zig/std/math/frexp.zig

172 lines
4.2 KiB
Zig

// Special Cases:
//
// - frexp(+-0) = +-0, 0
// - frexp(+-inf) = +-inf, 0
// - frexp(nan) = nan, undefined
const std = @import("../index.zig");
const math = std.math;
const assert = std.debug.assert;
fn frexp_result(comptime T: type) type {
return struct {
significand: T,
exponent: i32,
};
}
pub const frexp32_result = frexp_result(f32);
pub const frexp64_result = frexp_result(f64);
pub fn frexp(x: var) frexp_result(@typeOf(x)) {
const T = @typeOf(x);
return switch (T) {
f32 => frexp32(x),
f64 => frexp64(x),
else => @compileError("frexp not implemented for " ++ @typeName(T)),
};
}
fn frexp32(x: f32) frexp32_result {
var result: frexp32_result = undefined;
var y = @bitCast(u32, x);
const e = i32(y >> 23) & 0xFF;
if (e == 0) {
if (x != 0) {
// subnormal
result = frexp32(x * 0x1.0p64);
result.exponent -= 64;
} else {
// frexp(+-0) = (+-0, 0)
result.significand = x;
result.exponent = 0;
}
return result;
} else if (e == 0xFF) {
// frexp(nan) = (nan, undefined)
result.significand = x;
result.exponent = undefined;
// frexp(+-inf) = (+-inf, 0)
if (math.isInf(x)) {
result.exponent = 0;
}
return result;
}
result.exponent = e - 0x7E;
y &= 0x807FFFFF;
y |= 0x3F000000;
result.significand = @bitCast(f32, y);
return result;
}
fn frexp64(x: f64) frexp64_result {
var result: frexp64_result = undefined;
var y = @bitCast(u64, x);
const e = i32(y >> 52) & 0x7FF;
if (e == 0) {
if (x != 0) {
// subnormal
result = frexp64(x * 0x1.0p64);
result.exponent -= 64;
} else {
// frexp(+-0) = (+-0, 0)
result.significand = x;
result.exponent = 0;
}
return result;
} else if (e == 0x7FF) {
// frexp(nan) = (nan, undefined)
result.significand = x;
result.exponent = undefined;
// frexp(+-inf) = (+-inf, 0)
if (math.isInf(x)) {
result.exponent = 0;
}
return result;
}
result.exponent = e - 0x3FE;
y &= 0x800FFFFFFFFFFFFF;
y |= 0x3FE0000000000000;
result.significand = @bitCast(f64, y);
return result;
}
test "math.frexp" {
const a = frexp(f32(1.3));
const b = frexp32(1.3);
assert(a.significand == b.significand and a.exponent == b.exponent);
const c = frexp(f64(1.3));
const d = frexp64(1.3);
assert(c.significand == d.significand and c.exponent == d.exponent);
}
test "math.frexp32" {
const epsilon = 0.000001;
var r: frexp32_result = undefined;
r = frexp32(1.3);
assert(math.approxEq(f32, r.significand, 0.65, epsilon) and r.exponent == 1);
r = frexp32(78.0234);
assert(math.approxEq(f32, r.significand, 0.609558, epsilon) and r.exponent == 7);
}
test "math.frexp64" {
const epsilon = 0.000001;
var r: frexp64_result = undefined;
r = frexp64(1.3);
assert(math.approxEq(f64, r.significand, 0.65, epsilon) and r.exponent == 1);
r = frexp64(78.0234);
assert(math.approxEq(f64, r.significand, 0.609558, epsilon) and r.exponent == 7);
}
test "math.frexp32.special" {
var r: frexp32_result = undefined;
r = frexp32(0.0);
assert(r.significand == 0.0 and r.exponent == 0);
r = frexp32(-0.0);
assert(r.significand == -0.0 and r.exponent == 0);
r = frexp32(math.inf(f32));
assert(math.isPositiveInf(r.significand) and r.exponent == 0);
r = frexp32(-math.inf(f32));
assert(math.isNegativeInf(r.significand) and r.exponent == 0);
r = frexp32(math.nan(f32));
assert(math.isNan(r.significand));
}
test "math.frexp64.special" {
var r: frexp64_result = undefined;
r = frexp64(0.0);
assert(r.significand == 0.0 and r.exponent == 0);
r = frexp64(-0.0);
assert(r.significand == -0.0 and r.exponent == 0);
r = frexp64(math.inf(f64));
assert(math.isPositiveInf(r.significand) and r.exponent == 0);
r = frexp64(-math.inf(f64));
assert(math.isNegativeInf(r.significand) and r.exponent == 0);
r = frexp64(math.nan(f64));
assert(math.isNan(r.significand));
}