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compiler_rt: Make long double trig impls non-generic
This commit is contained in:
mihael
parent
ad10c76007
commit
4ccac1de41
@ -123,36 +123,52 @@ pub fn cos(x: f64) callconv(.c) f64 {
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};
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}
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fn coslGeneric(comptime T: type, x: T) T {
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pub fn cosx(x: f80) callconv(.c) f80 {
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(T)) {
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if (se < 0x3fff - math.floatMantissaBits(f80)) {
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// raise inexact if x!=0
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return 1.0 + x;
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}
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return trig.cosl(T, x, 0.0);
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return trig.cosx(x, 0.0);
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}
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var y: [2]T = undefined;
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const n = rem_pio2l(T, x, &y);
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var y: [2]f80 = undefined;
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const n = rem_pio2l(f80, x, &y);
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return switch (n & 3) {
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0 => trig.cosl(T, y[0], y[1]),
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1 => -trig.sinl(T, y[0], y[1], 1),
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2 => -trig.cosl(T, y[0], y[1]),
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else => trig.sinl(T, y[0], y[1], 1),
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0 => trig.cosx(y[0], y[1]),
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1 => -trig.sinx(y[0], y[1], 1),
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2 => -trig.cosx(y[0], y[1]),
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else => trig.sinx(y[0], y[1], 1),
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};
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}
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pub fn cosx(x: f80) callconv(.c) f80 {
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return coslGeneric(f80, x);
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}
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pub fn cosq(x: f128) callconv(.c) f128 {
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return coslGeneric(f128, x);
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(f128)) {
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// raise inexact if x!=0
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return 1.0 + x;
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}
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return trig.cosq(x, 0.0);
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}
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var y: [2]f128 = undefined;
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const n = rem_pio2l(f128, x, &y);
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return switch (n & 3) {
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0 => trig.cosq(y[0], y[1]),
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1 => -trig.sinq(y[0], y[1], 1),
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2 => -trig.cosq(y[0], y[1]),
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else => trig.sinq(y[0], y[1], 1),
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};
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}
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pub fn cosl(x: c_longdouble) callconv(.c) c_longdouble {
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@ -133,39 +133,58 @@ pub fn sin(x: f64) callconv(.c) f64 {
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};
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}
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fn sinlGeneric(comptime T: type, x: T) T {
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fn sinx(x: f80) callconv(.c) f80 {
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - (math.floatMantissaBits(T) / 2)) {
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if (se < 0x3fff - (math.floatMantissaBits(f80) / 2)) {
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// raise inexact if x!=0 and underflow if subnormal
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if (compiler_rt.want_float_exceptions) {
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mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
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}
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return x;
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}
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return trig.sinl(T, x, 0.0, 0);
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return trig.sinx(x, 0.0, 0);
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}
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var y: [2]T = undefined;
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const n = rem_pio2l(T, x, &y);
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var y: [2]f80 = undefined;
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const n = rem_pio2l(f80, x, &y);
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return switch (n & 3) {
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0 => trig.sinl(T, y[0], y[1], 1),
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1 => trig.cosl(T, y[0], y[1]),
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2 => -trig.sinl(T, y[0], y[1], 1),
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else => -trig.cosl(T, y[0], y[1]),
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0 => trig.sinx(y[0], y[1], 1),
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1 => trig.cosx(y[0], y[1]),
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2 => -trig.sinx(y[0], y[1], 1),
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else => -trig.cosx(y[0], y[1]),
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};
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}
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pub fn sinx(x: f80) callconv(.c) f80 {
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return sinlGeneric(f80, x);
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}
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pub fn sinq(x: f128) callconv(.c) f128 {
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return sinlGeneric(f128, x);
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - (math.floatMantissaBits(f128) / 2)) {
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// raise inexact if x!=0 and underflow if subnormal
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if (compiler_rt.want_float_exceptions) {
