Numbers

A number in MzScheme is one of the following:

• a fixnum exact integer (30 bits plus a sign bit)
• a bignum exact integer (cannot be represented in a fixnum)
• a fraction exact rational (represented by two exact integers)
• a flonum inexact rational (double-precision floating-point number)
• a complex number; the real and imaginary parts are either both inexact numbers or both exact numbers

The following are inexact numerical constants: +inf.0 (infinity), -inf.0 (negative infinity), +nan.0 (not a number), and -nan.0 (same as +nan.0). They have no exact form. Dividing by an inexact zero returns +inf.0 or -inf.0, depending on the sign of the dividend. The infinities are integers, and they answer #t for both even? and odd?; +nan.0 is not an integer and is not = to itself, but +nan.0 is eqv? to itself. No numerical operator distinguishes the inexact numbers 0.0 and -0.0, so (= 0.0 (/ -1 +inf.0)) is #t.

All multi-argument arithmetic procedures operate pairwise on arguments from right to left. When an arithmetic operation is applied to a combination of exact and inexact values, the exact values are first converted to inexact values. All numbers are either inexact or exact in both real and imaginary parts (i.e., an inexact ``real'' number is not even exactly real because its imaginary part is 0.0).

The string->number procedure works on all number representations and exact integer radix values in the range 2 to 16 (inclusive). The number->string procedure accepts all number types and the radix values 2, 8, 10, and 16; however, if an inexact number is provided with a radix other than 10, the exn:application:math:radix exception is raised.

The add1 and sub1 procedures work on any number:

• (add1 n) returns .
• (sub1 n) returns .

The following procedures work on exact integers in their (semi-infinite) two's complement representation:

• (bitwise-ior n ) returns the bitwise ``inclusive or'' of the ns.
• (bitwise-and n ) returns the bitwise ``and'' of the ns.
• (bitwise-xor n ) returns the bitwise ``exclusive or'' of the ns.
• (bitwise-not n) returns the bitwise ``not'' of n.
• (arithmetic-shift n m) returns the bitwise ``shift'' of n. The integer n is shifted left by m bits; i.e., m new zeros are introduced as rightmost digits. If m is negative, n is shifted right by -m bits; i.e., the rightmost -m digits are dropped.

The random procedure generates pseudo-random integers:

• (random n) returns a random integer in the range 0 to where n is an integer between 1 and , inclusive. The number is provided by the current psuedo-random number generator, which maintains an internal state for generating numbers.
• (random-seed n) seeds the current pseudo-random number generator with n, an integer between 0 and , inclusive. Seeding a generator sets its internal state deterministically; seeding a generator with a particular number forces it to produce a sequence of pseudo-random numbers that is the same across runs and across platforms.
• (current-pseudo-random-generator) returns the current pseudo-random number generator, and (current-pseudo-random-generator prg) sets the current generator to prg. See also section 9.4.1.15.
• (make-pseudo-random-generator) returns a new pseudo-random number generator. The new generator is seeded with a number derived from (current-milliseconds).
• (pseudo-random-generator? v) return #t if v is a pseudo-random number generator, #f otherwise.