authorgravatar for andrew@ziglang.orgAndrew Kelley <andrew@ziglang.org> 2018-04-24 23:47:37-04:00
committergravatar for andrew@ziglang.orgAndrew Kelley <andrew@ziglang.org> 2018-04-24 23:47:37-04:00
log7270f35c934ab5075c9d9128b5f5752c11d77056
tree7d2791171cceaf8f81a3353afed564d45d3e5308
parente5175d432ef01e078ef247ea0a781243219ddfb6
parent27cbb44993389ae042a03266743379c0f15a523e

Merge remote-tracking branch 'origin/master' into float-printing

30 files changed, 1540 insertions(+), 12 deletions(-)

CMakeLists.txt+22
...@@ -498,6 +498,28 @@ set(ZIG_STD_FILES...@@ -498,6 +498,28 @@ set(ZIG_STD_FILES
498 "math/tan.zig"498 "math/tan.zig"
499 "math/tanh.zig"499 "math/tanh.zig"
500 "math/trunc.zig"500 "math/trunc.zig"
501 "math/complex/abs.zig"
502 "math/complex/acosh.zig"
503 "math/complex/acos.zig"
504 "math/complex/arg.zig"
505 "math/complex/asinh.zig"
506 "math/complex/asin.zig"
507 "math/complex/atanh.zig"
508 "math/complex/atan.zig"
509 "math/complex/conj.zig"
510 "math/complex/cosh.zig"
511 "math/complex/cos.zig"
512 "math/complex/exp.zig"
513 "math/complex/index.zig"
514 "math/complex/ldexp.zig"
515 "math/complex/log.zig"
516 "math/complex/pow.zig"
517 "math/complex/proj.zig"
518 "math/complex/sinh.zig"
519 "math/complex/sin.zig"
520 "math/complex/sqrt.zig"
521 "math/complex/tanh.zig"
522 "math/complex/tan.zig"
501 "mem.zig"523 "mem.zig"
502 "net.zig"524 "net.zig"
503 "os/child_process.zig"525 "os/child_process.zig"
src/bigint.cpp+5
...@@ -86,6 +86,11 @@ static void to_twos_complement(BigInt *dest, const BigInt *op, size_t bit_count)...@@ -86,6 +86,11 @@ static void to_twos_complement(BigInt *dest, const BigInt *op, size_t bit_count)
86 size_t digits_to_copy = bit_count / 64;86 size_t digits_to_copy = bit_count / 64;
87 size_t leftover_bits = bit_count % 64;87 size_t leftover_bits = bit_count % 64;
88 dest->digit_count = digits_to_copy + ((leftover_bits == 0) ? 0 : 1);88 dest->digit_count = digits_to_copy + ((leftover_bits == 0) ? 0 : 1);
89 if (dest->digit_count == 1 && leftover_bits == 0) {
90 dest->data.digit = op_digits[0];
91 if (dest->data.digit == 0) dest->digit_count = 0;
92 return;
93 }
89 dest->data.digits = allocate_nonzero<uint64_t>(dest->digit_count);94 dest->data.digits = allocate_nonzero<uint64_t>(dest->digit_count);
90 for (size_t i = 0; i < digits_to_copy; i += 1) {95 for (size_t i = 0; i < digits_to_copy; i += 1) {
91 uint64_t digit = (i < op->digit_count) ? op_digits[i] : 0;96 uint64_t digit = (i < op->digit_count) ? op_digits[i] : 0;
src/ir.cpp+3
...@@ -3147,6 +3147,9 @@ static IrInstruction *ir_gen_block(IrBuilder *irb, Scope *parent_scope, AstNode...@@ -3147,6 +3147,9 @@ static IrInstruction *ir_gen_block(IrBuilder *irb, Scope *parent_scope, AstNode
3147 if (block_node->data.block.name == nullptr || incoming_blocks.length == 0) {3147 if (block_node->data.block.name == nullptr || incoming_blocks.length == 0) {
3148 return noreturn_return_value;3148 return noreturn_return_value;
3149 }3149 }
3150
3151 ir_set_cursor_at_end_and_append_block(irb, scope_block->end_block);
3152 return ir_build_phi(irb, parent_scope, block_node, incoming_blocks.length, incoming_blocks.items, incoming_values.items);
3150 } else {3153 } else {
3151 incoming_blocks.append(irb->current_basic_block);3154 incoming_blocks.append(irb->current_basic_block);
3152 incoming_values.append(ir_mark_gen(ir_build_const_void(irb, parent_scope, block_node)));3155 incoming_values.append(ir_mark_gen(ir_build_const_void(irb, parent_scope, block_node)));
std/crypto/throughput_test.zig+7-10
...@@ -1,17 +1,13 @@...@@ -1,17 +1,13 @@
1// Modify the HashFunction variable to the one wanted to test.1// Modify the HashFunction variable to the one wanted to test.
2//2//
3// NOTE: The throughput measurement may be slightly lower than other measurements since we run
4// through our block alignment functions as well. Be aware when comparing against other tests.
5//
6// ```3// ```
7// zig build-exe --release-fast --library c throughput_test.zig4// zig build-exe --release-fast throughput_test.zig
8// ./throughput_test5// ./throughput_test
9// ```6// ```
107
11const std = @import("std");8const std = @import("std");
12const c = @cImport({9const time = std.os.time;
13 @cInclude("time.h");10const Timer = time.Timer;
14});
15const HashFunction = @import("md5.zig").Md5;11const HashFunction = @import("md5.zig").Md5;
1612
17const MiB = 1024 * 1024;13const MiB = 1024 * 1024;
...@@ -28,13 +24,14 @@ pub fn main() !void {...@@ -28,13 +24,14 @@ pub fn main() !void {
28 var h = HashFunction.init();24 var h = HashFunction.init();
29 var offset: usize = 0;25 var offset: usize = 0;
3026
31 const start = c.clock();27 var timer = try Timer.start();
28 const start = timer.lap();
32 while (offset < BytesToHash) : (offset += block.len) {29 while (offset < BytesToHash) : (offset += block.len) {
33 h.update(block[0..]);30 h.update(block[0..]);
34 }31 }
35 const end = c.clock();32 const end = timer.read();
3633
37 const elapsed_s = f64(end - start) / f64(c.CLOCKS_PER_SEC);34 const elapsed_s = f64(end - start) / time.ns_per_s;
38 const throughput = u64(BytesToHash / elapsed_s);35 const throughput = u64(BytesToHash / elapsed_s);
3936
40 try stdout.print("{}: {} MiB/s\n", @typeName(HashFunction), throughput / (1 * MiB));37 try stdout.print("{}: {} MiB/s\n", @typeName(HashFunction), throughput / (1 * MiB));
std/math/complex/abs.zig created+18
...@@ -0,0 +1,18 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn abs(z: var) @typeOf(z.re) {
8 const T = @typeOf(z.re);
9 return math.hypot(T, z.re, z.im);
10}
11
12const epsilon = 0.0001;
13
14test "complex.cabs" {
15 const a = Complex(f32).new(5, 3);
16 const c = abs(a);
17 debug.assert(math.approxEq(f32, c, 5.83095, epsilon));
18}
std/math/complex/acos.zig created+21
...@@ -0,0 +1,21 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn acos(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const q = cmath.asin(z);
10 return Complex(T).new(T(math.pi) / 2 - q.re, -q.im);
11}
12
13const epsilon = 0.0001;
14
15test "complex.cacos" {
16 const a = Complex(f32).new(5, 3);
17 const c = acos(a);
18
19 debug.assert(math.approxEq(f32, c.re, 0.546975, epsilon));
20 debug.assert(math.approxEq(f32, c.im, -2.452914, epsilon));
21}
std/math/complex/acosh.zig created+21
...@@ -0,0 +1,21 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn acosh(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const q = cmath.acos(z);
10 return Complex(T).new(-q.im, q.re);
