authorgravatar for hi@mihaelm.commihael <hi@mihaelm.com> 2026-04-02 23:53:13+02:00
committergravatar for hi@mihaelm.commihael <hi@mihaelm.com> 2026-04-02 23:54:20+02:00
log4ccac1de416bff8846352ef3bf2fb592c5a419a9
tree989d270f4df185757eea5cd3c31cf6479c55cc0c
parentad10c7600793547393848528e7d4a608d9fde59e
signaturebadge-check Signed by SSH key SHA256:aoFoShdYLdrqMichqKXSSieTKUfACUIDJHsKc4V2tQg

`compiler_rt`: Make `long double` trig impls non-generic

5 files changed, 336 insertions(+), 236 deletions(-)

lib/compiler_rt/cos.zig+30-14
......@@ -123,36 +123,52 @@ pub fn cos(x: f64) callconv(.c) f64 {
123123 };
124124}
125125
126fn coslGeneric(comptime T: type, x: T) T {
126pub fn cosx(x: f80) callconv(.c) f80 {
127127 const se = ld.signExponent(x) & 0x7fff;
128128 if (se == 0x7fff) {
129129 return x - x;
130130 }
131131
132132 if (@abs(x) < trig.pi_4) {
133 if (se < 0x3fff - math.floatMantissaBits(T)) {
133 if (se < 0x3fff - math.floatMantissaBits(f80)) {
134134 // raise inexact if x!=0
135135 return 1.0 + x;
136136 }
137 return trig.cosl(T, x, 0.0);
137 return trig.cosx(x, 0.0);
138138 }
139139
140 var y: [2]T = undefined;
141 const n = rem_pio2l(T, x, &y);
140 var y: [2]f80 = undefined;
141 const n = rem_pio2l(f80, x, &y);
142142 return switch (n & 3) {
143 0 => trig.cosl(T, y[0], y[1]),
144 1 => -trig.sinl(T, y[0], y[1], 1),
145 2 => -trig.cosl(T, y[0], y[1]),
146 else => trig.sinl(T, y[0], y[1], 1),
143 0 => trig.cosx(y[0], y[1]),
144 1 => -trig.sinx(y[0], y[1], 1),
145 2 => -trig.cosx(y[0], y[1]),
146 else => trig.sinx(y[0], y[1], 1),
147147 };
148148}
149149
150pub fn cosx(x: f80) callconv(.c) f80 {
151 return coslGeneric(f80, x);
152}
153
154150pub fn cosq(x: f128) callconv(.c) f128 {
155 return coslGeneric(f128, x);
151 const se = ld.signExponent(x) & 0x7fff;
152 if (se == 0x7fff) {
153 return x - x;
154 }
155
156 if (@abs(x) < trig.pi_4) {
157 if (se < 0x3fff - math.floatMantissaBits(f128)) {
158 // raise inexact if x!=0
159 return 1.0 + x;
160 }
161 return trig.cosq(x, 0.0);
162 }
163
164 var y: [2]f128 = undefined;
165 const n = rem_pio2l(f128, x, &y);
166 return switch (n & 3) {
167 0 => trig.cosq(y[0], y[1]),
168 1 => -trig.sinq(y[0], y[1], 1),
169 2 => -trig.cosq(y[0], y[1]),
170 else => trig.sinq(y[0], y[1], 1),
171 };
156172}
157173
158174pub fn cosl(x: c_longdouble) callconv(.c) c_longdouble {
lib/compiler_rt/sin.zig+33-14
......@@ -133,39 +133,58 @@ pub fn sin(x: f64) callconv(.c) f64 {
133133 };
134134}
135135
136fn sinlGeneric(comptime T: type, x: T) T {
136fn sinx(x: f80) callconv(.c) f80 {
137137 const se = ld.signExponent(x) & 0x7fff;
138138 if (se == 0x7fff) {
139139 return x - x;
140140 }
141141
142142 if (@abs(x) < trig.pi_4) {
143 if (se < 0x3fff - (math.floatMantissaBits(T) / 2)) {
143 if (se < 0x3fff - (math.floatMantissaBits(f80) / 2)) {
144144 // raise inexact if x!=0 and underflow if subnormal
145145 if (compiler_rt.want_float_exceptions) {
146146 mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
