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These are the standard complex multiplication/division functions required by the C standard (Annex G). Don't get me started on the standard's handling of complex-infinity...
63 lines
2.3 KiB
Zig
63 lines
2.3 KiB
Zig
const std = @import("std");
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const isNan = std.math.isNan;
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const isInf = std.math.isInf;
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const scalbn = std.math.scalbn;
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const ilogb = std.math.ilogb;
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const max = std.math.max;
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const fabs = std.math.fabs;
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const maxInt = std.math.maxInt;
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const minInt = std.math.minInt;
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const isFinite = std.math.isFinite;
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const copysign = std.math.copysign;
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const Complex = @import("mulc3.zig").Complex;
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/// Implementation based on Annex G of C17 Standard (N2176)
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pub inline fn divc3(comptime T: type, a: T, b: T, c_in: T, d_in: T) Complex(T) {
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var c = c_in;
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var d = d_in;
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// logbw used to prevent under/over-flow
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const logbw = ilogb(max(fabs(c), fabs(d)));
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const logbw_finite = logbw != maxInt(i32) and logbw != minInt(i32);
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const ilogbw = if (logbw_finite) b: {
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c = scalbn(c, -logbw);
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d = scalbn(d, -logbw);
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break :b logbw;
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} else 0;
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const denom = c * c + d * d;
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const result = Complex(T){
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.real = scalbn((a * c + b * d) / denom, -ilogbw),
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.imag = scalbn((b * c - a * d) / denom, -ilogbw),
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};
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// Recover infinities and zeros that computed as NaN+iNaN;
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// the only cases are non-zero/zero, infinite/finite, and finite/infinite, ...
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if (isNan(result.real) and isNan(result.imag)) {
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const zero: T = 0.0;
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const one: T = 1.0;
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if ((denom == 0.0) and (!isNan(a) or !isNan(b))) {
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return .{
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.real = copysign(std.math.inf(T), c) * a,
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.imag = copysign(std.math.inf(T), c) * b,
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};
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} else if ((isInf(a) or isInf(b)) and isFinite(c) and isFinite(d)) {
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const boxed_a = copysign(if (isInf(a)) one else zero, a);
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const boxed_b = copysign(if (isInf(b)) one else zero, b);
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return .{
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.real = std.math.inf(T) * (boxed_a * c - boxed_b * d),
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.imag = std.math.inf(T) * (boxed_b * c - boxed_a * d),
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};
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} else if (logbw == maxInt(i32) and isFinite(a) and isFinite(b)) {
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const boxed_c = copysign(if (isInf(c)) one else zero, c);
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const boxed_d = copysign(if (isInf(d)) one else zero, d);
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return .{
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.real = 0.0 * (a * boxed_c + b * boxed_d),
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.imag = 0.0 * (b * boxed_c - a * boxed_d),
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};
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}
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}
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return result;
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}
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