11}
12
13const epsilon = 0.0001;
14
15test "complex.cacosh" {
16 const a = Complex(f32).new(5, 3);
17 const c = acosh(a);
18
19 debug.assert(math.approxEq(f32, c.re, 2.452914, epsilon));
20 debug.assert(math.approxEq(f32, c.im, 0.546975, epsilon));
21}
std/math/complex/arg.zig created+18
...@@ -0,0 +1,18 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn arg(z: var) @typeOf(z.re) {
8 const T = @typeOf(z.re);
9 return math.atan2(T, z.im, z.re);
10}
11
12const epsilon = 0.0001;
13
14test "complex.carg" {
15 const a = Complex(f32).new(5, 3);
16 const c = arg(a);
17 debug.assert(math.approxEq(f32, c, 0.540420, epsilon));
18}
std/math/complex/asin.zig created+27
...@@ -0,0 +1,27 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn asin(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const x = z.re;
10 const y = z.im;
11
12 const p = Complex(T).new(1.0 - (x - y) * (x + y), -2.0 * x * y);
13 const q = Complex(T).new(-y, x);
14 const r = cmath.log(q.add(cmath.sqrt(p)));
15
16 return Complex(T).new(r.im, -r.re);
17}
18
19const epsilon = 0.0001;
20
21test "complex.casin" {
22 const a = Complex(f32).new(5, 3);
23 const c = asin(a);
24
25 debug.assert(math.approxEq(f32, c.re, 1.023822, epsilon));
26 debug.assert(math.approxEq(f32, c.im, 2.452914, epsilon));
27}
std/math/complex/asinh.zig created+22
...@@ -0,0 +1,22 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn asinh(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const q = Complex(T).new(-z.im, z.re);
10 const r = cmath.asin(q);
11 return Complex(T).new(r.im, -r.re);
12}
13
14const epsilon = 0.0001;
15
16test "complex.casinh" {
17 const a = Complex(f32).new(5, 3);
18 const c = asinh(a);
19
20 debug.assert(math.approxEq(f32, c.re, 2.459831, epsilon));
21 debug.assert(math.approxEq(f32, c.im, 0.533999, epsilon));
22}
std/math/complex/atan.zig created+130
...@@ -0,0 +1,130 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn atan(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 return switch (T) {
10 f32 => atan32(z),
11 f64 => atan64(z),
12 else => @compileError("atan not implemented for " ++ @typeName(z)),
13 };
14}
15
16fn redupif32(x: f32) f32 {
17 const DP1 = 3.140625;
18 const DP2 = 9.67502593994140625e-4;
19 const DP3 = 1.509957990978376432e-7;
20
21 var t = x / math.pi;
22 if (t >= 0.0) {
23 t += 0.5;
24 } else {
25 t -= 0.5;
26 }
27
28 const u = f32(i32(t));
29 return ((x - u * DP1) - u * DP2) - t * DP3;
30}
31
32fn atan32(z: &const Complex(f32)) Complex(f32) {
33 const maxnum = 1.0e38;
34
35 const x = z.re;
36 const y = z.im;
37
38 if ((x == 0.0) and (y > 1.0)) {
39 // overflow
40 return Complex(f32).new(maxnum, maxnum);
41 }
42
43 const x2 = x * x;
44 var a = 1.0 - x2 - (y * y);
45 if (a == 0.0) {
46 // overflow
47 return Complex(f32).new(maxnum, maxnum);
48 }
49
50 var t = 0.5 * math.atan2(f32, 2.0 * x, a);
51 var w = redupif32(t);
52
53 t = y - 1.0;
54 a = x2 + t * t;
55 if (a == 0.0) {
56 // overflow
57 return Complex(f32).new(maxnum, maxnum);
58 }
59
60 t = y + 1.0;
61 a = (x2 + (t * t)) / a;
62 return Complex(f32).new(w, 0.25 * math.ln(a));
63}
64
65fn redupif64(x: f64) f64 {
66 const DP1 = 3.14159265160560607910;
67 const DP2 = 1.98418714791870343106e-9;
68 const DP3 = 1.14423774522196636802e-17;
69
70 var t = x / math.pi;
71 if (t >= 0.0) {
72 t += 0.5;
73 } else {
74 t -= 0.5;
75 }
76
77 const u = f64(i64(t));
78 return ((x - u * DP1) - u * DP2) - t * DP3;
79}
80
81fn atan64(z: &const Complex(f64)) Complex(f64) {
82 const maxnum = 1.0e308;
83
84 const x = z.re;
85 const y = z.im;
86
87 if ((x == 0.0) and (y > 1.0)) {
88 // overflow
89 return Complex(f64).new(maxnum, maxnum);
90 }
91
92 const x2 = x * x;
93 var a = 1.0 - x2 - (y * y);
94 if (a == 0.0) {
95 // overflow
96 return Complex(f64).new(maxnum, maxnum);
97 }
98
99 var t = 0.5 * math.atan2(f64, 2.0 * x, a);
100 var w = redupif64(t);
101
102 t = y - 1.0;
103 a = x2 + t * t;
104 if (a == 0.0) {
105 // overflow
106 return Complex(f64).new(maxnum, maxnum);
107 }
108
109 t = y + 1.0;
110 a = (x2 + (t * t)) / a;
111 return Complex(f64).new(w, 0.25 * math.ln(a));
112}
113
114const epsilon = 0.0001;
115
116test "complex.catan32" {
117 const a = Complex(f32).new(5, 3);
118 const c = atan(a);
119
120 debug.assert(math.approxEq(f32, c.re, 1.423679, epsilon));
121 debug.assert(math.approxEq(f32, c.im, 0.086569, epsilon));
122}
123
124test "complex.catan64" {
125 const a = Complex(f64).new(5, 3);
126 const c = atan(a);
127
128 debug.assert(math.approxEq(f64, c.re, 1.423679, epsilon));
129 debug.assert(math.approxEq(f64, c.im, 0.086569, epsilon));
130}
std/math/complex/atanh.zig created+22
...@@ -0,0 +1,22 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn atanh(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const q = Complex(T).new(-z.im, z.re);
10 const r = cmath.atan(q);
11 return Complex(T).new(r.im, -r.re);
12}
13
14const epsilon = 0.0001;
15
16test "complex.catanh" {
17 const a = Complex(f32).new(5, 3);
18 const c = atanh(a);
19
20 debug.assert(math.approxEq(f32, c.re, 0.146947, epsilon));
21 debug.assert(math.approxEq(f32, c.im, 1.480870, epsilon));
22}
std/math/complex/conj.zig created+17
...@@ -0,0 +1,17 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn conj(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 return Complex(T).new(z.re, -z.im);
10}
11
12test "complex.conj" {
13 const a = Complex(f32).new(5, 3);
14 const c = a.conjugate();
15
16 debug.assert(c.re == 5 and c.im == -3);
17}
std/math/complex/cos.zig created+21
...@@ -0,0 +1,21 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn cos(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const p = Complex(T).new(-z.im, z.re);
10 return cmath.cosh(p);
11}
12
13const epsilon = 0.0001;
14
15test "complex.ccos" {
16 const a = Complex(f32).new(5, 3);
17 const c = cos(a);
18
19 debug.assert(math.approxEq(f32, c.re, 2.855815, epsilon));
20 debug.assert(math.approxEq(f32, c.im, 9.606383, epsilon));
21}
std/math/complex/cosh.zig created+165
...@@ -0,0 +1,165 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7const ldexp_cexp = @import("ldexp.zig").ldexp_cexp;
8
9pub fn cosh(z: var) Complex(@typeOf(z.re)) {
10 const T = @typeOf(z.re);
11 return switch (T) {
12 f32 => cosh32(z),
13 f64 => cosh64(z),
14 else => @compileError("cosh not implemented for " ++ @typeName(z)),
15 };
16}
17
18fn cosh32(z: &const Complex(f32)) Complex(f32) {
19 const x = z.re;
20 const y = z.im;
21
22 const hx = @bitCast(u32, x);