147147 }
148148 return x;
149149 }
150 return trig.sinl(T, x, 0.0, 0);
150 return trig.sinx(x, 0.0, 0);
151151 }
152152
153 var y: [2]T = undefined;
154 const n = rem_pio2l(T, x, &y);
153 var y: [2]f80 = undefined;
154 const n = rem_pio2l(f80, x, &y);
155155 return switch (n & 3) {
156 0 => trig.sinl(T, y[0], y[1], 1),
157 1 => trig.cosl(T, y[0], y[1]),
158 2 => -trig.sinl(T, y[0], y[1], 1),
159 else => -trig.cosl(T, y[0], y[1]),
156 0 => trig.sinx(y[0], y[1], 1),
157 1 => trig.cosx(y[0], y[1]),
158 2 => -trig.sinx(y[0], y[1], 1),
159 else => -trig.cosx(y[0], y[1]),
160160 };
161161}
162162
163pub fn sinx(x: f80) callconv(.c) f80 {
164 return sinlGeneric(f80, x);
165}
166
167163pub fn sinq(x: f128) callconv(.c) f128 {
168 return sinlGeneric(f128, x);
164 const se = ld.signExponent(x) & 0x7fff;
165 if (se == 0x7fff) {
166 return x - x;
167 }
168
169 if (@abs(x) < trig.pi_4) {
170 if (se < 0x3fff - (math.floatMantissaBits(f128) / 2)) {
171 // raise inexact if x!=0 and underflow if subnormal
172 if (compiler_rt.want_float_exceptions) {
173 mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
174 }
175 return x;
176 }
177 return trig.sinq(x, 0.0, 0);
178 }
179
180 var y: [2]f128 = undefined;
181 const n = rem_pio2l(f128, x, &y);
182 return switch (n & 3) {
183 0 => trig.sinq(y[0], y[1], 1),
184 1 => trig.cosq(y[0], y[1]),
185 2 => -trig.sinq(y[0], y[1], 1),
186 else => -trig.cosq(y[0], y[1]),
187 };
169188}
170189
171190pub fn sinl(x: c_longdouble) callconv(.c) c_longdouble {
lib/compiler_rt/sincos.zig+54-17
......@@ -192,11 +192,7 @@ pub fn sincos(x: f64, r_sin: *f64, r_cos: *f64) callconv(.c) void {
192192 }
193193}
194194
195fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
196 if (T != f80 and T != f128) {
197 @compileError("`sincoslGeneric` implemented only for `f80` and `f128`, got: " ++ @typeName(T));
198 }
199
195pub fn sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
200196 const se = ld.signExponent(x) & 0x7fff;
201197 if (se == 0x7fff) {
202198 const result = x - x;
......@@ -206,7 +202,7 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
206202 }
207203
208204 if (@abs(x) < trig.pi_4) {
209 if (se < 0x3fff - math.floatMantissaBits(T)) {
205 if (se < 0x3fff - math.floatMantissaBits(f80)) {
210206 // raise underflow if subnormal
211207 if (compiler_rt.want_float_exceptions and se == 0) {
212208 mem.doNotOptimizeAway(x * 0x1p-120);
......@@ -216,15 +212,15 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
216212 r_cos.* = 1.0 + x;
217213 return;
218214 }
219 r_sin.* = trig.sinl(T, x, 0.0, 0);
220 r_cos.* = trig.cosl(T, x, 0.0);
215 r_sin.* = trig.sinx(x, 0.0, 0);
216 r_cos.* = trig.cosx(x, 0.0);
221217 return;
222218 }
223219
224 var y: [2]T = undefined;
225 const n = rem_pio2l(T, x, &y);
226 const s = trig.sinl(T, y[0], y[1], 1);
227 const c = trig.cosl(T, y[0], y[1]);
220 var y: [2]f80 = undefined;
221 const n = rem_pio2l(f80, x, &y);
222 const s = trig.sinx(y[0], y[1], 1);
223 const c = trig.cosx(y[0], y[1]);