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mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
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}
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return x;
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}
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return trig.sinq(x, 0.0, 0);
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}
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var y: [2]f128 = undefined;
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const n = rem_pio2l(f128, x, &y);
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return switch (n & 3) {
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0 => trig.sinq(y[0], y[1], 1),
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1 => trig.cosq(y[0], y[1]),
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2 => -trig.sinq(y[0], y[1], 1),
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else => -trig.cosq(y[0], y[1]),
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};
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}
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pub fn sinl(x: c_longdouble) callconv(.c) c_longdouble {
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@ -192,11 +192,7 @@ pub fn sincos(x: f64, r_sin: *f64, r_cos: *f64) callconv(.c) void {
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}
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}
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fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
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if (T != f80 and T != f128) {
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@compileError("`sincoslGeneric` implemented only for `f80` and `f128`, got: " ++ @typeName(T));
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}
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pub fn sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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const result = x - x;
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@ -206,7 +202,7 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(T)) {
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if (se < 0x3fff - math.floatMantissaBits(f80)) {
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// raise underflow if subnormal
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if (compiler_rt.want_float_exceptions and se == 0) {
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mem.doNotOptimizeAway(x * 0x1p-120);
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@ -216,15 +212,15 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
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r_cos.* = 1.0 + x;
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return;
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}
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r_sin.* = trig.sinl(T, x, 0.0, 0);
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r_cos.* = trig.cosl(T, x, 0.0);
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r_sin.* = trig.sinx(x, 0.0, 0);
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r_cos.* = trig.cosx(x, 0.0);
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return;
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}
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var y: [2]T = undefined;
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const n = rem_pio2l(T, x, &y);
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const s = trig.sinl(T, y[0], y[1], 1);
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const c = trig.cosl(T, y[0], y[1]);
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var y: [2]f80 = undefined;
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const n = rem_pio2l(f80, x, &y);
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const s = trig.sinx(y[0], y[1], 1);
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const c = trig.cosx(y[0], y[1]);
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switch (n & 3) {
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0 => {
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r_sin.* = s;
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@ -245,12 +241,53 @@ fn sincoslGeneric(comptime T: type, x: T, r_sin: *T, r_cos: *T) void {
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}
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}
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pub fn sincosx(x: f80, r_sin: *f80, r_cos: *f80) callconv(.c) void {
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return sincoslGeneric(f80, x, r_sin, r_cos);
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}
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pub fn sincosq(x: f128, r_sin: *f128, r_cos: *f128) callconv(.c) void {
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return sincoslGeneric(f128, x, r_sin, r_cos);
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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const result = x - x;
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r_sin.* = result;
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r_cos.* = result;
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return;
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}
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if (@abs(x) < trig.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(f128)) {
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// raise underflow if subnormal
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if (compiler_rt.want_float_exceptions and se == 0) {
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mem.doNotOptimizeAway(x * 0x1p-120);
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}
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r_sin.* = x;
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// raise inexact if x!=0
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r_cos.* = 1.0 + x;
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return;
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}
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r_sin.* = trig.sinq(x, 0.0, 0);
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r_cos.* = trig.cosq(x, 0.0);
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return;
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}
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var y: [2]f128 = undefined;
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const n = rem_pio2l(f128, x, &y);
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const s = trig.sinq(y[0], y[1], 1);
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const c = trig.cosq(y[0], y[1]);
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switch (n & 3) {
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0 => {
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r_sin.* = s;
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r_cos.* = c;
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},