23 const ix = hx & 0x7fffffff;
24
25 const hy = @bitCast(u32, y);
26 const iy = hy & 0x7fffffff;
27
28 if (ix < 0x7f800000 and iy < 0x7f800000) {
29 if (iy == 0) {
30 return Complex(f32).new(math.cosh(x), y);
31 }
32 // small x: normal case
33 if (ix < 0x41100000) {
34 return Complex(f32).new(math.cosh(x) * math.cos(y), math.sinh(x) * math.sin(y));
35 }
36
37 // |x|>= 9, so cosh(x) ~= exp(|x|)
38 if (ix < 0x42b17218) {
39 // x < 88.7: exp(|x|) won't overflow
40 const h = math.exp(math.fabs(x)) * 0.5;
41 return Complex(f32).new(math.copysign(f32, h, x) * math.cos(y), h * math.sin(y));
42 }
43 // x < 192.7: scale to avoid overflow
44 else if (ix < 0x4340b1e7) {
45 const v = Complex(f32).new(math.fabs(x), y);
46 const r = ldexp_cexp(v, -1);
47 return Complex(f32).new(x, y * math.copysign(f32, 1, x));
48 }
49 // x >= 192.7: result always overflows
50 else {
51 const h = 0x1p127 * x;
52 return Complex(f32).new(h * h * math.cos(y), h * math.sin(y));
53 }
54 }
55
56 if (ix == 0 and iy >= 0x7f800000) {
57 return Complex(f32).new(y - y, math.copysign(f32, 0, x * (y - y)));
58 }
59
60 if (iy == 0 and ix >= 0x7f800000) {
61 if (hx & 0x7fffff == 0) {
62 return Complex(f32).new(x * x, math.copysign(f32, 0, x) * y);
63 }
64 return Complex(f32).new(x, math.copysign(f32, 0, (x + x) * y));
65 }
66
67 if (ix < 0x7f800000 and iy >= 0x7f800000) {
68 return Complex(f32).new(y - y, x * (y - y));
69 }
70
71 if (ix >= 0x7f800000 and (hx & 0x7fffff) == 0) {
72 if (iy >= 0x7f800000) {
73 return Complex(f32).new(x * x, x * (y - y));
74 }
75 return Complex(f32).new((x * x) * math.cos(y), x * math.sin(y));
76 }
77
78 return Complex(f32).new((x * x) * (y - y), (x + x) * (y - y));
79}
80
81fn cosh64(z: &const Complex(f64)) Complex(f64) {
82 const x = z.re;
83 const y = z.im;
84
85 const fx = @bitCast(u64, x);
86 const hx = u32(fx >> 32);
87 const lx = @truncate(u32, fx);
88 const ix = hx & 0x7fffffff;
89
90 const fy = @bitCast(u64, y);
91 const hy = u32(fy >> 32);
92 const ly = @truncate(u32, fy);
93 const iy = hy & 0x7fffffff;
94
95 // nearly non-exceptional case where x, y are finite
96 if (ix < 0x7ff00000 and iy < 0x7ff00000) {
97 if (iy | ly == 0) {
98 return Complex(f64).new(math.cosh(x), x * y);
99 }
100 // small x: normal case
101 if (ix < 0x40360000) {
102 return Complex(f64).new(math.cosh(x) * math.cos(y), math.sinh(x) * math.sin(y));
103 }
104
105 // |x|>= 22, so cosh(x) ~= exp(|x|)
106 if (ix < 0x40862e42) {
107 // x < 710: exp(|x|) won't overflow
108 const h = math.exp(math.fabs(x)) * 0.5;
109 return Complex(f64).new(h * math.cos(y), math.copysign(f64, h, x) * math.sin(y));
110 }
111 // x < 1455: scale to avoid overflow
112 else if (ix < 0x4096bbaa) {
113 const v = Complex(f64).new(math.fabs(x), y);
114 const r = ldexp_cexp(v, -1);
115 return Complex(f64).new(x, y * math.copysign(f64, 1, x));
116 }
117 // x >= 1455: result always overflows
118 else {
119 const h = 0x1p1023;
120 return Complex(f64).new(h * h * math.cos(y), h * math.sin(y));
121 }
122 }
123
124 if (ix | lx == 0 and iy >= 0x7ff00000) {
125 return Complex(f64).new(y - y, math.copysign(f64, 0, x * (y - y)));
126 }
127
128 if (iy | ly == 0 and ix >= 0x7ff00000) {
129 if ((hx & 0xfffff) | lx == 0) {
130 return Complex(f64).new(x * x, math.copysign(f64, 0, x) * y);
131 }
132 return Complex(f64).new(x * x, math.copysign(f64, 0, (x + x) * y));
133 }
134
135 if (ix < 0x7ff00000 and iy >= 0x7ff00000) {
136 return Complex(f64).new(y - y, x * (y - y));
137 }
138
139 if (ix >= 0x7ff00000 and (hx & 0xfffff) | lx == 0) {
140 if (iy >= 0x7ff00000) {
141 return Complex(f64).new(x * x, x * (y - y));
142 }
143 return Complex(f64).new(x * x * math.cos(y), x * math.sin(y));
144 }
145
146 return Complex(f64).new((x * x) * (y - y), (x + x) * (y - y));
147}
148
149const epsilon = 0.0001;
150
151test "complex.ccosh32" {
152 const a = Complex(f32).new(5, 3);
153 const c = cosh(a);
154
155 debug.assert(math.approxEq(f32, c.re, -73.467300, epsilon));
156 debug.assert(math.approxEq(f32, c.im, 10.471557, epsilon));
157}
158
159test "complex.ccosh64" {
160 const a = Complex(f64).new(5, 3);
161 const c = cosh(a);
162
163 debug.assert(math.approxEq(f64, c.re, -73.467300, epsilon));
164 debug.assert(math.approxEq(f64, c.im, 10.471557, epsilon));
165}
std/math/complex/exp.zig created+140
...@@ -0,0 +1,140 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7const ldexp_cexp = @import("ldexp.zig").ldexp_cexp;
8
9pub fn exp(z: var) Complex(@typeOf(z.re)) {
10 const T = @typeOf(z.re);
11
12 return switch (T) {
13 f32 => exp32(z),
14 f64 => exp64(z),
15 else => @compileError("exp not implemented for " ++ @typeName(z)),
16 };
17}
18
19fn exp32(z: &const Complex(f32)) Complex(f32) {
20 @setFloatMode(this, @import("builtin").FloatMode.Strict);
21
22 const exp_overflow = 0x42b17218; // max_exp * ln2 ~= 88.72283955
23 const cexp_overflow = 0x43400074; // (max_exp - min_denom_exp) * ln2
24
25 const x = z.re;
26 const y = z.im;
27
28 const hy = @bitCast(u32, y) & 0x7fffffff;
29 // cexp(x + i0) = exp(x) + i0
30 if (hy == 0) {
31 return Complex(f32).new(math.exp(x), y);
32 }
33
34 const hx = @bitCast(u32, x);
35 // cexp(0 + iy) = cos(y) + isin(y)
36 if ((hx & 0x7fffffff) == 0) {
37 return Complex(f32).new(math.cos(y), math.sin(y));
38 }
39
40 if (hy >= 0x7f800000) {
41 // cexp(finite|nan +- i inf|nan) = nan + i nan
42 if ((hx & 0x7fffffff) != 0x7f800000) {
43 return Complex(f32).new(y - y, y - y);
44 }
45 // cexp(-inf +- i inf|nan) = 0 + i0
46 else if (hx & 0x80000000 != 0) {
47 return Complex(f32).new(0, 0);
48 }
49 // cexp(+inf +- i inf|nan) = inf + i nan
50 else {
51 return Complex(f32).new(x, y - y);
52 }
53 }
54
55 // 88.7 <= x <= 192 so must scale
56 if (hx >= exp_overflow and hx <= cexp_overflow) {
57 return ldexp_cexp(z, 0);
58 }
59 // - x < exp_overflow => exp(x) won't overflow (common)
60 // - x > cexp_overflow, so exp(x) * s overflows for s > 0
61 // - x = +-inf
62 // - x = nan
63 else {
64 const exp_x = math.exp(x);
65 return Complex(f32).new(exp_x * math.cos(y), exp_x * math.sin(y));
66 }
67}
68
69fn exp64(z: &const Complex(f64)) Complex(f64) {
70 const exp_overflow = 0x40862e42; // high bits of max_exp * ln2 ~= 710
71 const cexp_overflow = 0x4096b8e4; // (max_exp - min_denorm_exp) * ln2
72
73 const x = z.re;
74 const y = z.im;
75
76 const fy = @bitCast(u64, y);
77 const hy = u32(fy >> 32) & 0x7fffffff;
78 const ly = @truncate(u32, fy);
79
80 // cexp(x + i0) = exp(x) + i0
81 if (hy | ly == 0) {