228224 switch (n & 3) {
229225 0 => {
230226 r_sin.* = s;
......@@ -245,12 +241,53 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
245241 }
246242}
247243
248pub fn sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
249 return sincoslGeneric(f80, x, r_sin, r_cos);
250}
251
252244pub fn sincosq(x: f128, r_sin: *f128, r_cos: *f128) callconv(.c) void {
253 return sincoslGeneric(f128, x, r_sin, r_cos);
245 const se = ld.signExponent(x) & 0x7fff;
246 if (se == 0x7fff) {
247 const result = x - x;
248 r_sin.* = result;
249 r_cos.* = result;
250 return;
251 }
252
253 if (@abs(x) < trig.pi_4) {
254 if (se < 0x3fff - math.floatMantissaBits(f128)) {
255 // raise underflow if subnormal
256 if (compiler_rt.want_float_exceptions and se == 0) {
257 mem.doNotOptimizeAway(x * 0x1p-120);
258 }
259 r_sin.* = x;
260 // raise inexact if x!=0
261 r_cos.* = 1.0 + x;
262 return;
263 }
264 r_sin.* = trig.sinq(x, 0.0, 0);
265 r_cos.* = trig.cosq(x, 0.0);
266 return;
267 }
268
269 var y: [2]f128 = undefined;
270 const n = rem_pio2l(f128, x, &y);
271 const s = trig.sinq(y[0], y[1], 1);
272 const c = trig.cosq(y[0], y[1]);
273 switch (n & 3) {
274 0 => {
275 r_sin.* = s;
276 r_cos.* = c;
277 },
278 1 => {
279 r_sin.* = c;
280 r_cos.* = -s;
281 },
282 2 => {
283 r_sin.* = -s;
284 r_cos.* = -c;
285 },
286 else => {
287 r_sin.* = -c;
288 r_cos.* = s;
289 },
290 }
254291}
255292
256293pub fn sincosl(x: c_longdouble, r_sin: *c_longdouble, r_cos: *c_longdouble) callconv(.c) void {
lib/compiler_rt/tan.zig+24-15
......@@ -120,37 +120,46 @@ pub fn tan(x: f64) callconv(.c) f64 {
120120 return kernel.tan(y[0], y[1], n & 1 != 0);
121121}
122122
123fn tanlGeneric(comptime T: type, x: T) T {
124 if (!(T == f80 or T == f128)) {
125 @compileError("`tanlGeneric` implemented only for `f80` and `f128`, got: " ++ T);
126 }
127
123pub fn tanx(x: f80) callconv(.c) f80 {
128124 const se = ld.signExponent(x) & 0x7fff;
129125 if (se == 0x7fff) {
130126 return x - x;
131127 }
132128
133129 if (@abs(x) < kernel.pi_4) {
134 if (se < 0x3fff - math.floatMantissaBits(T) / 2) {
130 if (se < 0x3fff - math.floatMantissaBits(f80) / 2) {
135131 if (compiler_rt.want_float_exceptions) {
136132 mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
137133 }
138134 return x;
139135 }
140 return kernel.tanl(T, x, 0.0, 0);
136 return kernel.tanx(x, 0.0, 0);
141137 }
142138
143 var y: [2]T = undefined;
144 const n = rem_pio2l(T, x, &y);
145 return kernel.tanl(T, y[0], y[1], n & 1);
146}
147
148pub fn tanx(x: f80) callconv(.c) f80 {
149 return tanlGeneric(f80, x);
139 var y: [2]f80 = undefined;
140 const n = rem_pio2l(f80, x, &y);
141 return kernel.tanx(y[0], y[1], n & 1);
150142}
151143
152144pub fn tanq(x: f128) callconv(.c) f128 {
153 return tanlGeneric(f128, x);
145 const se = ld.signExponent(x) & 0x7fff;
146 if (se == 0x7fff) {
147 return x - x;
148 }
149
150 if (@abs(x) < kernel.pi_4) {
151 if (se < 0x3fff - math.floatMantissaBits(f128) / 2) {
152 if (compiler_rt.want_float_exceptions) {