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1 => {
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r_sin.* = c;
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r_cos.* = -s;
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},
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2 => {
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r_sin.* = -s;
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r_cos.* = -c;
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},
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else => {
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r_sin.* = -c;
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r_cos.* = s;
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},
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}
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}
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pub fn sincosl(x: c_longdouble, r_sin: *c_longdouble, r_cos: *c_longdouble) callconv(.c) void {
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@ -120,37 +120,46 @@ pub fn tan(x: f64) callconv(.c) f64 {
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return kernel.tan(y[0], y[1], n & 1 != 0);
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}
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fn tanlGeneric(comptime T: type, x: T) T {
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if (!(T == f80 or T == f128)) {
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@compileError("`tanlGeneric` implemented only for `f80` and `f128`, got: " ++ T);
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}
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pub fn tanx(x: f80) callconv(.c) f80 {
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < kernel.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(T) / 2) {
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if (se < 0x3fff - math.floatMantissaBits(f80) / 2) {
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if (compiler_rt.want_float_exceptions) {
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mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
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}
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return x;
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}
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return kernel.tanl(T, x, 0.0, 0);
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return kernel.tanx(x, 0.0, 0);
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}
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var y: [2]T = undefined;
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const n = rem_pio2l(T, x, &y);
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return kernel.tanl(T, y[0], y[1], n & 1);
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}
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pub fn tanx(x: f80) callconv(.c) f80 {
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return tanlGeneric(f80, x);
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var y: [2]f80 = undefined;
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const n = rem_pio2l(f80, x, &y);
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return kernel.tanx(y[0], y[1], n & 1);
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}
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pub fn tanq(x: f128) callconv(.c) f128 {
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return tanlGeneric(f128, x);
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const se = ld.signExponent(x) & 0x7fff;
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if (se == 0x7fff) {
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return x - x;
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}
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if (@abs(x) < kernel.pi_4) {
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if (se < 0x3fff - math.floatMantissaBits(f128) / 2) {
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if (compiler_rt.want_float_exceptions) {
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mem.doNotOptimizeAway(if (se == 0) x * 0x1p-120 else x + 0x1p120);
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}
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return x;
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}
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return kernel.tanq(x, 0.0, 0);
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}
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var y: [2]f128 = undefined;
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const n = rem_pio2l(f128, x, &y);
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return kernel.tanq(y[0], y[1], n & 1);
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}
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pub fn tanl(x: c_longdouble) callconv(.c) c_longdouble {
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@ -80,49 +80,43 @@ pub fn cosdf(x: f64) f32 {
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return @floatCast(((1.0 + z * C0) + w * C1) + (w * z) * r);
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}
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pub fn cosl(comptime T: type, x: T, y: T) T {
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const impl = switch (T) {
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f80 => struct {
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const C1: T = 0.0416666666666666666136;
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const C2: f64 = -0.0013888888888888874;
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const C3: f64 = 0.000024801587301571716;
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const C4: f64 = -0.00000027557319215507120;
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const C5: f64 = 0.0000000020876754400407278;
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const C6: f64 = -1.1470297442401303e-11;
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const C7: f64 = 4.7383039476436467e-14;
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inline fn poly(z: T) T {
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return z * (C1 + z * (C2 + z * (C3 + z * (C4 +
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z * (C5 + z * (C6 + z * C7))))));
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}
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},
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f128 => struct {
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const C1: T = 0.04166666666666666666666666666666658424671;
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const C2: T = -0.001388888888888888888888888888863490893732;
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const C3: T = 0.00002480158730158730158730158600795304914210;
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const C4: T = -0.2755731922398589065255474947078934284324e-6;
