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sincos.zig (8779B) - Raw


      1 const std = @import("std");
      2 const builtin = @import("builtin");
      3 const arch = builtin.cpu.arch;
      4 const math = std.math;
      5 const mem = std.mem;
      6 const trig = @import("trig.zig");
      7 const rem_pio2 = @import("rem_pio2.zig").rem_pio2;
      8 const rem_pio2f = @import("rem_pio2f.zig").rem_pio2f;
      9 const common = @import("common.zig");
     10 
     11 pub const panic = common.panic;
     12 
     13 comptime {
     14     @export(&__sincosh, .{ .name = "__sincosh", .linkage = common.linkage, .visibility = common.visibility });
     15     @export(&sincosf, .{ .name = "sincosf", .linkage = common.linkage, .visibility = common.visibility });
     16     @export(&sincos, .{ .name = "sincos", .linkage = common.linkage, .visibility = common.visibility });
     17     @export(&__sincosx, .{ .name = "__sincosx", .linkage = common.linkage, .visibility = common.visibility });
     18     if (common.want_ppc_abi) {
     19         @export(&sincosq, .{ .name = "sincosf128", .linkage = common.linkage, .visibility = common.visibility });
     20     }
     21     @export(&sincosq, .{ .name = "sincosq", .linkage = common.linkage, .visibility = common.visibility });
     22     @export(&sincosl, .{ .name = "sincosl", .linkage = common.linkage, .visibility = common.visibility });
     23 }
     24 
     25 pub fn __sincosh(x: f16, r_sin: *f16, r_cos: *f16) callconv(.c) void {
     26     // TODO: more efficient implementation
     27     var big_sin: f32 = undefined;
     28     var big_cos: f32 = undefined;
     29     sincosf(x, &big_sin, &big_cos);
     30     r_sin.* = @as(f16, @floatCast(big_sin));
     31     r_cos.* = @as(f16, @floatCast(big_cos));
     32 }
     33 
     34 pub fn sincosf(x: f32, r_sin: *f32, r_cos: *f32) callconv(.c) void {
     35     const sc1pio2: f64 = 1.0 * math.pi / 2.0; // 0x3FF921FB, 0x54442D18
     36     const sc2pio2: f64 = 2.0 * math.pi / 2.0; // 0x400921FB, 0x54442D18
     37     const sc3pio2: f64 = 3.0 * math.pi / 2.0; // 0x4012D97C, 0x7F3321D2
     38     const sc4pio2: f64 = 4.0 * math.pi / 2.0; // 0x401921FB, 0x54442D18
     39 
     40     const pre_ix = @as(u32, @bitCast(x));
     41     const sign = pre_ix >> 31 != 0;
     42     const ix = pre_ix & 0x7fffffff;
     43 
     44     // |x| ~<= pi/4
     45     if (ix <= 0x3f490fda) {
     46         // |x| < 2**-12
     47         if (ix < 0x39800000) {
     48             // raise inexact if x!=0 and underflow if subnormal
     49             if (common.want_float_exceptions) {
     50                 if (ix < 0x00100000) {
     51                     mem.doNotOptimizeAway(x / 0x1p120);
     52                 } else {
     53                     mem.doNotOptimizeAway(x + 0x1p120);
     54                 }
     55             }
     56             r_sin.* = x;
     57             r_cos.* = 1.0;
     58             return;
     59         }
     60         r_sin.* = trig.__sindf(x);
     61         r_cos.* = trig.__cosdf(x);
     62         return;
     63     }
     64 
     65     // |x| ~<= 5*pi/4
     66     if (ix <= 0x407b53d1) {
     67         // |x| ~<= 3pi/4
     68         if (ix <= 0x4016cbe3) {
     69             if (sign) {
     70                 r_sin.* = -trig.__cosdf(x + sc1pio2);
     71                 r_cos.* = trig.__sindf(x + sc1pio2);
     72             } else {
     73                 r_sin.* = trig.__cosdf(sc1pio2 - x);
     74                 r_cos.* = trig.__sindf(sc1pio2 - x);
     75             }
     76             return;
     77         }
     78         //  -sin(x+c) is not correct if x+c could be 0: -0 vs +0