153 mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
154 }
155 return x;
156 }
157 return kernel.tanq(x, 0.0, 0);
158 }
159
160 var y: [2]f128 = undefined;
161 const n = rem_pio2l(f128, x, &y);
162 return kernel.tanq(y[0], y[1], n & 1);
154163}
155164
156165pub fn tanl(x: c_longdouble) callconv(.c) c_longdouble {
lib/compiler_rt/trig.zig+195-176
......@@ -80,49 +80,43 @@ pub fn cosdf(x: f64) f32 {
8080 return @floatCast(((1.0 + z * C0) + w * C1) + (w * z) * r);
8181}
8282
83pub fn cosl(comptime T: type, x: T, y: T) T {
84 const impl = switch (T) {
85 f80 => struct {
86 const C1: T = 0.0416666666666666666136;
87
88 const C2: f64 = -0.0013888888888888874;
89 const C3: f64 = 0.000024801587301571716;
90 const C4: f64 = -0.00000027557319215507120;
91 const C5: f64 = 0.0000000020876754400407278;
92 const C6: f64 = -1.1470297442401303e-11;
93 const C7: f64 = 4.7383039476436467e-14;
94
95 inline fn poly(z: T) T {
96 return z * (C1 + z * (C2 + z * (C3 + z * (C4 +
97 z * (C5 + z * (C6 + z * C7))))));
98 }
99 },
100 f128 => struct {
101 const C1: T = 0.04166666666666666666666666666666658424671;
102 const C2: T = -0.001388888888888888888888888888863490893732;
103 const C3: T = 0.00002480158730158730158730158600795304914210;
104 const C4: T = -0.2755731922398589065255474947078934284324e-6;
105 const C5: T = 0.2087675698786809897659225313136400793948e-8;
106 const C6: T = -0.1147074559772972315817149986812031204775e-10;
107 const C7: T = 0.4779477332386808976875457937252120293400e-13;
108
109 const C8: f64 = -0.1561920696721507929516718307820958119868e-15;
110 const C9: f64 = 0.4110317413744594971475941557607804508039e-18;
111 const C10: f64 = -0.8896592467191938803288521958313920156409e-21;
112 const C11: f64 = 0.1601061435794535138244346256065192782581e-23;
113
114 inline fn poly(z: T) T {
115 return z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
116 z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
117 }
118 },
119 else => @compileError("cosl supports only f80 and f128, got: " ++ @typeName(T)),
120 };
83pub fn cosx(x: f80, y: f80) f80 {
84 const C1: f80 = 0.0416666666666666666136;
85 const C2: f64 = -0.0013888888888888874;
86 const C3: f64 = 0.000024801587301571716;
87 const C4: f64 = -0.00000027557319215507120;
88 const C5: f64 = 0.0000000020876754400407278;
89 const C6: f64 = -1.1470297442401303e-11;
90 const C7: f64 = 4.7383039476436467e-14;
12191
12292 const z = x * x;
123 const r = impl.poly(z);
93 const r = z * (C1 + z * (C2 + z * (C3 + z * (C4 +
94 z * (C5 + z * (C6 + z * C7))))));
12495 const hz = 0.5 * z;
12596 const w = 1.0 - hz;
97
98 return w + (((1.0 - w) - hz) + (z * r - x * y));
99}
100
101pub fn cosq(x: f128, y: f128) f128 {
102 const C1: f128 = 0.04166666666666666666666666666666658424671;
103 const C2: f128 = -0.001388888888888888888888888888863490893732;
104 const C3: f128 = 0.00002480158730158730158730158600795304914210;
105 const C4: f128 = -0.2755731922398589065255474947078934284324e-6;