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const C5: T = 0.2087675698786809897659225313136400793948e-8;
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const C6: T = -0.1147074559772972315817149986812031204775e-10;
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const C7: T = 0.4779477332386808976875457937252120293400e-13;
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const C8: f64 = -0.1561920696721507929516718307820958119868e-15;
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const C9: f64 = 0.4110317413744594971475941557607804508039e-18;
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const C10: f64 = -0.8896592467191938803288521958313920156409e-21;
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const C11: f64 = 0.1601061435794535138244346256065192782581e-23;
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inline fn poly(z: T) T {
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return z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
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z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
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}
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},
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else => @compileError("cosl supports only f80 and f128, got: " ++ @typeName(T)),
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};
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pub fn cosx(x: f80, y: f80) f80 {
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const C1: f80 = 0.0416666666666666666136;
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const C2: f64 = -0.0013888888888888874;
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const C3: f64 = 0.000024801587301571716;
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const C4: f64 = -0.00000027557319215507120;
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const C5: f64 = 0.0000000020876754400407278;
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const C6: f64 = -1.1470297442401303e-11;
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const C7: f64 = 4.7383039476436467e-14;
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const z = x * x;
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const r = impl.poly(z);
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const r = z * (C1 + z * (C2 + z * (C3 + z * (C4 +
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z * (C5 + z * (C6 + z * C7))))));
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const hz = 0.5 * z;
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const w = 1.0 - hz;
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return w + (((1.0 - w) - hz) + (z * r - x * y));
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}
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pub fn cosq(x: f128, y: f128) f128 {
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const C1: f128 = 0.04166666666666666666666666666666658424671;
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const C2: f128 = -0.001388888888888888888888888888863490893732;
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const C3: f128 = 0.00002480158730158730158730158600795304914210;
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const C4: f128 = -0.2755731922398589065255474947078934284324e-6;
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const C5: f128 = 0.2087675698786809897659225313136400793948e-8;
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const C6: f128 = -0.1147074559772972315817149986812031204775e-10;
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const C7: f128 = 0.4779477332386808976875457937252120293400e-13;
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const C8: f64 = -0.1561920696721507929516718307820958119868e-15;
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const C9: f64 = 0.4110317413744594971475941557607804508039e-18;
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const C10: f64 = -0.8896592467191938803288521958313920156409e-21;
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const C11: f64 = 0.1601061435794535138244346256065192782581e-23;
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const z = x * x;
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const r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
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z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
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const hz = 0.5 * z;
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const w = 1.0 - hz;
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||||
|
||||
return w + (((1.0 - w) - hz) + (z * r - x * y));
|
||||
}
|
||||
|
||||
@ -172,58 +166,6 @@ pub fn sin(x: f64, y: f64, iy: i32) f64 {
|
||||
}
|
||||
}
|
||||
|
||||
pub fn sinl(comptime T: type, x: T, y: T, iy: i32) T {
|
||||
const impl = switch (T) {
|
||||
f80 => struct {
|
||||
const S1: T = -0.166666666666666666671;
|
||||
|
||||
const S2: f64 = 0.0083333333333333332;
|
||||
const S3: f64 = -0.00019841269841269427;
|
||||
const S4: f64 = 0.0000027557319223597490;
|
||||
const S5: f64 = -0.000000025052108218074604;
|
||||
const S6: f64 = 1.6059006598854211e-10;
|
||||
const S7: f64 = -7.6429779983024564e-13;
|
||||
const S8: f64 = 2.6174587166648325e-15;
|
||||
|
||||
inline fn poly(z: T) T {
|
||||
return S2 + z * (S3 + z * (S4 + z * (S5 +
|
||||
z * (S6 + z * (S7 + z * S8)))));
|
||||
}
|
||||
},
|
||||
f128 => struct {
|
||||
const S1: T = -0.16666666666666666666666666666666666606732416116558;
|
||||
const S2: T = 0.0083333333333333333333333333333331135404851288270047;
|
||||
const S3: T = -0.00019841269841269841269841269839935785325638310428717;
|
||||
const S4: T = 0.27557319223985890652557316053039946268333231205686e-5;
|
||||
const S5: T = -0.25052108385441718775048214826384312253862930064745e-7;
|
||||
const S6: T = 0.16059043836821614596571832194524392581082444805729e-9;
|
||||
const S7: T = -0.76471637318198151807063387954939213287488216303768e-12;
|
||||
const S8: T = 0.28114572543451292625024967174638477283187397621303e-14;
|
||||
|
||||
const S9: f64 = -0.82206352458348947812512122163446202498005154296863e-17;
|
||||
const S10: f64 = 0.19572940011906109418080609928334380560135358385256e-19;
|
||||
const S11: f64 = -0.38680813379701966970673724299207480965452616911420e-22;
|
||||
const S12: f64 = 0.64038150078671872796678569586315881020659912139412e-25;
|
||||
|
||||
inline fn poly(z: T) T {
|
||||
return S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
|
||||
z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
|
||||
}
|
||||
},
|
||||
else => @compileError("sinl supports only f80 and f128, got: " ++ @typeName(T)),
|
||||
};
|
||||
|
||||
const z = x * x;
|
||||
const v = z * x;
|
||||
const r = impl.poly(z);
|
||||
|
||||
if (iy == 0) {
|
||||
return x + v * (impl.S1 + z * r);
|
||||
}
|
||||
|
||||
return x - ((z * (0.5 * y - v * r) - y) - v * impl.S1);
|
||||
}
|
||||
|
||||
pub fn sindf(x: f64) f32 {
|
||||
// |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]).