     79         r_sin.* = -trig.__sindf(if (sign) x + sc2pio2 else x - sc2pio2);
     80         r_cos.* = -trig.__cosdf(if (sign) x + sc2pio2 else x - sc2pio2);
     81         return;
     82     }
     83 
     84     // |x| ~<= 9*pi/4
     85     if (ix <= 0x40e231d5) {
     86         // |x| ~<= 7*pi/4
     87         if (ix <= 0x40afeddf) {
     88             if (sign) {
     89                 r_sin.* = trig.__cosdf(x + sc3pio2);
     90                 r_cos.* = -trig.__sindf(x + sc3pio2);
     91             } else {
     92                 r_sin.* = -trig.__cosdf(x - sc3pio2);
     93                 r_cos.* = trig.__sindf(x - sc3pio2);
     94             }
     95             return;
     96         }
     97         r_sin.* = trig.__sindf(if (sign) x + sc4pio2 else x - sc4pio2);
     98         r_cos.* = trig.__cosdf(if (sign) x + sc4pio2 else x - sc4pio2);
     99         return;
    100     }
    101 
    102     // sin(Inf or NaN) is NaN
    103     if (ix >= 0x7f800000) {
    104         const result = x - x;
    105         r_sin.* = result;
    106         r_cos.* = result;
    107         return;
    108     }
    109 
    110     // general argument reduction needed
    111     var y: f64 = undefined;
    112     const n = rem_pio2f(x, &y);
    113     const s = trig.__sindf(y);
    114     const c = trig.__cosdf(y);
    115     switch (n & 3) {
    116         0 => {
    117             r_sin.* = s;
    118             r_cos.* = c;
    119         },
    120         1 => {
    121             r_sin.* = c;
    122             r_cos.* = -s;
    123         },
    124         2 => {
    125             r_sin.* = -s;
    126             r_cos.* = -c;
    127         },
    128         else => {
    129             r_sin.* = -c;
    130             r_cos.* = s;
    131         },
    132     }
    133 }
    134 
    135 pub fn sincos(x: f64, r_sin: *f64, r_cos: *f64) callconv(.c) void {
    136     const ix = @as(u32, @truncate(@as(u64, @bitCast(x)) >> 32)) & 0x7fffffff;
    137 
    138     // |x| ~< pi/4
    139     if (ix <= 0x3fe921fb) {
    140         // if |x| < 2**-27 * sqrt(2)
    141         if (ix < 0x3e46a09e) {
    142             // raise inexact if x != 0 and underflow if subnormal
    143             if (common.want_float_exceptions) {
    144                 if (ix < 0x00100000) {
    145                     mem.doNotOptimizeAway(x / 0x1p120);
    146                 } else {
    147                     mem.doNotOptimizeAway(x + 0x1p120);
    148                 }
    149             }
    150             r_sin.* = x;
    151             r_cos.* = 1.0;
    152             return;
    153         }
    154         r_sin.* = trig.__sin(x, 0.0, 0);
    155         r_cos.* = trig.__cos(x, 0.0);
    156         return;
    157     }
    158 
    159     // sincos(Inf or NaN) is NaN
    160     if (ix >= 0x7ff00000) {
    161         const result = x - x;
    162         r_sin.* = result;
    163         r_cos.* = result;
    164         return;
    165     }
    166 
    167     // argument reduction needed
    168     var y: [2]f64 = undefined;
    169     const n = rem_pio2(x, &y);
    170     const s = trig.__sin(y[0], y[1], 1);
    171     const c = trig.__cos(y[0], y[1]);
    172     switch (n & 3) {
    173         0 => {
    174             r_sin.* = s;
    175             r_cos.* = c;
    176         },
    177         1 => {
    178             r_sin.* = c;
    179             r_cos.* = -s;
    180         },
    181         2 => {
    182             r_sin.* = -s;
    183             r_cos.* = -c;
    184         },
    185         else => {
    186             r_sin.* = -c;