106 const C5: f128 = 0.2087675698786809897659225313136400793948e-8;
107 const C6: f128 = -0.1147074559772972315817149986812031204775e-10;
108 const C7: f128 = 0.4779477332386808976875457937252120293400e-13;
109 const C8: f64 = -0.1561920696721507929516718307820958119868e-15;
110 const C9: f64 = 0.4110317413744594971475941557607804508039e-18;
111 const C10: f64 = -0.8896592467191938803288521958313920156409e-21;
112 const C11: f64 = 0.1601061435794535138244346256065192782581e-23;
113
114 const z = x * x;
115 const r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
116 z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
117 const hz = 0.5 * z;
118 const w = 1.0 - hz;
119
126120 return w + (((1.0 - w) - hz) + (z * r - x * y));
127121}
128122
......@@ -172,58 +166,6 @@ pub fn sin(x: f64, y: f64, iy: i32) f64 {
172166 }
173167}
174168
175pub fn sinl(comptime T: type, x: T, y: T, iy: i32) T {
176 const impl = switch (T) {
177 f80 => struct {
178 const S1: T = -0.166666666666666666671;
179
180 const S2: f64 = 0.0083333333333333332;
181 const S3: f64 = -0.00019841269841269427;
182 const S4: f64 = 0.0000027557319223597490;
183 const S5: f64 = -0.000000025052108218074604;
184 const S6: f64 = 1.6059006598854211e-10;
185 const S7: f64 = -7.6429779983024564e-13;
186 const S8: f64 = 2.6174587166648325e-15;
187
188 inline fn poly(z: T) T {
189 return S2 + z * (S3 + z * (S4 + z * (S5 +
190 z * (S6 + z * (S7 + z * S8)))));
191 }
192 },
193 f128 => struct {
194 const S1: T = -0.16666666666666666666666666666666666606732416116558;
195 const S2: T = 0.0083333333333333333333333333333331135404851288270047;
196 const S3: T = -0.00019841269841269841269841269839935785325638310428717;
197 const S4: T = 0.27557319223985890652557316053039946268333231205686e-5;
198 const S5: T = -0.25052108385441718775048214826384312253862930064745e-7;
199 const S6: T = 0.16059043836821614596571832194524392581082444805729e-9;
200 const S7: T = -0.76471637318198151807063387954939213287488216303768e-12;
201 const S8: T = 0.28114572543451292625024967174638477283187397621303e-14;
202
203 const S9: f64 = -0.82206352458348947812512122163446202498005154296863e-17;
204 const S10: f64 = 0.19572940011906109418080609928334380560135358385256e-19;
205 const S11: f64 = -0.38680813379701966970673724299207480965452616911420e-22;
206 const S12: f64 = 0.64038150078671872796678569586315881020659912139412e-25;
207
208 inline fn poly(z: T) T {
209 return S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
210 z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
211 }
212 },
213 else => @compileError("sinl supports only f80 and f128, got: " ++ @typeName(T)),
214 };
215
216 const z = x * x;
217 const v = z * x;
218 const r = impl.poly(z);
219
220 if (iy == 0) {
221 return x + v * (impl.S1 + z * r);
222 }
223
224 return x - ((z * (0.5 * y - v * r) - y) - v * impl.S1);
225}
226
227169pub fn sindf(x: f64) f32 {
228170 // |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]).