|
||||
const S1 = -0x15555554cbac77.0p-55; // -0.166666666416265235595
|
||||
@ -239,6 +181,52 @@ pub fn sindf(x: f64) f32 {
|
||||
return @floatCast((x + s * (S1 + z * S2)) + s * w * r);
|
||||
}
|
||||
|
||||
pub fn sinx(x: f80, y: f80, iy: i32) f80 {
|
||||
const S1: f80 = -0.166666666666666666671;
|
||||
const S2: f64 = 0.0083333333333333332;
|
||||
const S3: f64 = -0.00019841269841269427;
|
||||
const S4: f64 = 0.0000027557319223597490;
|
||||
const S5: f64 = -0.000000025052108218074604;
|
||||
const S6: f64 = 1.6059006598854211e-10;
|
||||
const S7: f64 = -7.6429779983024564e-13;
|
||||
const S8: f64 = 2.6174587166648325e-15;
|
||||
|
||||
const z = x * x;
|
||||
const v = z * x;
|
||||
const r = S2 + z * (S3 + z * (S4 + z * (S5 +
|
||||
z * (S6 + z * (S7 + z * S8)))));
|
||||
|
||||
if (iy == 0)
|
||||
return x + v * (S1 + z * r);
|
||||
|
||||
return x - ((z * (0.5 * y - v * r) - y) - v * S1);
|
||||
}
|
||||
|
||||
pub fn sinq(x: f128, y: f128, iy: i32) f128 {
|
||||
const S1: f128 = -0.16666666666666666666666666666666666606732416116558;
|
||||
const S2: f128 = 0.0083333333333333333333333333333331135404851288270047;
|
||||
const S3: f128 = -0.00019841269841269841269841269839935785325638310428717;
|
||||
const S4: f128 = 0.27557319223985890652557316053039946268333231205686e-5;
|
||||
const S5: f128 = -0.25052108385441718775048214826384312253862930064745e-7;
|
||||
const S6: f128 = 0.16059043836821614596571832194524392581082444805729e-9;
|
||||
const S7: f128 = -0.76471637318198151807063387954939213287488216303768e-12;
|
||||
const S8: f128 = 0.28114572543451292625024967174638477283187397621303e-14;
|
||||
const S9: f64 = -0.82206352458348947812512122163446202498005154296863e-17;
|
||||
const S10: f64 = 0.19572940011906109418080609928334380560135358385256e-19;
|
||||
const S11: f64 = -0.38680813379701966970673724299207480965452616911420e-22;
|
||||
const S12: f64 = 0.64038150078671872796678569586315881020659912139412e-25;
|
||||
|
||||
const z = x * x;
|
||||
const v = z * x;
|
||||
const r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
|
||||
z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
|
||||
|
||||
if (iy == 0)
|
||||
return x + v * (S1 + z * r);
|
||||
|
||||
return x - ((z * (0.5 * y - v * r) - y) - v * S1);
|
||||
}
|
||||
|
||||
/// kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
|
||||
/// Input x is assumed to be bounded by ~pi/4 in magnitude.
|
||||
/// Input y is the tail of x.