    187             r_cos.* = s;
    188         },
    189     }
    190 }
    191 
    192 pub fn __sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
    193     // TODO: more efficient implementation
    194     //return sincos_generic(f80, x, r_sin, r_cos);
    195     var big_sin: f128 = undefined;
    196     var big_cos: f128 = undefined;
    197     sincosq(x, &big_sin, &big_cos);
    198     r_sin.* = @as(f80, @floatCast(big_sin));
    199     r_cos.* = @as(f80, @floatCast(big_cos));
    200 }
    201 
    202 pub fn sincosq(x: f128, r_sin: *f128, r_cos: *f128) callconv(.c) void {
    203     // TODO: more correct implementation
    204     //return sincos_generic(f128, x, r_sin, r_cos);
    205     var small_sin: f64 = undefined;
    206     var small_cos: f64 = undefined;
    207     sincos(@as(f64, @floatCast(x)), &small_sin, &small_cos);
    208     r_sin.* = small_sin;
    209     r_cos.* = small_cos;
    210 }
    211 
    212 pub fn sincosl(x: c_longdouble, r_sin: *c_longdouble, r_cos: *c_longdouble) callconv(.c) void {
    213     switch (@typeInfo(c_longdouble).float.bits) {
    214         16 => return __sincosh(x, r_sin, r_cos),
    215         32 => return sincosf(x, r_sin, r_cos),
    216         64 => return sincos(x, r_sin, r_cos),
    217         80 => return __sincosx(x, r_sin, r_cos),
    218         128 => return sincosq(x, r_sin, r_cos),
    219         else => @compileError("unreachable"),
    220     }
    221 }
    222 
    223 pub const rem_pio2_generic = @compileError("TODO");
    224 
    225 /// Ported from musl sincosl.c. Needs the following dependencies to be complete:
    226 /// * rem_pio2_generic ported from __rem_pio2l.c
    227 /// * trig.sin_generic ported from __sinl.c
    228 /// * trig.cos_generic ported from __cosl.c
    229 inline fn sincos_generic(comptime F: type, x: F, r_sin: *F, r_cos: *F) void {
    230     const sc1pio4: F = 1.0 * math.pi / 4.0;
    231     const bits = @typeInfo(F).float.bits;
    232     const I = std.meta.Int(.unsigned, bits);
    233     const ix = @as(I, @bitCast(x)) & (math.maxInt(I) >> 1);
    234     const se: u16 = @truncate(ix >> (bits - 16));
    235 
    236     if (se == 0x7fff) {
    237         const result = x - x;
    238         r_sin.* = result;
    239         r_cos.* = result;
    240         return;
    241     }
    242 
    243     if (@as(F, @bitCast(ix)) < sc1pio4) {
    244         if (se < 0x3fff - math.floatFractionalBits(F) - 1) {
    245             // raise underflow if subnormal
    246             if (se == 0) {
    247                 if (common.want_float_exceptions) mem.doNotOptimizeAway(x * 0x1p-120);
    248             }
    249             r_sin.* = x;
    250             // raise inexact if x!=0
    251             r_cos.* = 1.0 + x;
    252             return;
    253         }
    254         r_sin.* = trig.sin_generic(F, x, 0, 0);
    255         r_cos.* = trig.cos_generic(F, x, 0);
    256         return;
    257     }
    258 
    259     var y: [2]F = undefined;
    260     const n = rem_pio2_generic(F, x, &y);
    261     const s = trig.sin_generic(F, y[0], y[1], 1);
    262     const c = trig.cos_generic(F, y[0], y[1]);
    263     switch (n & 3) {
    264         0 => {
    265             r_sin.* = s;
    266             r_cos.* = c;
    267         },
    268         1 => {
    269             r_sin.* = c;
    270             r_cos.* = -s;
    271         },
    272         2 => {
    273             r_sin.* = -s;
    274             r_cos.* = -c;
    275         },
    276         else => {
    277             r_sin.* = -c;
    278             r_cos.* = s;
    279         },
    280     }
    281 }