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; either the real and imaginary parts are both exact or inexact, or the number has an exact zero real part and an inexact imaginary part; a complex number with an inexact zero imaginary part is a real number

MzScheme extends the number syntax of R⁵RS in two ways:

• All input radixes (#b, #o, #d, and #x) allow ``decimal'' numbers that contain a period or exponent marker. For example, #b1.1 is equivalent to 1.5. In hexadecimal numbers, e always stands for a hexadecimal digit, not an exponent marker.
• 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). These names can also be used within complex constants, as in -inf.0+inf.0i.

The special inexact numbers +inf.0, -inf.0, and +nan.0 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?. The +nan.0 value is not an integer and is not = to itself, but +nan.0 is eqv? to itself. Similarly, (= 0.0 -0.0) is #t, but (eqv? 0.0 -0.0) is #f.

All multi-argument arithmetic procedures operate pairwise on arguments from left to right.

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:mismatch exception is raised.

The add1 and sub1 procedures work on any number:

• (add1 z) returns .
• (sub1 z) 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 k) returns a random exact integer in the range 0 to where k is an exact integer between 1 and , inclusive. The number is provided by the current pseudo-random number generator, which maintains an internal state for generating numbers.
• (random-seed k) seeds the current pseudo-random number generator with k, an exact 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 generator) sets the current generator to generator. See also section 9.4.1.13.
• (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) returns #t if v is a pseudo-random number generator, #f otherwise.