|
||||
@ -377,89 +365,29 @@ pub fn tandf(x: f64, odd: bool) f32 {
|
||||
return @floatCast(if (odd) -1.0 / r0 else r0);
|
||||
}
|
||||
|
||||
pub fn tanl(comptime T: type, x_: T, y_: T, odd: i32) T {
|
||||
pub fn tanx(x_: f80, y_: f80, odd: i32) f80 {
|
||||
const pio4: f80 = 0.785398163397448309628;
|
||||
const pio4lo: f80 = -1.25413940316708300586e-20;
|
||||
|
||||
const T3: f80 = 0.333333333333333333180;
|
||||
const T5: f80 = 0.133333333333333372290;
|
||||
const T7: f80 = 0.0539682539682504975744;
|
||||
const T9: f64 = 0.021869488536312216;
|
||||
const T11: f64 = 0.0088632355256619590;
|
||||
const T13: f64 = 0.0035921281113786528;
|
||||
const T15: f64 = 0.0014558334756312418;
|
||||
const T17: f64 = 0.00059003538700862256;
|
||||
const T19: f64 = 0.00023907843576635544;
|
||||
const T21: f64 = 0.000097154625656538905;
|
||||
const T23: f64 = 0.000038440165747303162;
|
||||
const T25: f64 = 0.000018082171885432524;
|
||||
const T27: f64 = 0.0000024196006108814377;
|
||||
const T29: f64 = 0.0000078293456938132840;
|
||||
const T31: f64 = -0.0000032609076735050182;
|
||||
const T33: f64 = 0.0000023261313142559411;
|
||||
|
||||
var x = x_;
|
||||
var y = y_;
|
||||
const impl = switch (T) {
|
||||
f80 => struct {
|
||||
const pio4: T = 0.785398163397448309628;
|
||||
const pio4lo: T = -1.25413940316708300586e-20;
|
||||
|
||||
const T3: T = 0.333333333333333333180;
|
||||
const T5: T = 0.133333333333333372290;
|
||||
const T7: T = 0.0539682539682504975744;
|
||||
const T9: f64 = 0.021869488536312216;
|
||||
const T11: f64 = 0.0088632355256619590;
|
||||
const T13: f64 = 0.0035921281113786528;
|
||||
const T15: f64 = 0.0014558334756312418;
|
||||
const T17: f64 = 0.00059003538700862256;
|
||||
const T19: f64 = 0.00023907843576635544;
|
||||
const T21: f64 = 0.000097154625656538905;
|
||||
const T23: f64 = 0.000038440165747303162;
|
||||
const T25: f64 = 0.000018082171885432524;
|
||||
const T27: f64 = 0.0000024196006108814377;
|
||||
const T29: f64 = 0.0000078293456938132840;
|
||||
const T31: f64 = -0.0000032609076735050182;
|
||||
const T33: f64 = 0.0000023261313142559411;
|
||||
|
||||
inline fn rpoly(w: T) T {
|
||||
return T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
|
||||
w * (T25 + w * (T29 + w * T33))))));
|
||||
}
|
||||
|
||||
inline fn vpoly(w: T) T {
|
||||
return T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
|
||||
w * (T27 + w * T31)))));
|
||||
}
|
||||
},
|
||||
f128 => struct {
|
||||
const pio4: T = 0x1.921fb54442d18469898cc51701b8p-1;
|
||||
const pio4lo: T = 0x1.cd129024e088a67cc74020bbea60p-116;
|
||||
|
||||
const T3: T = 0x1.5555555555555555555555555553p-2;
|
||||
const T5: T = 0x1.1111111111111111111111111eb5p-3;
|
||||
const T7: T = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5;
|
||||
const T9: T = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6;
|
||||
const T11: T = 0x1.226e355e6c23c8f5b4f5762322eep-7;
|
||||
const T13: T = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9;
|
||||
const T15: T = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10;
|
||||
