92 lines
3.4 KiB
Zig
92 lines
3.4 KiB
Zig
//
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// Zig has support for IEEE-754 floating-point numbers in these
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// specific sizes: f16, f32, f64, f128. Floating point literals
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// may be writen in scientific notation:
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//
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// const a1: f32 = 1200.0; // 1,200
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// const a2: f32 = 1.2e+3; // 1,200
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// const b1: f32 = -500_000.0; // -500,000
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// const b2: f32 = -5.0e+5; // -500,000
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//
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// Hex floats can't use the letter 'e' because that's a hex
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// digit, so we use a 'p' instead:
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//
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// const hex: f16 = 0x2A.F7p+3; // Wow, that's arcane!
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//
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// Be sure to use a float type that is large enough to store your
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// value (both in terms of significant digits and scale).
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// Rounding may or may not be okay, but numbers which are too
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// large or too small become inf or -inf (positive or negative
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// infinity)!
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//
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// const pi: f16 = 3.1415926535; // rounds to 3.140625
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// const av: f16 = 6.02214076e+23; // Avogadro's inf(inity)!
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//
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// A float literal has a decimal point. When performing math
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// operations with numeric literals, ensure the types match. Zig
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// does not perform unsafe type coercions behind your back:
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//
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// var foo: f16 = 13.5 * 5; // ERROR!
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// var foo: f16 = 13.5 * 5.0; // No problem, both are floats
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//
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// Please fix the two float problems with this program and
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// display the result as a whole number.
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const print = @import("std").debug.print;
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pub fn main() void {
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// The approximate weight of the Space Shuttle upon liftoff
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// (including boosters and fuel tank) was 2,200 tons.
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//
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// We'll convert this weight from tons to kilograms at a
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// conversion of 907.18kg to the ton.
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var shuttle_weight: f32 = 907.18 * 2200.0;
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// By default, float values are formatted in scientific
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// notation. Try experimenting with '{d}' and '{d:.3}' to see
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// how decimal formatting works.
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print("Shuttle liftoff weight: {d:.0}kg\n", .{shuttle_weight});
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}
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// Floating further:
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//
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// As an example, Zig's f16 is a IEEE 754 "half-precision" binary
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// floating-point format ("binary16"), which is stored in memory
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// like so:
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//
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// 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0
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// | |-------| |-----------------|
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// | exponent significand
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// |
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// sign
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//
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// This example is the decimal number 3.140625, which happens to
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// be the closest representation of Pi we can make with an f16
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// due to the way IEEE-754 floating points store digits:
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//
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// * Sign bit 0 makes the number positive.
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// * Exponent bits 10000 are a scale of 16.
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// * Significand bits 1001001000 are the decimal value 584.
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//
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// IEEE-754 saves space by modifying these values: the value
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// 01111 is always subtracted from the exponent bits (in our
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// case, 10000 - 01111 = 1, so our exponent is 2^1) and our
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// significand digits become the decimal value _after_ an
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// implicit 1 (so 1.1001001000 or 1.5703125 in decimal)! This
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// gives us:
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//
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// 2^1 * 1.5703125 = 3.140625
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//
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// Feel free to forget these implementation details immediately.
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// The important thing to know is that floating point numbers are
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// great at storing big and small values (f64 lets you work with
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// numbers on the scale of the number of atoms in the universe),
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// but digits may be rounded, leading to results which are less
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// precise than integers.
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//
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// Fun fact: sometimes you'll see the significand labeled as a
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// "mantissa" but Donald E. Knuth says not to do that.
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//
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// C compatibility fact: There is also a Zig floating point type
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// specifically for working with C ABIs called c_longdouble.
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