229171 const S1 = -0x15555554cbac77.0p-55; // -0.166666666416265235595
......@@ -239,6 +181,52 @@ pub fn sindf(x: f64) f32 {
239181 return @floatCast((x + s * (S1 + z * S2)) + s * w * r);
240182}
241183
184pub fn sinx(x: f80, y: f80, iy: i32) f80 {
185 const S1: f80 = -0.166666666666666666671;
186 const S2: f64 = 0.0083333333333333332;
187 const S3: f64 = -0.00019841269841269427;
188 const S4: f64 = 0.0000027557319223597490;
189 const S5: f64 = -0.000000025052108218074604;
190 const S6: f64 = 1.6059006598854211e-10;
191 const S7: f64 = -7.6429779983024564e-13;
192 const S8: f64 = 2.6174587166648325e-15;
193
194 const z = x * x;
195 const v = z * x;
196 const r = S2 + z * (S3 + z * (S4 + z * (S5 +
197 z * (S6 + z * (S7 + z * S8)))));
198
199 if (iy == 0)
200 return x + v * (S1 + z * r);
201
202 return x - ((z * (0.5 * y - v * r) - y) - v * S1);
203}
204
205pub fn sinq(x: f128, y: f128, iy: i32) f128 {
206 const S1: f128 = -0.16666666666666666666666666666666666606732416116558;
207 const S2: f128 = 0.0083333333333333333333333333333331135404851288270047;
208 const S3: f128 = -0.00019841269841269841269841269839935785325638310428717;
209 const S4: f128 = 0.27557319223985890652557316053039946268333231205686e-5;
210 const S5: f128 = -0.25052108385441718775048214826384312253862930064745e-7;
211 const S6: f128 = 0.16059043836821614596571832194524392581082444805729e-9;
212 const S7: f128 = -0.76471637318198151807063387954939213287488216303768e-12;
213 const S8: f128 = 0.28114572543451292625024967174638477283187397621303e-14;
214 const S9: f64 = -0.82206352458348947812512122163446202498005154296863e-17;
215 const S10: f64 = 0.19572940011906109418080609928334380560135358385256e-19;
216 const S11: f64 = -0.38680813379701966970673724299207480965452616911420e-22;
217 const S12: f64 = 0.64038150078671872796678569586315881020659912139412e-25;
218
219 const z = x * x;
220 const v = z * x;
221 const r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
222 z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
223
224 if (iy == 0)
225 return x + v * (S1 + z * r);
226
227 return x - ((z * (0.5 * y - v * r) - y) - v * S1);
228}
229
242230/// kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
243231/// Input x is assumed to be bounded by ~pi/4 in magnitude.
244232/// Input y is the tail of x.
......@@ -377,88 +365,112 @@ pub fn tandf(x: f64, odd: bool) f32 {
377365 return @floatCast(if (odd) -1.0 / r0 else r0);
378366}
379367
380pub fn tanl(comptime T: type, x_: T, y_: T, odd: i32) T {
368pub fn tanx(x_: f80, y_: f80, odd: i32) f80 {
369 const pio4: f80 = 0.785398163397448309628;
370 const pio4lo: f80 = -1.25413940316708300586e-20;
371
372 const T3: f80 = 0.333333333333333333180;
373 const T5: f80 = 0.133333333333333372290;
374 const T7: f80 = 0.0539682539682504975744;
375 const T9: f64 = 0.021869488536312216;
376 const T11: f64 = 0.0088632355256619590;
377 const T13: f64 = 0.0035921281113786528;
378 const T15: f64 = 0.0014558334756312418;
379 const T17: f64 = 0.00059003538700862256;
380 const T19: f64 = 0.00023907843576635544;
381 const T21: f64 = 0.000097154625656538905;
382 const T23: f64 = 0.000038440165747303162;
383 const T25: f64 = 0.000018082171885432524;
384 const T27: f64 = 0.0000024196006108814377;
385 const T29: f64 = 0.0000078293456938132840;
386 const T31: f64 = -0.0000032609076735050182;
387 const T33: f64 = 0.0000023261313142559411;
388
389 var x = x_;
390 var y = y_;
391 const big = @abs(x) >= 0.67434;
392 var sign: i8 = 0;
393
394 if (big) {
395 if (x < 0) {
396 sign = -1;
397 x = -x;
398 y = -y;
399 }
400 x = (pio4 - x) + (pio4lo - y);
401 y = 0.0;
402 }
403
404 var z = x * x;