const T17: T = 0x1.355824803674477dfcf726649efep-11;
|
||||
const T19: T = 0x1.f57d7734d1656e0aceb716f614c2p-13;
|
||||
const T21: T = 0x1.967e18afcb180ed942dfdc518d6cp-14;
|
||||
const T23: T = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15;
|
||||
const T25: T = 0x1.0b132d39f055c81be49eff7afd50p-16;
|
||||
const T27: T = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18;
|
||||
const T29: T = 0x1.5ef2daf21d1113df38d0fbc00267p-19;
|
||||
const T31: T = 0x1.1c77d6eac0234988cdaa04c96626p-20;
|
||||
const T33: T = 0x1.cd2a5a292b180e0bdd701057dfe3p-22;
|
||||
const T35: T = 0x1.75c7357d0298c01a31d0a6f7d518p-23;
|
||||
const T37: T = 0x1.2f3190f4718a9a520f98f50081fcp-24;
|
||||
const T39: f64 = 0.000000028443389121318352;
|
||||
const T41: f64 = 0.000000011981013102001973;
|
||||
const T43: f64 = 0.0000000038303578044958070;
|
||||
const T45: f64 = 0.0000000034664378216909893;
|
||||
const T47: f64 = -0.0000000015090641701997785;
|
||||
const T49: f64 = 0.0000000029449552300483952;
|
||||
const T51: f64 = -0.0000000022006995706097711;
|
||||
const T53: f64 = 0.0000000015468200913196612;
|
||||
const T55: f64 = -0.00000000061311613386849674;
|
||||
const T57: f64 = 1.4912469681508012e-10;
|
||||
|
||||
inline fn rpoly(w: T) T {
|
||||
return T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
|
||||
w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 +
|
||||
w * (T45 + w * (T49 + w * (T53 + w * T57))))))))))));
|
||||
}
|
||||
|
||||
inline fn vpoly(w: T) T {
|
||||
return T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
|
||||
w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 +
|
||||
w * (T47 + w * (T51 + w * T55)))))))))));
|
||||
}
|
||||
},
|
||||
else => @compileError("tanl supports only f80 and f128, got: " ++ @typeName(T)),
|
||||
};
|
||||
|
||||
const big = @abs(x) >= 0.67434;
|
||||
var sign: i8 = 0;
|
||||
|
||||
@ -469,20 +397,111 @@ pub fn tanl(comptime T: type, x_: T, y_: T, odd: i32) T {
|
||||
x = -x;
|
||||
y = -y;
|
||||
}
|
||||
x = (impl.pio4 - x) + (impl.pio4lo - y);
|
||||
x = (pio4 - x) + (pio4lo - y);
|
||||
y = 0.0;
|
||||
}
|
||||
|
||||
var z = x * x;
|
||||
var w = z * z;
|
||||
var r = impl.rpoly(w);
|
||||
var v = z * impl.vpoly(w);
|
||||
|
||||
var r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
|
||||
w * (T25 + w * (T29 + w * T33))))));
|
||||
|
||||
var v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
|
||||
w * (T27 + w * T31))))));
|
||||
|
||||
var s = z * x;
|
||||
r = y + z * (s * (r + v) + y) + impl.T3 * s;
|
||||
r = y + z * (s * (r + v) + y) + T3 * s;
|
||||
w = x + r;
|
||||
|
||||
if (big) {
|
||||
s = @as(T, @floatFromInt(1 - 2 * odd));
|
||||
s = @as(f80, @floatFromInt(1 - 2 * odd));
|
||||
v = s - 2.0 * (x + (r - w * w / (w + s)));
|
||||
return if (sign == -1) -v else v;
|
||||
}
|
||||
|
||||
if (odd == 0) {
|
||||
return w;
|
||||
}
|
||||
|
||||
// if allow error up to 2 ulp, simply return
|
||||
// -1.0 / (x+r) here
|
||||
//
|
||||
// compute -1.0 / (x+r) accurately
|
||||
z = w + 0x1p32 - 0x1p32;
|
||||
v = r - (z - x);
|
||||
const a = -1.0 / w;
|
||||
