253 lines
8.0 KiB
Zig
253 lines
8.0 KiB
Zig
// Ported from go, which is licensed under a BSD-3 license.
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// https://golang.org/LICENSE
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//
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// https://golang.org/src/math/pow.go
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const builtin = @import("builtin");
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const std = @import("../std.zig");
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const math = std.math;
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const expect = std.testing.expect;
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/// Returns x raised to the power of y (x^y).
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///
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/// Special Cases:
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/// - pow(x, +-0) = 1 for any x
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/// - pow(1, y) = 1 for any y
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/// - pow(x, 1) = x for any x
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/// - pow(nan, y) = nan
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/// - pow(x, nan) = nan
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/// - pow(+-0, y) = +-inf for y an odd integer < 0
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/// - pow(+-0, -inf) = +inf
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/// - pow(+-0, +inf) = +0
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/// - pow(+-0, y) = +inf for finite y < 0 and not an odd integer
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/// - pow(+-0, y) = +-0 for y an odd integer > 0
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/// - pow(+-0, y) = +0 for finite y > 0 and not an odd integer
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/// - pow(-1, +-inf) = 1
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/// - pow(x, +inf) = +inf for |x| > 1
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/// - pow(x, -inf) = +0 for |x| > 1
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/// - pow(x, +inf) = +0 for |x| < 1
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/// - pow(x, -inf) = +inf for |x| < 1
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/// - pow(+inf, y) = +inf for y > 0
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/// - pow(+inf, y) = +0 for y < 0
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/// - pow(-inf, y) = pow(-0, -y)
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/// - pow(x, y) = nan for finite x < 0 and finite non-integer y
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pub fn pow(comptime T: type, x: T, y: T) T {
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if (@typeInfo(T) == builtin.TypeId.Int) {
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return math.powi(T, x, y) catch unreachable;
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}
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if (T != f32 and T != f64) {
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@compileError("pow not implemented for " ++ @typeName(T));
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}
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// pow(x, +-0) = 1 for all x
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// pow(1, y) = 1 for all y
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if (y == 0 or x == 1) {
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return 1;
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}
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// pow(nan, y) = nan for all y
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// pow(x, nan) = nan for all x
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if (math.isNan(x) or math.isNan(y)) {
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return math.nan(T);
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}
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// pow(x, 1) = x for all x
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if (y == 1) {
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return x;
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}
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if (x == 0) {
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if (y < 0) {
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// pow(+-0, y) = +- 0 for y an odd integer
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if (isOddInteger(y)) {
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return math.copysign(T, math.inf(T), x);
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}
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// pow(+-0, y) = +inf for y an even integer
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else {
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return math.inf(T);
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}
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} else {
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if (isOddInteger(y)) {
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return x;
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} else {
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return 0;
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}
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}
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}
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if (math.isInf(y)) {
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// pow(-1, inf) = 1 for all x
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if (x == -1) {
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return 1.0;
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}
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// pow(x, +inf) = +0 for |x| < 1
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// pow(x, -inf) = +0 for |x| > 1
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else if ((math.fabs(x) < 1) == math.isPositiveInf(y)) {
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return 0;
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}
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// pow(x, -inf) = +inf for |x| < 1
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// pow(x, +inf) = +inf for |x| > 1
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else {
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return math.inf(T);
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}
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}
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if (math.isInf(x)) {
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if (math.isNegativeInf(x)) {
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return pow(T, 1 / x, -y);
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}
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// pow(+inf, y) = +0 for y < 0
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else if (y < 0) {
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return 0;
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}
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// pow(+inf, y) = +0 for y > 0
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else if (y > 0) {
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return math.inf(T);
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}
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}
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// special case sqrt
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if (y == 0.5) {
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return math.sqrt(x);
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}
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if (y == -0.5) {
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return 1 / math.sqrt(x);
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}
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const r1 = math.modf(math.fabs(y));
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var yi = r1.ipart;
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var yf = r1.fpart;
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if (yf != 0 and x < 0) {
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return math.nan(T);
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}
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if (yi >= 1 << (T.bit_count - 1)) {
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return math.exp(y * math.ln(x));
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}
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// a = a1 * 2^ae
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var a1: T = 1.0;
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var ae: i32 = 0;
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// a *= x^yf
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if (yf != 0) {
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if (yf > 0.5) {
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yf -= 1;
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yi += 1;
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}
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a1 = math.exp(yf * math.ln(x));