405 var w = z * z;
406
407 var r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
408 w * (T25 + w * (T29 + w * T33))))));
409
410 var v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
411 w * (T27 + w * T31))))));
412
413 var s = z * x;
414 r = y + z * (s * (r + v) + y) + T3 * s;
415 w = x + r;
416
417 if (big) {
418 s = @as(f80, @floatFromInt(1 - 2 * odd));
419 v = s - 2.0 * (x + (r - w * w / (w + s)));
420 return if (sign == -1) -v else v;
421 }
422
423 if (odd == 0) {
424 return w;
425 }
426
427 // if allow error up to 2 ulp, simply return
428 // -1.0 / (x+r) here
429 //
430 // compute -1.0 / (x+r) accurately
431 z = w + 0x1p32 - 0x1p32;
432 v = r - (z - x);
433 const a = -1.0 / w;
434 const t = a + 0x1p32 - 0x1p32;
435 s = 1.0 + t * z;
436 return t + a * (s + t * v);
437}
438
439pub fn tanq(x_: f128, y_: f128, odd: i32) f128 {
440 const pio4: f128 = 0x1.921fb54442d18469898cc51701b8p-1;
441 const pio4lo: f128 = 0x1.cd129024e088a67cc74020bbea60p-116;
442
443 const T3: f128 = 0x1.5555555555555555555555555553p-2;
444 const T5: f128 = 0x1.1111111111111111111111111eb5p-3;
445 const T7: f128 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5;
446 const T9: f128 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6;
447 const T11: f128 = 0x1.226e355e6c23c8f5b4f5762322eep-7;
448 const T13: f128 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9;
449 const T15: f128 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10;
450 const T17: f128 = 0x1.355824803674477dfcf726649efep-11;
451 const T19: f128 = 0x1.f57d7734d1656e0aceb716f614c2p-13;
452 const T21: f128 = 0x1.967e18afcb180ed942dfdc518d6cp-14;
453 const T23: f128 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15;
454 const T25: f128 = 0x1.0b132d39f055c81be49eff7afd50p-16;
455 const T27: f128 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18;
456 const T29: f128 = 0x1.5ef2daf21d1113df38d0fbc00267p-19;
457 const T31: f128 = 0x1.1c77d6eac0234988cdaa04c96626p-20;
458 const T33: f128 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22;
459 const T35: f128 = 0x1.75c7357d0298c01a31d0a6f7d518p-23;
460 const T37: f128 = 0x1.2f3190f4718a9a520f98f50081fcp-24;
461 const T39: f64 = 0.000000028443389121318352;
462 const T41: f64 = 0.000000011981013102001973;
463 const T43: f64 = 0.0000000038303578044958070;
464 const T45: f64 = 0.0000000034664378216909893;
465 const T47: f64 = -0.0000000015090641701997785;
466 const T49: f64 = 0.0000000029449552300483952;
467 const T51: f64 = -0.0000000022006995706097711;
468 const T53: f64 = 0.0000000015468200913196612;
469 const T55: f64 = -0.00000000061311613386849674;
470 const T57: f64 = 1.4912469681508012e-10;
471
381472 var x = x_;
382473 var y = y_;
383 const impl = switch (T) {
384 f80 => struct {
385 const pio4: T = 0.785398163397448309628;
386 const pio4lo: T = -1.25413940316708300586e-20;
387
388 const T3: T = 0.333333333333333333180;
389 const T5: T = 0.133333333333333372290;
390 const T7: T = 0.0539682539682504975744;
391 const T9: f64 = 0.021869488536312216;
392 const T11: f64 = 0.0088632355256619590;
393 const T13: f64 = 0.0035921281113786528;
394 const T15: f64 = 0.0014558334756312418;
395 const T17: f64 = 0.00059003538700862256;
396 const T19: f64 = 0.00023907843576635544;
397 const T21: f64 = 0.000097154625656538905;
398 const T23: f64 = 0.000038440165747303162;
399 const T25: f64 = 0.000018082171885432524;
400 const T27: f64 = 0.0000024196006108814377;
401 const T29: f64 = 0.0000078293456938132840;
402 const T31: f64 = -0.0000032609076735050182;
403 const T33: f64 = 0.0000023261313142559411;
404
405 inline fn rpoly(w: T) T {