const t = a + 0x1p32 - 0x1p32;
|
||||
s = 1.0 + t * z;
|
||||
return t + a * (s + t * v);
|
||||
}
|
||||
|
||||
pub fn tanq(x_: f128, y_: f128, odd: i32) f128 {
|
||||
const pio4: f128 = 0x1.921fb54442d18469898cc51701b8p-1;
|
||||
const pio4lo: f128 = 0x1.cd129024e088a67cc74020bbea60p-116;
|
||||
|
||||
const T3: f128 = 0x1.5555555555555555555555555553p-2;
|
||||
const T5: f128 = 0x1.1111111111111111111111111eb5p-3;
|
||||
const T7: f128 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5;
|
||||
const T9: f128 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6;
|
||||
const T11: f128 = 0x1.226e355e6c23c8f5b4f5762322eep-7;
|
||||
const T13: f128 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9;
|
||||
const T15: f128 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10;
|
||||
const T17: f128 = 0x1.355824803674477dfcf726649efep-11;
|
||||
const T19: f128 = 0x1.f57d7734d1656e0aceb716f614c2p-13;
|
||||
const T21: f128 = 0x1.967e18afcb180ed942dfdc518d6cp-14;
|
||||
const T23: f128 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15;
|
||||
const T25: f128 = 0x1.0b132d39f055c81be49eff7afd50p-16;
|
||||
const T27: f128 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18;
|
||||
const T29: f128 = 0x1.5ef2daf21d1113df38d0fbc00267p-19;
|
||||
const T31: f128 = 0x1.1c77d6eac0234988cdaa04c96626p-20;
|
||||
const T33: f128 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22;
|
||||
const T35: f128 = 0x1.75c7357d0298c01a31d0a6f7d518p-23;
|
||||
const T37: f128 = 0x1.2f3190f4718a9a520f98f50081fcp-24;
|
||||
const T39: f64 = 0.000000028443389121318352;
|
||||
const T41: f64 = 0.000000011981013102001973;
|
||||
const T43: f64 = 0.0000000038303578044958070;
|
||||
const T45: f64 = 0.0000000034664378216909893;
|
||||
const T47: f64 = -0.0000000015090641701997785;
|
||||
const T49: f64 = 0.0000000029449552300483952;
|
||||
const T51: f64 = -0.0000000022006995706097711;
|
||||
const T53: f64 = 0.0000000015468200913196612;
|
||||
const T55: f64 = -0.00000000061311613386849674;
|
||||
const T57: f64 = 1.4912469681508012e-10;
|
||||
|
||||
var x = x_;
|
||||
var y = y_;
|
||||
|
||||
const big = @abs(x) >= 0.67434;
|
||||
var sign: i8 = 0;
|
||||
|
||||
if (big) {
|
||||
if (x < 0) {
|
||||
sign = -1;
|
||||
x = -x;
|
||||
y = -y;
|
||||
}
|
||||
x = (pio4 - x) + (pio4lo - y);
|
||||
y = 0.0;
|
||||
}
|
||||
|
||||
var z = x * x;
|
||||
var w = z * z;
|
||||
|
||||
var r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
|
||||
w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 +
|
||||
w * (T45 + w * (T49 + w * (T53 + w * T57))))))))))));
|
||||
|
||||
var v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
|
||||
w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 +
|
||||
w * (T47 + w * (T51 + w * T55))))))))))));
|
||||
|
||||
var s = z * x;
|
||||
r = y + z * (s * (r + v) + y) + T3 * s;
|
||||
w = x + r;
|
||||
|
||||
if (big) {
|
||||
s = @as(f128, @floatFromInt(1 - 2 * odd));
|
||||
v = s - 2.0 * (x + (r - w * w / (w + s)));
|
||||
return if (sign == -1) -v else v;
|
||||
}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user