82 return Complex(f64).new(math.exp(x), y);
83 }
84
85 const fx = @bitCast(u64, x);
86 const hx = u32(fx >> 32);
87 const lx = @truncate(u32, fx);
88
89 // cexp(0 + iy) = cos(y) + isin(y)
90 if ((hx & 0x7fffffff) | lx == 0) {
91 return Complex(f64).new(math.cos(y), math.sin(y));
92 }
93
94 if (hy >= 0x7ff00000) {
95 // cexp(finite|nan +- i inf|nan) = nan + i nan
96 if (lx != 0 or (hx & 0x7fffffff) != 0x7ff00000) {
97 return Complex(f64).new(y - y, y - y);
98 }
99 // cexp(-inf +- i inf|nan) = 0 + i0
100 else if (hx & 0x80000000 != 0) {
101 return Complex(f64).new(0, 0);
102 }
103 // cexp(+inf +- i inf|nan) = inf + i nan
104 else {
105 return Complex(f64).new(x, y - y);
106 }
107 }
108
109 // 709.7 <= x <= 1454.3 so must scale
110 if (hx >= exp_overflow and hx <= cexp_overflow) {
111 const r = ldexp_cexp(z, 0);
112 return *r;
113 }
114 // - x < exp_overflow => exp(x) won't overflow (common)
115 // - x > cexp_overflow, so exp(x) * s overflows for s > 0
116 // - x = +-inf
117 // - x = nan
118 else {
119 const exp_x = math.exp(x);
120 return Complex(f64).new(exp_x * math.cos(y), exp_x * math.sin(y));
121 }
122}
123
124const epsilon = 0.0001;
125
126test "complex.cexp32" {
127 const a = Complex(f32).new(5, 3);
128 const c = exp(a);
129
130 debug.assert(math.approxEq(f32, c.re, -146.927917, epsilon));
131 debug.assert(math.approxEq(f32, c.im, 20.944065, epsilon));
132}
133
134test "complex.cexp64" {
135 const a = Complex(f32).new(5, 3);
136 const c = exp(a);
137
138 debug.assert(math.approxEq(f64, c.re, -146.927917, epsilon));
139 debug.assert(math.approxEq(f64, c.im, 20.944065, epsilon));
140}
std/math/complex/index.zig created+171
...@@ -0,0 +1,171 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4
5pub const abs = @import("abs.zig").abs;
6pub const acosh = @import("acosh.zig").acosh;
7pub const acos = @import("acos.zig").acos;
8pub const arg = @import("arg.zig").arg;
9pub const asinh = @import("asinh.zig").asinh;
10pub const asin = @import("asin.zig").asin;
11pub const atanh = @import("atanh.zig").atanh;
12pub const atan = @import("atan.zig").atan;
13pub const conj = @import("conj.zig").conj;
14pub const cosh = @import("cosh.zig").cosh;
15pub const cos = @import("cos.zig").cos;
16pub const exp = @import("exp.zig").exp;
17pub const log = @import("log.zig").log;
18pub const pow = @import("pow.zig").pow;
19pub const proj = @import("proj.zig").proj;
20pub const sinh = @import("sinh.zig").sinh;
21pub const sin = @import("sin.zig").sin;
22pub const sqrt = @import("sqrt.zig").sqrt;
23pub const tanh = @import("tanh.zig").tanh;
24pub const tan = @import("tan.zig").tan;
25
26pub fn Complex(comptime T: type) type {
27 return struct {
28 const Self = this;
29
30 re: T,
31 im: T,
32
33 pub fn new(re: T, im: T) Self {
34 return Self {
35 .re = re,
36 .im = im,
37 };
38 }
39
40 pub fn add(self: &const Self, other: &const Self) Self {
41 return Self {
42 .re = self.re + other.re,
43 .im = self.im + other.im,
44 };
45 }
46
47 pub fn sub(self: &const Self, other: &const Self) Self {
48 return Self {
49 .re = self.re - other.re,
50 .im = self.im - other.im,
51 };
52 }
53
54 pub fn mul(self: &const Self, other: &const Self) Self {
55 return Self {
56 .re = self.re * other.re - self.im * other.im,
57 .im = self.im * other.re + self.re * other.im,
58 };
59 }
60
61 pub fn div(self: &const Self, other: &const Self) Self {
62 const re_num = self.re * other.re + self.im * other.im;
63 const im_num = self.im * other.re - self.re * other.im;
64 const den = other.re * other.re + other.im * other.im;
65
66 return Self {
67 .re = re_num / den,
68 .im = im_num / den,
69 };
70 }
71
72 pub fn conjugate(self: &const Self) Self {
73 return Self {
74 .re = self.re,
75 .im = -self.im,
76 };
77 }
78
79 pub fn reciprocal(self: &const Self) Self {
80 const m = self.re * self.re + self.im * self.im;
81 return Self {
82 .re = self.re / m,
83 .im = -self.im / m,
84 };
85 }
86
87 pub fn magnitude(self: &const Self) T {
88 return math.sqrt(self.re * self.re + self.im * self.im);
89 }
90 };
91}
92
93const epsilon = 0.0001;
94
95test "complex.add" {
96 const a = Complex(f32).new(5, 3);
97 const b = Complex(f32).new(2, 7);
98 const c = a.add(b);
99
100 debug.assert(c.re == 7 and c.im == 10);
101}
102
103test "complex.sub" {
104 const a = Complex(f32).new(5, 3);
105 const b = Complex(f32).new(2, 7);
106 const c = a.sub(b);
107
108 debug.assert(c.re == 3 and c.im == -4);
109}
110
111test "complex.mul" {
112 const a = Complex(f32).new(5, 3);
113 const b = Complex(f32).new(2, 7);
114 const c = a.mul(b);
115
116 debug.assert(c.re == -11 and c.im == 41);
117}
118
119test "complex.div" {
120 const a = Complex(f32).new(5, 3);
121 const b = Complex(f32).new(2, 7);
122 const c = a.div(b);
123
124 debug.assert(math.approxEq(f32, c.re, f32(31)/53, epsilon) and
125 math.approxEq(f32, c.im, f32(-29)/53, epsilon));
126}
127
128test "complex.conjugate" {
129 const a = Complex(f32).new(5, 3);
130 const c = a.conjugate();
131
132 debug.assert(c.re == 5 and c.im == -3);
133}
134
135test "complex.reciprocal" {
136 const a = Complex(f32).new(5, 3);
137 const c = a.reciprocal();
138
139 debug.assert(math.approxEq(f32, c.re, f32(5)/34, epsilon) and
140 math.approxEq(f32, c.im, f32(-3)/34, epsilon));
141}
142
143test "complex.magnitude" {
144 const a = Complex(f32).new(5, 3);
145 const c = a.magnitude();
146
147 debug.assert(math.approxEq(f32, c, 5.83095, epsilon));
148}
149
150test "complex.cmath" {
151 _ = @import("abs.zig");
152 _ = @import("acosh.zig");
153 _ = @import("acos.zig");
154 _ = @import("arg.zig");
155 _ = @import("asinh.zig");
156 _ = @import("asin.zig");
157 _ = @import("atanh.zig");
158 _ = @import("atan.zig");
159 _ = @import("conj.zig");
160 _ = @import("cosh.zig");
161 _ = @import("cos.zig");
162 _ = @import("exp.zig");
163 _ = @import("log.zig");
164 _ = @import("pow.zig");
165 _ = @import("proj.zig");
166 _ = @import("sinh.zig");
167 _ = @import("sin.zig");
168 _ = @import("sqrt.zig");
169 _ = @import("tanh.zig");
170 _ = @import("tan.zig");
171}
std/math/complex/ldexp.zig created+75
...@@ -0,0 +1,75 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn ldexp_cexp(z: var, expt: i32) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9
10 return switch (T) {
11 f32 => ldexp_cexp32(z, expt),
12 f64 => ldexp_cexp64(z, expt),
13 else => unreachable,
14 };
15}
16
17fn frexp_exp32(x: f32, expt: &i32) f32 {
18 const k = 235; // reduction constant
