmd_band|BAND]]'' |
 | ''[[manual:chapter6:binary:cmd_bor|BOR]]'' | Bitwise OR | ''#1101010b #1100010b [[manual:chapter6:binary:cmd_bor|BOR]]'' |
 | ''[[manual:chapter6:binary:cmd_bxor|BXOR]]'' | Bitwise XOR | ''#1101010b #1100010b [[manual:chapter6:binary:cmd_bxor|BXOR]]'' |
-| ''[[manual:chapter6:binary:cmd_bnot|BNOT]]'' | Bitwise NOT (one's complement) | ''#11001b [[manual:chapter6:binary:cmd_bNOT|BNOT]]'' |
+| ''[[manual:chapter6:binary:cmd_bnot|BNOT]]'' | Bitwise NOT (One's Complement) | ''#11001b [[manual:chapter6:binary:cmd_bnot|BNOT]]'' |
+| ''[[manual:chapter6:binary:cmd_blsl|BLSL]]'' | Bitwise Logical Shift Left | ''#11001b 4 [[manual:chapter6:binary:cmd_blsl|BLSL]]'' |
+| ''[[manual:chapter6:binary:cmd_blsr|BLSR]]'' | Bitwise Logical Shift Right | ''#11001b 2 [[manual:chapter6:binary:cmd_blsr|BLSR]]'' |
+| ''[[manual:chapter6:binary:cmd_basr|BASR]]'' | Bitwise Arithmetic Shift Right | ''#215o 2 [[manual:chapter6:binary:cmd_basr|BASR]]'' |
+| ''[[manual:chapter6:binary:cmd_brl|BRL]]'' | Bitwise Rotate Left | ''#3FFh 4 [[manual:chapter6:binary:cmd_brl|BRL]]'' |
+| ''[[manual:chapter6:binary:cmd_brr|BRR]]'' | Bitwise Rotate Right | ''#3FFh 1 [[manual:chapter6:binary:cmd_brr|BRR]]'' |
+----
+==== Testing ====
+Real numbers form an ordered field and its elements can be compared: **newRPL** provides a full set of arithmetic and logic operators plus some specialized ones.
+All these operators (except ''[[manual:chapter6:operators:cmd_ovr_cmp|CMP]]'') return ''1'' __if the test is true__ and ''0'' __if the test is false__. Actually any value different from ''0'' is considered __true__, but conventionally the operators return always ''1'' when the test succeeds.
+The classical **arithmetic** test operators are ''[[manual:chapter6:operators:cmd_ovr_eq|==]]'' (equality), ''[[manual:chapter6:operators:cmd_ovr_noteq|≠]]'' (not equality), ''[[manual:chapter6:operators:cmd_ovr_lt|<]]'' (less than), ''[[manual:chapter6:operators:cmd_ovr_gt|>]]'' (greater than), ''[[manual:chapter6:operators:cmd_ovr_lte|≤]]'' (less than or equal), ''[[manual:chapter6:operators:cmd_ovr_gte|≥]]'' (greater than or equal).
+<code>
+:                          #10h
+:                       #10000b
+……………………………………………………………………………………
+==
+</code> yields ''1''.
+<code>
+:                          #11o
+:                           10.
+……………………………………………………………………………………
+<
+</code> yields ''0''.
+**Logical** test operators are ''[[[manual:chapter6:operators:cmd_ovr_and|AND]]'', ''[[[manual:chapter6:operators:cmd_ovr_or|OR]]'', ''[[[manual:chapter6:operators:cmd_ovr_xor|XOR]]'' and ''[[[manual:chapter6:operators:cmd_ovr_not|NOT]]''.
+These operators must not be confused with the similar named bitwise operators ''[[manual:chapter6:binary:cmd_band|BAND]]'', ''[[manual:chapter6:binary:cmd_bor|BOR]]'', ''[[manual:chapter6:binary:cmd_bxor|BXOR]]'' and ''[[manual:chapter6:binary:cmd_bnot|BNOT]]'' described earlier: while the latter operate on a bit-by-bit basis, the logical operators consider the //truth value// of their arguments. Some examples will help to clarify:
+<code>
+:                        #1000b
+:                       #11000b
+……………………………………………………………………………………
+BAND
+</code>
+yields ''#1000b'', but
+<code>
+:                        #1000b
+:                       #11000b
+……………………………………………………………………………………
+AND
+</code>
+yields ''1''. Similarly
+<code>
+:                        #1000b
+:                           #0b
+……………………………………………………………………………………
+BOR
+</code>
+yields ''#1000b'', but
+<code>
+:                        #1000b
+:                           #0b
+……………………………………………………………………………………
+AND
+</code>
+yields ''0''.
+Finally, **specialized** test operators perform particular tests: they are ''[[manual:chapter6:operators:cmd_ovr_cmp|CMP]]'', ''[[manual:chapter6:operators:cmd_ovr_same|SAME]]'' and ''[[manual:chapter6:operators:cmd_ovr_istrue|ISTRUE]]''.
+''[[manual:chapter6:operators:cmd_ovr_cmp|CMP]]'' returns the ''[[manual:chapter6:arithmetic:cmd_ovr_sign|SIGN]]'' of the difference between its arguments:
+<code>
+:                            -2
+:                             8
+……………………………………………………………………………………
+CMP
+</code>
+yields ''-1''.
+For real numbers
+  * ''[[manual:chapter6:operators:cmd_ovr_same|SAME]]'' and ''[[manual:chapter6:operators:cmd_ovr_eq|==]]'' are equivalent;
+  * ''[[manual:chapter6:operators:cmd_ovr_istrue|ISTRUE]]'' and ''« 0 [[manual:chapter6:operators:cmd_ovr_noteq|≠]] »'' are equivalent.
+----
+==== Special symbols ====
+Operations on real numbers aren't always defined on the whole field of real numbers: a notable example is the division, which is not defined if the divisor is ''0''. **newRPL** handles these occurrances defining two special symbols: ''∞'' (//infinity//) and ''NaN'' (//Not-a-Number//).
+The ''∞'' symbol is returned when attempting, as anticipated, a division by ''0'' or when the result of a function (e.g. ''[[manual:chapter6:transcendentals:cmd_tan|TAN]]'') diverges. Albeit ''∞'' must not be considered a number, it obeys to a number of rules. The following examples assume flag [[manual:appendix:flags#flag-103|-103]] is cleared.
+  * ''∞'' ''[[manual:chapter6:operators:cmd_ovr_add|+]]'' or ''[[manual:chapter6:operators:cmd_ovr_sub|-]]'' a finite number yields ''∞'';
+  * ''∞'' ''[[manual:chapter6:operators:cmd_ovr_mul|*]]'' or ''[[manual:chapter6:operators:cmd_ovr_div|/]]'' a finite number yields ''∞'';
+  * the sign rule in multiplication or division applies, therefore ''-∞'' is a valid object;
+  * sum, multiplication or power of ''∞'' with itself yields ''∞''.
+The ''NaN'' symbol is **newRPL** way of informing the user that the attempted calculation returns an //undefined// result: typical examples include the calculation of the difference ''∞ - ∞'' or the sine of ''∞''. In general any function that includes ''NaN'' among its arguments will yield ''NaN''.