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}
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// a *= x^yi
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const r2 = math.frexp(x);
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var xe = r2.exponent;
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var x1 = r2.significand;
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var i = @floatToInt(@IntType(true, T.bit_count), yi);
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while (i != 0) : (i >>= 1) {
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const overflow_shift = math.floatExponentBits(T) + 1;
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if (xe < -(1 << overflow_shift) or (1 << overflow_shift) < xe) {
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// catch xe before it overflows the left shift below
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// Since i != 0 it has at least one bit still set, so ae will accumulate xe
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// on at least one more iteration, ae += xe is a lower bound on ae
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// the lower bound on ae exceeds the size of a float exp
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// so the final call to Ldexp will produce under/overflow (0/Inf)
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ae += xe;
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break;
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}
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if (i & 1 == 1) {
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a1 *= x1;
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ae += xe;
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}
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x1 *= x1;
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xe <<= 1;
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if (x1 < 0.5) {
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x1 += x1;
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xe -= 1;
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}
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}
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// a *= a1 * 2^ae
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if (y < 0) {
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a1 = 1 / a1;
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ae = -ae;
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}
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return math.scalbn(a1, ae);
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}
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fn isOddInteger(x: f64) bool {
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const r = math.modf(x);
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return r.fpart == 0.0 and @floatToInt(i64, r.ipart) & 1 == 1;
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}
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test "math.pow" {
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const epsilon = 0.000001;
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expect(math.approxEq(f32, pow(f32, 0.0, 3.3), 0.0, epsilon));
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expect(math.approxEq(f32, pow(f32, 0.8923, 3.3), 0.686572, epsilon));
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expect(math.approxEq(f32, pow(f32, 0.2, 3.3), 0.004936, epsilon));
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expect(math.approxEq(f32, pow(f32, 1.5, 3.3), 3.811546, epsilon));
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expect(math.approxEq(f32, pow(f32, 37.45, 3.3), 155736.703125, epsilon));
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expect(math.approxEq(f32, pow(f32, 89.123, 3.3), 2722489.5, epsilon));
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expect(math.approxEq(f64, pow(f64, 0.0, 3.3), 0.0, epsilon));
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expect(math.approxEq(f64, pow(f64, 0.8923, 3.3), 0.686572, epsilon));
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expect(math.approxEq(f64, pow(f64, 0.2, 3.3), 0.004936, epsilon));
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expect(math.approxEq(f64, pow(f64, 1.5, 3.3), 3.811546, epsilon));
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expect(math.approxEq(f64, pow(f64, 37.45, 3.3), 155736.7160616, epsilon));
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expect(math.approxEq(f64, pow(f64, 89.123, 3.3), 2722490.231436, epsilon));
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}
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test "math.pow.special" {
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const epsilon = 0.000001;
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expect(pow(f32, 4, 0.0) == 1.0);
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expect(pow(f32, 7, -0.0) == 1.0);
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expect(pow(f32, 45, 1.0) == 45);
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expect(pow(f32, -45, 1.0) == -45);
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expect(math.isNan(pow(f32, math.nan(f32), 5.0)));
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expect(math.isPositiveInf(pow(f32, -math.inf(f32), 0.5)));
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expect(math.isPositiveInf(pow(f32, -0, -0.5)));
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expect(pow(f32, -0, 0.5) == 0);
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expect(math.isNan(pow(f32, 5.0, math.nan(f32))));
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expect(math.isPositiveInf(pow(f32, 0.0, -1.0)));
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//expect(math.isNegativeInf(pow(f32, -0.0, -3.0))); TODO is this required?
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expect(math.isPositiveInf(pow(f32, 0.0, -math.inf(f32))));
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expect(math.isPositiveInf(pow(f32, -0.0, -math.inf(f32))));
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expect(pow(f32, 0.0, math.inf(f32)) == 0.0);
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expect(pow(f32, -0.0, math.inf(f32)) == 0.0);
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expect(math.isPositiveInf(pow(f32, 0.0, -2.0)));
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expect(math.isPositiveInf(pow(f32, -0.0, -2.0)));
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expect(pow(f32, 0.0, 1.0) == 0.0);
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expect(pow(f32, -0.0, 1.0) == -0.0);
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expect(pow(f32, 0.0, 2.0) == 0.0);
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expect(pow(f32, -0.0, 2.0) == 0.0);
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expect(math.approxEq(f32, pow(f32, -1.0, math.inf(f32)), 1.0, epsilon));
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expect(math.approxEq(f32, pow(f32, -1.0, -math.inf(f32)), 1.0, epsilon));
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expect(math.isPositiveInf(pow(f32, 1.2, math.inf(f32))));
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expect(math.isPositiveInf(pow(f32, -1.2, math.inf(f32))));
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expect(pow(f32, 1.2, -math.inf(f32)) == 0.0);
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expect(pow(f32, -1.2, -math.inf(f32)) == 0.0);
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expect(pow(f32, 0.2, math.inf(f32)) == 0.0);
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expect(pow(f32, -0.2, math.inf(f32)) == 0.0);
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expect(math.isPositiveInf(pow(f32, 0.2, -math.inf(f32))));
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expect(math.isPositiveInf(pow(f32, -0.2, -math.inf(f32))));
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expect(math.isPositiveInf(pow(f32, math.inf(f32), 1.0)));
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expect(pow(f32, math.inf(f32), -1.0) == 0.0);
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//expect(pow(f32, -math.inf(f32), 5.0) == pow(f32, -0.0, -5.0)); TODO support negative 0?
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expect(pow(f32, -math.inf(f32), -5.2) == pow(f32, -0.0, 5.2));
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expect(math.isNan(pow(f32, -1.0, 1.2)));
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expect(math.isNan(pow(f32, -12.4, 78.5)));
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}
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test "math.pow.overflow" {
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expect(math.isPositiveInf(pow(f64, 2, 1 << 32)));
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expect(pow(f64, 2, -(1 << 32)) == 0);
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expect(math.isNegativeInf(pow(f64, -2, (1 << 32) + 1)));
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expect(pow(f64, 0.5, 1 << 45) == 0);
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expect(math.isPositiveInf(pow(f64, 0.5, -(1 << 45))));
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}
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