19 const kln2 = 162.88958740; // k * ln2
20
21 const exp_x = math.exp(x - kln2);
22 const hx = @bitCast(u32, exp_x);
23 *expt = i32(hx >> 23) - (0x7f + 127) + k;
24 return @bitCast(f32, (hx & 0x7fffff) | ((0x7f + 127) << 23));
25}
26
27fn ldexp_cexp32(z: &const Complex(f32), expt: i32) Complex(f32) {
28 var ex_expt: i32 = undefined;
29 const exp_x = frexp_exp32(z.re, &ex_expt);
30 const exptf = expt + ex_expt;
31
32 const half_expt1 = @divTrunc(exptf, 2);
33 const scale1 = @bitCast(f32, (0x7f + half_expt1) << 23);
34
35 const half_expt2 = exptf - half_expt1;
36 const scale2 = @bitCast(f32, (0x7f + half_expt2) << 23);
37
38 return Complex(f32).new(
39 math.cos(z.im) * exp_x * scale1 * scale2,
40 math.sin(z.im) * exp_x * scale1 * scale2,
41 );
42}
43
44fn frexp_exp64(x: f64, expt: &i32) f64 {
45 const k = 1799; // reduction constant
46 const kln2 = 1246.97177782734161156; // k * ln2
47
48 const exp_x = math.exp(x - kln2);
49
50 const fx = @bitCast(u64, x);
51 const hx = u32(fx >> 32);
52 const lx = @truncate(u32, fx);
53
54 *expt = i32(hx >> 20) - (0x3ff + 1023) + k;
55
56 const high_word = (hx & 0xfffff) | ((0x3ff + 1023) << 20);
57 return @bitCast(f64, (u64(high_word) << 32) | lx);
58}
59
60fn ldexp_cexp64(z: &const Complex(f64), expt: i32) Complex(f64) {
61 var ex_expt: i32 = undefined;
62 const exp_x = frexp_exp64(z.re, &ex_expt);
63 const exptf = i64(expt + ex_expt);
64
65 const half_expt1 = @divTrunc(exptf, 2);
66 const scale1 = @bitCast(f64, (0x3ff + half_expt1) << 20);
67
68 const half_expt2 = exptf - half_expt1;
69 const scale2 = @bitCast(f64, (0x3ff + half_expt2) << 20);
70
71 return Complex(f64).new(
72 math.cos(z.im) * exp_x * scale1 * scale2,
73 math.sin(z.im) * exp_x * scale1 * scale2,
74 );
75}
std/math/complex/log.zig created+23
...@@ -0,0 +1,23 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn log(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const r = cmath.abs(z);
10 const phi = cmath.arg(z);
11
12 return Complex(T).new(math.ln(r), phi);
13}
14
15const epsilon = 0.0001;
16
17test "complex.clog" {
18 const a = Complex(f32).new(5, 3);
19 const c = log(a);
20
21 debug.assert(math.approxEq(f32, c.re, 1.763180, epsilon));
22 debug.assert(math.approxEq(f32, c.im, 0.540419, epsilon));
23}
std/math/complex/pow.zig created+22
...@@ -0,0 +1,22 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn pow(comptime T: type, z: &const T, c: &const T) T {
8 const p = cmath.log(z);
9 const q = c.mul(p);
10 return cmath.exp(q);
11}
12
13const epsilon = 0.0001;
14
15test "complex.cpow" {
16 const a = Complex(f32).new(5, 3);
17 const b = Complex(f32).new(2.3, -1.3);
18 const c = pow(Complex(f32), a, b);
19
20 debug.assert(math.approxEq(f32, c.re, 58.049110, epsilon));
21 debug.assert(math.approxEq(f32, c.im, -101.003433, epsilon));
22}
std/math/complex/proj.zig created+24
...@@ -0,0 +1,24 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn proj(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9
10 if (math.isInf(z.re) or math.isInf(z.im)) {
11 return Complex(T).new(math.inf(T), math.copysign(T, 0, z.re));
12 }
13
14 return Complex(T).new(z.re, z.im);
15}
16
17const epsilon = 0.0001;
18
19test "complex.cproj" {
20 const a = Complex(f32).new(5, 3);
21 const c = proj(a);
22
23 debug.assert(c.re == 5 and c.im == 3);
24}
std/math/complex/sin.zig created+22
...@@ -0,0 +1,22 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn sin(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const p = Complex(T).new(-z.im, z.re);
10 const q = cmath.sinh(p);
11 return Complex(T).new(q.im, -q.re);
12}
13
14const epsilon = 0.0001;
15
16test "complex.csin" {
17 const a = Complex(f32).new(5, 3);
18 const c = sin(a);
19
20 debug.assert(math.approxEq(f32, c.re, -9.654126, epsilon));
21 debug.assert(math.approxEq(f32, c.im, 2.841692, epsilon));
22}
std/math/complex/sinh.zig created+164
...@@ -0,0 +1,164 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7const ldexp_cexp = @import("ldexp.zig").ldexp_cexp;
8
9pub fn sinh(z: var) Complex(@typeOf(z.re)) {
10 const T = @typeOf(z.re);
11 return switch (T) {
12 f32 => sinh32(z),
13 f64 => sinh64(z),
14 else => @compileError("tan not implemented for " ++ @typeName(z)),
15 };
16}
17
18fn sinh32(z: &const Complex(f32)) Complex(f32) {
19 const x = z.re;
20 const y = z.im;
21
22 const hx = @bitCast(u32, x);
23 const ix = hx & 0x7fffffff;
24
25 const hy = @bitCast(u32, y);
26 const iy = hy & 0x7fffffff;
27
28 if (ix < 0x7f800000 and iy < 0x7f800000) {
29 if (iy == 0) {
30 return Complex(f32).new(math.sinh(x), y);
31 }
32 // small x: normal case
33 if (ix < 0x41100000) {
34 return Complex(f32).new(math.sinh(x) * math.cos(y), math.cosh(x) * math.sin(y));
35 }
36
37 // |x|>= 9, so cosh(x) ~= exp(|x|)
38 if (ix < 0x42b17218) {
39 // x < 88.7: exp(|x|) won't overflow
40 const h = math.exp(math.fabs(x)) * 0.5;
41 return Complex(f32).new(math.copysign(f32, h, x) * math.cos(y), h * math.sin(y));
42 }
43 // x < 192.7: scale to avoid overflow
44 else if (ix < 0x4340b1e7) {
45 const v = Complex(f32).new(math.fabs(x), y);
46 const r = ldexp_cexp(v, -1);
47 return Complex(f32).new(x * math.copysign(f32, 1, x), y);
48 }
49 // x >= 192.7: result always overflows
50 else {
51 const h = 0x1p127 * x;
52 return Complex(f32).new(h * math.cos(y), h * h * math.sin(y));
53 }
54 }
55
56 if (ix == 0 and iy >= 0x7f800000) {
57 return Complex(f32).new(math.copysign(f32, 0, x * (y - y)), y - y);
58 }
59
60 if (iy == 0 and ix >= 0x7f800000) {
61 if (hx & 0x7fffff == 0) {
62 return Complex(f32).new(x, y);
63 }
64 return Complex(f32).new(x, math.copysign(f32, 0, y));
65 }
66
67 if (ix < 0x7f800000 and iy >= 0x7f800000) {
68 return Complex(f32).new(y - y, x * (y - y));
69 }
70
71 if (ix >= 0x7f800000 and (hx & 0x7fffff) == 0) {
72 if (iy >= 0x7f800000) {
73 return Complex(f32).new(x * x, x * (y - y));
74 }
75 return Complex(f32).new(x * math.cos(y), math.inf_f32 * math.sin(y));
76 }
77
78 return Complex(f32).new((x * x) * (y - y), (x + x) * (y - y));
79}
80
81fn sinh64(z: &const Complex(f64)) Complex(f64) {
82 const x = z.re;
83 const y = z.im;
84
85 const fx = @bitCast(u64, x);
86 const hx = u32(fx >> 32);
87 const lx = @truncate(u32, fx);
88 const ix = hx & 0x7fffffff;
89
90 const fy = @bitCast(u64, y);
91 const hy = u32(fy >> 32);
92 const ly = @truncate(u32, fy);
93 const iy = hy & 0x7fffffff;
94
95 if (ix < 0x7ff00000 and iy < 0x7ff00000) {
96 if (iy | ly == 0) {
97 return Complex(f64).new(math.sinh(x), y);
98 }
99 // small x: normal case
