1// Ported from musl, which is licensed under the MIT license:
2// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
3//
4// https://git.musl-libc.org/cgit/musl/tree/src/math/__rem_pio2.c
5
6const std = @import("std");
7const rem_pio2_large = @import("rem_pio2_large.zig").rem_pio2_large;
8const math = std.math;
9
10const toint = 1.5 / math.floatEps(f64);
11// pi/4
12const pio4 = 0x1.921fb54442d18p-1;
13// invpio2: 53 bits of 2/pi
14const invpio2 = 6.36619772367581382433e-01; // 0x3FE45F30, 0x6DC9C883
15// pio2_1: first 33 bit of pi/2
16const pio2_1 = 1.57079632673412561417e+00; // 0x3FF921FB, 0x54400000
17// pio2_1t: pi/2 - pio2_1
18const pio2_1t = 6.07710050650619224932e-11; // 0x3DD0B461, 0x1A626331
19// pio2_2: second 33 bit of pi/2
20const pio2_2 = 6.07710050630396597660e-11; // 0x3DD0B461, 0x1A600000
21// pio2_2t: pi/2 - (pio2_1+pio2_2)
22const pio2_2t = 2.02226624879595063154e-21; // 0x3BA3198A, 0x2E037073
23// pio2_3: third 33 bit of pi/2
24const pio2_3 = 2.02226624871116645580e-21; // 0x3BA3198A, 0x2E000000
25// pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
26const pio2_3t = 8.47842766036889956997e-32; // 0x397B839A, 0x252049C1
27
28fn medium(ix: u32, x: f64, y: *[2]f64) i32 {
29 var w: f64 = undefined;
30 var t: f64 = undefined;
31 var r: f64 = undefined;
32 var @"fn": f64 = undefined;
33 var n: i32 = undefined;
34 var ex: i32 = undefined;
35 var ey: i32 = undefined;
36 var ui: u64 = undefined;
37
38 // rint(x/(pi/2))
39 @"fn" = x * invpio2 + toint - toint;
40 n = @intFromFloat(@"fn");
41 r = x - @"fn" * pio2_1;
42 w = @"fn" * pio2_1t; // 1st round, good to 85 bits
43 // Matters with directed rounding.
44 if (r - w < -pio4) {
45 n -= 1;
46 @"fn" -= 1;
47 r = x - @"fn" * pio2_1;
48 w = @"fn" * pio2_1t;
49 } else if (r - w > pio4) {
50 n += 1;
51 @"fn" += 1;
52 r = x - @"fn" * pio2_1;
53 w = @"fn" * pio2_1t;
54 }
55 y[0] = r - w;
56 ui = @bitCast(y[0]);
57 ey = @intCast((ui >> 52) & 0x7ff);
58 ex = @intCast(ix >> 20);
59 if (ex - ey > 16) { // 2nd round, good to 118 bits
60 t = r;
61 w = @"fn" * pio2_2;
62 r = t - w;
63 w = @"fn" * pio2_2t - ((t - r) - w);
64 y[0] = r - w;
65 ui = @bitCast(y[0]);
66 ey = @intCast((ui >> 52) & 0x7ff);
67 if (ex - ey > 49) { // 3rd round, good to 151 bits, covers all cases
68 t = r;
69 w = @"fn" * pio2_3;
70 r = t - w;
71 w = @"fn" * pio2_3t - ((t - r) - w);
72 y[0] = r - w;
73 }
74 }
75 y[1] = (r - y[0]) - w;
76 return n;
77}
78
79// Returns the remainder of x rem pi/2 in y[0]+y[1]
80//
81// use rem_pio2_large() for large x
82//
83// caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
84pub fn rem_pio2(x: f64, y: *[2]f64) i32 {
85 var z: f64 = undefined;
