76 lines
2.2 KiB
Zig
76 lines
2.2 KiB
Zig
const std = @import("../../index.zig");
|
|
const debug = std.debug;
|
|
const math = std.math;
|
|
const cmath = math.complex;
|
|
const Complex = cmath.Complex;
|
|
|
|
pub fn ldexp_cexp(z: var, expt: i32) Complex(@typeOf(z.re)) {
|
|
const T = @typeOf(z.re);
|
|
|
|
return switch (T) {
|
|
f32 => ldexp_cexp32(z, expt),
|
|
f64 => ldexp_cexp64(z, expt),
|
|
else => unreachable,
|
|
};
|
|
}
|
|
|
|
fn frexp_exp32(x: f32, expt: &i32) f32 {
|
|
const k = 235; // reduction constant
|
|
const kln2 = 162.88958740; // k * ln2
|
|
|
|
const exp_x = math.exp(x - kln2);
|
|
const hx = @bitCast(u32, exp_x);
|
|
*expt = i32(hx >> 23) - (0x7f + 127) + k;
|
|
return @bitCast(f32, (hx & 0x7fffff) | ((0x7f + 127) << 23));
|
|
}
|
|
|
|
fn ldexp_cexp32(z: &const Complex(f32), expt: i32) Complex(f32) {
|
|
var ex_expt: i32 = undefined;
|
|
const exp_x = frexp_exp32(z.re, &ex_expt);
|
|
const exptf = expt + ex_expt;
|
|
|
|
const half_expt1 = @divTrunc(exptf, 2);
|
|
const scale1 = @bitCast(f32, (0x7f + half_expt1) << 23);
|
|
|
|
const half_expt2 = exptf - half_expt1;
|
|
const scale2 = @bitCast(f32, (0x7f + half_expt2) << 23);
|
|
|
|
return Complex(f32).new(
|
|
math.cos(z.im) * exp_x * scale1 * scale2,
|
|
math.sin(z.im) * exp_x * scale1 * scale2,
|
|
);
|
|
}
|
|
|
|
fn frexp_exp64(x: f64, expt: &i32) f64 {
|
|
const k = 1799; // reduction constant
|
|
const kln2 = 1246.97177782734161156; // k * ln2
|
|
|
|
const exp_x = math.exp(x - kln2);
|
|
|
|
const fx = @bitCast(u64, x);
|
|
const hx = u32(fx >> 32);
|
|
const lx = @truncate(u32, fx);
|
|
|
|
*expt = i32(hx >> 20) - (0x3ff + 1023) + k;
|
|
|
|
const high_word = (hx & 0xfffff) | ((0x3ff + 1023) << 20);
|
|
return @bitCast(f64, (u64(high_word) << 32) | lx);
|
|
}
|
|
|
|
fn ldexp_cexp64(z: &const Complex(f64), expt: i32) Complex(f64) {
|
|
var ex_expt: i32 = undefined;
|
|
const exp_x = frexp_exp64(z.re, &ex_expt);
|
|
const exptf = i64(expt + ex_expt);
|
|
|
|
const half_expt1 = @divTrunc(exptf, 2);
|
|
const scale1 = @bitCast(f64, (0x3ff + half_expt1) << 20);
|
|
|
|
const half_expt2 = exptf - half_expt1;
|
|
const scale2 = @bitCast(f64, (0x3ff + half_expt2) << 20);
|
|
|
|
return Complex(f64).new(
|
|
math.cos(z.im) * exp_x * scale1 * scale2,
|
|
math.sin(z.im) * exp_x * scale1 * scale2,
|
|
);
|
|
}
|