127 lines
3.7 KiB
Zig
127 lines
3.7 KiB
Zig
// Special Cases:
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//
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// - asinh(+-0) = +-0
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// - asinh(+-inf) = +-inf
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// - asinh(nan) = nan
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const math = @import("index.zig");
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const assert = @import("../debug.zig").assert;
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pub fn asinh(x: var) -> @typeOf(x) {
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const T = @typeOf(x);
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switch (T) {
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f32 => @inlineCall(asinh32, x),
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f64 => @inlineCall(asinh64, x),
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else => @compileError("asinh not implemented for " ++ @typeName(T)),
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}
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}
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// asinh(x) = sign(x) * log(|x| + sqrt(x * x + 1)) ~= x - x^3/6 + o(x^5)
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fn asinh32(x: f32) -> f32 {
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const u = @bitCast(u32, x);
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const i = u & 0x7FFFFFFF;
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const s = i >> 31;
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var rx = @bitCast(f32, i); // |x|
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// TODO: Shouldn't need this explicit check.
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if (math.isNegativeInf(x)) {
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return x;
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}
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// |x| >= 0x1p12 or inf or nan
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if (i >= 0x3F800000 + (12 << 23)) {
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rx = math.ln(rx) + 0.69314718055994530941723212145817656;
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}
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// |x| >= 2
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else if (i >= 0x3F800000 + (1 << 23)) {
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rx = math.ln(2 * x + 1 / (math.sqrt(x * x + 1) + x));
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}
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// |x| >= 0x1p-12, up to 1.6ulp error
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else if (i >= 0x3F800000 - (12 << 23)) {
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rx = math.log1p(x + x * x / (math.sqrt(x * x + 1) + 1));
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}
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// |x| < 0x1p-12, inexact if x != 0
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else {
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math.forceEval(x + 0x1.0p120);
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}
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if (s != 0) -rx else rx
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}
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fn asinh64(x: f64) -> f64 {
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const u = @bitCast(u64, x);
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const e = (u >> 52) & 0x7FF;
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const s = u >> 63;
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var rx = @bitCast(f64, u & (@maxValue(u64) >> 1)); // |x|
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if (math.isNegativeInf(x)) {
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return x;
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}
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// |x| >= 0x1p26 or inf or nan
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if (e >= 0x3FF + 26) {
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rx = math.ln(rx) + 0.693147180559945309417232121458176568;
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}
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// |x| >= 2
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else if (e >= 0x3FF + 1) {
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rx = math.ln(2 * x + 1 / (math.sqrt(x * x + 1) + x));
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}
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// |x| >= 0x1p-12, up to 1.6ulp error
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else if (e >= 0x3FF - 26) {
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rx = math.log1p(x + x * x / (math.sqrt(x * x + 1) + 1));
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}
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// |x| < 0x1p-12, inexact if x != 0
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else {
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math.forceEval(x + 0x1.0p120);
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}
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if (s != 0) -rx else rx
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}
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test "math.asinh" {
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assert(asinh(f32(0.0)) == asinh32(0.0));
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assert(asinh(f64(0.0)) == asinh64(0.0));
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}
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test "math.asinh32" {
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const epsilon = 0.000001;
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assert(math.approxEq(f32, asinh32(0.0), 0.0, epsilon));
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assert(math.approxEq(f32, asinh32(0.2), 0.198690, epsilon));
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assert(math.approxEq(f32, asinh32(0.8923), 0.803133, epsilon));
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assert(math.approxEq(f32, asinh32(1.5), 1.194763, epsilon));
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assert(math.approxEq(f32, asinh32(37.45), 4.316332, epsilon));
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assert(math.approxEq(f32, asinh32(89.123), 5.183196, epsilon));
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assert(math.approxEq(f32, asinh32(123123.234375), 12.414088, epsilon));
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}
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test "math.asinh64" {
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const epsilon = 0.000001;
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assert(math.approxEq(f64, asinh64(0.0), 0.0, epsilon));
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assert(math.approxEq(f64, asinh64(0.2), 0.198690, epsilon));
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assert(math.approxEq(f64, asinh64(0.8923), 0.803133, epsilon));
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assert(math.approxEq(f64, asinh64(1.5), 1.194763, epsilon));
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assert(math.approxEq(f64, asinh64(37.45), 4.316332, epsilon));
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assert(math.approxEq(f64, asinh64(89.123), 5.183196, epsilon));
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assert(math.approxEq(f64, asinh64(123123.234375), 12.414088, epsilon));
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}
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test "math.asinh32.special" {
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assert(asinh32(0.0) == 0.0);
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assert(asinh32(-0.0) == -0.0);
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assert(math.isPositiveInf(asinh32(math.inf(f32))));
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assert(math.isNegativeInf(asinh32(-math.inf(f32))));
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assert(math.isNan(asinh32(math.nan(f32))));
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}
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test "math.asinh64.special" {
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assert(asinh64(0.0) == 0.0);
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assert(asinh64(-0.0) == -0.0);
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assert(math.isPositiveInf(asinh64(math.inf(f64))));
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assert(math.isNegativeInf(asinh64(-math.inf(f64))));
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assert(math.isNan(asinh64(math.nan(f64))));
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}
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