86 var tx: [3]f64 = undefined;
87 var ty: [2]f64 = undefined;
88 var n: i32 = undefined;
89 var ix: u32 = undefined;
90 var sign: bool = undefined;
91 var i: i32 = undefined;
92 var ui: u64 = undefined;
93
94 ui = @bitCast(x);
95 sign = ui >> 63 != 0;
96 ix = @truncate((ui >> 32) & 0x7fffffff);
97 if (ix <= 0x400f6a7a) { // |x| ~<= 5pi/4
98 if ((ix & 0xfffff) == 0x921fb) { // |x| ~= pi/2 or 2pi/2
99 return medium(ix, x, y);
100 }
101 if (ix <= 0x4002d97c) { // |x| ~<= 3pi/4
102 if (!sign) {
103 z = x - pio2_1; // one round good to 85 bits
104 y[0] = z - pio2_1t;
105 y[1] = (z - y[0]) - pio2_1t;
106 return 1;
107 } else {
108 z = x + pio2_1;
109 y[0] = z + pio2_1t;
110 y[1] = (z - y[0]) + pio2_1t;
111 return -1;
112 }
113 } else {
114 if (!sign) {
115 z = x - 2 * pio2_1;
116 y[0] = z - 2 * pio2_1t;
117 y[1] = (z - y[0]) - 2 * pio2_1t;
118 return 2;
119 } else {
120 z = x + 2 * pio2_1;
121 y[0] = z + 2 * pio2_1t;
122 y[1] = (z - y[0]) + 2 * pio2_1t;
123 return -2;
124 }
125 }
126 }
127 if (ix <= 0x401c463b) { // |x| ~<= 9pi/4
128 if (ix <= 0x4015fdbc) { // |x| ~<= 7pi/4
129 if (ix == 0x4012d97c) { // |x| ~= 3pi/2
130 return medium(ix, x, y);
131 }
132 if (!sign) {
133 z = x - 3 * pio2_1;
134 y[0] = z - 3 * pio2_1t;
135 y[1] = (z - y[0]) - 3 * pio2_1t;
136 return 3;
137 } else {
138 z = x + 3 * pio2_1;
139 y[0] = z + 3 * pio2_1t;
140 y[1] = (z - y[0]) + 3 * pio2_1t;
141 return -3;
142 }
143 } else {
144 if (ix == 0x401921fb) { // |x| ~= 4pi/2 */
145 return medium(ix, x, y);
146 }
147 if (!sign) {
148 z = x - 4 * pio2_1;
149 y[0] = z - 4 * pio2_1t;
150 y[1] = (z - y[0]) - 4 * pio2_1t;
151 return 4;
152 } else {
153 z = x + 4 * pio2_1;
154 y[0] = z + 4 * pio2_1t;
155 y[1] = (z - y[0]) + 4 * pio2_1t;
156 return -4;
157 }
158 }
159 }
160 if (ix < 0x413921fb) { // |x| ~< 2^20*(pi/2), medium size
161 return medium(ix, x, y);
162 }
163 // all other (large) arguments
164 if (ix >= 0x7ff00000) { // x is inf or NaN
165 y[0] = x - x;
166 y[1] = y[0];
167 return 0;
168 }
169 // set z = scalbn(|x|,-ilogb(x)+23)
170 ui = @bitCast(x);
171 ui &= std.math.maxInt(u64) >> 12;
172 ui |= @as(u64, 0x3ff + 23) << 52;
173 z = @bitCast(ui);
174
175 i = 0;
176 while (i < 2) : (i += 1) {
177 tx[@intCast(i)] = @floatFromInt(@as(i32, @intFromFloat(z)));
178 z = (z - tx[@intCast(i)]) * 0x1p24;
179 }
180 tx[@intCast(i)] = z;
181 // skip zero terms, first term is non-zero
182 while (tx[@intCast(i)] == 0.0) {
183 i -= 1;
184 }
185 n = rem_pio2_large(tx[0..], ty[0..], @as(i32, @intCast((ix >> 20))) - (0x3ff + 23), i + 1, 1);
186 if (sign) {
187 y[0] = -ty[0];
188 y[1] = -ty[1];
189 return -n;
190 }
191 y[0] = ty[0];
192 y[1] = ty[1];
193 return n;
194}