100 if (ix < 0x40360000) {
101 return Complex(f64).new(math.sinh(x) * math.cos(y), math.cosh(x) * math.sin(y));
102 }
103
104 // |x|>= 22, so cosh(x) ~= exp(|x|)
105 if (ix < 0x40862e42) {
106 // x < 710: exp(|x|) won't overflow
107 const h = math.exp(math.fabs(x)) * 0.5;
108 return Complex(f64).new(math.copysign(f64, h, x) * math.cos(y), h * math.sin(y));
109 }
110 // x < 1455: scale to avoid overflow
111 else if (ix < 0x4096bbaa) {
112 const v = Complex(f64).new(math.fabs(x), y);
113 const r = ldexp_cexp(v, -1);
114 return Complex(f64).new(x * math.copysign(f64, 1, x), y);
115 }
116 // x >= 1455: result always overflows
117 else {
118 const h = 0x1p1023 * x;
119 return Complex(f64).new(h * math.cos(y), h * h * math.sin(y));
120 }
121 }
122
123 if (ix | lx == 0 and iy >= 0x7ff00000) {
124 return Complex(f64).new(math.copysign(f64, 0, x * (y - y)), y - y);
125 }
126
127 if (iy | ly == 0 and ix >= 0x7ff00000) {
128 if ((hx & 0xfffff) | lx == 0) {
129 return Complex(f64).new(x, y);
130 }
131 return Complex(f64).new(x, math.copysign(f64, 0, y));
132 }
133
134 if (ix < 0x7ff00000 and iy >= 0x7ff00000) {
135 return Complex(f64).new(y - y, x * (y - y));
136 }
137
138 if (ix >= 0x7ff00000 and (hx & 0xfffff) | lx == 0) {
139 if (iy >= 0x7ff00000) {
140 return Complex(f64).new(x * x, x * (y - y));
141 }
142 return Complex(f64).new(x * math.cos(y), math.inf_f64 * math.sin(y));
143 }
144
145 return Complex(f64).new((x * x) * (y - y), (x + x) * (y - y));
146}
147
148const epsilon = 0.0001;
149
150test "complex.csinh32" {
151 const a = Complex(f32).new(5, 3);
152 const c = sinh(a);
153
154 debug.assert(math.approxEq(f32, c.re, -73.460617, epsilon));
155 debug.assert(math.approxEq(f32, c.im, 10.472508, epsilon));
156}
157
158test "complex.csinh64" {
159 const a = Complex(f64).new(5, 3);
160 const c = sinh(a);
161
162 debug.assert(math.approxEq(f64, c.re, -73.460617, epsilon));
163 debug.assert(math.approxEq(f64, c.im, 10.472508, epsilon));
164}
std/math/complex/sqrt.zig created+133
...@@ -0,0 +1,133 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7// TODO when #733 is solved this can be @typeOf(z) instead of Complex(@typeOf(z.re))
8pub fn sqrt(z: var) Complex(@typeOf(z.re)) {
9 const T = @typeOf(z.re);
10
11 return switch (T) {
12 f32 => sqrt32(z),
13 f64 => sqrt64(z),
14 else => @compileError("sqrt not implemented for " ++ @typeName(z)),
15 };
16}
17
18fn sqrt32(z: &const Complex(f32)) Complex(f32) {
19 const x = z.re;
20 const y = z.im;
21
22 if (x == 0 and y == 0) {
23 return Complex(f32).new(0, y);
24 }
25 if (math.isInf(y)) {
26 return Complex(f32).new(math.inf(f32), y);
27 }
28 if (math.isNan(x)) {
29 // raise invalid if y is not nan
30 const t = (y - y) / (y - y);
31 return Complex(f32).new(x, t);
32 }
33 if (math.isInf(x)) {
34 // sqrt(inf + i nan) = inf + nan i
35 // sqrt(inf + iy) = inf + i0
36 // sqrt(-inf + i nan) = nan +- inf i
37 // sqrt(-inf + iy) = 0 + inf i
38 if (math.signbit(x)) {
39 return Complex(f32).new(math.fabs(x - y), math.copysign(f32, x, y));
40 } else {
41 return Complex(f32).new(x, math.copysign(f32, y - y, y));
42 }
43 }
44
45 // y = nan special case is handled fine below
46
47 // double-precision avoids overflow with correct rounding.
48 const dx = f64(x);
49 const dy = f64(y);
50
51 if (dx >= 0) {
52 const t = math.sqrt((dx + math.hypot(f64, dx, dy)) * 0.5);
53 return Complex(f32).new(f32(t), f32(dy / (2.0 * t)));
54 } else {
55 const t = math.sqrt((-dx + math.hypot(f64, dx, dy)) * 0.5);
56 return Complex(f32).new(f32(math.fabs(y) / (2.0 * t)), f32(math.copysign(f64, t, y)));
57 }
58}
59
60fn sqrt64(z: &const Complex(f64)) Complex(f64) {
61 // may encounter overflow for im,re >= DBL_MAX / (1 + sqrt(2))
62 const threshold = 0x1.a827999fcef32p+1022;
63
64 var x = z.re;
65 var y = z.im;
66
67 if (x == 0 and y == 0) {
68 return Complex(f64).new(0, y);
69 }
70 if (math.isInf(y)) {
71 return Complex(f64).new(math.inf(f64), y);
72 }
73 if (math.isNan(x)) {
74 // raise invalid if y is not nan
75 const t = (y - y) / (y - y);
76 return Complex(f64).new(x, t);
77 }
78 if (math.isInf(x)) {
79 // sqrt(inf + i nan) = inf + nan i
80 // sqrt(inf + iy) = inf + i0
81 // sqrt(-inf + i nan) = nan +- inf i
82 // sqrt(-inf + iy) = 0 + inf i
83 if (math.signbit(x)) {
84 return Complex(f64).new(math.fabs(x - y), math.copysign(f64, x, y));
85 } else {
86 return Complex(f64).new(x, math.copysign(f64, y - y, y));
87 }
88 }
89
90 // y = nan special case is handled fine below
91
92 // scale to avoid overflow
93 var scale = false;
94 if (math.fabs(x) >= threshold or math.fabs(y) >= threshold) {
95 x *= 0.25;
96 y *= 0.25;
97 scale = true;
98 }
99
100 var result: Complex(f64) = undefined;
101 if (x >= 0) {
102 const t = math.sqrt((x + math.hypot(f64, x, y)) * 0.5);
103 result = Complex(f64).new(t, y / (2.0 * t));
104 } else {
105 const t = math.sqrt((-x + math.hypot(f64, x, y)) * 0.5);
106 result = Complex(f64).new(math.fabs(y) / (2.0 * t), math.copysign(f64, t, y));
107 }
108
109 if (scale) {
110 result.re *= 2;
111 result.im *= 2;
112 }
113
114 return result;
115}
116
117const epsilon = 0.0001;
118
119test "complex.csqrt32" {
120 const a = Complex(f32).new(5, 3);
121 const c = sqrt(a);
122
123 debug.assert(math.approxEq(f32, c.re, 2.327117, epsilon));
124 debug.assert(math.approxEq(f32, c.im, 0.644574, epsilon));
125}
126
127test "complex.csqrt64" {
128 const a = Complex(f64).new(5, 3);
129 const c = sqrt(a);
130
131 debug.assert(math.approxEq(f64, c.re, 2.3271175190399496, epsilon));
132 debug.assert(math.approxEq(f64, c.im, 0.6445742373246469, epsilon));
133}
std/math/complex/tan.zig created+22
...@@ -0,0 +1,22 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn tan(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 const q = Complex(T).new(-z.im, z.re);
10 const r = cmath.tanh(q);
11 return Complex(T).new(r.im, -r.re);
12}
13
14const epsilon = 0.0001;
15
16test "complex.ctan" {
17 const a = Complex(f32).new(5, 3);
18 const c = tan(a);
19
20 debug.assert(math.approxEq(f32, c.re, -0.002708233, epsilon));
21 debug.assert(math.approxEq(f32, c.im, 1.004165, epsilon));
22}
std/math/complex/tanh.zig created+111
...@@ -0,0 +1,111 @@
1const std = @import("../../index.zig");
2const debug = std.debug;
3const math = std.math;
4const cmath = math.complex;
5const Complex = cmath.Complex;
6
7pub fn tanh(z: var) Complex(@typeOf(z.re)) {
8 const T = @typeOf(z.re);
9 return switch (T) {
10 f32 => tanh32(z),
11 f64 => tanh64(z),