406 return T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
407 w * (T25 + w * (T29 + w * T33))))));
408 }
409
410 inline fn vpoly(w: T) T {
411 return T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
412 w * (T27 + w * T31)))));
413 }
414 },
415 f128 => struct {
416 const pio4: T = 0x1.921fb54442d18469898cc51701b8p-1;
417 const pio4lo: T = 0x1.cd129024e088a67cc74020bbea60p-116;
418
419 const T3: T = 0x1.5555555555555555555555555553p-2;
420 const T5: T = 0x1.1111111111111111111111111eb5p-3;
421 const T7: T = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5;
422 const T9: T = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6;
423 const T11: T = 0x1.226e355e6c23c8f5b4f5762322eep-7;
424 const T13: T = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9;
425 const T15: T = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10;
426 const T17: T = 0x1.355824803674477dfcf726649efep-11;
427 const T19: T = 0x1.f57d7734d1656e0aceb716f614c2p-13;
428 const T21: T = 0x1.967e18afcb180ed942dfdc518d6cp-14;
429 const T23: T = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15;
430 const T25: T = 0x1.0b132d39f055c81be49eff7afd50p-16;
431 const T27: T = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18;
432 const T29: T = 0x1.5ef2daf21d1113df38d0fbc00267p-19;
433 const T31: T = 0x1.1c77d6eac0234988cdaa04c96626p-20;
434 const T33: T = 0x1.cd2a5a292b180e0bdd701057dfe3p-22;
435 const T35: T = 0x1.75c7357d0298c01a31d0a6f7d518p-23;
436 const T37: T = 0x1.2f3190f4718a9a520f98f50081fcp-24;
437 const T39: f64 = 0.000000028443389121318352;
438 const T41: f64 = 0.000000011981013102001973;
439 const T43: f64 = 0.0000000038303578044958070;
440 const T45: f64 = 0.0000000034664378216909893;
441 const T47: f64 = -0.0000000015090641701997785;
442 const T49: f64 = 0.0000000029449552300483952;
443 const T51: f64 = -0.0000000022006995706097711;
444 const T53: f64 = 0.0000000015468200913196612;
445 const T55: f64 = -0.00000000061311613386849674;
446 const T57: f64 = 1.4912469681508012e-10;
447
448 inline fn rpoly(w: T) T {
449 return T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
450 w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 +
451 w * (T45 + w * (T49 + w * (T53 + w * T57))))))))))));
452 }
453
454 inline fn vpoly(w: T) T {
455 return T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
456 w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 +
457 w * (T47 + w * (T51 + w * T55)))))))))));
458 }
459 },
460 else => @compileError("tanl supports only f80 and f128, got: " ++ @typeName(T)),
461 };
462474
463475 const big = @abs(x) >= 0.67434;
464476 var sign: i8 = 0;
......@@ -469,20 +481,27 @@ pub fn tanl(comptime T: type, x_: T, y_: T, odd: i32) T {
469481 x = -x;
470482 y = -y;
471483 }
472 x = (impl.pio4 - x) + (impl.pio4lo - y);
484 x = (pio4 - x) + (pio4lo - y);
473485 y = 0.0;
474486 }
475487
476488 var z = x * x;
477489 var w = z * z;
478 var r = impl.rpoly(w);
479 var v = z * impl.vpoly(w);
490
491 var r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
492 w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 +
493 w * (T45 + w * (T49 + w * (T53 + w * T57))))))))))));
494
495 var v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
496 w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 +
497 w * (T47 + w * (T51 + w * T55))))))))))));
498
480499 var s = z * x;
481 r = y + z * (s * (r + v) + y) + impl.T3 * s;
500 r = y + z * (s * (r + v) + y) + T3 * s;
482501 w = x + r;
483502
484503 if (big) {
485 s = @as(T, @floatFromInt(1 - 2 * odd));
504 s = @as(f128, @floatFromInt(1 - 2 * odd));
486505 v = s - 2.0 * (x + (r - w * w / (w + s)));
487506 return if (sign == -1) -v else v;
488507 }