12 else => @compileError("tan not implemented for " ++ @typeName(z)),
13 };
14}
15
16fn tanh32(z: &const Complex(f32)) Complex(f32) {
17 const x = z.re;
18 const y = z.im;
19
20 const hx = @bitCast(u32, x);
21 const ix = hx & 0x7fffffff;
22
23 if (ix >= 0x7f800000) {
24 if (ix & 0x7fffff != 0) {
25 const r = if (y == 0) y else x * y;
26 return Complex(f32).new(x, r);
27 }
28 const xx = @bitCast(f32, hx - 0x40000000);
29 const r = if (math.isInf(y)) y else math.sin(y) * math.cos(y);
30 return Complex(f32).new(xx, math.copysign(f32, 0, r));
31 }
32
33 if (!math.isFinite(y)) {
34 const r = if (ix != 0) y - y else x;
35 return Complex(f32).new(r, y - y);
36 }
37
38 // x >= 11
39 if (ix >= 0x41300000) {
40 const exp_mx = math.exp(-math.fabs(x));
41 return Complex(f32).new(math.copysign(f32, 1, x), 4 * math.sin(y) * math.cos(y) * exp_mx * exp_mx);
42 }
43
44 // Kahan's algorithm
45 const t = math.tan(y);
46 const beta = 1.0 + t * t;
47 const s = math.sinh(x);
48 const rho = math.sqrt(1 + s * s);
49 const den = 1 + beta * s * s;
50
51 return Complex(f32).new((beta * rho * s) / den, t / den);
52}
53
54fn tanh64(z: &const Complex(f64)) Complex(f64) {
55 const x = z.re;
56 const y = z.im;
57
58 const fx = @bitCast(u64, x);
59 const hx = u32(fx >> 32);
60 const lx = @truncate(u32, fx);
61 const ix = hx & 0x7fffffff;
62
63 if (ix >= 0x7ff00000) {
64 if ((ix & 0x7fffff) | lx != 0) {
65 const r = if (y == 0) y else x * y;
66 return Complex(f64).new(x, r);
67 }
68
69 const xx = @bitCast(f64, (u64(hx - 0x40000000) << 32) | lx);
70 const r = if (math.isInf(y)) y else math.sin(y) * math.cos(y);
71 return Complex(f64).new(xx, math.copysign(f64, 0, r));
72 }
73
74 if (!math.isFinite(y)) {
75 const r = if (ix != 0) y - y else x;
76 return Complex(f64).new(r, y - y);
77 }
78
79 // x >= 22
80 if (ix >= 0x40360000) {
81 const exp_mx = math.exp(-math.fabs(x));
82 return Complex(f64).new(math.copysign(f64, 1, x), 4 * math.sin(y) * math.cos(y) * exp_mx * exp_mx);
83 }
84
85 // Kahan's algorithm
86 const t = math.tan(y);
87 const beta = 1.0 + t * t;
88 const s = math.sinh(x);
89 const rho = math.sqrt(1 + s * s);
90 const den = 1 + beta * s * s;
91
92 return Complex(f64).new((beta * rho * s) / den, t / den);
93}
94
95const epsilon = 0.0001;
96
97test "complex.ctanh32" {
98 const a = Complex(f32).new(5, 3);
99 const c = tanh(a);
100
101 debug.assert(math.approxEq(f32, c.re, 0.999913, epsilon));
102 debug.assert(math.approxEq(f32, c.im, -0.000025, epsilon));
103}
104
105test "complex.ctanh64" {
106 const a = Complex(f64).new(5, 3);
107 const c = tanh(a);
108
109 debug.assert(math.approxEq(f64, c.re, 0.999913, epsilon));
110 debug.assert(math.approxEq(f64, c.im, -0.000025, epsilon));
111}
std/math/index.zig+5
...@@ -129,6 +129,9 @@ pub const cos = @import("cos.zig").cos;...@@ -129,6 +129,9 @@ pub const cos = @import("cos.zig").cos;
129pub const sin = @import("sin.zig").sin;129pub const sin = @import("sin.zig").sin;
130pub const tan = @import("tan.zig").tan;130pub const tan = @import("tan.zig").tan;
131131
132pub const complex = @import("complex/index.zig");
133pub const Complex = complex.Complex;
134
132test "math" {135test "math" {
133 _ = @import("nan.zig");136 _ = @import("nan.zig");
134 _ = @import("isnan.zig");137 _ = @import("isnan.zig");
...@@ -172,6 +175,8 @@ test "math" {...@@ -172,6 +175,8 @@ test "math" {
172 _ = @import("sin.zig");175 _ = @import("sin.zig");
173 _ = @import("cos.zig");176 _ = @import("cos.zig");
174 _ = @import("tan.zig");177 _ = @import("tan.zig");
178
179 _ = @import("complex/index.zig");
175}180}
176181
177182
std/mem.zig+82-2
...@@ -20,7 +20,7 @@ pub const Allocator = struct {...@@ -20,7 +20,7 @@ pub const Allocator = struct {
20 /// * alignment >= alignment of old_mem.ptr20 /// * alignment >= alignment of old_mem.ptr
21 ///21 ///
22 /// If `new_byte_count <= old_mem.len`:22 /// If `new_byte_count <= old_mem.len`:
23 /// * this function must return successfully. 23 /// * this function must return successfully.
24 /// * alignment <= alignment of old_mem.ptr24 /// * alignment <= alignment of old_mem.ptr
25 ///25 ///
26 /// The returned newly allocated memory is undefined.26 /// The returned newly allocated memory is undefined.
...@@ -174,6 +174,20 @@ pub fn dupe(allocator: &Allocator, comptime T: type, m: []const T) ![]T {...@@ -174,6 +174,20 @@ pub fn dupe(allocator: &Allocator, comptime T: type, m: []const T) ![]T {
174 return new_buf;174 return new_buf;
175}175}
176176
177/// Remove values from the beginning of a slice.
178pub fn trimLeft(comptime T: type, slice: []const T, values_to_strip: []const T) []const T {
179 var begin: usize = 0;
180 while (begin < slice.len and indexOfScalar(T, values_to_strip, slice[begin]) != null) : (begin += 1) {}
181 return slice[begin..];
182}
183
184/// Remove values from the end of a slice.
185pub fn trimRight(comptime T: type, slice: []const T, values_to_strip: []const T) []const T {
186 var end: usize = slice.len;
187 while (end > 0 and indexOfScalar(T, values_to_strip, slice[end - 1]) != null) : (end -= 1) {}
188 return slice[0..end];
189}
190
177/// Remove values from the beginning and end of a slice.191/// Remove values from the beginning and end of a slice.
178pub fn trim(comptime T: type, slice: []const T, values_to_strip: []const T) []const T {192pub fn trim(comptime T: type, slice: []const T, values_to_strip: []const T) []const T {
179 var begin: usize = 0;193 var begin: usize = 0;
...@@ -184,6 +198,8 @@ pub fn trim(comptime T: type, slice: []const T, values_to_strip: []const T) []co...@@ -184,6 +198,8 @@ pub fn trim(comptime T: type, slice: []const T, values_to_strip: []const T) []co
184}198}
185199
186test "mem.trim" {200test "mem.trim" {
201 assert(eql(u8, trimLeft(u8, " foo\n ", " \n"), "foo\n "));
202 assert(eql(u8, trimRight(u8, " foo\n ", " \n"), " foo"));
187 assert(eql(u8, trim(u8, " foo\n ", " \n"), "foo"));203 assert(eql(u8, trim(u8, " foo\n ", " \n"), "foo"));
188 assert(eql(u8, trim(u8, "foo", " \n"), "foo"));204 assert(eql(u8, trim(u8, "foo", " \n"), "foo"));
189}205}
...@@ -193,6 +209,17 @@ pub fn indexOfScalar(comptime T: type, slice: []const T, value: T) ?usize {...@@ -193,6 +209,17 @@ pub fn indexOfScalar(comptime T: type, slice: []const T, value: T) ?usize {
193 return indexOfScalarPos(T, slice, 0, value);209 return indexOfScalarPos(T, slice, 0, value);
194}210}
195211
212/// Linear search for the last index of a scalar value inside a slice.
213pub fn lastIndexOfScalar(comptime T: type, slice: []const T, value: T) ?usize {
214 var i: usize = slice.len;
215 while (i != 0) {
216 i -= 1;
217 if (slice[i] == value)
218 return i;
219 }
220 return null;
221}
222
196pub fn indexOfScalarPos(comptime T: type, slice: []const T, start_index: usize, value: T) ?usize {223pub fn indexOfScalarPos(comptime T: type, slice: []const T, start_index: usize, value: T) ?usize {
197 var i: usize = start_index;224 var i: usize = start_index;
198 while (i < slice.len) : (i += 1) {225 while (i < slice.len) : (i += 1) {
...@@ -206,6 +233,18 @@ pub fn indexOfAny(comptime T: type, slice: []const T, values: []const T) ?usize...@@ -206,6 +233,18 @@ pub fn indexOfAny(comptime T: type, slice: []const T, values: []const T) ?usize
206 return indexOfAnyPos(T, slice, 0, values);233 return indexOfAnyPos(T, slice, 0, values);
207}234}
208235
236pub fn lastIndexOfAny(comptime T: type, slice: []const T, values: []const T) ?usize {
237 var i: usize = slice.len;
238 while (i != 0) {
239 i -= 1;
240 for (values) |value| {
241 if (slice[i] == value)
242 return i;
243 }
244 }
245 return null;
246}
247
209pub fn indexOfAnyPos(comptime T: type, slice: []const T, start_index: usize, values: []const T) ?usize {248pub fn indexOfAnyPos(comptime T: type, slice: []const T, start_index: usize, values: []const T) ?usize {
210 var i: usize = start_index;249 var i: usize = start_index;
211 while (i < slice.len) : (i += 1) {250 while (i < slice.len) : (i += 1) {
...@@ -221,6 +260,22 @@ pub fn indexOf(comptime T: type, haystack: []const T, needle: []const T) ?usize...@@ -221,6 +260,22 @@ pub fn indexOf(comptime T: type, haystack: []const T, needle: []const T) ?usize
221 return indexOfPos(T, haystack, 0, needle);260 return indexOfPos(T, haystack, 0, needle);
222}261}
223262
263/// Find the index in a slice of a sub-slice, searching from the end backwards.
264/// To start looking at a different index, slice the haystack first.
265/// TODO is there even a better algorithm for this?
266pub fn lastIndexOf(comptime T: type, haystack: []const T, needle: []const T) ?usize {
267 if (needle.len > haystack.len)
268 return null;
269
270 var i: usize = haystack.len - needle.len;
271 while (true) : (i -= 1) {
272 if (mem.eql(T, haystack[i..i+needle.len], needle))
273 return i;
274 if (i == 0)
275 return null;
276 }
277}
278
224// TODO boyer-moore algorithm279// TODO boyer-moore algorithm
225pub fn indexOfPos(comptime T: type, haystack: []const T, start_index: usize, needle: []const T) ?usize {280pub fn indexOfPos(comptime T: type, haystack: []const T, start_index: usize, needle: []const T) ?usize {
226 if (needle.len > haystack.len)281 if (needle.len > haystack.len)
...@@ -237,9 +292,19 @@ pub fn indexOfPos(comptime T: type, haystack: []const T, start_index: usize, nee...@@ -237,9 +292,19 @@ pub fn indexOfPos(comptime T: type, haystack: []const T, start_index: usize, nee
237292
238test "mem.indexOf" {293test "mem.indexOf" {
239 assert(??indexOf(u8, "one two three four", "four") == 14);294 assert(??indexOf(u8, "one two three four", "four") == 14);
295 assert(??lastIndexOf(u8, "one two three two four", "two") == 14);
240 assert(indexOf(u8, "one two three four", "gour") == null);296 assert(indexOf(u8, "one two three four", "gour") == null);
297 assert(lastIndexOf(u8, "one two three four", "gour") == null);
241 assert(??indexOf(u8, "foo", "foo") == 0);298 assert(??indexOf(u8, "foo", "foo") == 0);
299 assert(??lastIndexOf(u8, "foo", "foo") == 0);
242 assert(indexOf(u8, "foo", "fool") == null);300 assert(indexOf(u8, "foo", "fool") == null);
301 assert(lastIndexOf(u8, "foo", "lfoo") == null);
302 assert(lastIndexOf(u8, "foo", "fool") == null);
303
304 assert(??indexOf(u8, "foo foo", "foo") == 0);
305 assert(??lastIndexOf(u8, "foo foo", "foo") == 4);
306 assert(??lastIndexOfAny(u8, "boo, cat", "abo") == 6);
307 assert(??lastIndexOfScalar(u8, "boo", 'o') == 2);
243}308}
244309
245/// Reads an integer from memory with size equal to bytes.len.310/// Reads an integer from memory with size equal to bytes.len.
...@@ -359,9 +424,24 @@ pub fn startsWith(comptime T: type, haystack: []const T, needle: []const T) bool...@@ -359,9 +424,24 @@ pub fn startsWith(comptime T: type, haystack: []const T, needle: []const T) bool
359 return if (needle.len > haystack.len) false else eql(T, haystack[0 .. needle.len], needle);424 return if (needle.len > haystack.len) false else eql(T, haystack[0 .. needle.len], needle);
360}425}
361426
427test "mem.startsWith" {
428 assert(startsWith(u8, "Bob", "Bo"));
429 assert(!startsWith(u8, "Needle in haystack", "haystack"));
430}
431
432pub fn endsWith(comptime T: type, haystack: []const T, needle: []const T) bool {
433 return if (needle.len > haystack.len) false else eql(T, haystack[haystack.len - needle.len ..], needle);
434}
435
436
437test "mem.endsWith" {
438 assert(endsWith(u8, "Needle in haystack", "haystack"));
439 assert(!endsWith(u8, "Bob", "Bo"));
440}
441
362pub const SplitIterator = struct {442pub const SplitIterator = struct {
363 buffer: []const u8,443 buffer: []const u8,
364 split_bytes: []const u8, 444 split_bytes: []const u8,
365 index: usize,445 index: usize,
366446
367 pub fn next(self: &SplitIterator) ?[]const u8 {447 pub fn next(self: &SplitIterator) ?[]const u8 {
test/cases/defer.zig+11
...@@ -41,3 +41,14 @@ fn testBreakContInDefer(x: usize) void {...@@ -41,3 +41,14 @@ fn testBreakContInDefer(x: usize) void {
41 assert(i == 5);41 assert(i == 5);
42 }42 }
43}43}
44
45test "defer and labeled break" {
46 var i = usize(0);
47
48 blk: {
49 defer i += 1;
50 break :blk;
51 }
52
53 assert(i == 1);
54}
test/cases/eval.zig+16
...@@ -513,3 +513,19 @@ test "array concat of slices gives slice" {...@@ -513,3 +513,19 @@ test "array concat of slices gives slice" {
513 assert(std.mem.eql(u8, c, "aoeuasdf"));513 assert(std.mem.eql(u8, c, "aoeuasdf"));
514 }514 }
515}515}
516
517test "comptime shlWithOverflow" {
518 const ct_shifted: u64 = comptime amt: {
519 var amt = u64(0);
520 _ = @shlWithOverflow(u64, ~u64(0), 16, &amt);
521 break :amt amt;
522 };
523
524 const rt_shifted: u64 = amt: {
525 var amt = u64(0);
526 _ = @shlWithOverflow(u64, ~u64(0), 16, &amt);
527 break :amt amt;
528 };
529
530 assert(ct_shifted == rt_shifted);
531}